Patent Publication Number: US-2022236753-A1

Title: Variable Reference Voltage Source

Description:
TECHNICAL FIELD 
     The present invention relates to a variable reference voltage source that does not require a measuring instrument for calibration. 
     BACKGROUND ART 
     A voltage source for calibration that outputs a known voltage is used for, for example, calibration of a sensor circuit that detects something. A correspondence relation between a digital value and a sensing target signal changes because of changes with time of an offset and a gain of an amplifier, an offset, linearity, and the like of an AD converter of the sensor circuit. In order to suppress the change without increasing maintenance operation, calibration of the amplifier and the AD converter is necessary. In the calibration of the offset and the gain of the amplifier and the offset of the AD converter, the known voltage is input to the amplifier and the calibration is performed according to a correlation between the known voltage and outputs of the amplifier and the AD converter. 
     Examples of a variable signal source that outputs a known voltage include an R-2R ladder circuit, a resistance string circuit (Non-Patent Literature 1), and a PWM circuit (Non-Patent Literature 2). The R-2R ladder circuit can configure a high-resolution and high-accuracy variable signal source with a relatively small number of resistance elements. The resistance string circuit has low power consumption and monotonicity. The PWM circuit has an advantage that performance is stable because the PWM circuit is configured by only a digital circuit. 
     CITATION LIST 
     Non-Patent Literature 
     Non-Patent Literature 1: Trimming for improving accuracy of a DAC (⅓) EDN Japan [searched on May 16, 2019], Internet (URL: http://ednjapn.com/edn/articles/1611/08/news012.html) 
     Non-Patent Literature 2: Secret trick! Realize a pseudo D/A converter using PWM [searched on May 16, 2019], Internet (URL: https://service.macnica.co.jp/library/107577) 
     SUMMARY OF THE INVENTION 
     Technical Problem 
     However, in order to improve the accuracy of these signal sources, it is necessary to prepare, on the outside of the signal sources, a measuring instrument serving as a reference and adjusting the signal sources. The R-2R circuit and the resistance string circuit need to finely adjust a value of the resistance element using the measuring instrument on the outside. In the PWM circuit, high accuracy is requested for frequency accuracy of a high-order low-pass filter for removing ripple noise appearing in an output. Therefore, adjustment using the measuring instrument on the outside is necessary. 
     In order to use the conventional signal source as a reference in this way, there is a problem in that work for preparing the measuring instrument on the outside of the reference signal source and adjusting the reference signal source is essential. 
     The present invention has been devised in view of this problem and an object of the present invention is to provide a variable reference voltage source for which a measuring instrument for calibration is unnecessary. 
     Means for Solving the Problem 
     A variable reference voltage source according to an aspect of the present invention is a variable reference voltage source that generates a variable reference voltage corresponding to setting data set from outside, the variable reference voltage source including: a control unit including a calibration control unit that controls operation for acquiring calibration data including calibration values of an offset voltage and a predetermined unit voltage of a determiner, which determines magnitudes of two voltages, and an output control unit that controls operation for generating, based on the calibration data, a variable reference voltage corresponding to the setting data set from the outside; a reference voltage unit that outputs a reference voltage; and an integrated-voltage generating unit that repeats, when the calibration control unit controls the operation, an integrating operation until an integrated voltage obtained by integrating at least two or more kinds of unit voltages becomes equal to the reference voltage and outputs, when the output control unit controls the operation, the variable reference voltage corresponding to the setting data. 
     Effects of the Invention 
     According to the present invention, it is possible to provide a variable reference voltage source for which a measuring instrument for calibration on the outside is unnecessary. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a functional block diagram showing a configuration example of a variable reference voltage source according to an embodiment of the present invention. 
         FIG. 2  is a flowchart showing a processing procedure of an intermediate-voltage integrating unit shown in  FIG. 1 . 
         FIG. 3  is a diagram schematically showing a relation between the number of times of integration and an integrated voltage. 
         FIG. 4  is a flowchart showing a processing procedure of an intermediate-voltage-excess integrating unit shown in  FIG. 1 . 
         FIG. 5  is a flowchart showing a processing procedure of a reference-voltage integrating unit shown in  FIG. 1 . 
         FIG. 6  is a flowchart showing a processing procedure of a positive-voltage-integration processing unit shown in  FIG. 1 . 
         FIG. 7  is a flowchart showing a processing procedure of a negative-voltage-integration processing unit shown in  FIG. 1 . 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     An embodiment of the present invention is explained below with reference to the drawings. The same components in a plurality of drawings are denoted by the same reference numerals and signs. Explanation of the components is not repeated. 
       FIG. 1  is a functional block diagram showing a functional configuration example of a variable reference voltage source according to the embodiment of the present invention. A variable reference voltage source  100  shown in  FIG. 1  generates a variable reference voltage corresponding to setting data set from the outside and outputs the variable reference voltage to an output  1 . The variable reference voltage source  100  includes a reference voltage unit  10 , a control unit  20 , and an integrated-voltage generating unit  30  having a plurality of unit voltages. The reference voltage unit  10  outputs a reference voltage Vref. 
     An offset and a predetermined unit voltage are included in the integrated-voltage generating unit  30  on the inside of the variable reference voltage source  100  and change with time because of a drift. Therefore, in order to keep accuracy, it is necessary to calibrate the offset and the unit voltage as explained below. The control unit  20  includes a calibration control unit  21  that controls operation for acquiring calibration data including calibration values of the offset and the predetermined unit voltage of the integrated-voltage generating unit  30  and an output control unit  22  that controls operation for generating a variable reference voltage corresponding to setting data set from the outside based on the calibration data. 
     The integrated-voltage generating unit  30  repeats, when the calibration control unit  21  controls the operation, an integrating operation until an integrated voltage obtained by integrating the predetermined unit voltage becomes equal to the reference voltage Vref and outputs, when the output control unit  22  controls the operation, a variable reference voltage corresponding to the setting data. 
     The integrated-voltage generating unit  30  includes an integrating unit  35 , a determiner  33 , a crossbar switch  32 , a threshold generating unit  34 , a determination-voltage switching unit  31 , and a polarity switching unit  36 . The integrating unit  35  generates an integrated voltage obtained by integrating a unit voltage. The determiner  33  includes positive and negative inputs, determines that a positive input voltage exceeds a negative input voltage at a calibration state time, and outputs a determination signal. The crossbar switch  32  is used for measurement of an offset voltage of the determiner  33 . The threshold generating unit  34  generates a bias voltage Vb and an intermediate potential V 1  of the integrating unit  35 . The determination-voltage switching unit  31  switches a voltage serving as a reference given to the determiner  33  through the crossbar switch  33  at the calibration state time. The polarity switching unit  36  switches a polarity of the unit voltage. 
     The integrating unit  35  is configured by an operational amplifier  350  including positive and negative inputs, an SW 4 , an SW 1 , an SW 2 , a capacitor C 1 , a capacitor C 2 , and a SW 3 . The SW 4  switches an integrating operation and an operation as a unity gain buffer of the operational amplifier  350 . The SW 1  and the SW 2  switch the magnitude of the unit voltage and a polarity at the time of a small unit voltage. The capacitor C 1  accumulates electric charges equivalent to one unit voltage. The capacitor C 2  accumulates electric charges equivalent to an integrated voltage. The SW 3  is used when the electric charges accumulated in the capacitor C 2  are reset. 
     Connection of the SW 1 , SW 2 , SW 3 , and SW 4 , the polarity switching unit  36 , the determination-voltage switching unit  31 , and the crossbar switch  32  is controlled according to CHG 1 , CHG 2 , RST, PRE, VGP, THR, and POL, which are operation control signals from the control unit  20 . 
     In the integrating unit  35 , integration processing at two kinds of unit voltages having different magnitudes and different polarities is possible. In the following explanation, a relation between operations and the numbers of times of integration at the unit voltages and an output of the operational amplifier  350  is explained and, thereafter, operation of calibration processing is explained. In the following explanation, integration processing at a small unit voltage having a positive polarity is described as first positive integration processing, integration processing at a small unit voltage having a negative polarity is described as first negative integration processing, integration processing at a large unit voltage having a positive polarity is described as second positive integration processing, and integration processing at a large unit voltage having a negative polarity is described as second negative integration processing. 
     Operation of the first positive integration processing is explained. This processing is configured by a first positive comparison step, a first positive charge accumulation step, and a first positive charge transfer step. In this processing, sp 1  and sp 2  of the polarity switching unit  36  are connected. In the first positive comparison step, connection of a 1  and b 1  of the SW 1 , connection of a 2  and b 2  of the SW 2 , and connection of a 4  and b 4  of the SW 4  are carried out. When an output of the operational amplifier  350  is represented as Vsp,0, electric charges Q1,0 and Q2,0 accumulated in the capacitor C 1  and the capacitor C 2  are respectively represented by the following expressions. 
     
       
         
           
             
               
                 
                   
                     
                       
                         Math 
                         . 
                             
                         1 
                       
                     
                     
                         
                     
                   
                   
                     
                       
                         Q1 
                         , 
                         
                           0 
                           = 
                           
                             C 
                             ⁢ 
                             1 
                             ⁢ 
                                 
                             Vref 
                           
                         
                       
                     
                     
                       
                         ( 
                         1 
                         ) 
                       
                     
                   
                   
                     
                       
                         
                           Q 
                           ⁢ 
                           2 
                         
                         , 
                         
                           0 
                           = 
                           
                             C 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               { 
                               
                                 
                                   
                                     
                                       A 
                                       + 
                                       1 
                                     
                                     A 
                                   
                                   ⁢ 
                                   Vsp 
                                 
                                 , 
                                 
                                   0 
                                   - 
                                   
                                     ( 
                                     
                                       Vofop 
                                       + 
                                       Vb 
                                     
                                     ) 
                                   
                                 
                               
                               } 
                             
                           
                         
                       
                     
                     
                       
                         ( 
                         2 
                         ) 
                       
                     
                   
                 
               
               
                   
               
             
           
         
       
     
     In Expression (2), A represents a gain of the operational amplifier  350  and Vofop represents an offset voltage of the operational amplifier  350 . When parasitic capacitance Cp connected to a negative input of the operational amplifier  350  and affecting the operation of the integration processing is considered, electric charges Qp,0 accumulated in Cp are represented by the following expression. 
     
       
         
           
             
               
                 
                   Math 
                   . 
                       
                   2 
                 
               
               
                   
               
             
             
               
                 
                   Qp 
                   , 
                   
                     0 
                     = 
                     
                       Cp 
                       ⁡ 
                       ( 
                       
                         
                           - 
                           
                             
                               Vsp 
                               , 
                               0 
                             
                             A 
                           
                         
                         + 
                         Vofop 
                         + 
                         Vb 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     In the first positive charge accumulation step, after a 4  and c 4  of the SW 4  are connected, a 2  and c 2  of the SW 2  are connected. Electric charges accumulated in C 2  are saved by connecting a 4  and c 4  of the SW 4 . The operational amplifier  350  operates as a unity gain buffer. An output Vspa,1 of the operational amplifier  350  at this time is represented by the following expression. 
     
       
         
           
             
               
                 
                   Math 
                   . 
                       
                   3 
                 
               
               
                   
               
             
             
               
                 
                   Vspa 
                   , 
                   
                     1 
                     = 
                     
                       
                         A 
                         
                           A 
                           + 
                           1 
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           Vofop 
                           + 
                           Vb 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     A differential voltage between the reference voltage Vref and Vspa,1 is applied to the capacitor C 1 . Electric charges Q1a,1, Q2a,1, and Qpa,1 accumulated in the capacitor C 1 , the capacitor C 2 , and Cp in this step are represented by the following expressions. 
     
       
         
           
             
               Math 
               . 
                   
               4 
             
             ⁢ 
             
               
                 
                   
                     
                       Q 
                       ⁢ 
                       1 
                       ⁢ 
                       a 
                     
                     , 
                     
                       1 
                       = 
                       
                         C 
                         ⁢ 
                         1 
                         ⁢ 
                         
                           { 
                           
                             Vref 
                             - 
                             
                               
                                 A 
                                 
                                   A 
                                   + 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                     
                   
                 
                 
                   
                     ( 
                     5 
                     ) 
                   
                 
               
               
                 
                   
                     
                       Q 
                       ⁢ 
                       2 
                       ⁢ 
                       a 
                     
                     , 
                     
                       1 
                       = 
                       
                         
                           Q 
                           ⁢ 
                           
                             2 
                             
                               , 
                               0 
                             
                           
                         
                         = 
                         
                           C 
                           ⁢ 
                           2 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   A 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                 
                                 ⁢ 
                                 Vsp 
                               
                               , 
                               
                                 0 
                                 - 
                                 Vofop 
                                 - 
                                 Vb 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
                 
                   
                     ( 
                     6 
                     ) 
                   
                 
               
               
                 
                   
                     
                       Q 
                       ⁢ 
                       pa 
                     
                     , 
                     
                       1 
                       = 
                       
                         Cp 
                         ⁢ 
                         
                           A 
                           
                             A 
                             + 
                             1 
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     ( 
                     7 
                     ) 
                   
                 
               
             
           
         
       
     
     In the first positive charge transfer step, after a 4  and b 4  of the SW 4  are connected, a 1  and c 1  of the SW 1  are connected. Since c 1  of the SW 1  is connected to V 1 , when an output of the operational amplifier  350  is represented as Vspb,1, electric charges Q1b,1, Q2b,1, and Qpb,1 accumulated in the capacitor C 1 , the capacitor C 2 , and Cp in this step are represented by the following expressions. 
     
       
         
           
             
               Math 
               . 
                   
               5 
             
             ⁢ 
             
               
                 
                   
                     
                       Q 
                       ⁢ 
                       1 
                       ⁢ 
                       b 
                     
                     , 
                     
                       1 
                       = 
                       
                         C 
                         ⁢ 
                         1 
                         ⁢ 
                         
                           { 
                           
                             
                               
                                 V 
                                 ⁢ 
                                 1 
                               
                               + 
                               
                                 
                                   1 
                                   A 
                                 
                                 ⁢ 
                                 Vspb 
                               
                             
                             , 
                             
                               1 
                               - 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                     
                   
                 
                 
                   
                     ( 
                     8 
                     ) 
                   
                 
               
               
                 
                   
                     
                       Q 
                       ⁢ 
                       2 
                       ⁢ 
                       b 
                     
                     , 
                     
                       1 
                       = 
                       
                         C 
                         ⁢ 
                         2 
                         ⁢ 
                         
                           { 
                           
                             
                               
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 A 
                               
                               ⁢ 
                               Vspb 
                             
                             , 
                             
                               1 
                               - 
                               
                                 ( 
                                 
                                   Vofop 
                                   - 
                                   Vb 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                     
                   
                 
                 
                   
                     ( 
                     9 
                     ) 
                   
                 
               
               
                 
                   
                     
                       Q 
                       ⁢ 
                       pb 
                     
                     , 
                     
                       1 
                       = 
                       
                         Cp 
                         ⁢ 
                         
                           { 
                           
                             
                               
                                 - 
                                 
                                   1 
                                   A 
                                 
                               
                               ⁢ 
                               Vspb 
                             
                             , 
                             
                               1 
                               + 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                     
                   
                 
                 
                   
                     ( 
                     10 
                     ) 
                   
                 
               
             
           
         
       
     
     Electric charges accumulated in a capacitor connected to the negative input of the operational amplifier  350  before and after the first positive charge transfer step are saved. Accordingly, a relational expression between Vspb,1 and Vsp,0 is as follows. 
     
       
         
           
             
               
                 
                                    
                   
                     Math 
                     . 
                         
                     6 
                   
                 
               
               
                   
               
             
             
               
                 
                   
                     
                       
                         - 
                         Q 
                       
                       ⁢ 
                       1 
                       ⁢ 
                       a 
                     
                     , 
                     
                       1 
                       + 
                       Qpa 
                     
                     , 
                     
                       1 
                       - 
                       
                         Q 
                         ⁢ 
                         2 
                         ⁢ 
                         a 
                       
                     
                     , 
                     
                       1 
                       = 
                       
                         
                           - 
                           Q 
                         
                         ⁢ 
                         1 
                         ⁢ 
                         b 
                       
                     
                     , 
                     
                       1 
                       + 
                       Qpb 
                     
                     , 
                     
                       1 
                       - 
                       
                         Q 
                         ⁢ 
                         2 
                         ⁢ 
                         b 
                       
                     
                     , 
                     
                       
                         1 
                         - 
                         
                           C 
                           ⁢ 
                           1 
                           ⁢ 
                           
                             { 
                             
                               Vref 
                               - 
                               
                                 
                                   A 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     Vofop 
                                     + 
                                     Vb 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                         
                         + 
                         
                           Cp 
                           ⁢ 
                           
                             A 
                             
                               A 
                               + 
                               1 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               Vofop 
                               + 
                               Vb 
                             
                             ) 
                           
                         
                         - 
                         
                           C 
                           ⁢ 
                           2 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                   A 
                                 
                                 ⁢ 
                                 Vsp 
                               
                               , 
                               
                                 0 
                                 - 
                                 Vofop 
                                 - 
                                 Vb 
                               
                             
                             ) 
                           
                         
                       
                       = 
                       
                         
                           
                             - 
                             C 
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   V 
                                   ⁢ 
                                   1 
                                 
                                 + 
                                 
                                   
                                     1 
                                     A 
                                   
                                   ⁢ 
                                   Vspb 
                                 
                               
                               , 
                               
                                 1 
                                 - 
                                 Vofop 
                                 - 
                                 Vb 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           Cp 
                           ⁡ 
                           ( 
                           
                             
                               
                                 - 
                                 
                                   1 
                                   
                                     A 
                                       
                                   
                                 
                               
                               ⁢ 
                               Vspb 
                             
                             , 
                             
                               1 
                               + 
                               Vofop 
                               + 
                               Vb 
                             
                           
                           ) 
                         
                         - 
                         
                           C 
                           ⁢ 
                           2 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                   A 
                                 
                                 ⁢ 
                                 Vspb 
                               
                               , 
                               
                                 1 
                                 - 
                                 Vofop 
                                 - 
                                 Vb 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       
                         ( 
                         
                           
                             
                               C 
                               ⁢ 
                               1 
                             
                             A 
                           
                           + 
                           
                             
                               Cp 
                               ⁢ 
                               2 
                             
                             A 
                           
                           + 
                           
                             
                               
                                 A 
                                 + 
                                 1 
                               
                               A 
                             
                             ⁢ 
                             C 
                             ⁢ 
                             2 
                           
                         
                         ) 
                       
                       ⁢ 
                       Vspb 
                     
                     , 
                     
                       1 
                       = 
                       
                         
                           C 
                           ⁢ 
                           1 
                           ⁢ 
                           
                             { 
                             
                               Vref 
                               - 
                               
                                 V 
                                 ⁢ 
                                 1 
                               
                               + 
                               
                                 
                                   1 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     Vofop 
                                     + 
                                     Vb 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                         
                         + 
                         
                           C 
                           ⁢ 
                           2 
                           ⁢ 
                           
                             
                               A 
                               + 
                               1 
                             
                             A 
                           
                           ⁢ 
                           Vsp 
                         
                       
                     
                     , 
                     
                       0 
                       + 
                       
                         Cp 
                         ⁢ 
                         
                           1 
                           
                             A 
                             + 
                             1 
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                       
                     
                   
                   ⁢ 
                   
 
                   
                     Vspb 
                     , 
                     
                       1 
                       = 
                       
                         
                           
                             
                               AC 
                               ⁢ 
                               1 
                             
                             
                               
                                 C 
                                 ⁢ 
                                 1 
                               
                               + 
                               Cp 
                               + 
                               
                                 
                                   ( 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 C 
                                 ⁢ 
                                 2 
                               
                             
                           
                           ⁢ 
                           
                             { 
                             
                               Vref 
                               - 
                               
                                 V 
                                 ⁢ 
                                 1 
                               
                               + 
                               
                                 
                                   1 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     Vofop 
                                     + 
                                     Vb 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                         
                         + 
                         
                           
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               2 
                             
                             
                               
                                 C 
                                 ⁢ 
                                 1 
                               
                               + 
                               Cp 
                               + 
                               
                                 
                                   ( 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 C 
                                 ⁢ 
                                 2 
                               
                             
                           
                           ⁢ 
                           Vsp 
                         
                       
                     
                     , 
                     
                       0 
                       + 
                       
                         
                           Cp 
                           
                             
                               C 
                               ⁢ 
                               1 
                             
                             + 
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           A 
                           
                             A 
                             + 
                             1 
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     A relation between the output Vsp,1 of the operational amplifier  350  and the electric charges Q2,1 and Qp,1 accumulated in the capacitor C 2  and Cp at the time when the processing transitions to the first positive comparison step again is an expression obtained by replacing Vsp,0 and Q2,0 and Qp,0 in Expression (2) and Expression (3) with Vsp,1 and Q2,1 and Qp,1. According to this relational expression, Vsp,1 and Vspb,1 are equal as follows. 
     
       
         
           
             
               
                 
                                    
                   
                     
                       Math 
                       . 
                           
                       7 
                     
                     ⁢ 
                     
 
                     	 
                     
                       Qpb 
                       , 
                       
                         1 
                         - 
                         
                           Q 
                           ⁢ 
                           2 
                           ⁢ 
                           b 
                         
                       
                       , 
                       
                         1 
                         = 
                         Qp 
                       
                       , 
                       
                         1 
                         - 
                         
                           Q 
                           ⁢ 
                           2 
                         
                       
                       , 
                       1 
                     
                     ⁢ 
                     
 
                     
                       
                         
                           Cp 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   - 
                                   
                                     1 
                                     A 
                                   
                                 
                                 ⁢ 
                                 Vspb 
                               
                               , 
                               
                                 1 
                                 + 
                                 
                                   ( 
                                   
                                     Vofop 
                                     + 
                                     Vb 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                         
                         - 
                         
                           C 
                           ⁢ 
                           2 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                   A 
                                 
                                 ⁢ 
                                 Vspb 
                               
                               , 
                               
                                 1 
                                 - 
                                 
                                   ( 
                                   
                                     Vofop 
                                     + 
                                     Vb 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                         
                       
                       = 
                       
                         
                           Cp 
                           ⁡ 
                           ( 
                           
                             
                               - 
                               
                                 
                                   Vsp 
                                   , 
                                   1 
                                 
                                 A 
                               
                             
                             + 
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                         - 
                         
                           C 
                           ⁢ 
                           2 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                   A 
                                 
                                 ⁢ 
                                 Vsp 
                               
                               , 
                               
                                 1 
                                 - 
                                 
                                   ( 
                                   
                                     Vofop 
                                     + 
                                     Vb 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                         
                       
                     
                     ⁢ 
                     
 
                     	 
                     
                       Vspb 
                       , 
                       
                         1 
                         = 
                         Vsp 
                       
                       , 
                       1 
                     
                   
                 
               
               
                   
               
             
           
         
       
     
     Accordingly, a relation between Vsp,1 and Vsp,0 is represented by the following expression. 
     
       
         
           
             
               
                 
                                    
                   
                     Math 
                     . 
                         
                     8 
                   
                 
               
               
                   
               
             
             
               
                 
                   Vsp 
                   , 
                   
                     1 
                     = 
                     
                       
                         
                           
                             AC 
                             ⁢ 
                             1 
                           
                           
                             
                               C 
                               ⁢ 
                               1 
                             
                             + 
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           { 
                           
                             Vref 
                             - 
                             
                               V 
                               ⁢ 
                               1 
                             
                             + 
                             
                               
                                 1 
                                 
                                   A 
                                   + 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                       + 
                       
                         
                           
                             
                               ( 
                               
                                 A 
                                 + 
                                 1 
                               
                               ) 
                             
                             ⁢ 
                             C 
                             ⁢ 
                             2 
                           
                           
                             
                               C 
                               ⁢ 
                               1 
                             
                             + 
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               2 
                             
                           
                         
                         ⁢ 
                         Vsp 
                       
                     
                   
                   , 
                   
                     0 
                     + 
                     
                       
                         Cp 
                         
                           
                             C 
                             ⁢ 
                             1 
                           
                           + 
                           Cp 
                           + 
                           
                             
                               ( 
                               
                                 A 
                                 + 
                                 1 
                               
                               ) 
                             
                             ⁢ 
                             C 
                             ⁢ 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         A 
                         
                           A 
                           + 
                           1 
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           Vofop 
                           + 
                           Vb 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     Expression (12) can be represented in the following form of a geometrical series. 
       Math. 9 
         Vsp, 1+ Bsp 0= Bsp 1( Vsp, 0+ Bsp 0) 
         Vsp, 1= Bsp 1 Vsp, 0+( Bsp 1−1) Bsp 0  (13)
 
     According to comparison of Expression (12) and Expression (13), Bsp1 is represented by the following expression. 
     
       
         
           
             
               
                 
                                    
                   
                     Math 
                     . 
                         
                     10 
                   
                 
               
               
                   
               
             
             
               
                 
                   
                     Bsp 
                     ⁢ 
                     1 
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             A 
                             + 
                             1 
                           
                           ) 
                         
                         ⁢ 
                         C 
                         ⁢ 
                         2 
                       
                       
                         
                           C 
                           ⁢ 
                           1 
                         
                         + 
                         Cp 
                         + 
                         
                           
                             ( 
                             
                               A 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           C 
                           ⁢ 
                           2 
                         
                       
                     
                     = 
                     
                       
                         1 
                         - 
                         
                           
                             
                               C 
                               ⁢ 
                               1 
                             
                             + 
                             Cp 
                           
                           
                             
                               C 
                               ⁢ 
                               1 
                             
                             + 
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               2 
                             
                           
                         
                       
                       = 
                       
                         1 
                         - 
                         
                           η 
                           ⁢ 
                           sp 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                                    
                   
                     
                       η 
                       ⁢ 
                       sp 
                     
                     = 
                     
                       
                         
                           C 
                           ⁢ 
                           1 
                         
                         + 
                         Cp 
                       
                       
                         
                           C 
                           ⁢ 
                           1 
                         
                         + 
                         Cp 
                         + 
                         
                           
                             ( 
                             
                               A 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           C 
                           ⁢ 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     (Bsp1−1)Bsp0=−ηsp Bsp0 is represented by the following expression. 
     
       
         
           
             
               
                 
                                    
                   
                     Math 
                     . 
                         
                     11 
                   
                 
               
               
                   
               
             
             
               
                 
                   
                     
                       - 
                       η 
                     
                     ⁢ 
                     spBsp 
                     ⁢ 
                     0 
                   
                   = 
                   
                     
                       
                         
                           AC 
                           ⁢ 
                           1 
                         
                         
                           
                             C 
                             ⁢ 
                             1 
                           
                           + 
                           Cp 
                           + 
                           
                             
                               ( 
                               
                                 A 
                                 + 
                                 1 
                               
                               ) 
                             
                             ⁢ 
                             C 
                             ⁢ 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         { 
                         
                           Vref 
                           - 
                           
                             V 
                             ⁢ 
                             1 
                           
                           + 
                           
                             
                               1 
                               
                                 A 
                                 + 
                                 1 
                               
                             
                             ⁢ 
                             
                               ( 
                               
                                 Vofop 
                                 + 
                                 Vb 
                               
                               ) 
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         Cp 
                         
                           
                             C 
                             ⁢ 
                             1 
                           
                           + 
                           Cp 
                           + 
                           
                             
                               ( 
                               
                                 A 
                                 + 
                                 1 
                               
                               ) 
                             
                             ⁢ 
                             C 
                             ⁢ 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         A 
                         
                           A 
                           + 
                           1 
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           Vofop 
                           + 
                           Vb 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     A voltage Vsp,k of the operational amplifier  350  at the time when the first positive integration processing is repeated k times is represented by the following expression. 
       Math. 12 
         Vsp,k+Bsp 0= Bsp 1 k ( Vsp, 0+ Bsp 0)=(1−η sp ) k ( Vsp, 0+ Bsp 0)
 
         Vsp,k =(1−η sp ) k ( Vsp, 0+ Bsp 0)− Bsp 0  (17)
 
     Operation of the first negative integration processing is explained. This processing is configured by a first negative comparison step, a first negative charge accumulation step, and a first negative charge transfer step. In this processing, sp 1  and sp 2  of the polarity switching unit  36  are connected. In the first negative comparison step, connection of a 1  and c 1  of the SW 1 , connection of a 2  and b 2  of the SW 2 , and connection of a 4  and b 4  of the SW 4  are carried out. When a voltage of the operational amplifier  350  at this time is represented as Vsn,0, electric charges accumulated in the capacitor C 2  and Cp are represented by expressions obtained by replacing Vsp,0 on the right sides of Expression (2) and Expression (3) with Vsn,0. 
     In the first negative charge accumulation step, after a 4  and c 4  of the SW 4  are connected, a 2  and c 2  of the SW 2  are connected. When an output of the operational amplifier  350  is represented as Vsna,1, a differential voltage between the reference voltage V 1  and Vsna,1 is applied to the capacitor C 1 . Electric charges Q1a,1 accumulated in the capacitor C 1  in this step are represented by the following expression. 
     
       
         
           
             
               
                 
                   Math 
                   . 
                       
                   13 
                 
               
               
                   
               
             
             
               
                 
                   
                     Q 
                     ⁢ 
                     1 
                     ⁢ 
                     a 
                   
                   , 
                   
                     1 
                     = 
                     
                       C 
                       ⁢ 
                       1 
                       ⁢ 
                       
                         { 
                         
                           
                             V 
                             ⁢ 
                             1 
                           
                           - 
                           
                             
                               A 
                               
                                 A 
                                 + 
                                 1 
                               
                             
                             ⁢ 
                             
                               ( 
                               
                                 Vofop 
                                 + 
                                 Vb 
                               
                               ) 
                             
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     Electric charges accumulated in the capacitor C 2  are represented by an expression obtained by replacing sp,0 on the right side of Expression (6) with Vsn,0. Electric charges accumulated in Cp are represented by Expression (7). 
     In the first negative charge transfer step, after a 4  and b 4  of the SW 4  are connected, a 1  and b 1  of the SW 1  are connected. When an output of the operational amplifier  350  at this time is represented as Vsnb,1, electric charges accumulated in the capacitor C 1  are represented by the following expression. 
     
       
         
           
             
               
                 
                   Math 
                   . 
                       
                   14 
                 
               
               
                   
               
             
             
               
                 
                   
                     Q 
                     ⁢ 
                     1 
                     ⁢ 
                     b 
                   
                   , 
                   
                     1 
                     = 
                     
                       C 
                       ⁢ 
                       1 
                       ⁢ 
                       
                         { 
                         
                           
                             Vref 
                             + 
                             
                               
                                 1 
                                 A 
                               
                               ⁢ 
                               Vsnb 
                             
                           
                           , 
                           
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Vofop 
                                 + 
                                 Vb 
                               
                               ) 
                             
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     Electric charges accumulated in the capacitor C 2  and Cp are represented by expressions obtained by replacing Vspb,1 on the right sides of Expression (9) and Expression (10) with Vsnb,1. Electric charges accumulated in the capacitor connected to the negative input of the operational amplifier  350  before and after the first negative charge transfer step are saved. Accordingly, a relational expression between Vsnb,1 and Vsn,0 is as follows. 
     
       
         
           
             
               
                 
                                    
                   
                     Math 
                     . 
                         
                     15 
                   
                 
               
               
                   
               
             
             
               
                 
                   
                     
                       
                         - 
                         Q 
                       
                       ⁢ 
                       1 
                       ⁢ 
                       a 
                     
                     , 
                     
                       1 
                       + 
                       Qpa 
                     
                     , 
                     
                       1 
                       - 
                       
                         Q 
                         ⁢ 
                         2 
                         ⁢ 
                         a 
                       
                     
                     , 
                     
                       1 
                       = 
                       
                         
                           - 
                           Q 
                         
                         ⁢ 
                         1 
                         ⁢ 
                         b 
                       
                     
                     , 
                     
                       1 
                       + 
                       Qpb 
                     
                     , 
                     
                       1 
                       - 
                       
                         Q 
                         ⁢ 
                         2 
                         ⁢ 
                         b 
                       
                     
                     , 
                     
                       
                         1 
                         - 
                         
                           C 
                           ⁢ 
                           1 
                           ⁢ 
                           
                             { 
                             
                               
                                 V 
                                 ⁢ 
                                 1 
                               
                               - 
                               
                                 
                                   A 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     Vofop 
                                     + 
                                     Vb 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                         
                         + 
                         
                           Cp 
                           ⁢ 
                           
                             A 
                             
                               A 
                               + 
                               1 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               Vofop 
                               + 
                               Vb 
                             
                             ) 
                           
                         
                         - 
                         
                           C 
                           ⁢ 
                           2 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                   A 
                                 
                                 ⁢ 
                                 Vsp 
                               
                               , 
                               
                                 0 
                                 - 
                                 Vofop 
                                 - 
                                 Vb 
                               
                             
                             ) 
                           
                         
                       
                       = 
                       
                         
                           
                             - 
                             C 
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                             ( 
                             
                               
                                 Vref 
                                 + 
                                 
                                   
                                     1 
                                     A 
                                   
                                   ⁢ 
                                   Vsnb 
                                 
                               
                               , 
                               
                                 1 
                                 - 
                                 Vofop 
                                 - 
                                 Vb 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           Cp 
                           ⁡ 
                           ( 
                           
                             
                               
                                 - 
                                 
                                   1 
                                   
                                     A 
                                       
                                   
                                 
                               
                               ⁢ 
                               Vsnb 
                             
                             , 
                             
                               1 
                               + 
                               Vofop 
                               + 
                               Vb 
                             
                           
                           ) 
                         
                         - 
                         
                           C 
                           ⁢ 
                           2 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                   A 
                                 
                                 ⁢ 
                                 Vsnb 
                               
                               , 
                               
                                 1 
                                 - 
                                 Vofop 
                                 - 
                                 Vb 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       
                         ( 
                         
                           
                             
                               C 
                               ⁢ 
                               1 
                             
                             A 
                           
                           + 
                           
                             
                               Cp 
                               ⁢ 
                               2 
                             
                             A 
                           
                           + 
                           
                             
                               
                                 A 
                                 + 
                                 1 
                               
                               A 
                             
                             ⁢ 
                             C 
                             ⁢ 
                             2 
                           
                         
                         ) 
                       
                       ⁢ 
                       Vsnb 
                     
                     , 
                     
                       1 
                       = 
                       
                         
                           C 
                           ⁢ 
                           1 
                           ⁢ 
                           
                             { 
                             
                               
                                 V 
                                 ⁢ 
                                 1 
                               
                               - 
                               Vref 
                               + 
                               
                                 
                                   1 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     Vofop 
                                     + 
                                     Vb 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                         
                         + 
                         
                           C 
                           ⁢ 
                           2 
                           ⁢ 
                           
                             
                               A 
                               + 
                               1 
                             
                             A 
                           
                           ⁢ 
                           Vsn 
                         
                       
                     
                     , 
                     
                       0 
                       + 
                       
                         Cp 
                         ⁢ 
                         
                           1 
                           
                             A 
                             + 
                             1 
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                       
                     
                   
                   ⁢ 
                   
 
                   
                     Vsnb 
                     , 
                     
                       1 
                       = 
                       
                         
                           
                             
                               AC 
                               ⁢ 
                               1 
                             
                             
                               
                                 C 
                                 ⁢ 
                                 1 
                               
                               + 
                               Cp 
                               + 
                               
                                 
                                   ( 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 C 
                                 ⁢ 
                                 2 
                               
                             
                           
                           ⁢ 
                           
                             { 
                             
                               
                                 - 
                                 Vref 
                               
                               + 
                               
                                 V 
                                 ⁢ 
                                 1 
                               
                               + 
                               
                                 
                                   1 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     Vofop 
                                     + 
                                     Vb 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                         
                         + 
                         
                           
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               2 
                             
                             
                               
                                 C 
                                 ⁢ 
                                 1 
                               
                               + 
                               Cp 
                               + 
                               
                                 
                                   ( 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 C 
                                 ⁢ 
                                 2 
                               
                             
                           
                           ⁢ 
                           Vsp 
                         
                       
                     
                     , 
                     
                       0 
                       + 
                       
                         
                           Cp 
                           
                             
                               C 
                               ⁢ 
                               1 
                             
                             + 
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           A 
                           
                             A 
                             + 
                             1 
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                   
               
             
           
         
       
     
     An output Vsn,1 of the operational amplifier  350  and Vsnb,1 at the time when the processing transitions to the first positive comparison step again are equal. Therefore, a relational expression between Vsn1 and Vsn,0 is represented by the following expression. 
     
       
         
           
             
               
                 
                                    
                   
                     Math 
                     . 
                         
                     16 
                   
                 
               
               
                   
               
             
             
               
                 
                   Vsn 
                   , 
                   
                     1 
                     = 
                     
                       
                         
                           
                             AC 
                             ⁢ 
                             1 
                           
                           
                             
                               C 
                               ⁢ 
                               1 
                             
                             + 
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           { 
                           
                             
                               - 
                               Vref 
                             
                             + 
                             
                               V 
                               ⁢ 
                               1 
                             
                             + 
                             
                               
                                 1 
                                 
                                   A 
                                   + 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                       + 
                       
                         
                           
                             
                               ( 
                               
                                 A 
                                 + 
                                 1 
                               
                               ) 
                             
                             ⁢ 
                             C 
                             ⁢ 
                             2 
                           
                           
                             
                               C 
                               ⁢ 
                               1 
                             
                             + 
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               2 
                             
                           
                         
                         ⁢ 
                         Vsp 
                       
                     
                   
                   , 
                   
                     0 
                     + 
                     
                       
                         Cp 
                         
                           
                             C 
                             ⁢ 
                             1 
                           
                           + 
                           Cp 
                           + 
                           
                             
                               ( 
                               
                                 A 
                                 + 
                                 1 
                               
                               ) 
                             
                             ⁢ 
                             C 
                             ⁢ 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         A 
                         
                           A 
                           + 
                           1 
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           Vofop 
                           + 
                           Vb 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     According to the same development of formula as that in the first positive integration processing, a voltage Vsn,k of the operational amplifier  350  at the time when the first negative integration processing is repeated k times is represented by the following expression. 
     
       
         
           
             
               Math 
               . 
               
                   
               
               ⁢ 
               17 
             
             ⁢ 
             
                 
             
           
         
       
       
         
           
             
               
                 
                   
                     Vsn 
                     , 
                     
                       k 
                       = 
                       
                         
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   η 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   sn 
                                 
                               
                               ) 
                             
                             k 
                           
                           ⁢ 
                           
                             ( 
                             
                               Vsn 
                               , 
                               
                                 0 
                                 + 
                                 
                                   Bsn 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   0 
                                 
                               
                             
                             ) 
                           
                         
                         - 
                         
                           Bsn 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                     
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       η 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       sn 
                     
                     = 
                     
                       
                         
                           
                             C 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           + 
                           Cp 
                         
                         
                           
                             C 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           + 
                           Cp 
                           + 
                           
                             
                               ( 
                               
                                 A 
                                 + 
                                 1 
                               
                               ) 
                             
                             ⁢ 
                             C2 
                           
                         
                       
                       = 
                       
                         
                           
                             η 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             sp 
                           
                           - 
                           
                             η 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             snBsn 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                         
                         = 
                         
                           
                             
                               
                                 AC 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                               
                                 
                                   C 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 + 
                                 Cp 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       A 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   C 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                             
                             ⁢ 
                             
                               { 
                               
                                 
                                   - 
                                   Vref 
                                 
                                 + 
                                 
                                   V 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 + 
                                 
                                   
                                     1 
                                     
                                       A 
                                       + 
                                       1 
                                     
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       Vofop 
                                       + 
                                       Vb 
                                     
                                     ) 
                                   
                                 
                               
                               } 
                             
                           
                           + 
                         
                       
                     
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
             
               
                 
                   
                     Cp 
                     
                       
                         C 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       + 
                       Cp 
                       + 
                       
                         
                           ( 
                           
                             A 
                             + 
                             1 
                           
                           ) 
                         
                         ⁢ 
                         C 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                   
                   ⁢ 
                   
                     A 
                     
                       A 
                       + 
                       1 
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       Vofop 
                       + 
                       Vb 
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     Operation of the second positive integration processing is explained. This processing is configured by a second positive charge accumulation/comparison step and a second positive charge transfer step. In this processing, sp 1  and sp 2  of the polarity switching unit are connected and a 4  and b 4  of the SW 4  are connected. In the second positive charge accumulation/comparison step, a 1  and b 1  of the SW 1  are connected and a 2  and b 2  of the SW 2  are connected. When an output of the operational amplifier  350  is represented as Vlp,0, electric charges Q2,0 and Qp,0 accumulated in the capacitor C 2  and Cp are represented by expressions obtained by replacing Vsp,0 on the right sides of Expression (2) and Expression (3) with Vlp,0. Electric charges accumulated in the capacitor C 1  are represented by Expression (1). 
     In the second positive charge transfer step, a 2  and c 2  of the SW 2  are connected. When an output of the operational amplifier  350  at this time is represented as Vlpa,1, electric charges Q2a,1 and Qpa,1 accumulated in the capacitor C 2  and Cp are represented by expressions obtained by replacing Vspb.1 on the right sides of Expression (9) and Expression (10) with Vlpa,1. In the electric charges Q1a,1 accumulated in the capacitor C 1 , since connection of the SW 1 , the SW 2 , and the SW 4  is the same as that in the first negative integration processing, Q1a,1 is represented by an expression obtained by replacing Vsnb,1 on the right side of Expression (19) with Vlpa,1. A relational expression between Vlp,0 and Vlpa,1 is represented by the following expression. 
     
       
         
           
             
               
                 
                   
                     
                       Math 
                       . 
                       
                           
                       
                       ⁢ 
                       18 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
 
                     
                     - 
                     
                       Q 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                       ⁢ 
                       a 
                     
                   
                   , 
                   
                     1 
                     + 
                     Qpa 
                   
                   , 
                   
                     1 
                     - 
                     
                       Q 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                       ⁢ 
                       a 
                     
                   
                   , 
                   
                     1 
                     = 
                     
                       
                         - 
                         Q 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   , 
                   
                     1 
                     + 
                     Qp 
                   
                   , 
                   
                     1 
                     - 
                     
                       Q 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   , 
                   
                     
                       1 
                       - 
                       
                         C 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         
                           { 
                           
                             
                               Vref 
                               + 
                               
                                 
                                   1 
                                   A 
                                 
                                 ⁢ 
                                 V 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 lpa 
                               
                             
                             , 
                             
                               1 
                               - 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                       + 
                       
                         Cp 
                         ⁢ 
                         
                           { 
                           
                             
                               
                                 - 
                                 
                                   1 
                                   A 
                                 
                               
                               ⁢ 
                               Vlpa 
                             
                             , 
                             
                               1 
                               + 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                       - 
                       
                         C 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         
                           { 
                           
                             
                               
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 A 
                               
                               ⁢ 
                               Vlpa 
                             
                             , 
                             
                               1 
                               - 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                     
                     = 
                     
                       - 
                       
                           
                         
                           
                             
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                               ⁢ 
                               Vref 
                             
                             + 
                             
                               Cp 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     - 
                                     
                                       
                                         Vlp 
                                         ⁢ 
                                         .0 
                                       
                                       A 
                                     
                                   
                                   + 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                             
                             - 
                             
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 { 
                                 
                                   
                                     
                                       
                                         A 
                                         + 
                                         1 
                                       
                                       A 
                                     
                                     ⁢ 
                                     Vlp 
                                   
                                   , 
                                   
                                     0 
                                     - 
                                     
                                       ( 
                                       
                                         Vofop 
                                         + 
                                         Vb 
                                       
                                       ) 
                                     
                                   
                                 
                                 } 
                               
                               ⁢ 
                               
                                 
 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     
                                       C 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                     A 
                                   
                                   + 
                                   
                                     
                                       Cp 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                     A 
                                   
                                   + 
                                   
                                     
                                       
                                         A 
                                         + 
                                         1 
                                       
                                       A 
                                     
                                     ⁢ 
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               Vlpa 
                             
                           
                           , 
                           
                               
                           
                           ⁢ 
                           
                             
 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             1 
                             = 
                             
                               
                                 C 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     Vofop 
                                     + 
                                     Vb 
                                   
                                   ) 
                                 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     
                                       
                                         Cp 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                       
                                       A 
                                     
                                     + 
                                     
                                       C 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                       ⁢ 
                                       
                                         
                                           A 
                                           + 
                                           1 
                                         
                                         A 
                                       
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 Vlp 
                               
                             
                           
                           , 
                           
                             0 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
 
                             
                             ⁢ 
                             Vlpa 
                           
                           , 
                           
                             1 
                             = 
                             
                               
                                 
                                   
                                     AC 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   
                                     
                                       C 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                     + 
                                     Cp 
                                     + 
                                     
                                       
                                         ( 
                                         
                                           A 
                                           + 
                                           1 
                                         
                                         ) 
                                       
                                       ⁢ 
                                       C 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     Vofop 
                                     + 
                                     Vb 
                                   
                                   ) 
                                 
                               
                               + 
                               
                                 
                                   
                                     Cp 
                                     + 
                                     
                                       
                                         ( 
                                         
                                           A 
                                           + 
                                           1 
                                         
                                         ) 
                                       
                                       ⁢ 
                                       C 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                   
                                   
                                     
                                       C 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                     + 
                                     Cp 
                                     + 
                                     
                                       
                                         ( 
                                         
                                           A 
                                           + 
                                           1 
                                         
                                         ) 
                                       
                                       ⁢ 
                                       C 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                   
                                 
                                 ⁢ 
                                 Vlp 
                               
                             
                           
                           , 
                           0 
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     A voltage Vlp,1 of the operational amplifier  350  and Vlpa1 at the time when the processing transitions to the second positive charge accumulation/comparison step again are equal. Therefore, a relational expression between Vlp,1 and V1p,0 is represented by the following expression. 
     
       
         
           
             
               
                 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     19 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   Vlp 
                   , 
                   
                     1 
                     = 
                     
                       
                         
                           
                             AC 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           
                             
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             + 
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                       
                       + 
                       
                         
                           
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           
                             
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             + 
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                         
                         ⁢ 
                         Vlp 
                       
                     
                   
                   , 
                   0 
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     According to the same development of formula as that in the first positive integration processing, a voltage Vlp,k of the operational amplifier  350  at the time when the second positive integration processing is repeated k times is represented by the following expression. 
     
       
         
           
             
               
                 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     20 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   Vpl 
                   , 
                   
                     k 
                     = 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 η 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 lp 
                               
                             
                             ) 
                           
                           k 
                         
                         ⁢ 
                         
                           ( 
                           
                             Vlp 
                             , 
                             
                               0 
                               + 
                               
                                 Blp 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 0 
                               
                             
                           
                           ) 
                         
                       
                       - 
                       
                         Blp 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                       
                     
                   
                 
               
               
                 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     25 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       η 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       lp 
                     
                     = 
                     
                       
                         C 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       
                         
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         + 
                         Cp 
                         + 
                         
                           
                             ( 
                             
                               A 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                     
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     26 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       - 
                       η 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     lp 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Blp 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                   
                   = 
                   
                     
                       
                         AC 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       
                         
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         + 
                         Cp 
                         + 
                         
                           
                             ( 
                             
                               A 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         Vofop 
                         + 
                         Vb 
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     27 
                     ) 
                   
                 
               
             
           
         
       
     
     Operation of the second negative integration processing is explained. This processing is configured by a second negative charge accumulation/comparison step and a negative charge transfer step. In this processing, sp 1  and sp 3  of the polarity switching unit  36  are connected and a 4  and b 4  of the SW 4  are connected. In the second negative charge accumulation/comparison step, a 1  and b 1  of the SW 1  are connected and a 2  and b 2  of the SW 2  are connected. When an output of the operational amplifier  350  is represented as Vln,0, electric charges Q2,0 and Qp,0 accumulated in the capacitor C 2  and Cp are represented by expressions obtained by replacing Vsp,0 on the right sides of Expressions (2) and Expression (3) with Vln,0. Electric charges Q1,0 accumulated in the capacitor C 1  are represented by the following expression (28). 
       Math. 21 
         Q 1,0= C 1( V ref− V ref)=0  (28)
 
     In the second negative charge transfer step, a 2  and c 2  of the SW 2  are connected. When an output of the operational amplifier  350  at this time is represented as Vlna,1, electric charges Q2a,1 and Qpa,1 accumulated in the capacitor C 2  and Cp are represented by expressions obtained by replacing Vspb,1 on the right sides of Expression (9) and Expression (10) with Vlna,1. In electric charges Q1a,1 accumulated in the capacitor C 1 , since connection of the SW 1 , the SW 2 , and the SW 4  is the same as that in the first negative integration processing, Q1a,1 is represented by an expression obtained by replacing Vsnb,1 on the right side of Expression (19) with Vlna,1. A relational expression between V1p,0 and Vlpa,1 is represented by the following expression. 
     
       
         
           
             
               
                 Math 
                 . 
                 
                     
                 
                 ⁢ 
                 22 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
 
               
               - 
               
                 Q 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 1 
                 ⁢ 
                 a 
               
             
             , 
             
               1 
               + 
               Qpa 
             
             , 
             
               1 
               - 
               
                 Q 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 2 
                 ⁢ 
                 a 
               
             
             , 
             
               1 
               = 
               
                 
                   - 
                   Q 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 1 
               
             
             , 
             
               1 
               + 
               Qp 
             
             , 
             
               1 
               - 
               
                 Q 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 2 
               
             
             , 
             
               
                 1 
                 - 
                 
                   C 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                   ⁢ 
                   
                     { 
                     
                       
                         Vref 
                         + 
                         
                           
                             1 
                             A 
                           
                           ⁢ 
                           Vlna 
                         
                       
                       , 
                       
                         1 
                         - 
                         
                           ( 
                           
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                       
                     
                     } 
                   
                 
                 + 
                 
                   Cp 
                   ⁢ 
                   
                     { 
                     
                       
                         
                           - 
                           
                             1 
                             A 
                           
                         
                         ⁢ 
                         Vlna 
                       
                       , 
                       
                         1 
                         + 
                         
                           ( 
                           
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                       
                     
                     } 
                   
                 
                 - 
                 
                   C 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                   ⁢ 
                   
                     { 
                     
                       
                         
                           
                             A 
                             + 
                             1 
                           
                           A 
                         
                         ⁢ 
                         Vlna 
                       
                       , 
                       
                         1 
                         - 
                         
                           ( 
                           
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                       
                     
                     } 
                   
                 
               
               = 
               
                 
                   Cp 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         - 
                         
                           
                             Vln 
                             , 
                             0 
                           
                           A 
                         
                       
                       + 
                       Vofop 
                       + 
                       Vb 
                     
                     ) 
                   
                 
                 - 
                 
                   C 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                   ⁢ 
                   
                     { 
                     
                       
                         
                           
                             A 
                             + 
                             1 
                           
                           A 
                         
                         ⁢ 
                         Vln 
                       
                       , 
                       
                         0 
                         - 
                         
                           ( 
                           
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                       
                     
                     } 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
             ⁢ 
             
               
                 
                   ( 
                   
                     
                       
                         C 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       A 
                     
                     + 
                     
                       
                         Cp 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       A 
                     
                     + 
                     
                       
                         
                           A 
                           + 
                           1 
                         
                         A 
                       
                       ⁢ 
                       C 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   ) 
                 
                 ⁢ 
                 Vlna 
               
               , 
               
                   
               
               ⁢ 
               
                 1 
                 = 
                 
                   
                     C 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                       ( 
                       
                         
                           - 
                           Vref 
                         
                         + 
                         Vofop 
                         + 
                         Vb 
                       
                       ) 
                     
                   
                   + 
                   
                     
                       ( 
                       
                         
                           
                             Cp 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                           A 
                         
                         + 
                         
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                           ⁢ 
                           
                             
                               A 
                               + 
                               1 
                             
                             A 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     Vln 
                   
                 
               
               , 
               0 
             
             ⁢ 
             
                 
             
           
         
       
       
         
           
             Vlna 
             , 
             
               1 
               = 
               
                 
                   
                     
                       AC 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                     
                       
                         C 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       + 
                       Cp 
                       + 
                       
                         
                           ( 
                           
                             A 
                             + 
                             1 
                           
                           ) 
                         
                         ⁢ 
                         C 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         - 
                         Vref 
                       
                       + 
                       Vofop 
                       + 
                       Vb 
                     
                     ) 
                   
                 
                 + 
                 
                   
                     
                       Cp 
                       + 
                       
                         
                           ( 
                           
                             A 
                             + 
                             1 
                           
                           ) 
                         
                         ⁢ 
                         C 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     
                       
                         C 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       + 
                       Cp 
                       + 
                       
                         
                           ( 
                           
                             A 
                             + 
                             1 
                           
                           ) 
                         
                         ⁢ 
                         C 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                   
                   ⁢ 
                   Vln 
                 
               
             
             , 
             0 
           
         
       
     
     A voltage Vln,1 of the operational amplifier  350  and Vlna1 at the time when the processing transitions to the second negative charge accumulation/comparison step again are equal. Therefore, a relational expression between Vln,1 and Vln,0 is represented by the following expression. 
     
       
         
           
             
               
                 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     23 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   Vln 
                   , 
                   
                     1 
                     = 
                     
                       
                         
                           
                             AC 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           
                             
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             + 
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               - 
                               Vref 
                             
                             + 
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                       
                       + 
                       
                         
                           
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           
                             
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             + 
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                         
                         ⁢ 
                         Vln 
                       
                     
                   
                   , 
                   0 
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
           
         
       
     
     According to the same development of formula as that in the first positive integration processing, a voltage Vln,k of the operational amplifier  350  at the time when the second negative integration processing is repeated k times is represented by the following expressions. 
     
       
         
           
             
               
                 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     24 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Vln 
                     , 
                     
                       k 
                       = 
                       
                         
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   η 
                                   ⁢ 
                                   ln 
                                 
                               
                               ) 
                             
                             k 
                           
                           ⁢ 
                           
                             ( 
                             
                               Vln 
                               , 
                               
                                 0 
                                 + 
                                 
                                   
                                     B 
                                     ⁢ 
                                     ln 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   0 
                                 
                               
                             
                             ) 
                           
                         
                         - 
                         
                           
                             B 
                             ⁢ 
                             ln 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                     
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     30 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       η 
                       ⁢ 
                       ln 
                     
                     = 
                     
                       
                         C 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       
                         
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         + 
                         Cp 
                         + 
                         
                           
                             ( 
                             
                               A 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                     
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     31 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       - 
                       
                         η 
                         ⁢ 
                         ln 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       B 
                       ⁢ 
                       ln 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                   
                   = 
                   
                     
                       
                         AC 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       
                         
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         + 
                         Cp 
                         + 
                         
                           
                             ( 
                             
                               A 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           - 
                           Vref 
                         
                         + 
                         Vofop 
                         + 
                         Vb 
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     32 
                     ) 
                   
                 
               
             
           
         
       
     
     Processing in the calibration control unit  21  is explained below. The calibration control unit  21  is configured by an intermediate-voltage integrating unit  210 , an intermediate-voltage-excess integrating unit  211 , and a reference-voltage integrating unit  212 . 
     A processing flow of the intermediate-voltage integrating unit  210  is shown in  FIG. 2 . When the processing is started, in initialization processing, the intermediate-voltage integrating unit  210  connects st 1  and st 3  of the determination-voltage switching unit  31  and performs connection and disconnection of the SW 3  to reset electric charges accumulated in the capacitor C 2  (step S 1 ). Thereafter, the intermediate-voltage integrating unit  210  executes second positive integration processing (step S 2 ) and second positive integration and comparison processing (step S 3 ) until an integrated voltage Vo, which is an output voltage of the integrating unit  35 , becomes larger than V 1 . In the second positive integration and comparison processing, the intermediate-voltage integrating unit  210  monitors an output of the determiner  33  in the case in which s 11  and S 13  of the crossbar switch  32  are connected and s 12  and s 14  of the crossbar switch  32  are connected and in the case in which s 11  and s 14  of the crossbar switch  32  are connected and s 12  and s 13  of the crossbar switch  32  are connected. The processing transitions to the next first negative integration processing (step S 4 ) when the integrated voltage becomes larger than V 1  in both the cases. 
     An offset voltage Vofc is present on a positive input side of the determiner  33 . When s 11  and s 13  are connected and s 12  and s 14  are connected, a positive input of the determiner  33  is equivalently Vo+Vofc and a negative input of the determiner  33  is V 1 . A determination signal of an output of the determiner  33  is a low voltage signal when Vo is small and is a high voltage signal when Vo is large. When s 11  and s 14  are connected and s 12  and s 13  are connected, the positive input of the determiner  33  is equivalently V 1 +Vofc and the negative input of the determiner  33  is Vo. The determination signal is the high voltage signal when Vo is small and is the low voltage signal when Vo is large. Accordingly, the second positive integration processing and the second positive integration and comparison processing are executed until the determination signal becomes the high voltage signal when s 11  and s 13  are connected and s 12  and s 14  are connected and the determination signal becomes the low voltage signal when the s 11  and s 14  are connected and s 12  and s 13  are connected. When the number of times of the second positive integration processing at the time when Vo&gt;V 1  for the first time in both of the case in which s 11  and s 13  are connected and s 12  and s 14  are connected and the case in which s 11  and s 14  are connected and s 12  and s 13  are connected is represented as km21+1, km21 is defined as the number of times of intermediate potential second positive integration processing. 
     After the processing transitions to the first negative integration processing, the intermediate-voltage integrating unit  210  repeats the first negative integration processing (step S 4 ) and the first negative integration and comparison processing (step S 5 ) until Vo&lt;V 1  in both of the case in which the s 11  and s 13  are connected and s 12  and s 14  are connected and the case in which s 11  and s 14  are connected and s 12  and s 13  are connected. 
     An example of a relation between an integrated voltage and the number of times of integration is shown in  FIG. 3 . A unit voltage in the second positive integration processing is represented as VG2 and a unit voltage in the first negative integration processing is represented as VG1. In  FIG. 2 , Vofc&gt;0. After once Vo&gt;V 1 +Vofc in the second positive integration processing, V 1 +Vofc&gt;Vo according to the first negative integration processing. When the first negative integration processing is further continued, V 1 −Vofc&gt;Vo. When the number of times of integration at the time when V 1 +Vofc&gt;Vo for the first time according to the first negative integration processing after the number of times of integration is km21+1 is represented as km11p+1 (counted from km21+1), km11p is defined as the number of times of intermediate potential first negative integration processing 1. 
     An integrated voltage Vo at the time when, after the capacitor C 2  is reset, the second positive integration processing is repeated km21+1 times and the first negative integration processing is repeated km11p times is calculated. Since this is the same operation as the operation of the unity gain buffer at the time when the capacitor C 2  is reset, when an output of the operational amplifier is represented as Vlp,0, Vlp,0 is represented by the following expression. 
     
       
         
           
             
               
                 
                   Math 
                   . 
                   
                       
                   
                   ⁢ 
                   25 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   Vlp 
                   , 
                   
                     0 
                     = 
                     
                       
                         A 
                         
                           A 
                           + 
                           1 
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           Vofop 
                           + 
                           Vb 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
           
         
       
     
     Vo is calculated by performing development of formula with Vsn,0 of Expression (21) as Vlp, km21+1. Vo is the following expression when development of formula is performed using Maclaurin&#39;s expansion with k1=km11p, k2=km21+1 and ηlp«1 and ηsn«1. 
     
       
         
           
             
               
                 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     26 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   Vo 
                   = 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 η 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 sn 
                               
                             
                             ) 
                           
                           
                             k 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         ⁢ 
                         
                           { 
                           
                             
                               
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       η 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       lp 
                                     
                                   
                                   ) 
                                 
                                 
                                   k 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Vlp 
                                   , 
                                   
                                     0 
                                     + 
                                     
                                       Blp 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       0 
                                     
                                   
                                 
                                 ) 
                               
                             
                             - 
                             
                               Blp 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               0 
                             
                             + 
                             
                               Bsn 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               0 
                             
                           
                           } 
                         
                       
                       - 
                       
                         Bsn 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                       
                     
                     = 
                     
                       
                         
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   η 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   sn 
                                 
                               
                               ) 
                             
                             
                               k 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   η 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   lp 
                                 
                               
                               ) 
                             
                             
                               k 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               Vlp 
                               , 
                               
                                 0 
                                 + 
                                 
                                   Blp 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   0 
                                 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   η 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   sn 
                                 
                               
                               ) 
                             
                             
                               k 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   - 
                                   Blp 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 0 
                               
                               + 
                               
                                 Bsn 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 0 
                               
                             
                             ) 
                           
                         
                         - 
                         
                           Bsn 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                       = 
                       
                         
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   η 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   sn 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   k 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 - 
                                 
                                   η 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   lp 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   k 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 Vlp 
                                 , 
                                 
                                   0 
                                   + 
                                   
                                     Blp 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     0 
                                   
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   η 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   sn 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   k 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     - 
                                     Blp 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   0 
                                 
                                 + 
                                 
                                   Bsn 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   0 
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             Bsn 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                         
                         = 
                         
                             
                           
                             Vlp 
                             , 
                             
                               
                                 0 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       
                                         - 
                                         η 
                                       
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       lp 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       k 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       Vlp 
                                       , 
                                       
                                         0 
                                         + 
                                         
                                           Blp 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           0 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       
                                         - 
                                         η 
                                       
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       sn 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       k 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       Vlp 
                                       , 
                                       
                                         0 
                                         + 
                                         
                                           Bsn 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           0 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                               = 
                               
                                 
                                   
                                     
                                       A 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         Vofop 
                                         + 
                                         Vb 
                                       
                                       ) 
                                     
                                   
                                   + 
                                   
                                     k 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     
                                       { 
                                       
                                         
                                           
                                             - 
                                             
                                               
                                                 C 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 1 
                                               
                                               
                                                 
                                                   C 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   1 
                                                 
                                                 + 
                                                 Cp 
                                                 + 
                                                 
                                                   
                                                     ( 
                                                     
                                                       A 
                                                       + 
                                                       1 
                                                     
                                                     ) 
                                                   
                                                   ⁢ 
                                                   C 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   2 
                                                 
                                               
                                             
                                           
                                           ⁢ 
                                           
                                             A 
                                             
                                               A 
                                               + 
                                               1 
                                             
                                           
                                           ⁢ 
                                           
                                             ( 
                                             
                                               Vofop 
                                               + 
                                               Vb 
                                             
                                             ) 
                                           
                                         
                                         + 
                                         
                                           
                                             
                                               AC 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               1 
                                             
                                             
                                               
                                                 C 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 1 
                                               
                                               + 
                                               Cp 
                                               + 
                                               
                                                 
                                                   ( 
                                                   
                                                     A 
                                                     + 
                                                     1 
                                                   
                                                   ) 
                                                 
                                                 ⁢ 
                                                 C 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 2 
                                               
                                             
                                           
                                           ⁢ 
                                           
                                             ( 
                                             
                                               Vofop 
                                               + 
                                               Vb 
                                             
                                             ) 
                                           
                                         
                                       
                                       } 
                                     
                                   
                                   + 
                                   
                                     k 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                     ⁢ 
                                     
                                       { 
                                       
                                         
                                           
                                             - 
                                             
                                               
                                                 
                                                   C 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   1 
                                                 
                                                 + 
                                                 Cp 
                                               
                                               
                                                 
                                                   C 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   1 
                                                 
                                                 + 
                                                 Cp 
                                                 + 
                                                 
                                                   
                                                     ( 
                                                     
                                                       A 
                                                       + 
                                                       1 
                                                     
                                                     ) 
                                                   
                                                   ⁢ 
                                                   C 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   2 
                                                 
                                               
                                             
                                           
                                           ⁢ 
                                           
                                             A 
                                             
                                               A 
                                               + 
                                               1 
                                             
                                           
                                           ⁢ 
                                           
                                             ( 
                                             
                                               Vofop 
                                               + 
                                               Vb 
                                             
                                             ) 
                                           
                                         
                                         + 
                                         
                                           
                                             
                                               AC 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               1 
                                             
                                             
                                               
                                                 C 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 1 
                                               
                                               + 
                                               Cp 
                                               + 
                                               
                                                 
                                                   ( 
                                                   
                                                     A 
                                                     + 
                                                     1 
                                                   
                                                   ) 
                                                 
                                                 ⁢ 
                                                 C 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 2 
                                               
                                             
                                           
                                           ⁢ 
                                           
                                             { 
                                             
                                               
                                                 - 
                                                 Vref 
                                               
                                               + 
                                               
                                                 V 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 1 
                                               
                                               + 
                                               
                                                 
                                                   1 
                                                   
                                                     A 
                                                     + 
                                                     1 
                                                   
                                                 
                                                 ⁢ 
                                                 
                                                   ( 
                                                   
                                                     Vofop 
                                                     + 
                                                     Vb 
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             } 
                                           
                                         
                                         + 
                                         
                                           
                                             Cp 
                                             
                                               
                                                 C 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 1 
                                               
                                               + 
                                               Cp 
                                               + 
                                               
                                                 
                                                   ( 
                                                   
                                                     A 
                                                     + 
                                                     1 
                                                   
                                                   ) 
                                                 
                                                 ⁢ 
                                                 C 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 2 
                                               
                                             
                                           
                                           ⁢ 
                                           
                                             A 
                                             
                                               A 
                                               + 
                                               1 
                                             
                                           
                                           ⁢ 
                                           
                                             ( 
                                             
                                               Vofop 
                                               + 
                                               Vb 
                                             
                                             ) 
                                           
                                         
                                       
                                       } 
                                     
                                   
                                 
                                 = 
                                 
                                   
                                     k 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     
                                       
                                         AC 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         1 
                                       
                                       
                                         
                                           C 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           1 
                                         
                                         + 
                                         Cp 
                                         + 
                                         
                                           
                                             ( 
                                             
                                               A 
                                               + 
                                               1 
                                             
                                             ) 
                                           
                                           ⁢ 
                                           C 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           2 
                                         
                                       
                                     
                                     ⁢ 
                                     
                                       A 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         Vofop 
                                         + 
                                         Vb 
                                       
                                       ) 
                                     
                                   
                                   + 
                                   
                                     k 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                     ⁢ 
                                     
                                       
                                         AC 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         1 
                                       
                                       
                                         
                                           C 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           1 
                                         
                                         + 
                                         Cp 
                                         + 
                                         
                                           
                                             ( 
                                             
                                               A 
                                               + 
                                               1 
                                             
                                             ) 
                                           
                                           ⁢ 
                                           C 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           2 
                                         
                                       
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           - 
                                           Vref 
                                         
                                         + 
                                         
                                           V 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           1 
                                         
                                       
                                       ) 
                                     
                                   
                                   + 
                                   
                                     
                                       A 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         Vofop 
                                         + 
                                         Vb 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Vo 
                     = 
                     
                       
                         k 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         VG 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         k 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         VG 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       + 
                       Vofb 
                     
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                   ( 
                   34 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       VG 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                     = 
                     
                       
                         
                           AC 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         
                           
                             C 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           + 
                           Cp 
                           + 
                           
                             
                               ( 
                               
                                 A 
                                 + 
                                 1 
                               
                               ) 
                             
                             ⁢ 
                             C 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         A 
                         
                           A 
                           + 
                           1 
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           Vofop 
                           + 
                           Vb 
                         
                         ) 
                       
                     
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                   ( 
                   35 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       VG 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                     = 
                     
                       
                         
                           AC 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         
                           
                             C 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           + 
                           Cp 
                           + 
                           
                             
                               ( 
                               
                                 A 
                                 + 
                                 1 
                               
                               ) 
                             
                             ⁢ 
                             C 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           Vref 
                           - 
                           
                             V 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         ) 
                       
                     
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                   ( 
                   36 
                   ) 
                 
               
             
             
               
                 
                   
                     Vofb 
                     = 
                     
                       
                         A 
                         
                           A 
                           + 
                           1 
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           Vofop 
                           + 
                           Vb 
                         
                         ) 
                       
                     
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                   ( 
                   37 
                   ) 
                 
               
             
           
         
       
     
     The following expression holds at the time when V1+Vofc=Vo. 
       Math. 27 
         V 1+ V olk=( km 21+1) VG 2−( km 11 p+δkm 11 p ) VG 1+ V ofb  (38)
 
     In Expression (38), δkm11p is a real number equal to or larger than 0 and smaller than 1 and represents a difference between an integrated voltage and Vref+Vofc at the time when VG1δkm11p is the number of times of integration km11p. 
     When the number of times of integration at the time when V1−Vofc&gt;Vo for the first time according to the first negative integration processing after the number of times of integration is km21+1 is represented as km11n+1, km11n is defined as the number of times of intermediate potential first negative integration processing 2. The following expression holds at the time when V1−Vofc=Vo. 
       Math. 28 
         V 1− V ofc=( km 21+1) VG 2−( km 11 n+δkm 11 n )  VG 1+ V ofb  (39)
 
     A processing flow of the intermediate-voltage-excess integrating unit  211  is shown in  FIG. 4 . This processing is different from the processing of the intermediate-voltage integrating unit  211  in that excess second positive integration processing (step S 13 ) is carried out before first negative integration and comparison processing (step S 15 ). Second positive integration processing is carried out in the excess second positive integration processing (step S 13 ). Therefore, an expression that holds at the time when V1+Vofc=V0 and at the time when V1−Vofc=Vo is the following expression. 
       Math. 29 
         V 1+ V ofc=( km 21+2)  VG 2−( km 12 p+δkm 12p)  VG 1+ V ofb  (40)
 
         V 1− V ofc=( km 21+2)  VG 2−( km 12 n+δkm 12 n )  VG 1+ V ofb  (41)
 
     A processing flow of the reference-voltage integrating unit  212  is shown in  FIG. 5 . This processing is different from the processing of the intermediate-voltage integrating unit  212  in processing for inputting a reference voltage to the determiner  33  and comparing an integrated voltage and the reference voltage. Accordingly, st 1  and st 2  of the determination-voltage switching unit  31  are connected in initialization processing. An expression that holds at the time when Vref+Vofc=Vo and at the time when Vref−Vofc=Vo is the following expression. 
       Math. 30 
         V ref+ V ofc=( kr 2+1)  VG 2−( kr 1 p+δkr 1 p )  VG 1+ V ofb  (42)
 
         V ref− V ofc=( kr 2+2)  VG 2−( kr 1 n+δkr 1 n )  VG 1+ V ofb  (43)
 
     When the operations of the intermediate-voltage integrating unit  210 , the intermediate-voltage-excess integrating unit  211 , and the reference-voltage integrating unit  212  are completed, the reference-voltage integrating unit  212  derives calibration values of VG2 and VG1. Vofc is cancelled from Expression (38) according to Expression (43) to obtain the following expressions. 
       Math. 31 
         V 1=( km 21+1)  VG 2− Km 11  VG 1+ V ofb  (44)
 
         V 1=( km 21+2)  VG 2− Km 12  VG 1+ V ofb  (45)
 
         V ref=( kr 2+1)  VG 2− Kr 1 VG 1+ V ofb  (46)
 
     In Expression (44), Km11=(km11p+δkm11p+km11n+δkm11n)/2. In Expression (45), Km12=(km12p+δkm12p+km12n+δkm12n)/2. In Expression (46), Kr1=(kr1p+δkr1p+kr1n+δkr1n)/2. The following expression holds from Expression (35) and Expression (36). 
     
       
         
           
             
               
                 
                   Math 
                   . 
                   
                       
                   
                   ⁢ 
                   32 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       VG 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                     
                       VG 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   = 
                   
                     Vofb 
                     
                       Vref 
                       - 
                       Vi 
                     
                   
                 
               
               
                 
                   ( 
                   47 
                   ) 
                 
               
             
           
         
       
     
     The following relational expression holds between VG1 and VG2 from Expression (44) and Expression (45). 
       Math. 33 
       0= VG 2−( Km 12− Km 11)  VG 1
 
         VG 2=( Km 12− Km 11)  VG 1  (48)
 
     When Expression (48) is substituted in Expression (47), Expression (49) is obtained. 
       Math. 34 
         V ofb=( Km 12− Km 11)( V ref− V 1)  (49)
 
     When a difference between Expression (46) and Expression (44) is calculated, the following Expression (50) is obtained. 
       Math. 35 
         V ref− V 1=( kr 2− km 21)  VG 2−( Kr 1− Km 11) VG 1=( kr 2− km 21)( Km 12− Km 11)  VG 1−( Kr 1− Km 11) VG 1  (50)
 
     An expression of VG1 is obtained by substituting Expression (50), Expression (49), and Expression (48) in Expression (46). 
     
       
         
           
             
               
                 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     36 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   Vref 
                   = 
                   
                     
                       
                         ( 
                         
                           
                             kr 
                             2 
                           
                           + 
                           1 
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             Km 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                           - 
                           
                             Km 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             11 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       VG 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                     - 
                     
                         
                       
                         Kr 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         VG 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         
                             
                           
                             + 
                             
                                 
                               
                                 
                                   ( 
                                   
                                     
                                       Km 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       12 
                                     
                                     - 
                                     
                                       Km 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       11 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   { 
                                   
                                     
                                       
                                         ( 
                                         
                                           
                                             kr 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             2 
                                           
                                           - 
                                           
                                             km 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             21 
                                           
                                         
                                         ) 
                                       
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         ( 
                                         
                                           
                                             Km 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             12 
                                           
                                           - 
                                           
                                             Km 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             11 
                                           
                                         
                                         ) 
                                       
                                       ⁢ 
                                       VG 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                     - 
                                     
                                       
                                         ( 
                                         
                                           
                                             Kr 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             1 
                                           
                                           - 
                                           
                                             Km 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             11 
                                           
                                         
                                         ) 
                                       
                                       ⁢ 
                                       VG 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                   
                                   } 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           VG 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         = 
                           
                         ⁢ 
                         
                           Vref 
                           
                             
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           kr 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           2 
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           Km 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           12 
                                         
                                         - 
                                         
                                           Km 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           11 
                                         
                                       
                                       ) 
                                     
                                   
                                   - 
                                 
                               
                             
                             
                               
                                 
                                   
                                     Kr 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   
                                     ( 
                                     
                                       
                                         Km 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         12 
                                       
                                       - 
                                       
                                         Km 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         11 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   ( 
                                   
                                     
                                       
                                         ( 
                                         
                                           
                                             kr 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             2 
                                           
                                           - 
                                           
                                             km 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             21 
                                           
                                         
                                         ) 
                                       
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         ( 
                                         
                                           
                                             Km 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             12 
                                           
                                           - 
                                           
                                             Km 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             11 
                                           
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       ( 
                                       
                                         
                                           Kr 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           1 
                                         
                                         - 
                                         
                                           Km 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           11 
                                         
                                       
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                     
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           Vref 
                           
                             
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           kr 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           2 
                                         
                                         - 
                                         
                                           km 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           21 
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     
                                       
                                         ( 
                                         
                                           
                                             Km 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             12 
                                           
                                           - 
                                           
                                             Km 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             11 
                                           
                                         
                                         ) 
                                       
                                       2 
                                     
                                   
                                   + 
                                 
                               
                             
                             
                               
                                 
                                   ( 
                                   
                                     
                                       kr 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                     + 
                                     1 
                                     - 
                                     
                                       Kr 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                     + 
                                     
                                       Km 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       11 
                                     
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         Km 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         12 
                                       
                                       - 
                                       
                                         Km 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         11 
                                       
                                     
                                     ) 
                                   
                                   - 
                                   
                                     Kr 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   51 
                   ) 
                 
               
             
           
         
       
     
     Expressions of Vofb and VG2 are obtained as described below. 
     
       
         
           
             
               
                 
                   Math 
                   . 
                   
                       
                   
                   ⁢ 
                   37 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     VG 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             Km 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             12 
                           
                           - 
                           
                             Km 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             11 
                           
                         
                         ) 
                       
                       ⁢ 
                       Vref 
                     
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     kr 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                   - 
                                   
                                     km 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     21 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   ( 
                                   
                                     
                                       Km 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       12 
                                     
                                     - 
                                     
                                       Km 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       11 
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                             
                             + 
                           
                         
                       
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     kr 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                   + 
                                   1 
                                   - 
                                   
                                     Kr 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   
                                     Km 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     11 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     Km 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     12 
                                   
                                   - 
                                   
                                     Km 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     11 
                                   
                                 
                                 ) 
                               
                             
                             - 
                             
                               Kr 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   52 
                   ) 
                 
               
             
             
               
                 
                   Vofb 
                   = 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       kr 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                     - 
                                     
                                       km 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       21 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     ( 
                                     
                                       
                                         Km 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         12 
                                       
                                       - 
                                       
                                         Km 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         11 
                                       
                                     
                                     ) 
                                   
                                   2 
                                 
                               
                               - 
                             
                           
                         
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     Kr 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   - 
                                   
                                     Km 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     11 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     Km 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     12 
                                   
                                   - 
                                   
                                     Km 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     11 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       kr 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                     - 
                                     
                                       km 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     ( 
                                     
                                       
                                         Km 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         12 
                                       
                                       - 
                                       
                                         Km 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         11 
                                       
                                     
                                     ) 
                                   
                                   2 
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               ( 
                               
                                 
                                   kr 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                                 + 
                                 1 
                                 - 
                                 
                                   Kr 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 + 
                                 
                                   Km 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   11 
                                 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     Km 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     12 
                                   
                                   - 
                                   
                                     Km 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     11 
                                   
                                 
                                 ) 
                               
                               - 
                               
                                 Kr 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                           
                         
                       
                     
                     ⁢ 
                     Vref 
                   
                 
               
               
                 
                   ( 
                   53 
                   ) 
                 
               
             
           
         
       
     
     Calibration values of VG1, VG2, and Vofb can be obtained according to km21, km11, km12, kr2, and kr1 obtained by the above processing. 
     When a variable reference voltage is output, the number of times of integration for enabling a voltage closest to a value requested by setting data to be output is calculated using the calibration values obtained by the calibration processing explained above and integration processing is executed. When the value requested by the setting data is a value larger than Vofb, the processing in a positive-voltage-integration processing unit  221  of the output control unit  22  is executed. When the value requested by the setting data is a value smaller than Vofb, the processing in a negative-voltage-integration processing unit  222  is executed. 
     A processing flow of the positive-voltage-integration processing unit  221  is shown in  FIG. 6 . In initialization processing, the positive-voltage-integration processing unit  221  performs connection and disconnection of the SW 3  and resets electric charges accumulated in the capacitor C 2  (step S 20 ). Thereafter, the positive-voltage-integration processing unit  221  executes second positive integration processing (step S 21 ) and first positive integration processing (step S 22 ) by the numbers of times of integration k2 and k1 for enabling a voltage closest to a value requested by setting data calculated by the output control unit  22  to be output. The positive-voltage-integration processing unit  221  derives the integrated voltage Vo after the execution of these kinds of processing below. An initial value of the second positive integration processing (step S 21 ) is the same as Expression (33). Since the first positive integration processing is executed k1 times after the second positive integration processing is executed k2 times, Vo is the following expression from Expression (25) and Expression (17). 
     
       
         
           
             
               
                 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     38 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           Vo 
                           = 
                           
                             
                               
                                 
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       
                                         η 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         sp 
                                       
                                     
                                     ) 
                                   
                                   
                                     k 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   { 
                                   
                                     
                                       
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             
                                               η 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               lp 
                                             
                                           
                                           ) 
                                         
                                         
                                           k 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           2 
                                         
                                       
                                       ⁢ 
                                       
                                         ( 
                                         
                                           Vlp 
                                           , 
                                           
                                             0 
                                             + 
                                             
                                               Blp 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               0 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       Blp 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       0 
                                     
                                     + 
                                     
                                       Bsp 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       0 
                                     
                                   
                                   } 
                                 
                               
                               - 
                               
                                 Bsp 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 0 
                               
                             
                             = 
                             
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           η 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           sp 
                                         
                                       
                                       ) 
                                     
                                     
                                       k 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                   
                                   ⁢ 
                                   
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           η 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           lp 
                                         
                                       
                                       ) 
                                     
                                     
                                       k 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       Vlp 
                                       , 
                                       
                                         0 
                                         + 
                                         
                                           Blp 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           0 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           η 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           sp 
                                         
                                       
                                       ) 
                                     
                                     
                                       k 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                   
                                   ⁢ 
                                   
                                     { 
                                     
                                       
                                         
                                           - 
                                           Blp 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         0 
                                       
                                       + 
                                       
                                         Bsp 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         0 
                                       
                                     
                                     } 
                                   
                                 
                                 - 
                                 
                                   Bsp 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   0 
                                 
                               
                               = 
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           k 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           1 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           η 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           sp 
                                         
                                         - 
                                         
                                           k 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           2 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           η 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           lp 
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         Vlp 
                                         , 
                                         
                                           0 
                                           + 
                                           
                                             Blp 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             0 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                   + 
                                   
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           k 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           1 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           η 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           sp 
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     
                                       { 
                                       
                                         
                                           
                                             - 
                                             Blp 
                                           
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           0 
                                         
                                         + 
                                         
                                           Bsp 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           0 
                                         
                                       
                                       } 
                                     
                                   
                                   - 
                                   
                                     Bsp 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     0 
                                   
                                 
                                 = 
                                 Vlp 
                               
                             
                           
                         
                         , 
                         0 
                       
                         
                     
                     - 
                     
                       
                           
                           
                       
                       ⁢ 
                       
                           
                           
                       
                       ⁢ 
                       k 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       η 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         sp 
                         ⁡ 
                         
                           ( 
                           
                             
                               V 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               lp 
                             
                             , 
                             
                               0 
                               + 
                               
                                 Bsp 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 0 
                               
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                       k 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       η 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         lp 
                         ⁡ 
                         
                           ( 
                           
                             Vlp 
                             , 
                             
                               0 
                               + 
                               
                                 Blp 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 0 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         
                           A 
                           
                             A 
                             + 
                             1 
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                       
                       + 
                       
                         k 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         
                           { 
                           
                             
                               
                                 - 
                                 
                                   A 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 
                                   
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   Cp 
                                 
                                 
                                   
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   Cp 
                                   + 
                                   
                                     
                                       ( 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     ⁢ 
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                               
                             
                             + 
                             
                               
                                 
                                   AC 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 
                                   
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   Cp 
                                   + 
                                   
                                     
                                       ( 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     ⁢ 
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                               
                               ⁢ 
                               
                                 { 
                                 
                                   Vref 
                                   - 
                                   
                                     V 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   
                                     
                                       A 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         Vofop 
                                         + 
                                         Vb 
                                       
                                       ) 
                                     
                                   
                                 
                                 } 
                               
                             
                             + 
                             
                               
                                 
                                   C 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 
                                   
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   Cp 
                                   + 
                                   
                                     
                                       ( 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     ⁢ 
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                               
                               ⁢ 
                               
                                 A 
                                 
                                   A 
                                   + 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                       + 
                       
                         k 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         
                           { 
                           
                             
                               
                                 - 
                                 
                                   A 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 
                                   C 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 
                                   
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   Cp 
                                   + 
                                   
                                     
                                       ( 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     ⁢ 
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                               
                             
                             + 
                             
                               
                                 
                                   AC 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 
                                   
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   Cp 
                                   + 
                                   
                                     
                                       ( 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     ⁢ 
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             A 
                             
                               A 
                               + 
                               1 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               Vofop 
                               + 
                               Vb 
                             
                             ) 
                           
                         
                         + 
                         
                           k 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                             
                               AC 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             
                               
                                 C 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                               + 
                               Cp 
                               + 
                               
                                 
                                   ( 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 C 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               Vref 
                               - 
                               
                                 V 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           k 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                           ⁢ 
                           
                             
                               AC 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             
                               
                                 C 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                               + 
                               Cp 
                               + 
                               
                                 
                                   ( 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 C 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                           
                           ⁢ 
                           
                             A 
                             
                               A 
                               + 
                               1 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               Vofop 
                               + 
                               Vb 
                             
                             ) 
                           
                         
                       
                       = 
                       
                         
                           k 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           VG 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                         + 
                         
                           k 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           VG 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         + 
                         Vofb 
                       
                     
                   
                 
               
               
                 
                   ( 
                   54 
                   ) 
                 
               
             
           
         
       
     
     Since the first positive integration processing is not executed in the calibration processing but the calibration values of VG2, VG1, and Vofb are obtained in the calibration processing, it is possible to output a known voltage if the processing of the positive-voltage-integration processing unit  221  is executed. 
     A processing flow of the negative-voltage-integration processing unit  222  is shown in  FIG. 7 . In initialization processing, the negative-voltage-integration processing unit  222  performs connection and disconnection of the SW 3  and resets electric charges accumulated in C 2  (step S 30 ). Thereafter, the negative-voltage-integration processing unit  222  executes second negative integration processing (step S 31 ) and first negative integration processing (step S 32 ) by the numbers of times of integration k2 and k1 for enabling a voltage closest to a value requested by setting data calculated by the output control unit  22  to be output. The negative-voltage-integration processing unit  222  derives the integrated voltage Vo in this case below. An initial value Vln,0 of the second negative integration processing is the same as the right side of Expression (33). Since the first negative integration processing is executed k1 times after the second negative integration processing is executed k2 times, Vo is the following expression from Expression (30) and Expression (21). 
     
       
         
           
             
               
                 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     39 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           Vo 
                           = 
                           
                             
                               
                                 
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       
                                         η 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         sn 
                                       
                                     
                                     ) 
                                   
                                   
                                     k 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   { 
                                   
                                     
                                       
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             
                                               η 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               ln 
                                             
                                           
                                           ) 
                                         
                                         
                                           k 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           2 
                                         
                                       
                                       ⁢ 
                                       
                                         ( 
                                         
                                           Vln 
                                           , 
                                           
                                             0 
                                             + 
                                             
                                               Bln 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               0 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       Bln 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       0 
                                     
                                     + 
                                     
                                       Bsn 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       0 
                                     
                                   
                                   } 
                                 
                               
                               - 
                               
                                 Bsn 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 0 
                               
                             
                             = 
                             
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           η 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           sn 
                                         
                                       
                                       ) 
                                     
                                     
                                       k 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                   
                                   ⁢ 
                                   
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           η 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           ln 
                                         
                                       
                                       ) 
                                     
                                     
                                       k 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       Vln 
                                       , 
                                       
                                         0 
                                         + 
                                         
                                           Bln 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           0 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           η 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           sn 
                                         
                                       
                                       ) 
                                     
                                     
                                       k 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                   
                                   ⁢ 
                                   
                                     { 
                                     
                                       
                                         
                                           - 
                                           Bln 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         0 
                                       
                                       + 
                                       
                                         Bsn 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         0 
                                       
                                     
                                     } 
                                   
                                 
                                 - 
                                 
                                   Bsn 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   0 
                                 
                               
                               = 
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           k 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           1 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           η 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           sn 
                                         
                                         - 
                                         
                                           k 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           2 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           η 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           ln 
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         Vln 
                                         , 
                                         
                                           0 
                                           + 
                                           
                                             Bln 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             0 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                   + 
                                   
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           k 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           1 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           η 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           sn 
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     
                                       { 
                                       
                                         
                                           
                                             - 
                                             Bln 
                                           
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           0 
                                         
                                         + 
                                         
                                           Bsn 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           0 
                                         
                                       
                                       } 
                                     
                                   
                                   - 
                                   
                                     Bsn 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     0 
                                   
                                 
                                 = 
                                 Vln 
                               
                             
                           
                         
                         , 
                         0 
                       
                         
                     
                     - 
                     
                       
                           
                           
                       
                       ⁢ 
                       
                           
                           
                       
                       ⁢ 
                       k 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       η 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         sn 
                         ⁡ 
                         
                           ( 
                           
                             
                               V 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               ln 
                             
                             , 
                             
                               0 
                               + 
                               
                                 Bsn 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 0 
                               
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                       k 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       η 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ln 
                         ⁡ 
                         
                           ( 
                           
                             Vln 
                             , 
                             
                               0 
                               + 
                               Bln0 
                             
                           
                           ) 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         
                           A 
                           
                             A 
                             + 
                             1 
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                       
                       + 
                       
                         k 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         
                           { 
                           
                             
                               
                                 A 
                                 
                                   A 
                                   + 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 
                                   
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   Cp 
                                 
                                 
                                   
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   Cp 
                                   + 
                                   
                                     
                                       ( 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     ⁢ 
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                               
                             
                             + 
                             
                               
                                 
                                   AC 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 
                                   
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   Cp 
                                   + 
                                   
                                     
                                       ( 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     ⁢ 
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                               
                               ⁢ 
                               
                                 { 
                                 
                                   
                                     - 
                                     Vref 
                                   
                                   - 
                                   
                                     V 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   
                                     
                                       A 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         Vofop 
                                         + 
                                         Vb 
                                       
                                       ) 
                                     
                                   
                                 
                                 } 
                               
                             
                             + 
                             
                               
                                 
                                   C 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 
                                   
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   Cp 
                                   + 
                                   
                                     
                                       ( 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     ⁢ 
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                               
                               ⁢ 
                               
                                 A 
                                 
                                   A 
                                   + 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                       + 
                       
                         k 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         
                           { 
                           
                             
                               
                                 - 
                                 
                                   A 
                                   
                                     A 
                                     + 
                                     1 
                                   
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 
                                   C 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 
                                   
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   Cp 
                                   + 
                                   
                                     
                                       ( 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     ⁢ 
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                               
                             
                             + 
                             
                               
                                 
                                   AC 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 
                                   
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   Cp 
                                   + 
                                   
                                     
                                       ( 
                                       
                                         A 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     ⁢ 
                                     C 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     - 
                                     Vref 
                                   
                                   + 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                     
                     = 
                     
                       
                         
                           A 
                           
                             A 
                             + 
                             1 
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             Vofop 
                             + 
                             Vb 
                           
                           ) 
                         
                       
                       + 
                       
                         k 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         
                           
                             AC 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           
                             
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             + 
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               - 
                               Vref 
                             
                             + 
                             
                               V 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         k 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         
                           
                             AC 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           
                             
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             + 
                             Cp 
                             + 
                             
                               
                                 ( 
                                 
                                   A 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           { 
                           
                             
                               - 
                               Vref 
                             
                             + 
                             
                               
                                 A 
                                 
                                   A 
                                   + 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Vofop 
                                   + 
                                   Vb 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     = 
                     
                       
                         k 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         VG 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         m 
                       
                       - 
                       
                         k 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         VG 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       + 
                       Vofb 
                     
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                   ( 
                   55 
                   ) 
                 
               
             
             
               
                 
                   
                     VG 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     m 
                   
                   = 
                   
                     
                       
                         AC 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       
                         
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         + 
                         Cp 
                         + 
                         
                           
                             ( 
                             
                               A 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       { 
                       
                         
                           - 
                           Vref 
                         
                         + 
                         
                           
                             A 
                             
                               A 
                               + 
                               1 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               Vofop 
                               + 
                               Vb 
                             
                             ) 
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   56 
                   ) 
                 
               
             
           
         
       
     
     An integration unit VG2m of the second negative integration processing is correlated with VG2 by the following expression and can be calibrated by already obtained calibration values of VG2 and Vofb. 
     
       
         
           
             
               
                 
                   Math 
                   . 
                   
                       
                   
                   ⁢ 
                   40 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     VG 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     m 
                   
                   = 
                   
                     
                       
                         
                           - 
                           Vref 
                         
                         + 
                         Vofob 
                       
                       Vofb 
                     
                     ⁢ 
                     VG 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
               
               
                 
                   ( 
                   57 
                   ) 
                 
               
             
           
         
       
     
     Therefore, it is possible to output the known voltage even in this case. 
     The variable reference voltage source  100  explained above is a variable reference voltage source that generates a variable reference voltage corresponding to setting data set from the outside. The variable reference voltage source  100  includes the control unit  20 , the reference voltage unit  10  that outputs a reference voltage, and the integrated-voltage generating unit  30 . The control unit  20  includes the calibration control unit  21  that controls operation for acquiring calibration data including calibration values of an offset voltage and a predetermined unit voltage of the determiner  33 , which determines magnitudes of two voltages, and the output control unit  22  that controls operation for generating a variable reference voltage corresponding to setting data set from the outside based on the calibration data. The integrated-voltage generating unit  30  repeats, when the calibration control unit  21  controls the operation, an integrating operation until an integrated voltage obtained by integrating at least two or more kinds of unit voltages becomes equal to a reference voltage and outputs, when the output control unit  22  controls the operation, a variable reference voltage corresponding to the setting data. Consequently, it is possible to provide a variable reference voltage source for which a measuring instrument for calibration is unnecessary on the outside. 
     The variable reference voltage source  100  according to this embodiment can calibrate itself with remote operation without requiring a measuring instrument for calibration. Therefore, the variable reference voltage source  100  of the present invention is suitably used in combination with a large number of sensor circuits present in remote locations. 
     That is, even if an operator does not visit sites where a large number of sensor circuits are disposed, it is possible to calibrate, with remote operation, a variable reference voltage used by the respective sensor circuits. 
     Note that the present invention is not limited to the embodiment explained above. Modifications of the present invention are possible within a range of the gist described in claims. 
     REFERENCE SIGNS LIST 
       10  Reference voltage unit 
       20  Control unit 
       21  Calibration control unit 
       22  Output control unit 
       30  Integrated-voltage generating unit 
       31  Determination-voltage switching unit 
       32  Crossbar switch 
       33  Determiner 
       34  Threshold generating unit 
       35  Integrating unit 
       36  Polarity switching unit 
       210  Intermediate-voltage integrating unit 
       211  Intermediate-voltage-excess integrating unit 
       212  Reference-voltage integrating unit 
       221  Positive-voltage-integration processing unit 
       222  Negative-voltage-integration processing unit