Patent Publication Number: US-11031870-B2

Title: Drive signal generating circuit and power supply circuit

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application claims priority pursuant to 35 U.S.C. § 119 from Japanese patent application number 2019-018072, filed on Feb. 4, 2019, the entire disclosure of which is hereby incorporated by reference herein. 
     BACKGROUND 
     Technical Field 
     The present disclosure relates to a drive signal generating circuit and a power supply circuit. 
     Description of the Related Art 
     A typical power factor correction circuit (hereinafter referred to as PFC circuit) improves the power factor of a power supply by causing an inductor current flowing through an inductor of the PFC circuit to be similar in waveform to a rectified voltage obtained by rectifying an AC voltage (for example, Japanese Patent Application Publication No. 2014-235993). 
     In the PFC circuit disclosed in Japanese Patent Application Publication No. 2014-235993, the inductor current that is similar in waveform to the rectified voltage is produced based on a voltage obtained by dividing the rectified voltage with resistors. In such a circuit, power is consumed by the resistors that are used for dividing the rectified voltage even while the PFC circuit is not operating, thereby increasing power consumption of the PFC circuit. 
     The present invention has been achieved in view of such an issue as above, and an object thereof is to provide a drive signal generating circuit capable of reducing power consumption of a PFC circuit. 
     SUMMARY 
     A main aspect of the present disclosure for solving an issue described above is a drive signal generating circuit that generates a drive signal based on an output voltage generated from an AC voltage and an inductor current flowing through an inductor, the inductor being configured to be applied with a rectified voltage from a rectifier circuit that rectifies the AC voltage, the drive signal being used for turning on and off a transistor that controls the inductor current, the drive signal generating circuit comprising: a command-value output unit that outputs a command value for increasing the inductor current when the output voltage is lower than a target level and reducing the inductor current when the output voltage is higher than the target level; a rectified-voltage calculation unit that calculates the rectified voltage based on an inductance of the inductor and an amount of change in the inductor current in a predetermined time period, the inductor current being a current that increases from zero when the transistor is turned on and decreases to zero when the transistor is turned off; an ON-period calculation unit that calculates an ON period in a switching period of the transistor based on the calculated rectified voltage, the command value, the switching period, and the output voltage, the ON period being a time period for causing the output voltage to reach the target level and for changing the inductor current according to the rectified voltage; and a drive signal output unit that outputs the drive signal based on the calculated ON period and the switching period 
     According to the present disclosure, it is possible to provide a drive signal generating circuit capable of reducing power consumption of a PFC circuit. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating an example of an AC-DC converter  10 ; 
         FIG. 2  is a diagram illustrating a configuration of a power factor correction IC  25 ; 
         FIG. 3  is a diagram illustrating an example of a waveform in the case where an inductor current IL continuously flows; 
         FIG. 4  is a diagram illustrating an example of a waveform in the case where an inductor current IL intermittently flows; 
         FIG. 5  is a diagram illustrating details of a waveform in the case where an inductor current IL intermittently flows; 
         FIG. 6  is a diagram illustrating an example of blocks implemented in a DSP  43 ; 
         FIG. 7  is a diagram illustrating an example of a signal output unit  61 ; 
         FIG. 8  is a diagram illustrating an example of a signal output unit  62 ; and 
         FIG. 9  is a flowchart illustrating an example of processing executed by a power factor correction IC  25 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     At least the following matters are clarified by the description of this specification and the accompanying drawings. 
     Embodiments 
     &lt;&lt;&lt;Overview of AC-DC Converter  10 &gt;&gt;&gt; 
       FIG. 1  is a diagram illustrating the configuration of an AC-DC converter  10  according to an embodiment of the present invention. The AC-DC converter  10  is a power supply circuit of a boost chopper type that generates an output voltage Vout at a target level from an AC voltage Vac of a commercial power supply. 
     The AC-DC converter  10  (power supply circuit) includes a full-wave rectifier circuit  20 , capacitors  21  and  22 , an inductor  23 , a diode  24 , a power factor correction IC  25 , an NMOS transistor  26 , and resistors  30  to  32 . 
     The full-wave rectifier circuit  20  full-wave rectifies an input predetermined AC voltage Vac and outputs the result to the capacitor  21  and the inductor  23  as a rectified voltage Vr. In an embodiment of the present disclosure, a voltage concerning the AC voltage Vac indicates a voltage between two terminals of the full-wave rectifier circuit  20  and a voltage concerning others indicates a potential difference with respect to reference potential (GND point in  FIG. 1 ). The same applies hereinafter. The AC voltage Vac is, for example, a voltage having an effective value of 140 to 240 V and a frequency of 50 to 60 Hz. 
     The capacitor  21  smoothes the rectified voltage Vr. The capacitor  22 , the inductor  23 , the diode  24 , and the NMOS transistor  26  configure a boost chopper circuit. Thus, a charging voltage of the capacitor  22  results in a DC output voltage Vout. In an embodiment of the present disclosure, a voltage of a node connected with a drain electrode of the NMOS transistor  26 , the inductor  23 , and the diode  24  is given as a voltage Vsw. 
     The power factor correction IC  25  (drive signal generating circuit) is an integrated circuit that controls switching of the NMOS transistor  26  such that the output voltage Vout reaches a target level (for example, 400 V) while improving the power factor of the AC-DC converter  10 . That is, the power factor correction IC  25  is a control circuit that performs control such that the AC-DC converter  10  operates as a PFC circuit. The power factor correction IC  25  drives the NMOS transistor  26  based on an inductor current IL flowing through the inductor  23  and the output voltage Vout. Details of the power factor correction IC  25  will be described below. The power factor correction IC  25  includes terminals CS, FB, and OUT. In an embodiment of the present disclosure, terminals of the power factor correction IC  25  other than the terminal CS and the like are omitted for convenience. 
     The NMOS transistor  26  is a switching device for controlling electric power to a load  11  of the AC-DC converter  10 . In an embodiment of the present disclosure, the NMOS transistor  26  is an N-type Metal Oxide Semiconductor (MOS) transistor. However, the NMOS transistor  26  may be, for example, a bipolar transistor or an Insulated Gate Bipolar Transistor (IGBT). A gate electrode of the NMOS transistor  26  is connected to a terminal OUT. 
     The resistors  30  and  31  configure a voltage divider circuit that divides the output voltage Vout and generates a feedback voltage Vfb used in switching the NMOS transistor  26 . The feedback voltage Vfb generated at a node, to which the resistors  30  and  31  are connected, is applied to the terminal FB. 
     The resistor  32  is a resistor for detecting the inductor current IL, and has one end connected to a source electrode of the NMOS transistor  26  and the other end connected to the terminal CS. 
     &lt;&lt;&lt;Power Factor Correction IC  25 &gt;&gt;&gt; 
     ==Configuration of Power Factor Correction IC  25 == 
       FIG. 2  is a diagram illustrating the configuration of the power factor correction IC  25 . The power factor correction IC  25  includes a clock generation circuit  40 , AD converters (ADCs: Analog-to-Digital Converters)  41  and  42 , a digital signal processing circuit (DSP)  43 , and a drive signal output circuit  44 . 
     The clock generation circuit  40  outputs a clock signal Sck having a cycle equal to a cycle in which the NMOS transistor  26  performs switching (hereinafter referred to as the “switching period T”). The clock signal Sck has a frequency of, for example, 50 to 100 kHz. 
     The AD converter  41  converts the feedback voltage Vfb into a digital value. The AD converter  42  converts a voltage indicating the inductor current IL detected by the resistor  32  into a digital value. In an embodiment of the present disclosure, a voltage indicating the inductor current IL to be processed in the DSP  43  is referred to as the inductor current IL, for convenience. The AD converters  41  and  42  in an embodiment of the present disclosure sample input signals (inductor current IL and the feedback voltage Vfb), for example, at timing when the logic level of the clock signal Sck changes, that is, at a double frequency of the clock signal Sck. It is assumed here that the sampling frequency of the AD converters  41  and  42  is the double frequency (100 to 200 kHz) of the clock signal Sck. However, the sampling frequency may be a higher frequency including the timing when the logic level of the clock signal Sck changes. 
     The DSP  43  is a circuit that generates a command voltage VD 1 , VD 2  serving as a reference of a drive signal Vg based on the feedback voltage Vfb, the inductor current IL. As explained in detail below, the command voltage VD 1  is a voltage for operating the AC-DC converter  10  as a PFC circuit in a continuous mode. The “continuous mode” is a mode in which the inductor current IL continuously flows. On the other hand, the command voltage VD 2  is a voltage for operating the AC-DC converter  10  as a PFC circuit in a discontinuous mode. The “discontinuous mode” is a mode in which the inductor current IL intermittently flows, that is, a mode in which there is a time period during which the inductor current IL is zero in each switching period. A “critical mode” for switching ON when an inductor current becomes zero may be dealt with as in the “continuous mode” or may be dealt with as in the “discontinuous mode”. 
     The DSP  43  includes a DSP core  50  and a memory  51  that stores a program to be executed by the DSP core  50  and various types of information. As explained in detail below, the DSP core  50  executes the programs to thereby cause the DSP  43  to implement various circuits and/or functional blocks such as an adder, a subtractor, a multiplier, a divider, a filter, an amplifier circuit, and the like. 
     The drive signal output circuit  44  (drive signal output unit) outputs the drive signal Vg for turning on and off the NMOS transistor  26  to the terminal OUT, based on the command voltage VD 1  or the command voltage VD 2 . 
     The drive signal output circuit  44  includes a DA converter (DAC: Digital-to-Analog Converter)  55 , an oscillator circuit  56 , a comparator  57 , and a gate driver  58 . 
     The DAC  55  converts the command voltage VD 1  or the command voltage VD 2 , which is a digital value output from the DSP  43 , into an analog value, and outputs the result as a command voltage Vx (=VD 1  or VD 2 ). 
     The oscillator circuit  56  outputs an oscillator voltage Vosc of a triangular wave based on the clock signal Sck. Specifically, the oscillator circuit  56  outputs the oscillator voltage Vosc having an instantaneous value that increases when the clock signal Sck changes to a high level (hereinafter referred to as high) and decreases when the clock signal Sck changes to a low level (hereinafter referred to as low). 
     The comparator  57  (comparison unit) outputs a low signal when the command voltage Vx is higher than the oscillator voltage Vosc, and outputs a high signal when the command voltage Vx is lower than the oscillator voltage Vosc. 
     The gate driver  58  (output unit) outputs, to the terminal OUT, the drive signal Vg for turning on the NMOS transistor  26  based on the high signal output from the comparator  57  and turning off the NMOS transistor  26  based on the low signal. Thus, in an embodiment of the present disclosure, when the command voltage VD 1 , VD 2  (or the command voltage Vx) rises, off-duty Doff of the NMOS transistor  26  increases. 
     ===Waveform of Inductor Current IL=== 
     &lt;&lt;Case where Inductor Current IL Continuously Flows&gt;&gt; 
       FIG. 3  is a diagram illustrating an example of a waveform in the case where the inductor current IL continuously flows. For example, when the clock signal Sck goes high at time t 0  in  FIG. 3 , the instantaneous value of the oscillator voltage Vosc increases. When the oscillator voltage Vosc becomes higher than the command voltage Vx at time t 1 , the drive signal Vg goes high and the NMOS transistor  26  is turned on. As a result, the inductor current IL increases and the voltage Vsw decreases to substantially 0 V. When the clock signal Sck goes low at time t 2 , the instantaneous value of the oscillator voltage Vosc decreases. When the oscillator voltage Vosc becomes lower than the command voltage Vx at time t 3 , the drive signal Vg goes low. As a result, the NMOS transistor  26  is turned off, the inductor current IL decreases, and the voltage Vsw changes to the level of the output voltage Vout. 
     At time t 4  when the switching period T has elapsed from the time t 0 , the clock signal Sck goes high and thus the oscillator voltage Vosc increases. At time t 5 , the oscillator voltage Vosc becomes higher than the command voltage Vx, and thus the NMOS transistor  26  is turned on and the inductor current IL increases as is the case with the time t 1 . In the following time period from time t 6  to time t 8 , the operation from the time t 2  to the time t 6  is repeated. 
     As explained above, the AD converter  42  samples the inductor current IL at the timing when the logic level of the clock signal Sck changes. Specifically, at timing (for example, the time t 2 ) when the clock signal Sck goes low, the AD converter  42  samples the inductor current IL to acquire the inductor current IL as a sampling value Isp. At timing (for example, the time t 4 ) when the clock signal Sck goes high, the AD converter  42  samples the inductor current IL to acquire the inductor current IL as a sampling value Isb. 
     The timing when the clock signal Sck goes low at the time t 2  is at a peak of the triangular wave (at a time when the instantaneous value of the oscillator voltage Voc is the maximum). Thus, the timing when the sampling value Isp is acquired is in the middle of a time period in which the NMOS transistor  26  is ON (a time period during which the drive signal Vg is high). The timing in the middle of an ON period Ton corresponds to timing when a half (Ton/2) of the ON period Ton has elapsed since the NMOS transistor  26  has been turned on. 
     The timing when the clock signal Sck goes high at the time t 4  is at a bottom of the triangular wave (at a time when the instantaneous value of oscillator voltage Vosc is the minimum). Thus, the timing when the sampling value Isb is acquired is in the middle of a time period in which the NMOS transistor  26  is OFF (a time period in which the drive signal Vg is low). The timing in the middle of an OFF period Toff corresponds to timing when a half (Toff/2) of the OFF period Toff has elapsed since the NMOS transistor  26  has been turned off. 
     When the inductor current IL has a continuous waveform, the inductor current IL increases in the ON period Ton of the NMOS transistor  26  (for example, the time t 1  to the time t 3 ) and decreases in the OFF period Toff (for example, the time t 3  to the time t 5 ) of the NMOS transistor  26 . The amount of change (amount of increase) in the inductor current IL in the ON period Ton and the amount of change (amount of decrease) in the inductor current IL in the OFF period Toff are equal. Thus, when the inductor current IL has a continuous waveform, the sampling value Isp acquired in the middle of the ON period Ton (time t 2 ) and the sampling value Isb acquired in the middle of the OFF period Toff (time t 4 ) are equal. 
     &lt;&lt;Case where Inductor Current IL Intermittently Flows&gt;&gt; 
       FIG. 4  is a diagram illustrating an example of a waveform in the case where the inductor current IL intermittently flows. When the clock signal Sck goes high at time t 10  in  FIG. 4 , the instantaneous value of the oscillator voltage Vosc increases. When the oscillator voltage Vosc becomes higher than the command voltage Vx at time t 11 , the drive signal Vg goes high and the NMOS transistor  26  is turned on. As a result, the inductor current IL increases from zero. 
     When the clock signal Sck goes low at time t 12 , the instantaneous value of the oscillator voltage Vosc decreases. When the oscillator voltage Vosc becomes lower than the command voltage Vx at time t 13 , the drive signal Vg goes low. As a result, the NMOS transistor  26  is turned off and the inductor current IL decreases. 
     At time t 14  when the switching period T has elapsed since the time t 10 , the clock signal Sck goes high, and thus the instantaneous value of the oscillator voltage Vosc increases. However, at this timing, since the NMOS transistor  26  is off, the inductor current IL decreases to zero at time t 15 . 
     When the oscillator voltage Vosc becomes higher than the command voltage Vx at time t 16 , the NMOS transistor  26  is turned on, and thus the inductor current IL increases from zero. Accordingly, the inductor current IL remains zero from the time t 15  to the time t 16  at the time when the oscillator voltage Vosc becomes higher than the command voltage Vx. In a time period from the time t 15  to the time t 16 , the voltage Vsw drops from the voltage Vout to a voltage Vrec. 
     At time t 17  when the clock signal Sck goes low, the instantaneous value of the oscillator voltage Vosc decreases as in the time t 12 . In a time period from the time t 17  to time t 19 , the operation from the time  12  to the time t 17  is repeated. 
     At timing when the clock signal Sck goes low (for example, the time t 12 ), the AD converter  42  in an embodiment of the present disclosure samples the inductor current IL to acquire the inductor current IL as the sampling value Isp. At timing when the clock signal Sck goes high (for example, the time t 14 ), the AD converter  42  samples the inductor current IL to acquire the inductor current IL as the sampling value Isb. 
     The time t 12  is at a peak of the triangular wave (oscillator voltage Vosc). Thus, the timing when the sampling value Isp is acquired is in the middle of the ON period of the NMOS transistor  26 . 
     The time t 14  is at a bottom of the triangular wave (oscillator voltage Vosc). Thus, the timing when the sampling value Isb is acquired is in the middle of the OFF period of the NMOS transistor  26 . 
     In the case where the inductor current IL has a discontinuous waveform, a change in the inductor current IL when the NMOS transistor  26  is ON and a change in the inductor current IL when the NMOS transistor  26  is OFF are equal under the same voltage conditions of the rectified voltage Vr and the output voltage Vout. However, the inductor current IL increases over the ON period Ton, but the inductor current IL becomes zero during a part (for example, the time t 15  to the time t 16 ) of the OFF period Toff (for example, the time t 13  to the time t 16 ). That is, the inductor current IL decreases to zero within a time period shorter than the OFF period Toff. 
     Thus, when the inductor current IL has a discontinuous waveform, the sampling value Isp acquired in the middle of the ON period Ton (time t 12 ) is different from the sampling value Isb acquired in the middle of the OFF period Toff (time t 14 ). Since the inductor current IL cannot take a negative value due to the circuit configuration, the current stops changing at this point in time. 
     Accordingly, as is apparent from  FIGS. 3 and 4 , it is possible to figure out whether the inductor current IL has a continuous waveform or a discontinuous waveform by acquiring the sampling values Isp and Isb. 
     &lt;&lt;Method for Calculating ON Period Ton in Discontinuous Mode&gt;&gt; 
     An explanation will be given of a method of calculating the ON period Ton for causing the inductor current IL to be similar in waveform to the rectified voltage Vr when the PFC circuit is operated in the discontinuous mode. 
       FIG. 5  is a diagram for describing details of a waveform in the case where the inductor current IL has a discontinuous waveform.  FIG. 5  is the same as an excerpt from  FIG. 4 . Thus, explanation of the clock signal Sck, the oscillator voltage Vosc, and the like is omitted. 
     First, when the drive signal Vg goes high at time t 20 , the inductor current IL increases from zero. At time t 21  when a half (Ton/2) of the ON period Ton has elapsed since the time t 20 , the inductor current IL is sampled to acquire the sampling value Isp. 
     At time t 22  when a half (Ton/2) of the ON period Ton has elapsed since the time t 21 , the drive signal Vg goes low and the inductor current IL decreases. At time t 23  when a half (Toff/2) of the OFF period Toff has elapsed since the time t 22 , the inductor current IL is sampled to acquire the sampling value Isb. 
     At time t 24 , the inductor current IL decreases to zero. When the drive signal Vg goes high at time t 25 , the inductor current IL increases from zero. 
     When a peak current value of the inductor current IL at the time t 22  is given as “Ip”, the current value Ip is given by Expression (1).
 
 IP=Vr ×( T on/ L )  (1)
 
     where “Vr” is the rectified voltage Vr described above, and “L” is the inductance of the inductor  23 . 
     A reset time Tr until the inductor current IL has decreased to zero is given by Expression (2). 
     
       
         
           
             
               
                 
                   
                     
                       
                         Tr 
                         = 
                           
                         ⁢ 
                         
                           L 
                           × 
                           
                             Ip 
                             / 
                             
                               ( 
                               
                                 Vout 
                                 - 
                                 Vr 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             ( 
                             
                               L 
                               × 
                               Vr 
                               × 
                               
                                 ( 
                                 
                                   Ton 
                                   / 
                                   L 
                                 
                                 ) 
                               
                             
                             ) 
                           
                           / 
                           
                             ( 
                             
                               Vout 
                               - 
                               Vr 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           Ton 
                           × 
                           
                             Vr 
                             / 
                             
                               ( 
                               
                                 Vout 
                                 - 
                                 Vr 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     An average current Im (average value) of the inductor current IL is given by Expression (3). 
     
       
         
           
             
               
                 
                   
                     
                       
                         Im 
                         = 
                           
                         ⁢ 
                         
                           Ip 
                           × 
                           
                             
                               ( 
                               
                                 Ton 
                                 + 
                                 Tr 
                               
                               ) 
                             
                             / 
                             
                               ( 
                               
                                 2 
                                 × 
                                 T 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             = 
                               
                             ⁢ 
                             
                               ( 
                               
                                 
                                   ( 
                                   
                                     Vr 
                                     × 
                                     Vout 
                                   
                                   ) 
                                 
                                 / 
                                 
                                   ( 
                                   
                                     
                                       ( 
                                       
                                         Vout 
                                         - 
                                         Vr 
                                       
                                       ) 
                                     
                                     × 
                                     2 
                                     × 
                                     T 
                                     × 
                                     L 
                                   
                                   ) 
                                 
                               
                               ) 
                             
                           
                           ) 
                         
                         × 
                         Ton 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     When the average current Im is made proportional to the rectified voltage Vr, that is, when a waveform of the inductor current IL is caused to be similar in waveform to the rectified voltage Vr, those other than the rectified voltage Vr in Expression (3) needs to be a constant “k”. That is, variables and the like included in Expression (3) need to satisfy the relation of Expression (4).
 
( V out/( V out− Vr )×2× T×L )))× T on2= k   (4)
 
     In such a case, Expression (3) results in Im=Vr×k. From Expression (4), the ON period Ton is calculated as follows:
 
 T on=(2× T×L×k (1− Vr/V out))½  (5)
 
     When the switching period T is constant and a change in the inductance L caused by DC superimposition can be ignored, and when assuming that a coefficient “2×T×L×k” is a coefficient “a”, Expression (5) results in Expression (6).
 
 T on= a ×(1− Vr/V out)½  (6)
 
     When a value obtained by normalizing “Vr/Vout” is given as “Vrm” in Expression (6), Expression (6) results in Expression (7).
 
 T on= a ×(1− Vrm )½  (7)
 
     As explained in detail below, since the coefficient “k” is a coefficient corresponding to an amplitude command value of the average current Im, Expression (5) holds the coefficient “k”, even if the inductance L is unknown. Thus, when the switching period T is constant, it is possible to calculate the ON period Ton for causing the inductor current IL to be similar in waveform to the rectified voltage Vr, by substituting the rectified voltage Vr and the output voltage Vout into Expression (6). 
     &lt;&lt;Method for Calculating Rectified Voltage Vr in Discontinuous Mode&gt;&gt; 
     As explained above, in order to calculate the ON period Ton for causing the inductor current IL to be similar in waveform to the rectified voltage Vr, the rectified voltage Vr needs to be figured out. A method for calculating the rectified voltage Vr will be explained below with reference to  FIG. 5 . 
     First, in the discontinuous mode, the inductor current IL increases from zero. The sampling value Isp is acquired in the middle (Ton/2) of the ON period Ton. Thus, Expression (8) holds based on the amount of change (amount of increase from zero to the current value Isp) in the inductor current IL in a predetermined time period (Ton/2).
 
 L×Isp=Vr ×( T on/2)  (8)
 
     From Expression (8), the rectified voltage Vr is given by Expression (9).
 
 Vr =(2× L×Isp )/ T on  (9)
 
     Thus, if the inductance L of the inductor  23  can be obtained from Expression (9), the rectified voltage Vr can be calculated. 
     &lt;&lt;Method for Calculating Inductance L&gt;&gt; 
     A method for calculating the inductance L of the inductor  23  will be explained. When the amount of decrease in the inductor current IL from a start of the OFF period Toff (time t 22 ) to the time t 23  is given as ΔI, Expression (10) holds.
 
 L×ΔI =( V out− Vr )×( T off/2)  (10)
 
     When Expression (9) is substituted into Expression (10), Expressions (11) and (12) are obtained.
 
 L×ΔI=V out×( T off/2)− L×Isp ×( T off/ T on)  (11)
 
 L ×(Δ I+Isp ×( T off/ T on))= V out×( T off/2)  (12)
 
     The time t 23  is timing when a half of the OFF period Toff has elapsed since the time t 22  and the sampling value Isb is acquired. Thus, the relation of Expression (13) holds between ΔI and the sampling values Isp and Isb.
 
Δ I= 2× Isp−Isb   (13)
 
     Thus, the inductance L is calculated by the following Expression (14).
 
 L =( V out×( T off/2))/((2 +T off/ T on)× Isp−Isb )  (14)
 
     Thus, the inductance L is calculated based on the sampling value Isp acquired at the timing of the time t 21  (Ton/2) in the ON period Ton and the sampling value Isb acquired at the timing of the time t 23  (Toff/2) in the OFF period Toff. 
     Expression (14) holds only when the sampling value Isb acquired at the OFF period Toff is positive (Isb&gt;0), that is, the sampling value Isb is not zero. 
     When the inductance L is obtained by Expression (14), the rectified voltage Vr is calculated from Expression (9). Further, when the rectified voltage Vr is calculated, the ON period Ton for causing the inductor current IL to be similar in waveform to the rectified voltage Vr can be calculated from Expression (6). 
     ==DSP  43 == 
       FIG. 6  is an example of blocks implemented in the DSP  43 . The DSP core  50  executes predetermined programs, thereby implementing a determination unit  60  and signal output units  61  and  62  in the DSP  43 . 
     The determination unit  60  determines, based on the inductor current IL, whether the AC-DC converter  10  is operated as the PFC circuit in the continuous mode or operated as the PFC circuit in the discontinuous mode. Specifically, when a difference between the sampling value Isp and the sampling value Isb is smaller than a predetermined value X 1  (for example, 0.1 mA), the determination unit  60  determines that the inductor current IL has a continuous waveform and operates the signal output unit  61  for the continuous mode. On the other hand, when the difference between the sampling value Isp and the sampling value Isb is larger than the predetermined value X, the determination unit  60  determines that the inductor current IL has a discontinuous waveform and operates the signal output unit  62  for the discontinuous mode. 
     The signal output unit  61  (first signal output unit) generates, based on the feedback voltage Vfb and the inductor current IL, the command voltage VD 1  (first signal) for operating the AC-DC converter  10  as the PFC circuit in the continuous mode. 
     The signal output unit  62  (second signal output unit) generates, based on the feedback voltage Vfb and the inductor current IL, the command voltage VD 2  (second signal) for operating the AC-DC converter  10  as the PFC circuit in the discontinuous mode. 
     In an embodiment of the present disclosure, the feedback voltage Vfb is an output voltage feedback value output from the AD converter  41 . However, for convenience, the output voltage feedback value is simply referred to as the feedback voltage Vfb. 
     &lt;&lt;Details of Signal Output Unit  61 » 
       FIG. 7  is an example of a processing flow (so-called signal flowchart) with functional blocks implemented in the signal output unit  61 . The signal output unit  61  generates the command voltage VD 1  serving as a reference of the drive signal Vg based on the feedback voltage Vfb and the inductor current IL. 
     The signal output unit  61  includes subtractors  70 ,  73 , and  75 , a voltage regulator (AVR: Automatic Voltage Regulator)  71 , a multiplier  72 , a current regulator  74  (ACR: Automatic Current Regulator), a delay device  76 , and a divider  77 . 
     The subtractor  70  subtracts the feedback voltage Vfb from a reference voltage Vref serving as a reference of the output voltage Vout (for example, 400 V) at the target level and calculates an error E 1  between the reference voltage Vref and the feedback voltage Vfb. 
     The voltage regulator  71  outputs, according to the error E 1 , a command voltage VA for causing the feedback voltage Vfb to reach the reference voltage Vref. 
     The multiplier  72  multiplies the command voltage VA and an output from the delay device  76  explained below together and outputs the multiplication result as a reference current Iref serving as the reference of the inductor current IL. In an embodiment of the present disclosure, the reference current Iref is a current command value output from the multiplier  72 . However, for convenience, the current command value is simply referred to as the reference current Iref. 
     The subtractor  73  subtracts the inductor current IL from the reference current Iref and calculates an error E 2  between the reference current Iref and the inductor current IL. 
     The current regulator  74  outputs, according to the error E 2 , a command voltage VB for causing the inductor current IL to reach the current value of the reference current Iref. The current regulator  74  in an embodiment of the present disclosure outputs a positive command voltage VB when the reference current Iref is larger than the inductor current IL and outputs a negative command voltage VB when the reference current Iref is smaller than the inductor current IL. 
     The subtractor  75  subtracts the command voltage VB from an output of the delay device  76  and calculates a command voltage VC. As explained in detail below, the output of the delay device  76  is a previously output command voltage VC. 
     The delay device  76  delays the command voltage VC by a predetermined time period (for example, a time period per one sample of the DSP  43 ) and outputs the command voltage VC. 
     The current regulator  74  and the subtractor  75  output the command voltage VC for causing the inductor current IL to reach the current value of the reference current Iref. Specifically, the current regulator  74  and the subtractor  75  output the command voltage VC for increasing the inductor current IL when the inductor current IL is smaller than the reference current Iref and reducing the inductor current IL when the inductor current IL is larger than the reference current Iref. 
     The subtractor  75  subtracts (adds if the command voltage VB is negative), from (to) the command voltage VC of the immediately preceding sample, the command voltage VB needed for causing the inductor current IL to reach the reference current Iref and outputs the command voltage VC as a new command voltage VC. With such a configuration, the current regulator  74  does not need to greatly change the command voltage VB. Thus, a control characteristic in a current feedback loop is improved. 
     The divider  77  is a block for dividing the command voltage VC by a voltage (for example, the feedback voltage Vfb) obtained by dividing the output voltage Vout. 
     ==Operation (Continuous Mode) of Power Factor Correction IC  25  Using Signal Output Unit  61 == 
     An explanation will be given of an operation of the power factor correction IC  25  using the signal output unit  61  when the determination unit  60  has determined that the inductor current IL has a continuous waveform. First, an explanation will be given of an operation concerning a current loop and a voltage loop, in a feedback loop of the power factor correction IC  25 . 
     &lt;&lt;Current Loop&gt;&gt; 
     For example, when the operation of the power factor correction IC  25  is started, the voltage regulator  71  of the signal output unit  61  outputs the command voltage VA according to the error E 1 , and the multiplier  72  outputs the reference current Iref according to the command voltage VA. 
     For example, when the reference current Iref is larger than the inductor current IL, a positive command voltage VB is output from the current regulator  74 . As a result, the subtractor  75  subtracts the positive command voltage VB from the previously output command voltage VC. Thus, the command voltage VC output from the subtractor  75  drops. The divider  77  divides the command voltage VC by, for example, the feedback voltage Vfb. Thus, the command voltage VD 1  also drops. The feedback voltage Vfb is substantially constant in a time period in which the divider  77  executes division processing (for example, a time period equivalent to one sample of the DSP  43 ). 
     As a result, since the voltage Vx also drops, a duty ratio Doff decreases (that is, a time period in which the NMOS transistor  26  is ON increases), so that the inductor current IL increases to reach the reference current Iref consequently. 
     On the other hand, for example, when the reference current Iref is smaller than the inductor current IL, a negative command voltage VB is output from the current regulator  74 . As a result, the subtractor  75  adds the command voltage VB to the previously output command voltage VC, so that the command voltage VC rises. As a result, since the command voltage VD 1  and the command voltage Vx also rise, the duty ratio Doff increases (that is, the time period in which the NMOS transistor  26  is ON decreases), so that the inductor current IL decreases to reach the reference current Iref consequently. 
     That is, in the power factor correction IC  25 , the current loop is formed such that the inductor current IL will reach the reference current Iref. An operation for causing the inductor current IL to reach the reference current Iref, serving as a target value, is performed at the level of the instantaneous value of the reference current Iref. Thus, as explained in detail below, if the reference current Iref is a rectified sinusoidal waveform, the inductor current IL will have a similar waveform. 
     &lt;&lt;Voltage Loop&gt;&gt; 
     Next, an explanation will be given of an operation concerning the voltage loop in the feedback loop of the power factor correction IC  25 . When an average value of the rectified voltage Vr is constant and the output voltage Vout rises from the target level (for example, 400V), the feedback voltage Vfb also rises. When the command voltage VA drops with a rise in the feedback voltage Vfb, an average value of the reference current Iref also decreases. As a result, an average value of the inductor current IL also decreases and the amount of charge on the capacitor  22  decreases, and thus the output voltage Vout drops. 
     On the other hand, when the average value of the rectified voltage Vr is constant and the output voltage Vout drops from the target level, the feedback voltage Vfb also drops. When the command voltage VA rises with a drop in the feedback voltage Vfb, the average value of the reference current Iref also increases. As a result, the average value of the inductor current IL increases and the amount of charge on the capacitor  22  increases, and thus the output voltage Vout rises. 
     In this way, the power factor correction IC  25  performs feedback control such that the output voltage Vout reaches the target level. 
     &lt;&lt;Power Factor Correction&gt;&gt; 
     As explained above, the current loop and the voltage loop are formed as the feedback loop in the power factor correction IC  25  using the signal output unit  61 . That is, the power factor correction IC  25  is a control circuit of a current mode control type. 
     The control circuit of the current mode control type controls a direct current or a low frequency component of the inductor current IL so as to be a value close to the reference current Iref. On the other hand, direct-current impedance or low-frequency impedance of the inductor  23  in  FIG. 1  is designed to be extremely small, and its direct-current voltage or low-frequency component voltage is negligibly small. That is, it is possible to utilize a principle that “Vr≈Vsw(ave) may be assumed as an approximate value”. 
     Under a condition that the output voltage Vout is constant, it is possible to estimate the rectified voltage Vr by figuring out the duty ratio Doff, that is, the command voltage Vx, instead of the average voltage Vsw (ave). Similarly, in the power factor correction IC  25  using the signal output unit  61  that controls the output voltage Vout so as to be constant, the current voltage Vr and the command voltages VC and VD 1  have similar waveforms. 
     In an embodiment of the present disclosure, the command voltage VC similar in waveform to the rectified voltage Vr is input to the multiplier  72 . The multiplier  72  sets the multiplication result of the command voltage VA and the command voltage VC as the reference current Iref. As a result, the waveform of the reference current Iref will also be a rectified sinusoidal waveform similar to the waveform of the rectified voltage Vr. Accordingly, the power factor of a power supply is improved. 
     Incidentally, the output voltage Vout has been explained as being constant, however, in actuality, the instantaneous value of the output voltage Vout may not be regarded as being constant, due to being affected by a ripple voltage when the capacitor  22  smoothes a voltage output from the diode  24 . 
     Specifically, the output voltage Vout in an embodiment of the present disclosure includes a ripple component (ripple voltage) due to a change in the instantaneous value of the AC voltage Vac, which is a commercial power supply. In general, the double frequency component of the AC voltage Vac is predominant. Thus, the command voltage VC generated by the feedback voltage Vfb that is obtained by dividing the output voltage Vout also includes a ripple component at the double frequency component of the AC voltage Vac. 
     A specific explanation will be given of an operation when the command voltage VC is divided by the feedback voltage Vfb. For example, the output voltage Vout and the feedback voltage Vfb may be larger than the average values by 10% due to the ripple component explained above. When the divider  77  divides the command voltage VC by “1.1” at timing when the feedback voltage Vfb is 1.1 times of the average value, the command voltage VD 1  is expressed by VD 1 =VC×(1/1.1). Thus, the duty ratio “Doff” in an OFF period also results in “1/1.1” times. 
     However, in this case, the amplitude of the voltage Vsw is also 1.1 times similarly to the output voltage Vout, and thus an average voltage Vsw(ave) is the same as the average voltage Vsw(ave) when the output voltage Vout is at a desired level. Accordingly, a proportional relationship between the command voltage VC and the rectified voltage Vr is maintained. 
     In this way, the divider  77  divides the command voltage VC by, for example, the feedback voltage Vfb, and thus a ripple component in the command voltage VC is suppressed. 
     Since a waveform of the command voltage VC becomes similar to the waveform of the rectified voltage Vr, a waveform of the reference current Iref results in being similar to the waveform of the rectified voltage Vr. As a result, in an embodiment of the present disclosure, even when the output voltage Vout is affected by the ripple component, the power factor of the power supply is improved. 
     &lt;&lt;Details of Signal Output Unit  62 » 
       FIG. 8  is a diagram illustrating an example of blocks included in the signal output unit  62 . When the PFC circuit is operated in the discontinuous mode, the signal output unit  62  generates the command voltage VD 2  for causing the inductor current IL to be similar in waveform to the rectified voltage Vr while causing the output voltage Vout to reach the target level. The signal output unit  62  includes a subtractor  90 , a voltage regulator (AVR)  91 , a mode determination unit  92 , an inductance calculation unit  93 , a storage unit  94 , a rectified-voltage calculation unit  95 , and an ON-period calculation unit  96 . 
     The subtractor  90  subtracts the feedback voltage Vfb from the reference voltage Vref serving as the reference of the output voltage Vout (for example, 400 V) at the target level, and calculates an error E 3  between the reference voltage Vref and the feedback voltage Vfb. 
     The voltage regulator  91  outputs a command value Vk for causing the feedback voltage Vfb to reach the reference voltage Vref, according to the error E 3 . As explained in detail below, the command value Vk corresponds to the coefficient “k” explained in Expression (4). The subtractor  90  and the voltage regulator  91  correspond to a command-value output unit. 
     The mode determination unit  92  determines whether the inductance L of the inductor  23  can be calculated, based on the sampling value Isb of the inductor current IL. Specifically, when the sampling value Isb is not zero, Expression (14) described above can be calculated. Thus, when the sampling value Isb is larger than a predetermined value X 2  (for example, 0.1 A) that is slightly larger than zero, the mode determination unit  92  determines that a mode is such a mode that the inductance L can be calculated (hereinafter referred to as the “mode A”). When the sampling value Isb is smaller than the predetermined value X 2 , the mode determination unit  92  determines that a mode is such the mode that the inductance L cannot be calculated (hereinafter referred to as the “mode B”). 
     The inductance calculation unit  93  calculates the inductance L based on the sampling value Isp acquired after the time period Ton/2 has elapsed since the start of the ON period Ton, the sampling value Isb acquired after the time period Toff/2 has elapsed since the start of the OFF period Toff, and the feedback voltage Vfb. The inductance L is calculated based on Expressions (8) to (14) described above. 
     The storage unit  94  stores the inductance L calculated by the inductance calculation unit  93  and the switching period T. The inductance calculation unit  93  updates information stored in the storage unit  94  every time the inductance calculation unit  93  calculates the inductance L. 
     The rectified-voltage calculation unit  95  calculates the rectified voltage Vr based on the inductance L stored in the storage unit  94  and the sampling value Isp acquired after the time period Ton/2 has elapsed since the start of the ON period Ton. The rectified voltage Vr is calculated based on Expression (9) described above. 
     The ON-period calculation unit  96  calculates the ON period Ton based on the command value Vk, the feedback voltage Vfb, the rectified voltage Vr, the switching period T, and the inductance L. The ON-period calculation unit  96  calculates The ON period Ton based on Expression (6) described above. The ON-period calculation unit  96  outputs the command value VD 2  corresponding to the calculated ON period Ton to cause the ON period of the NMOS transistor  26  to reach the calculated ON period Ton based on the instantaneous value of the oscillator voltage Vosc, for example. As a result, when the PFC circuit is operated in the discontinuous mode, the above described expression Im=Vr×k holds. Thus, the average current Im of the inductor current IL becomes similar in waveform to the rectified voltage Vr. 
     &lt;&lt;Voltage Loop&gt;&gt; 
     The voltage loop of the signal output unit  62  will be explained. When the output voltage Vout is lower than the target level, that is, when the feedback voltage Vfb is lower than the reference voltage Vref, the voltage regulator  91  increases the command value Vk according to the error E 3 . Since the command value Vk corresponds to the coefficient “k” explained in Expression (4), the ON time Ton becomes longer as the command value Vk (coefficient “k”) increases. Thus, the inductor current IL increases. As a result, the output voltage Vout rises. 
     On the other hand, when the output voltage Vout is higher than the target level, that is, when the feedback voltage Vfb is higher than the reference voltage Vref, the voltage regulator  91  reduces the command value Vk according to the error E 3 . When the command value Vk (coefficient “k”) decreases, the ON period Ton becomes shorter as the inductor current IL decreases. As a result, the output voltage Vout drops. In this way, the signal output unit  62  can cause the output voltage Vout to reach the target level. 
     ===Processing Executed by Power Factor Correction IC  25 === 
       FIG. 9  is a flowchart illustrating an example of process S 10  executed in the power factor correction IC  25 . First, every time the inductor current IL is sampled at the AD converter  42  of the DSP  43 , the determination unit  60  acquires the sampling values Isp and Isb (S 20 ). Then, the determination unit  60  determines whether the inductor current IL has a continuous waveform or a discontinuous waveform (S 21 ) based on whether the difference between the sampling value Isp and the sampling value Isb is larger than the predetermined value X 1 . When having determined that the inductor current IL has a continuous waveform (continuous in S 21 ), the determination unit  60  operates the signal output unit  61  (S 22 ). As a result, the command voltage VD 1  is output from the signal output unit  61 . Thus, the AC-DC converter  10  operates as the PFC circuit in the continuous mode. 
     On the other hand, when the determination unit  60  determine that the inductor current IL has a discontinuous waveform (discontinuous in S 21 ), the mode determination unit  92  of the signal output unit  62  determines whether the current mode is the mode A in which the inductance L can be calculated or the mode B in which the inductance L cannot be calculated (S 23 ) based on the sampling value Isb. 
     When the mode determination unit  92  determines that the current mode is the mode A (mode A in S 23 ), the inductance calculation unit  93  calculates the inductance L and stores the calculation result in the storage unit  94  (S 24 ). 
     The inductance L may change according to a direct current or a low frequency current flowing through the inductor  23 . However, when the current mode is the mode A, the inductance L is calculated every time the inductor current IL is sampled. As explained above, a sampling frequency of the AD converter  42  is, for example, 100 to 200 kHz, which is sufficiently higher than 50 to 60 Hz of the AC voltage Vac. 
     Thus, in an embodiment of the present disclosure, even when the inductance L changes, it is possible to accurately calculate the inductance L. 
     When the inductance L is calculated in the process S 24  or the mode determination unit  92  determines that the current mode is the mode B (mode B in S 23 ), the rectified-voltage calculation unit  95  calculates the rectified voltage Vr based on the inductance L and the sampling value Isp (S 25 ). 
     When the rectified voltage Vr is calculated, the ON-period calculation unit  96  calculates the ON period Ton based on the rectified voltage Vr, the switching period T, the inductance L, the command voltage Vk, and the feedback voltage Vfb corresponding to the output voltage Vout (S 26 ). The ON-period calculation unit  96  outputs the command voltage VD 2  corresponding to the ON period Ton such that switching of the NMOS transistor  26  is performed in the calculated ON period Ton (S 27 ). As a result, the AC-DC converter  10  operates as the PFC circuit in the discontinuous mode. 
     In this way, the DSP  43  of the power factor correction IC  25  executes the process S 10  every time the inductor current IL is sampled. In the AC-DC converter  10 , in both of the continuous mode and the discontinuous mode, the waveform of the inductor current IL is similar to the waveform of the rectified voltage Vr, and the power factor is improved. 
     &lt;&lt;=Summary=== 
     The AC-DC converter  10  in an embodiment of the present disclosure has been explained above. When the inductor current IL discontinuously changes, the power factor correction IC  25  calculates the rectified voltage Vr based on the amount of change (Isp) in the inductor current IL that changes in the predetermined time period (Ton/2) and the inductance L (see, for example, Expression (9)). The ON-period calculation unit  96  calculates the ON period Ton for causing the inductor current IL to be similar in waveform to the rectified voltage Vr, based on the calculated rectified voltage Vr. Thus, the power factor correction IC  25  can cause the inductor current IL to be similar in waveform to the rectified voltage Vr without detecting the rectified voltage Vr with a resistor or the like. Accordingly, the power factor correction IC  25  is capable of reducing power consumption of the AC-DC converter  10 . 
     The rectified-voltage calculation unit  95  may calculate the rectified voltage Vr based on the amount of change ΔI in the inductor current IL that changes in the predetermined time period (Toff/2) and the inductance L (see Expression (10)). However, when the rectified-voltage calculation unit  95  calculates the rectified voltage Vr using the amount of change in the inductor current IL in the OFF period Toff, the rectified-voltage calculation unit  95  needs to use the output voltage Vout as well. Thus, it is possible to further reduce processing amount when the rectified voltage Vr is calculated based on the amount of change in the inductor current IL in the ON period Ton. 
     The rectified-voltage calculation unit  95  uses the sampling value Isp at the time when the predetermined time period (Ton/2) has elapsed since the inductor current IL has started to increase from zero (see Expression (9)). When the AC-DC converter  10  is operated as the PFC circuit in the discontinuous mode, the inductor current IL increases from zero invariably at the start of the ON period Ton. Accordingly, the amount of change in the inductor current IL changing from zero in the predetermined time period (Ton/2) can be figured out by the sampling value Isp in the predetermined time period (Ton/2). It is unnecessary to calculate a difference in current value between two points at different timings. Thus, it is possible to reduce the processing amount in the DSP  43 , by acquiring the inductor current IL at such timing. 
     In an embodiment of the present disclosure, the drive signal Vg for turning on and off the NMOS transistor  26  is generated based on the oscillator voltage Vosc of the triangular wave and the command voltage Vx. In the triangular wave, arising period in which the instantaneous value increases and a falling period in which the instantaneous value decreases are equal. Thus, a peak (including a peak on the bottom side) of the triangular wave is in the middle of the ON period Ton or the OFF period Toff. In an embodiment of the present disclosure, the inductor current IL is sampled at timing of the peak of the triangular wave after the NMOS transistor  26  is turned on. Accordingly, the sampling value Isp is acquired always at the timing after the time period Ton/2 has elapsed since the start of the ON period Ton, and thus the DSP  43  does not need to calculate such timing. 
     In an embodiment of the present disclosure, the inductance calculation unit  93  calculates the inductance L. However, the present disclosure is not limited to this. For example, a user of the AC-DC converter  10  may previously store, in the storage unit  94 , a value of the inductance L of the inductor  23  to be actually used. In such a case, it is possible to calculate the rectified voltage Vr without calculating the inductance L. 
     As explained above, the coefficient “k” corresponds to the amplitude command value of the average current Im. Thus, even if the inductance L is unknown, the ON period ton can be calculated, since Expression (5) holds with the coefficient “k” being controlled. However, when the ON-period calculation unit  96  calculates the ON period Ton considering the inductance L, the voltage regulator  91  needs only control the coefficient “k” (command voltage Vk). Accordingly, it is possible to prevent increase in gain or the like of the voltage regulator  91  more than necessary, thereby facilitating design of the voltage loop (feedback loop) and being able to stabilize the operation of the AC-DC converter  10 . 
     The DSP  43  includes: the signal output unit  61  for operating the AC-DC converter  10  as the PFC circuit in the continuous mode; and the signal output unit  62  for operating the AC-DC converter  10  as the PFC circuit in the discontinuous mode. Thus, even when the inductor current IL has obtained a continuous waveform or a discontinuous waveform, it is possible to improve the power factor. 
     In an embodiment of the present disclosure, the DSP  43  executes the programs to implement the subtractor  70  and the like. However, the present disclosure is not limited to this. For example, all of the blocks (for example, the subtractor  70  and the voltage regulator  71 ) of the DSP  43  may be implemented with hardware circuit (s) that does not use software (programs). Here, the “hardware circuit” indicates a circuit including circuit elements such as a resistor, a capacitor, a transistor, and the like, a digital circuit such as a logic circuit and the like, and an analog circuit such as an operational amplifier and the like. It should be noted that the terms “ . . . er/or or . . . device”, “ . . . circuit”, and “ . . . unit” are used for blocks having predetermined functions implemented by an integrated circuit. For example, “multiplier”, “multiplier circuit”, or “multiplier unit” is used for a block having a function of multiplying one signal by another signal. 
     Embodiments of the present disclosure described above are simply to facilitate understanding of the present disclosure and are not in any way to be construed as limiting the present disclosure. The present disclosure may variously be changed or altered without departing from its gist and encompass equivalents thereof. 
     For example, the determination unit  60  and the signal output units  61  and  62  are implemented in the DSP  43 . However, the present disclosure is not limited to this, but only the signal output unit  62  may be implemented. In this case, the DSP  43  operates the AC-DC converter  10  as the PFC circuit in the discontinuous mode.