PATENT DOCUMENT

Abstract:
In a delta sigma modulator including first and second integration circuits connected in cascade, each as a component thereof, first and second power source terminals for supplying first and second different power source voltages to the first and second integration circuits are provided. The first power source voltage is supplied to the former-stage first integration circuit having a SNR which is largely affected by the magnitude of the power source voltage. The second power source voltage lower than the first power source voltage is supplied to the latter-stage second integration circuit having a SNR which is not largely affected by the magnitude of the power source voltage.

Full Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a delta sigma modulator which includes an integration circuit and a quantizer connected in cascade, each as a component thereof, and also comprises a first power source terminal connected to the former-stage integration circuit, and a second power source terminal connected to the latter-stage quantizer to allow a reduction in power consumption without degrading a SNR (Signal to Noise Ratio). 
     The present invention also relates to a delta sigma modulator which includes a first integration circuit and a second integration circuit connected in cascade, each as a component thereof, and also comprises a first power source terminal connected to the former-stage first integration circuit and a second power source terminal connected to the latter-stage second integration circuit to allow a reduction in power consumption without degrading the SNR. 
     The present invention further relates to a delta sigma modulator which has a plurality of delta sigma modulation type quantization loops connected in cascade in multiple stages, and also comprises a first power source terminal connected to a first integration circuit composing the first-stage delta sigma modulation type quantization loop, and a second power source terminal connected to a second integration circuit composing second and subsequent delta sigma modulation type quantization loops to allow a reduction in power consumption without degrading the SNR. 
     2. Description of the Related Art 
     A system using a delta sigma modulator has been conventionally known, and used in an AD converter for digital audio equipment or the like. When the system is used in portable equipment, in particular, low power consumption is considered to be important. 
     Conventionally, an oversampling AD converter often referred to as a delta sigma AD converter has been well known. The delta sigma AD converter digitizes an analog signal at an extremely high oversampling rate, and simultaneously performs noise shaping for shifting noise to a high frequency range, and a digital filtering process after the noise shaping. This allows the delta sigma AD converter to implement an effective resolution higher than a quantized output of a delta sigma modulator. Thereafter, the effective sampling rate is returned to a Nyquist rate using decimation. 
     The noise shaping is a technique which lowers the level of quantization noise showing a uniform-level frequency distribution in a low frequency range in which an original signal is present by an differential/integral operation in accordance with delta sigma modulation without changing the frequency characteristics of the original signal, and conversely raises the level of quantization noise in a high frequency range in which a sampling frequency is present. 
     The effect of the noise shaping is larger as the order of a delta sigma modulation is higher, i.e., the number of stages of integrators composing a delta sigma modulator is larger. Accordingly, the noise shaping effect of a second-order delta sigma modulator is higher than that of a first-order delta sigma modulator. 
       FIG. 13  shows a structure of a single-loop second-order delta sigma modulator as a conventional embodiment. A delta sigma modulator  1  comprises first and second integration circuits  10  and  11 , amplifiers  20  and  21  each having an amplification factor a 1 , an amplifier  22  having an amplification factor a 2 , a quantizer  2 , adders/subtractors  3  and  4 , and DA converters  30  and  31 . The delta sigma modulator  1  operates with a power source voltage VDD 1  supplied from a power source terminal  600 . 
     The first integration circuit  10  receives a signal obtained by subtracting, from a signal obtained by passing an analog input signal Ain through the amplifier  20 , a signal obtained by passing a feedback reference voltage (positive voltage+Vr 1  or negative voltage−Vr 1 ) generated from the DA converter  30  through the amplifier  21  by means of the adder/subtractor  3 . 
     The second integration circuit  11  receives a signal obtained by subtracting, from an output of the first integration circuit  10 , a signal obtained by passing a feedback reference voltage (positive voltage+Vr 1  or negative voltage−Vr 1 ) generated from the DA converter  31  through the amplifier  22  by means of the adder/subtractor  4 . 
     The quantizer  2  quantizes an output of the second integration circuit  11  to a 1-bit digital output signal Dout. 
     The DA converters  30  and  31  generate the feedback reference voltage (positive voltage+Vr 1  or negative voltage−Vr 1 ) mentioned above from the 1-bit digital output signal Dout of the quantizer  2 . 
     Typically, the 1-bit digital output signal Dout of the delta sigma modulator  1  is inputted to a digital filter circuit for the retrieval of a needed signal band. The delta sigma modulator  1  composes an AD converter. 
     As a result, when the digital output signal Dout of the delta sigma modulator  1  is normalized such that a digital full scale value equals 1, it can be given by the following transmission function: 
     
       
         
           
             
               
                 
                   
                     
                       
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     where the digital full scale value corresponds to the voltage±Vr 1  of an analog value, and Q represents quantization noise generated in the quantizer  2 . 
     A description will be given to a specific circuit structure for implementing the delta sigma modulator  1  of  FIG. 13  with reference to  FIG. 14 . 
       FIG. 14  is a circuit diagram showing an example of the specific circuit structure of a single-loop second-order delta sigma modulator  101  using a switched capacitor circuit. The first and second integration circuits  10  and  11 , the DA converters  30  and  31 , and the adders/subtractors  3  and  4  of  FIG. 13  are composed of the switched capacitor circuit comprising switches  41  to  52  and  61  to  72 , capacitors C 11  to C 14  and C 21  to C 24 , operational amplifiers  6  and  7 , and buffers  5  and  8  in  FIG. 14 . VDD 1  is a power source voltage supplied to the second-order delta sigma modulator  101 .  601  is a power source terminal. 
     The analog input signal Ain is integrated by the operational amplifier  6  using the reference voltage Vr 1  as well as charging and discharging between the capacitors C 11  and C 14 . 
     A feedback signal is processed as follows. The digital output signal Dout is converted by the buffer circuit  5  to digital signals S 1   p  and S 1   n . Then, by turning ON/OFF the switches  46  and  50  in accordance with the levels of the digital signals S 1   p  and S 1   n , a DA conversion using the reference voltage Vr 1  and a zero voltage is performed. The DA converted voltage is integrated by the operational amplifier  6  using the charging and discharging between the capacitors C 12  and C 13 . 
     In this manner, the first integration circuit  10  and the DA converter  30  are constructed. The amplification factor a 1  of the amplifier  20  shown in  FIG. 13  corresponds to the capacitance ratio C 11 /C 14 , while the amplification factor a 1  of the amplifier  21  shown in  FIG. 13  corresponds to the capacitance ratios C 12 /C 14  and C 13 /C 14 . 
     Next, the output signal of the operational amplifier  6  is integrated by the operational amplifier  7  using the reference voltage Vr 1  as well as the charging and discharging between the capacitors C 21  and C 24 . 
     The feedback signal is processed as follows. The digital output signal Dout is converted by the buffer circuit  5  to the digital signals S 1   p and S 1   n . Then, by turning ON/OFF the switches  66  and  70  in accordance with the levels of the digital signals S 1   p and S 1   n , a DA conversion using the reference voltage Vr 1  and a zero voltage is performed. The DA converted voltage is integrated by the operational amplifier  7  using the charging and discharging between the capacitors C 22  and C 23 . 
     In this manner, the second integration circuit  11  and the DA converter  31  are constructed. The amplification factor a 2  of the amplifier  22  shown in  FIG. 13  corresponds to the capacitance ratios C 22 /C 24  and C 23 /C 24 . 
     The output signal of the operational amplifier  7  is quantized by a comparator  12 , and outputted as the 1-bit digital signal Dout. The comparator  12  corresponds to the quantizer  2  of  FIG. 13 . 
     The buffer circuit  5  outputs the digital signals S 1   p and S 1   n  which are each in-phase or anti-phase with the 1-bit digital output signal Dout of the delta sigma modulator  101 . The switches  46  and  66  are under the ON/OFF control of the digital signal S 1   n . The switches  50  and  70  are under the ON/OFF control of the digital signal S 1   p , which is opposite to the ON/OFF control over the switches  46  and  66 . 
     The buffer circuit  8  receives a control clock for the switched capacitor circuit, and outputs digital signals φ 1   p  and φ 1   n  which are each in-phase or anti-phase with the control clock. The switches  41 ,  44 ,  45 ,  48 ,  51 ,  52 ,  61 ,  64 ,  65 ,  68 ,  71  and  72  are under the ON/OFF control of the digital signal φ 1   p . The switches  42 ,  43 ,  47 ,  49 ,  62 ,  63 ,  67 , and  69  are under the ON/OFF control of the digital signal φ 1   n , which is opposite to the control over the switches  41 ,  44 ,  45 ,  48 ,  51 ,  52 ,  61 ,  64 ,  65 ,  68 ,  71  and  72 . 
     As shown in  FIG. 15 , the buffer circuit  5  comprises an inverter IN 1  composed of a P-channel transistor  81 A and an N-channel transistor  82 A, an inverter IN 2  composed of a P-channel transistor  81 B and an N-channel transistor  82 B, and an inverter IN 3  composed of a P-channel transistor  81 C and an N-channel transistor  82 C. A signal which is in-phase with the signal inputted to an input terminal IN is outputted from an output terminal OUTp, while a signal which is anti-phase with the signal inputted to the input terminal IN is outputted from an output terminal OUTn. 
     The buffer circuit  8  has the same structure as that of the buffer circuit  5 . 
     The switches  41  to  52  and  61  to  72  are each composed of, e.g., an N-channel transistor  83  shown in  FIG. 16 , and intermittently interrupts (ON/OFF) a signal with the timing of a signal CLK (clock) inputted to the gate thereof. The signal CLK is supplied from each of the buffer circuits  5  and  8 . 
       FIG. 17  shows an example of respective circuits which implement the operational amplifiers  6  and  7 , and the comparator  12 . These circuits are composed of P-channel transistors  84 A to  84 C, N-channel transistors  85 A and  85 B, and current sources  86 A and  86 B. 
     The reference voltage Vr 1  is supplied by, e.g., dividing the power source voltage VDD 1  with resistors  405 A and  405 B, and amplifying the divided voltage with an operational amplifier  406 , as shown in  FIG. 18 . 
     Thus, the delta sigma modulator shown in  FIG. 13  is composed of the switched capacitor circuit. 
     As a CMOS circuit has been increasingly scaled down from 0.35 μm to 0.18 μm, and to 0.13 μm, the operation voltage thereof has also been reduced from 3.3 V to 1.8 V, and to 1.2 V. To reduce the power consumption of a delta sigma modulator, it is effective to minimize the power source voltage thereof, and operate the delta sigma modulator. 
     However, when the delta sigma modulator is operated with a lowered power source voltage, the dynamic range of the circuit is narrowed so that it is necessary to simultaneously reduce the amplitude of the input signal as well as the feedback reference voltage. As a result, the SNR (Signal to Noise Ratio) during an AD conversion deteriorates. In addition, a voltage for driving the MOS switch of the switched capacitor circuit also lowers to lead to the problem that the ON resistance of the switch increases, and the turning ON/OFF of the switch becomes difficult. Thus, it is not easy to lower the power source voltage of an analog circuit. 
     A description will be given hereinbelow to the ON resistance of the switch mentioned above. The ON resistance of the switch of  FIG. 16  can be given by:
 
 Ron≈ 1/(μ* Cox*W/L* ( Vgs−Vt ))
 
where μ is a mobility, Cox is the thickness of a gate oxide film, W is a gate width, L is a gate length, Vgs is a gate-source drive voltage, and Vt is a threshold. Accordingly, when the voltage Vgs decreases, the ON resistance Ron increases.
 
     Even microfabrication processes using design rules of 0.18 μm or below have many examples in which a transistor adapted to perform a 3.3 V operation by varying the thickness of the gate oxide film is embedded for an external interface (I/F). As a result, there is disclosed a method which lowers power consumption by using a 3.3 V transistor for an analog circuit such as a delta sigma modulator, and operates, with a low power source voltage, only a digital circuit such as a digital filter connected in a stage subsequent thereto or the like (see Japanese Unexamined Patent Publication No. HEI 6-283980). 
     SUMMARY OF THE INVENTION 
     It is therefore an object of the present invention to provide a delta sigma modulator which allows a reduction in power consumption without degrading the SNR during an AD conversion. 
     A delta sigma modulator in accordance with a first aspect of the present invention is a delta sigma modulator including an integration circuit, and a quantizer for quantizing an output of the integration circuit, an output of the quantizer being feedbacked to the input side of the integration circuit, the delta sigma modulator comprising: a first power source terminal for supplying a first operation power source voltage to the integration circuit; and a second power source terminal for supplying a second operation power source voltage lower than the first operation power source voltage to the quantizer. 
     The arrangement makes it possible to reduce power consumption without degrading the SNR on the whole by supplying a higher power source voltage to the former-stage integration circuit in which noise has not been reduced, and a reduction in power source voltage largely affects the SNR, while supplying a lower power source voltage to the latter-stage quantizer in which noise has been already reduced by noise shaping performed by the integration circuit, and a reduction in power source voltage does not largely affect the SNR. 
     In the former-stage integration circuit, the noise of an input signal has not eventually been attenuated. Therefore, by supplying the higher power source voltage, it is possible to eliminate the need to reduce the amplitude of the input signal, and prevent the deterioration of the SNR. In the latter-stage quantizer, on the other hand, the noise of an input signal is attenuated by noise shaping so that, even when power consumption is reduced by supplying the lower power source voltage, the SNR is not degraded thereby. As a result, it is possible to implement a delta sigma modulator with reduced power consumption without degrading the SNR on the whole. 
     In the delta sigma modulator in accordance with the first aspect of the present invention mentioned above, the integration circuit preferably includes an operational amplifier supplied with the first operation power source voltage, and the quantizer preferably includes a comparator supplied with the second operation power source voltage. 
     In the delta sigma modulator in accordance with the first aspect of the present invention mentioned above, the integration circuit may include a capacitor, a switch for intermittently interrupting a charge/discharge current to the capacitor, and a drive circuit supplied with the first operation power source voltage to drive the switch, and the quantizer may include a operational amplifier supplied with the second operation power source voltage. The drive circuit mentioned above preferably receives a signal in accordance with a level of a power source voltage supplied to the second power source terminal, and outputs a signal in accordance with a level of a power source voltage supplied to the first power source terminal. 
     In the delta sigma modulator in accordance with the first aspect of the present invention mentioned above, the integration circuit may include an operational amplifier supplied with the first operation power source voltage, a capacitor, a switch for intermittently interrupting a charge/discharge current to the capacitor, and a drive circuit supplied with the first operation power source voltage to drive the switch, and the quantizer may include a comparator supplied with the second operation power source voltage. The drive circuit mentioned above preferably receives a signal in accordance with a level of a power source voltage supplied to the second power source terminal, and outputs a signal in accordance with a level of a power source voltage supplied to the first power source terminal. 
     In the delta sigma modulator in accordance with the first aspect of the present invention mentioned above, a feedback path from an output terminal of the quantizer to the input side of the integration circuit is preferably provided with a DA converter receiving the output of the quantizer to generate a feedback reference voltage to be inputted to the integration circuit. The feedback reference voltage mentioned above is preferably generated based on a power source voltage supplied to the first power source terminal. 
     A delta sigma modulator in accordance with a second aspect of the present invention is a delta sigma modulator including a first integration circuit, a second integration circuit for integrating an output of the first integration circuit, and a quantizer for quantizing an output of the second integration circuit, an output of the quantizer being feedbacked to the input side of the first integration circuit, the delta sigma modulator comprising: a first power source terminal for supplying a first operation power source voltage to the first integration circuit; and a second power source terminal for supplying a second operation power source voltage lower than the first operation power source voltage to the second integration circuit. 
     The arrangement makes it possible to reduce power consumption without degrading the SNR on the whole by supplying a higher power source voltage to the former-stage first integration circuit in which noise has not been reduced, and a reduction in power source voltage largely affects the SNR, while supplying a lower power source voltage to the latter-stage second integration circuit in which noise has been already reduced by noise shaping performed by the first integration circuit, and a reduction in power source voltage does not largely affect the SNR. 
     In the former-stage first integration circuit, the noise of an input signal has not eventually been attenuated. Therefore, by supplying the higher power source voltage, it is possible to eliminate the need to reduce the amplitude of the input signal, and prevent the deterioration of the SNR. In the latter-stage second integration circuit, on the other hand, the noise of an input signal is attenuated by noise shaping performed by the former-stage integration circuit so that, even when power consumption is reduced by supplying the lower power source voltage, the SNR is not degraded thereby. As a result, it is possible to implement a delta sigma modulator with reduced power consumption without degrading the SNR on the whole. 
     In the delta sigma modulator in accordance with the second aspect of the present invention mentioned above, the second operation power source voltage is preferably supplied from the second power source terminal to the quantizer. 
     In the delta sigma modulator in accordance with the second aspect of the present invention mentioned above, the first integration circuit preferably includes a first operational amplifier supplied with the first operation power source voltage, and the second integration circuit preferably includes a second operational amplifier supplied with the second operation power source voltage. 
     In the delta sigma modulator in accordance with the second aspect of the present invention mentioned above, the first integration circuit may include a first capacitor, a first switch for intermittently interrupting a charge/discharge current to the first capacitor, and a first drive circuit supplied with the first operation power source voltage to drive the first switch, and the second integration circuit may include a second capacitor, a second switch for intermittently interrupting a charge/discharge current to the second capacitor, and a second drive circuit supplied with the second operation power source voltage to drive the second switch. The first drive circuit mentioned above preferably receives a signal in accordance with a level of a power source voltage supplied to the second power source terminal, and outputs a signal in accordance with a level of a power source voltage supplied to the first power source terminal. 
     In the delta sigma modulator in accordance with the second aspect of the present invention mentioned above, the first integration circuit may include a first operational amplifier supplied with the first operation power source voltage, a first capacitor, a first switch for intermittently interrupting a charge/discharge current to the first capacitor, and a first drive circuit supplied with the first operation power source voltage to drive the first switch, and the second integration circuit may include a second operational amplifier supplied with the second operation power source voltage, a second capacitor, a second switch for intermittently interrupting a charge/discharge current to the second capacitor, and a second drive circuit supplied with the second operation power source voltage to drive the second switch. The first drive circuit mentioned above preferably receives a signal in accordance with a level of a power source voltage supplied to the second power source terminal, and outputs a signal in accordance with a level of a power source voltage supplied to the first power source terminal. 
     In the delta sigma modulator in accordance with the second aspect of the present invention mentioned above, a feedback path from an output terminal of the quantizer to the input side of each of the first and second integration circuits is preferably provided with a DA converter receiving the output of the quantizer to generate a feedback reference voltage to be inputted to each of the first and second integration circuits. The feedback reference voltage mentioned above is preferably generated based on a power source voltage supplied to the first power source terminal. 
     In the delta sigma modulator in accordance with the second aspect of the present invention mentioned above, feedback paths from an output terminal of the quantizer to the input sides of the first and second integration circuits may be provided with first and second DA converters receiving the output of the quantizer to generate first and second feedback reference voltages to be inputted to the first and second integration circuits. The first and second feedback reference voltages are preferably generated based on respective power source voltages supplied to the first and second power source terminals. 
     A delta sigma modulator in accordance with a third aspect of the present invention is a delta sigma modulator comprising: a first-stage delta sigma modulation type quantization loop including a first integration circuit, and a first quantizer for quantizing an output of the first integration circuit, an output of the first quantizer being feedbacked to the input side of the first integration circuit; a subsequent-stage delta sigma modulation type quantization loop connected in cascade to the first-stage delta sigma modulation type quantization loop, and including a second integration circuit, and a second quantizer for quantizing an output of the second integration circuit, an output of the second quantizer being feedbacked to the input side of the second integration circuit; and a noise removal circuit receiving an output of the first-stage delta sigma modulation type quantization loop, and an output of the subsequent-stage delta sigma modulation type quantization loop to remove noise included in the output of the first-stage delta sigma modulation type quantization loop, the delta sigma modulator further comprising: a first power source terminal for supplying a first operation power source voltage to the first integration circuit; and a second power source terminal for supplying a second operation power source voltage lower than the first operation power source voltage to the second integration circuit. 
     The arrangement makes it possible to reduce power consumption without degrading the SNR on the whole by supplying a higher power source voltage to the first integration circuit in the first-stage delta sigma modulation type quantization loop in which noise has not been reduced, and a reduction in power source voltage largely affects the SNR, while supplying a lower power source voltage to the second integration circuit in the subsequent-stage delta sigma modulation type quantization loop in which noise has been already reduced by noise shaping performed by the first integration circuit, and a reduction in power source voltage does not largely affect the SNR. 
     In the former-stage first integration circuit, the noise of an input signal has not eventually been attenuated. Therefore, by supplying the higher power source voltage, it is possible to eliminate the need to reduce the amplitude of the input signal, and prevent the deterioration of the SNR. In the latter-stage second integration circuit, on the other hand, the noise of an input signal is attenuated by noise shaping performed by the former-stage integration circuit so that, even when power consumption is reduced by supplying the lower power source voltage, the SNR is not degraded thereby. As a result, it is possible to implement a delta sigma modulator with reduced power consumption without degrading the SNR on the whole. 
     In the delta sigma modulator in accordance with the third aspect of the present invention mentioned above, the second operation power source voltage is preferably supplied from the second power source terminal to each of the first and second quantizers. 
     In the delta sigma modulator in accordance with the third aspect of the present invention mentioned above, the first integration circuit preferably includes a first operational amplifier supplied with the first operation power source voltage, and the second integration circuit preferably includes a second operational amplifier supplied with the second operation power source voltage. 
     In the delta sigma modulator in accordance with the third aspect of the present invention mentioned above, the first integration circuit may include a first capacitor, a first switch for intermittently interrupting a charge/discharge current to the first capacitor, and a first drive circuit supplied with the first operation power source voltage to drive the first switch, and the second integration circuit may include a second capacitor, a second switch for intermittently interrupting a charge/discharge current to the second capacitor, and a second drive circuit supplied with the second operation power source voltage to drive the second switch. The first drive circuit mentioned above preferably receives a signal in accordance with a level of a power source voltage supplied to the second power source terminal, and outputs a signal in accordance with a level of a power source voltage supplied to the first power source terminal. 
     In the delta sigma modulator in accordance with the third aspect of the present invention mentioned above, the first integration circuit may include a first operational amplifier supplied with the first operation power source voltage, a first capacitor, a first switch for intermittently interrupting a charge/discharge current to the first capacitor, and a first drive circuit supplied with the first operation power source voltage to drive the first switch, and the second integration circuit may include a second operational amplifier supplied with the second operation power source voltage, a second capacitor, a second switch for intermittently interrupting a charge/discharge current to the second capacitor, and a second drive circuit supplied with the second operation power source voltage to drive the second switch. The first drive circuit mentioned above preferably receives a signal in accordance with a level of a power source voltage supplied to the second power source terminal, and outputs a signal in accordance with a level of a power source voltage supplied to the first power source terminal. 
     In the delta sigma modulator in accordance with the third aspect of the present invention mentioned above, a feedback path from an output terminal of the first quantizer to the input side of the first integration circuit is preferably provided with a first DA converter receiving the output of the first quantizer to generate a first feedback reference voltage to be inputted to the first integration circuit, and a feedback path from an output terminal of the second quantizer to the input side of the second integration circuit is preferably provided with a second DA converter receiving the output of the second quantizer to generate a second feedback reference voltage to be inputted to the second integration circuit. The first and second feedback reference voltages mentioned above are preferably generated based on respective power source voltages supplied to the first and second power source terminals. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram showing a structure of a delta sigma modulator in a first embodiment of the present invention; 
         FIG. 2  is a circuit diagram showing an example of a circuit in the delta sigma modulator in the first embodiment; 
         FIG. 3  is a circuit diagram showing an example of a buffer circuit; 
         FIGS. 4A and 4B  are circuit diagrams each showing an example of a reference voltage generation circuit; 
         FIG. 5  is a block diagram showing a structure of a delta sigma modulator in a second embodiment of the present invention; 
         FIG. 6  is a block diagram showing a structure of a delta sigma modulator in a third embodiment of the present invention; 
         FIG. 7  is a circuit diagram showing an example of a circuit in the delta sigma modulator in the third embodiment; 
         FIG. 8  is a circuit diagram showing an example of a buffer circuit; 
         FIG. 9  is a circuit diagram showing an example of a circuit in a delta sigma modulator in a fourth embodiment of the present invention; 
         FIG. 10  is a circuit diagram showing an example of a circuit in a delta sigma modulator in a fifth embodiment of the present invention; 
         FIG. 11  is a circuit diagram showing an example of a circuit in a delta sigma modulator in a sixth embodiment of the present invention; 
         FIGS. 12A to 12D  are circuit diagrams each showing an example of a circuit in a delta sigma modulator in a seventh embodiment of the present invention; 
         FIG. 13  is a block diagram showing a structure of a conventional delta sigma modulator; 
         FIG. 14  is a circuit diagram showing an example of a circuit in the conventional delta sigma modulator; 
         FIG. 15  is a circuit diagram showing an example of a buffer circuit; 
         FIG. 16  is a circuit diagram showing an example of a switch circuit; 
         FIG. 17  is a circuit diagram showing an example of respective circuits in an operational amplifier and a comparator; and 
         FIG. 18  is a circuit diagram showing an example of a reference voltage generation circuit. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring now to the drawings, the embodiments of the present invention will be described hereinbelow. 
       FIG. 1  shows a structure of a single-loop second-order delta sigma modulator as a first embodiment of the present invention. The delta sigma modulator comprises first and second integration circuits  110  and  111 , amplifiers  120  and  121  each having an amplification factor a 0 , an amplifier  122  having an amplification factor a 2 , a quantizer  102  made of, e.g., a comparator, adders/subtractors  103  and  104 , and DA converters  130  and  131 . The delta sigma modulator operates with respective power source voltages VDD 1  and VDD 2  (VDD 1 &gt;VDD 2 ) supplied from power source terminals  701  and  702 . 
     The first integration circuit  110  operates with the power source voltage VDD 1  supplied from the first power source terminal  701 , and receives a signal obtained by subtracting, from a signal obtained by passing an analog input signal Ain through the amplifier  120 , a signal obtained by passing a first feedback reference voltage (positive voltage+Vr 1  or negative voltage−Vr 1 ) generated from the DA converter  130  through the amplifier  121  by means of the adder/subtractor  103 . 
     The second integration circuit  111  operates with the power source voltage VDD 2  supplied from the second power source terminal  702 , and receives a signal obtained by subtracting, from an output Ao of the first integration circuit  110 , a signal obtained by passing a second feedback reference voltage (positive voltage+Vr 2  or negative voltage−Vr 2 ) generated from the DA converter  131  through the amplifier  122  by means of the adder/subtractor  104 . 
     The quantizer  102  operates with the power source voltage VDD 2  supplied from the second power source terminal  702 , and quantizes an output of the second integration circuit  111  to a 1-bit digital output signal Dout. 
     The first DA converter  130  generates the first feedback reference voltage (positive voltage+Vr 1  or negative voltage−Vr 1 ) mentioned above from the 1-bit digital output signal Dout from the quantizer  102 . 
     The second DA converter  131  generates the second feedback reference voltage (positive voltage+Vr 2  or negative voltage−Vr 2 ) mentioned above from the 1-bit digital output signal Dout from the quantizer  102 . 
     Typically, the 1-bit digital output signal Dout of the delta sigma modulator is inputted to a digital filter circuit for the retrieval of a needed signal band. The delta sigma modulator composes an AD converter. 
     At this time, to prevent the occurrence of distortion in an output signal of the second integration circuit  111 , it is necessary to operate the delta sigma modulator by setting the amplification factor a 0  of each of the amplifiers  120  and  121  and the feedback reference voltages (Vr 1  and Vr 2 ) of the DA converters  130  and  131  such that the signals inputted to the second integration circuit  111 , i.e., an output of the first integration circuit  110  and an output of the second DA converter  131  are in a range under the voltage VDD 2 . 
     The 1-bit digital output signal Dout as an output of the delta sigma modulator shown in  FIG. 1  can be given by the following transmission function: 
     
       
         
           
             
               
                 
                   Dout 
                   ≅ 
                   
                     
                       Ain 
                       
                         2 
                         · 
                         
                           Vr 
                           1 
                         
                       
                     
                     + 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 Z 
                                 
                                   - 
                                   1 
                                 
                               
                             
                             ) 
                           
                           2 
                         
                         ⁢ 
                         
                           Q 
                           · 
                           2 
                           · 
                           
                             Vr 
                             2 
                           
                         
                       
                       
                         
                           
                             
                               
                                 2 
                                 · 
                                 
                                   Vr 
                                   2 
                                 
                                 · 
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           1 
                                           - 
                                           
                                             
                                               ( 
                                               
                                                 2 
                                                 - 
                                                 
                                                   a 
                                                   2 
                                                 
                                               
                                               ) 
                                             
                                             ⁢ 
                                             
                                               Z 
                                               
                                                 - 
                                                 1 
                                               
                                             
                                           
                                           + 
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                             ( 
                                             
                                               1 
                                               + 
                                               
                                                 a 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 2 
                                               
                                             
                                             ) 
                                           
                                           ⁢ 
                                           
                                             Z 
                                             
                                               - 
                                               2 
                                             
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 2 
                                 · 
                                 
                                   Vr 
                                   1 
                                 
                                 · 
                                 a 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 0 
                                 · 
                                 
                                   Z 
                                   
                                     - 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
               
             
           
         
       
     
     when it is assumed that the values of Vr 2  and a 0  are set to satisfy Vr 2 =Vr 1 ·a 0 /a 1 , Expression 3 shown below is given: 
     
       
         
           
             
               
                 
                   
                     
                       
                         Dout 
                         ≅ 
                           
                         ⁢ 
                         
                           
                             Ain 
                             
                               2 
                               · 
                               
                                 Vr 
                                 1 
                               
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     Z 
                                     
                                       - 
                                       1 
                                     
                                   
                                 
                                 ) 
                               
                               2 
                             
                             ⁢ 
                             
                               Q 
                               · 
                               2 
                               · 
                               
                                 Vr 
                                 2 
                               
                             
                           
                           
                             2 
                             · 
                             
                               Vr 
                               2 
                             
                             · 
                             
                               [ 
                               
                                 1 
                                 - 
                                 
                                   
                                     ( 
                                     
                                       2 
                                       - 
                                       
                                         a 
                                         2 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     
                                       - 
                                       1 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       1 
                                       + 
                                       
                                         a 
                                         1 
                                       
                                       - 
                                       
                                         a 
                                         2 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     
                                       - 
                                       2 
                                     
                                   
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             Ain 
                             
                               2 
                               · 
                               
                                 Vr 
                                 1 
                               
                             
                           
                           + 
                           
                             
                               
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       Z 
                                       
                                         - 
                                         1 
                                       
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                               ⁢ 
                               Q 
                             
                             
                               1 
                               - 
                               
                                 
                                   ( 
                                   
                                     2 
                                     - 
                                     
                                       a 
                                       2 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   Z 
                                   
                                     - 
                                     1 
                                   
                                 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     
                                       a 
                                       1 
                                     
                                     - 
                                     
                                       a 
                                       2 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   Z 
                                   
                                     - 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
               
             
           
         
       
     
     The arrangement allows the settings of, e.g., VDD 1 =3.3 V and VDD 2 =1.8 V or 1.6 V, and allows a reduction in the power consumption of the second integration circuit  111  and the circuits subsequent thereto. In addition, noise added in the second integration circuit  111  and the circuits subsequent thereto in the delta sigma modulator is attenuated by the effect of noise shaping. 
     Thus, in the delta sigma modulator in the embodiment of the present invention, the amplitude of a signal in the second and subsequent-stage integration circuits in which the noise is attenuated by noise shaping is reduced, while the amplitude of a signal in the first-stage integration circuit in which the noise is not attenuated is held large. Accordingly, there is no deterioration of the SNR resulting from a reduction in the operation power source voltage of the second and subsequent-stage integration circuits. In addition, because the area of a 1.8 V transistor is generally smaller than that of a 3.3 V transistor, a reduction in circuit area can also be achieved by using the 3.3 V transistor as a transistor used in the circuit connected to the power source voltage VDD 1 , while using the 1.8 V transistor as a transistor used in the circuit connected to the power source voltage VDD 2 . 
     Next, a description will be given to a specific example of the circuit of the first embodiment of the present invention with reference to  FIG. 2 . 
     The integration circuits  110  and  111 , the DA converters  130  and  131 , the adders/subtractors  103  and  104 , and the amplifiers  120 ,  121 , and  122  of  FIG. 1  are composed of a switched capacitor circuit comprising switches  141  to  152  and  161  to  172 , capacitors C 111  to C 114  and C 121  to C 124 , operational amplifiers  106  and  107 , and buffers  105  and  108  in  FIG. 2 . 
     Specifically, the integration circuit  110 , the DA converter  130 , the adder/subtractor  103 , and the amplifiers  120  and  121  are composed of the switches  141  to  152 , the capacitors C 111  to C 114 , the operational amplifier  106 , and the buffers  105  and  108  in  FIG. 2 . 
     On the other hand, the integration circuit  111 , the DA converter  131 , the adder/subtractor  104 , and the amplifier  122  are composed of the switches  161  to  172 , the capacitors C 121  to C 124 , the operational amplifier  107 , and the buffers  105  and  108  in  FIG. 2 . 
     VDD 1  and VDD 2  denote power source voltages supplied to the second-order delta sigma modulator, while  703  and  704  denote power source terminals. In  FIG. 2 , the reference numerals  200  and  201  denote circuit blocks composing the integration circuits and the DA converters. 
     The analog input signal Ain is integrated by the operational amplifier  106  using the first reference voltage Vr 1  as well as charging and discharging between the capacitors C 111  and C 114 . 
     The feedback signal is processed as follows. The digital output signal Dout is converted by the buffer circuit  105  to the digital signals S 1   p and S 1   n . Then, by turning ON/OFF the switches  146  and  150  in accordance with the levels of the digital signals S 1   p and S 1   n , a DA conversion using the reference voltage Vr 1  and a zero voltage is performed. The DA converted voltage is integrated by the operational amplifier  6  using charging and discharging between the capacitors C 112  and C 113 . 
     The amplification factor ac of the amplifier  120  of  FIG. 1  corresponds to the capacitance ratio C 111 /C 114 , and the amplification factor a 0  of the amplifier  121  of  FIG. 1  corresponds to the capacitance ratios C 112 /C 114  and C 113 /C 114 . 
     Next, an output signal of the operational amplifier  106  is level-converted using the first and second reference voltages Vr 1  and Vr 2 , and integrated by the operational amplifier  107  using charging and discharging between the capacitors C 121  and C 124 . 
     The feedback signal is processed as follows. The digital output signal Dout is converted by the buffer circuit  105  to the digital signals S 1   p and S 1   n . Then, by turning ON/OFF the switches  166  and  170  in accordance with the levels of the digital signals S 1   p and S 1   n , a DA conversion using the reference voltage Vr 1  and a zero voltage is performed. The DA converted voltage is integrated by the operational amplifier  107  using charging and discharging between the capacitors C 122  and C 123 . 
     In this manner, the second integration circuit  111  and the DA converter  131  are constructed. To the power source terminal of the operational amplifier  107 , the second power source terminal  704  is connected. The amplification factor of the amplifier  122  shown in  FIG. 1  corresponds to the capacitance ratios C 122 /C 124  and C 123 /C 124 . 
     The output signal of the operational amplifier  107  is quantized by a quantizer  202  made of a comparator connected to the second power source terminal  704 , and outputted as the 1-bit digital output signal Dout. 
     The buffer circuits  105  and  108  are composed of a circuit shown in  FIG. 3 . The VDD 2 -based digital signal inputted to a terminal IN is outputted as a VDD 1 -based in-phase signal and a VDD 1 -based anti-phase signal from terminals OUT 1   p  and OUT 1   n , respectively, while a VDD 2 -based in-phase signal and a VDD 2 -based anti-phase signal are outputted from terminals OUT 2   p  and OUT 2   n , respectively, to drive the respective switches. 
     As shown in  FIGS. 4A and 4B , the reference voltage Vr 1  is generated by resistance division of the power source voltage VDD 1  or the like, and the reference voltage Vr 2  is generated by resistance division of the power source voltage VDD 2  or the like. In  FIGS. 4A and 4B ,  506  and  507  denote operational amplifiers. 
     In this manner, the delta sigma modulator shown in  FIG. 1  can be implemented with the switched capacitor circuit. 
     Next, a description will be given to a second embodiment of the present invention with reference to  FIG. 5 .  FIG. 5  shows an example in which the delta sigma modulator of the first embodiment is applied to a cascaded delta sigma modulator. The cascaded delta sigma modulator is characterized in that it can implement a higher-order delta sigma modulation type AD converter with a larger number of stages of integration circuits. A description will be given hereinbelow to a fourth-order cascaded delta sigma modulator. 
     The fourth-order cascaded delta sigma modulator comprises a first second-order delta sigma modulation type quantization loop  300 , a second second-order delta sigma modulation type quantization loop  301  connected in cascade to the first delta sigma modulation type quantization loop  300 , and a noise removal circuit  302 A for removing noise by combining the outputs of the first and second second-order delta sigma modulation type quantization loops  300  and  301 . The cascaded delta sigma modulator operates with the power source voltages VDD 1  and VDD 2  supplied from power source terminals  801  and  802 . 
     The first second-order delta sigma modulation type quantization loop  300  comprises first and second integration circuits  210  and  211 , amplifiers  220  and  221  each having an amplification factor a 0 , an amplifier  222  having an amplification factor a 12 , a quantizer  302 , adders/subtractors  203  and  204 , and DA converters  230  and  231 . 
     The first integration circuit  210  receives a signal obtained by subtracting, from a signal obtained by passing the analog input signal Ain through the amplifier  220 , a signal obtained by passing the first feedback reference voltage (positive voltage+Vr 1  or negative voltage−Vr 1 ) generated from the first DA converter  230  through the amplifier  221  by means of the adder/subtractor  203 , and operates with the power source voltage VDD 1  supplied from the first power source terminal  801 . 
     The second integration circuit  211  receives a signal obtained by subtracting, from an output of the first integration circuit  210 , a signal obtained by passing the second feedback reference voltage (positive voltage+Vr 2  or negative voltage−Vr 2 ) generated from the second DA converter  231  through the amplifier  222  by means of the adder/subtractor  204 , and operates with the power source voltage VDD 2  supplied from the second power source terminal  802 . 
     The quantizer  302  is made of, e.g., a comparator, and quantizes an output of the second integration circuit  211  to the 1-bit digital signal, and operates with the power source voltage VDD 2 . 
     The first and second DA converters  230  and  231  generate the first and second feedback reference voltages mentioned above from the 1-bit digital output signal of the quantizer  302 . 
     The second second-order delta sigma modulation type quantization loop  301  comprises third and fourth integration circuits  310  and  311 , amplifiers  320  and  321  each having an amplification factor a 21 , an amplifier  322  having an amplification factor a 22 , a quantizer  402 , adders/subtractors  303  and  304 , and DA converters  330  and  331 . The second second-order delta sigma modulation type quantization loop  301  receives a differential signal between an input to the quantizer  302  of the first second-order delta sigma modulation type quantization loop  300  and an output of the DA converter  231  of the first second-order delta sigma modulation type quantization loop  300 , i.e., a quantization error generated by the quantizer  302  of the first second-order delta sigma modulation type quantization loop  300 . The differential signal mentioned above is calculated by the adder/subtractor  404 . 
     The third integration circuit  310  receives a signal obtained by subtracting, from a signal obtained by passing an input signal made of the quantization error generated by the quantizer  302  of the first second-order delta sigma modulation type quantization loop  300  through the amplifier  320 , a signal obtained by passing the first feedback reference voltage (positive voltage+Vr 2  or negative voltage−Vr 2 ) generated from the third DA converter  330  through the amplifier  321  by means of the adder/subtractor  303 , and operates with the power source voltage VDD 2 . 
     The fourth integration circuit  311  receives a signal obtained by subtracting, from an output of the third integration circuit  310 , a signal obtained by passing the second feedback reference voltage (positive voltage+Vr 2  or negative voltage−Vr 2 ) generated from the fourth DA converter  330  through the amplifier  322  by means of the adder/subtractor  304 , and operates with the power source voltage VDD 2 . 
     The quantizer  402  quantizes an output of the fourth integration circuit  311  to the 1-bit digital output signal Dout, and operates with the power source voltage VDD 2 . 
     The third and fourth DA converters  330  and  331  generate the first and second feedback reference voltages each mentioned above from the 1-bit digital output signal Dout of the quantizer  402 . 
     The noise removal circuit  302 A operates with the power source voltage VDD 2 , and provides a signal obtained by subtracting, from a signal obtained by delaying an output signal of the quantizer  302  of the first quantization loop  300  in a delayer  9 , a signal obtained by differentiating an output signal of the quantizer of the second second-order delta sigma modulation type quantization loop  301  in a differentiator  109  by means of the adder/subtractor  403  as an output signal of the cascaded delta sigma modulator. 
     Respective outputs Y 1  and Y 2  of the second-order delta sigma modulation type quantization loops  300  and  301  can be given by the following transmission functions: 
     
       
         
           
             
               
                 
                   
                     Y 
                     1 
                   
                   ≅ 
                   
                     
                       Ain 
                       
                         2 
                         · 
                         
                           Vr 
                           1 
                         
                       
                     
                     + 
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             
                               Z 
                               
                                 - 
                                 1 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           
                             Q 
                             1 
                           
                           · 
                           2 
                           · 
                           
                             Vr 
                             2 
                           
                         
                       
                       
                         
                           
                             
                               
                                 2 
                                 · 
                                 
                                   Vr 
                                   2 
                                 
                                 · 
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           1 
                                           - 
                                           
                                             
                                               ( 
                                               
                                                 2 
                                                 - 
                                                 
                                                   a 
                                                   2 
                                                 
                                               
                                               ) 
                                             
                                             ⁢ 
                                             
                                               Z 
                                               
                                                 - 
                                                 1 
                                               
                                             
                                           
                                           + 
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                             ( 
                                             
                                               1 
                                               + 
                                               
                                                 a 
                                                 1 
                                               
                                               - 
                                               
                                                 a 
                                                 2 
                                               
                                             
                                             ) 
                                           
                                           ⁢ 
                                           
                                             Z 
                                             
                                               - 
                                               2 
                                             
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 2 
                                 · 
                                 
                                   Vr 
                                   1 
                                 
                                 · 
                                 a 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 0 
                                 · 
                                 
                                   Z 
                                   
                                     - 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   4 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           Y 
                           2 
                         
                         ≅ 
                           
                         ⁢ 
                         
                           
                             
                               
                                 Q 
                                 1 
                               
                               · 
                               2 
                               · 
                               
                                 Vr 
                                 2 
                               
                             
                             
                               2 
                               · 
                               
                                 Vr 
                                 2 
                               
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   Z 
                                   
                                     - 
                                     1 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               
                                 Q 
                                 2 
                               
                               · 
                               2 
                               · 
                               
                                 Vr 
                                 2 
                               
                             
                           
                           
                             2 
                             · 
                             
                               Vr 
                               2 
                             
                             · 
                             
                               [ 
                               
                                 1 
                                 - 
                                 
                                   
                                     ( 
                                     
                                       2 
                                       - 
                                       
                                         a 
                                         22 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     
                                       - 
                                       1 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       1 
                                       + 
                                       
                                         a 
                                         21 
                                       
                                       - 
                                       
                                         a 
                                         22 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     
                                       - 
                                       2 
                                     
                                   
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             Q 
                             1 
                           
                           + 
                           
                             
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     Z 
                                     
                                       - 
                                       1 
                                     
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 Q 
                                 2 
                               
                             
                             
                               [ 
                               
                                 1 
                                 - 
                                 
                                   
                                     ( 
                                     
                                       2 
                                       - 
                                       
                                         a 
                                         22 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     
                                       - 
                                       1 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       1 
                                       + 
                                       
                                         a 
                                         21 
                                       
                                       - 
                                       
                                         a 
                                         22 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     
                                       - 
                                       2 
                                     
                                   
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   5 
                 
               
             
           
         
       
     
     when it is assumed that the values of Vr 2  and a 0  are set to satisfy Vr 2 =Vr 1 ·a 0 /a 11 , as in the case with Expression 3, Expression 6 shown below is given: 
     
       
         
           
             
               
                 
                   
                     Y 
                     1 
                   
                   ≅ 
                   
                     
                       Ain 
                       
                         2 
                         · 
                         
                           Vr 
                           1 
                         
                       
                     
                     + 
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             
                               Z 
                               
                                 - 
                                 1 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           Q 
                           1 
                         
                       
                       
                         [ 
                         
                           
                             
                               
                                 1 
                                 - 
                                 
                                   
                                     ( 
                                     
                                       2 
                                       - 
                                       
                                         a 
                                         12 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     
                                       - 
                                       1 
                                     
                                   
                                 
                                 + 
                               
                             
                           
                           
                             
                               
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     
                                       a 
                                       11 
                                     
                                     - 
                                     
                                       a 
                                       12 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   Z 
                                   
                                     - 
                                     2 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   6 
                 
               
             
           
         
       
     
     Accordingly, the 1-bit digital output signal Dout as the output of the cascaded delta sigma modulator is given by Expression 7 shown below: 
     
       
         
           
             
               
                 
                   Dout 
                   = 
                   
                     
                       Ain 
                       
                         2 
                         · 
                         
                           Vr 
                           1 
                         
                       
                     
                     + 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 Z 
                                 
                                   - 
                                   1 
                                 
                               
                             
                             ) 
                           
                           4 
                         
                         ⁢ 
                         
                           Q 
                           2 
                         
                       
                       
                         
                           
                             
                               1 
                               - 
                               
                                 
                                   ( 
                                   
                                     2 
                                     - 
                                     
                                       a 
                                       22 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   Z 
                                   
                                     - 
                                     1 
                                   
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   
                                     a 
                                     11 
                                   
                                   - 
                                   
                                     a 
                                     22 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 Z 
                                 
                                   - 
                                   2 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   7 
                 
               
             
           
         
       
     
     From the foregoing result, it can be seen that, by comprising the first power source terminal  801  connected to the first integration circuit  210  and the second power source terminal  802  connected to the second integration circuit  211  in the same manner as in the first embodiment, the settings of, e.g., VDD 1 =3.3 V and VDD 2 =1.8 V or 1.6 V are allowed, and a delta sigma modulator which allows a reduction in power consumption without degrading the SNR can be implemented. 
     The cascaded delta sigma modulator shown in the second embodiment of the present invention can be constructed to have a three or more stage configuration. Although the delta sigma modulation type quantization loop in each of the stages is composed of two stages of integration circuits, it can be composed of one stage of an integration circuit or three or more stages of integration circuits. In addition, it is not necessary for all the quantization loops to have the same numbers of stages of integration circuits. 
       FIG. 6  shows an example of a feed forward delta sigma modulator as a third embodiment of the present invention. 
     The delta sigma modulator of  FIG. 6  comprises first and second integration circuits  410  and  411 , amplifiers  420  and  421  each having the amplification factor a 0 , an amplifier  422  having an amplification factor C 1 , adders/subtractors  503  and  504 , a quantizer  502 , and a DA converter  430 . 
     The first integration circuit  410  receives a signal obtained by subtracting, from a signal obtained by passing the analog input signal Ain through the amplifier  420 , a signal obtained by passing the feedback reference voltage (positive voltage+Vr 1  or negative voltage−Vr 1 ) generated from the DA converter  430  through the amplifier  421  by means of the adder/subtractor  403 , and operates with the power source voltage VDD 1  supplied from a first power source terminal  901 . 
     The second integration circuit  411  receives an output of the first integration circuit  410 , and operates with the power source voltage VDD 2  supplied from a second power source terminal  902 . 
     The quantizer  502  quantizes a signal obtained by adding up an output of the second integration circuit  411  and a signal obtained bypassing the output of the first integration circuit  410  through the amplifier  422  by means of the adder  404  to the 1-bit digital output signal Dout, and operates with the power source voltage VDD 2 . 
     The DA converter  430  generates the feedback reference voltage mentioned above from the 1-bit digital output signal Dout of the quantizer  502 , and operates with the power source voltage VDD 2 . 
     At this time, to prevent the occurrence of distortion in the output signal, it is necessary to operate the delta sigma modulator by setting the amplification factor a 0  of each of the amplifiers  420  and  421  and the feedback reference voltage (Vr 1 ) of the DA converter  430  such that the signal inputted to the second integration circuit  411  and the adder  404 , i.e., the output of the first integration circuit  410  is in a range under the power source voltage VDD 2 , in the same manner as in the first embodiment. 
     The 1-bit digital output signal Dout as an output of the delta sigma modulator shown in  FIG. 6  can be given by the following transmission function: 
     
       
         
           
             
               
                 
                   Dout 
                   ≅ 
                   
                     
                       Ain 
                       
                         2 
                         · 
                         
                           Vr 
                           1 
                         
                       
                     
                     + 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 Z 
                                 
                                   - 
                                   1 
                                 
                               
                             
                             ) 
                           
                           2 
                         
                         ⁢ 
                         
                           Q 
                           · 
                           2 
                           · 
                           
                             Vr 
                             2 
                           
                         
                       
                       
                         
                           
                             
                               
                                 2 
                                 · 
                                 
                                   
                                     Vr 
                                     2 
                                   
                                   ⁡ 
                                   
                                     [ 
                                     
                                       1 
                                       - 
                                       
                                         2 
                                         ⁢ 
                                         
                                           Z 
                                           
                                             - 
                                             1 
                                           
                                         
                                       
                                       + 
                                       
                                         Z 
                                         
                                           - 
                                           2 
                                         
                                       
                                     
                                     ] 
                                   
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               2 
                               · 
                               
                                 Vr 
                                 1 
                               
                               · 
                               
                                 
                                   a 
                                   0 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     
                                       
                                         c 
                                         1 
                                       
                                       · 
                                       
                                         Z 
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           
                                             c 
                                             1 
                                           
                                         
                                         ) 
                                       
                                       ⁢ 
                                       
                                         Z 
                                         
                                           - 
                                           2 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   8 
                 
               
             
           
         
       
     
     when it is assumed that the values of Vr 2  and a 0  are set to satisfy Vr 2 =Vr 1 ·a 0 /a 1 , Expression 9 shown below is given: 
     
       
         
           
             
               
                 
                   
                     
                       
                         Dout 
                         ≅ 
                           
                         ⁢ 
                         
                           
                             Ain 
                             
                               2 
                               · 
                               
                                 Vr 
                                 1 
                               
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   Z 
                                   
                                     - 
                                     1 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               
                                 Q 
                                 2 
                               
                               · 
                               2 
                               · 
                               
                                 Vr 
                                 2 
                               
                             
                           
                           
                             2 
                             · 
                             
                               Vr 
                               2 
                             
                             · 
                             
                               [ 
                               
                                 1 
                                 - 
                                 
                                   
                                     ( 
                                     
                                       2 
                                       - 
                                       
                                         
                                           a 
                                           1 
                                         
                                         · 
                                         
                                           c 
                                           1 
                                         
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     
                                       - 
                                       1 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       1 
                                       + 
                                       
                                         a 
                                         1 
                                       
                                       - 
                                       
                                         
                                           a 
                                           1 
                                         
                                         · 
                                         
                                           c 
                                           1 
                                         
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     
                                       - 
                                       2 
                                     
                                   
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             Ain 
                             
                               2 
                               · 
                               
                                 Vr 
                                 1 
                               
                             
                           
                           + 
                           
                             
                               
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       Z 
                                       
                                         - 
                                         1 
                                       
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                               ⁢ 
                               Q 
                             
                             
                               1 
                               - 
                               
                                 
                                   ( 
                                   
                                     2 
                                     - 
                                     
                                       
                                         a 
                                         1 
                                       
                                       · 
                                       
                                         c 
                                         1 
                                       
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   Z 
                                   
                                     - 
                                     1 
                                   
                                 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     
                                       a 
                                       1 
                                     
                                     - 
                                     
                                       
                                         a 
                                         1 
                                       
                                       · 
                                       
                                         c 
                                         1 
                                       
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   Z 
                                   
                                     - 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   9 
                 
               
             
           
         
       
     
     In the arrangement, by comprising the first power source terminal  901  connected to the first integration circuit  410  and the second power source terminal  902  connected to the second integration circuit  411  in the same manner as in the first embodiment, the settings of, e.g., Vdd 1 =3.3 V and Vdd 2 =1.8 V or 1.6 V are allowed, and a delta sigma modulator which allows a reduction in power consumption without degrading the SNR can be implemented. 
     The feed forward delta sigma modulator shown in the third embodiment of the present invention can also compose the cascaded delta sigma modulator as shown in  FIG. 5 . 
     Next, a description will be given to a specific example of a circuit in the third embodiment of the present invention with reference to  FIG. 7 . 
     The integration circuits  410  and  411 , the DA converter  430 , the adders/subtractors  503  and  504 , and the amplifiers  420 ,  421 , and  422  of  FIG. 6  are composed of a switched capacitor circuit comprising switches  241  to  252 ,  261  to  271 , capacitors C 31  to C 34 , C 41 , C 42 , and C 51  to C 53 , and operational amplifiers  206  and  207 , as shown in  FIG. 7 . 
     Specifically, the integration circuit  410 , the DA converter  430 , the adder/subtractor  503 , and the amplifiers  420  and  421  are composed of the switches  241  to  252 , the capacitors C 31  to C 34 , and the operational amplifier  206 , as shown in  FIG. 7 . 
     On the other hand, the integration circuit  411  is composed of the switches  261  to  271 , the capacitors C 41  and C 42 , and the operational amplifier  207 . 
     The adder/subtractor  504 , the amplifier  422 , and the quantizer  502  are composed of the switches  261  to  271 , the capacitors C 51  to C 53 , and a comparator (operational amplifier)  302 . 
     The reference numeral  2001  denotes a circuit block composing the integration circuit and the DA converter. The reference numeral  2002  denotes a circuit block composing the integration circuit. The reference numeral  2003  denotes a circuit block composing the quantizer and the feed forward circuit. 
     The analog input signal Ain is integrated by the operational amplifier  206  using the first reference voltage Vr 1  as well as charging and discharging between the capacitors C 31  and C 34 . 
     The feedback signal is processed as follows. The digital output signal Dout is converted by a buffer circuit  205  to the digital signals S 1   p and S 1   n . Then, by turning ON/OFF the switches  246  and  250  in accordance with the levels of the digital signals S 1   p  and S 1   n , a DA conversion using the reference voltage Vr 1  and a zero voltage is performed. The DA converted voltage is integrated by the operational amplifier  206  using charging and discharging between the capacitors C 32  and C 33 . 
     In this manner, the first integration circuit  410  and the DA converter  430  shown in  FIG. 6  are constructed. The amplification factor of the amplifier  420  shown in  FIG. 7  corresponds to the capacitance ratio C 31 /C 34 , and the amplification factor of the amplifier  421  shown in  FIG. 7  corresponds to the capacitance ratios C 32 /C 34 , and C 33 /C 34 . The switches  241  to  252 , and the operational amplifier  206  operate with the power source voltage VDD 1  supplied from a first power source terminal  1001 . 
     Next, an output signal of the operational amplifier  206  is integrated by the operational amplifier  207  using the first and second reference voltages Vr 1  and Vr 2  as well as charging and discharging between the capacitors C 41  and C 42 . 
     In this manner, the second integration circuit  411  is constructed. The switches  261  to  264  and the operational amplifier  207  operate with the power source voltage VDD 2 . 
     Next, the output signals of the operational amplifiers  206  and  207  are added up using the first and second reference voltages Vr 1  and Vr 2  as well as charging and discharging between the capacitors C 51 , C 52 , and C 53 . The amplification factor of the amplifier  422  shown in  FIG. 6  corresponds to the capacitance ratio C 52 /C 53 . The switches  265  to  271  operate with the power source voltage VDD 2 . 
     The buffer circuit is composed of a circuit shown in  FIG. 8 . The VDD 2 -based digital signal inputted to the terminal IN is outputted as a VDD 1 -based in-phase signal and a VDD 1 -based anti-phase signal from the terminals OUTp and OUTn. 
     In this manner, the delta sigma modulator shown in  FIG. 6  can be implemented by the switched capacitor circuit. 
       FIG. 9  shows a structure of a single-loop first-order delta sigma modulator of a fourth embodiment of the present invention. The delta sigma modulator  300  comprises the integration circuit  210 , the quantizer  302 , and the DA converter  230 . 
     The integration circuit  210  receives a signal obtained by subtracting, from a signal obtained by passing the analog input signal Ain through the amplifier  220 , a signal obtained by passing the first feedback reference voltage (positive voltage+Vr 1  or negative voltage−Vr 1 ) generated from the DA converter  230  through the amplifier  221  by means of the adder/subtractor  203 , and operates with the power source voltage (VDD 1 ) supplied from the first power source terminal  801 . The quantizer  302  quantizes an output Ao of the first integration circuit  210  to the 1-bit digital signal (Dout), and operates with the power source voltage VDD 2 . The DA converter  230  generates the first feedback reference voltage mentioned above from a digital output of the quantizer  302 . 
     At this time, to prevent the occurrence of distortion in an output signal of the quantizer  302 , it is necessary to operate the delta sigma modulator by setting the amplification factor a 0  of each of the amplifiers  220  and  221  and the feedback reference voltage (Vr 1 ) of the DA converter  230  such that the signal inputted to the quantizer  302 , i.e., the output of the integration circuit  210  is in a range under the voltage VDD 2 . 
     The output Dout of the delta sigma modulator shown in  FIG. 9  can be given by the following transmission function: 
     
       
         
           
             
               
                 
                   Dout 
                   ≅ 
                   
                     
                       Ain 
                       
                         2 
                         · 
                         
                           Vr 
                           1 
                         
                       
                     
                     + 
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             
                               Z 
                               
                                 - 
                                 1 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           Q 
                           · 
                           2 
                           · 
                           
                             Vr 
                             2 
                           
                         
                       
                       
                         
                           2 
                           · 
                           
                             Vr 
                             1 
                           
                           · 
                           a 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           0 
                           · 
                           
                             Z 
                             
                               - 
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   10 
                 
               
             
           
         
       
     
     The arrangement allows the settings of, e.g., Vdd 1 =3.3 V and Vdd 2 =1.8 V or 1.6 V, and allows a reduction in the power consumption of the quantizer  302  and the circuits subsequent thereto. Thus, in the delta sigma modulator according to the present invention, the amplitude of a signal in the quantizer  302  in which noise is attenuated is reduced, while the amplitude of a signal in the first-stage integration circuit  210  in which the noise is not attenuated is maintained. Accordingly, there is no deterioration of the SNR resulting from a reduction in the operation power source voltage. In addition, because the area of a 1.8 V transistor is generally smaller than that of a 3.3 V transistor, a reduction in circuit area can also be achieved by using the 3.3 V transistor with a high operation power source voltage as a transistor used in the circuit connected to the power source voltage VDD 1 , while using the 1.8 V transistor as a transistor used in the circuit connected to the power source voltage VDD 2 . 
     Next, a delta sigma modulator according to a fifth embodiment of the present invention will be shown using  FIG. 10 .  FIG. 10  shows an example in which the first embodiment is applied to a cascaded delta sigma modulator. The cascaded delta sigma modulator is characterized in that it can implement a higher-order delta sigma modulation type AD converter with a larger number of stages of integration circuits. A description will be given hereinbelow to a third-order cascaded delta sigma modulator. 
     The third-order cascaded delta sigma modulator comprises the second-order delta sigma modulation type quantization loop  300 , a first-order delta sigma modulation type quantization loop  301 A connected in cascade to the second-order delta sigma modulation type quantization loop  300 , and the noise removal circuit  302 A for removing noise by combining the outputs of the second-order delta sigma modulation type quantization loop  300  and the first-order delta sigma modulation type quantization loop  301 A. 
     The second-order delta sigma modulation type quantization loop  300  comprises the first and second integration circuits  210  and  211 , the quantizer  302 , and the first and second DA converters  230  and  231 . 
     The first integration circuit  210  receives a signal obtained by subtracting, from a signal obtained by passing the analog input signal Ain through the amplifier  220 , a signal obtained by passing the first feedback reference voltage (positive voltage+Vr 1  or negative voltage−Vr 1 ) generated from the first DA converter  230  through the amplifier  221  by means of the adder/subtractor  203 , and operates with the power source voltage (VDD 1 ) supplied from the first power source terminal  801 . 
     The second integration circuit  211  receives a signal obtained by subtracting, from an output of the first integration circuit  210 , a signal obtained by passing the second feedback reference voltage (positive voltage+Vr 2  or negative voltage−Vr 2 ) generated from the second DA converter  231  through the amplifier  222  by means of the adder/subtractor  204 , and operates with the power source voltage (VDD 2 ) supplied from the second power source terminal. 
     The quantizer  302  quantizes an output of the second integration circuit  211  to the 1-bit digital signal, and operates with the voltage VDD 2 . 
     The first DA converter  230  generates the first feedback reference voltage mentioned above from a digital output of the quantizer  302 . 
     The second DA converter  231  generates the second feedback reference voltage mentioned above from the digital output of the quantizer  302 . 
     The first-order delta sigma modulation type quantization loop  301 A comprises the third integration circuit  310 , the second quantizer  402 , and the third DA converter  330 . 
     The first-order delta sigma modulation type quantization loop  301 A receives a differential signal between an input to the quantizer  302  of the second-order delta sigma modulation type quantization loop  300  and an output of the DA converter  231  of the second-order delta sigma modulation type quantization loop  300 , i.e., a quantization error generated by the quantizer  302  of the second-order delta sigma modulation type quantization loop  300 . 
     The third integration circuit  310  receives a signal obtained by subtracting, from a signal obtained by passing the input signal mentioned above through the amplifier  320 , a signal obtained by passing the second feedback reference voltage (positive voltage+Vr 2  or negative voltage−Vr 2 ) generated from the third DA converter  330  through the amplifier  321  by means of the adder/subtractor  303 , and operates with the voltage VDD 2 . 
     The quantizer  402  quantizes an output of the third integration circuit  310  to the 1-bit digital signal, and operates with the voltage VDD 2 . 
     The third DA converter  330  comprises the third DA converter  331  for generating the second feedback reference voltage mentioned above from the digital output of the quantizer  402 . 
     The noise removal circuit operates with the voltage VDD 2 , and provides a signal obtained by subtracting, from a signal obtained by delaying the output signal of the quantizer  302  of the second-order delta sigma modulation type quantization loop  300  in the delayer  9 , a signal obtained by differentiating an output signal of the quantizer  402  of the first-order delta sigma modulation type quantization loop  301 A in the differentiator  109  by means of the adder/subtractor  403  as an output signal of the cascaded delta sigma modulator. 
     Respective outputs Y 1  and Y 2  of the second-order delta sigma modulation type quantization loop  300  and the first-order delta sigma modulation type quantization loop  301 A can be respectively given by the following transmission functions: 
     
       
         
           
             
               
                 
                   
                     Y 
                     1 
                   
                   ≅ 
                   
                     
                       Ain 
                       
                         2 
                         · 
                         
                           Vr 
                           1 
                         
                       
                     
                     + 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 Z 
                                 
                                   - 
                                   1 
                                 
                               
                             
                             ) 
                           
                           2 
                         
                         ⁢ 
                         
                           
                             Q 
                             1 
                           
                           · 
                           2 
                           · 
                           
                             Vr 
                             2 
                           
                         
                       
                       
                         
                           
                             
                               
                                 2 
                                 · 
                                 
                                   Vr 
                                   2 
                                 
                                 · 
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           1 
                                           - 
                                           
                                             
                                               ( 
                                               
                                                 2 
                                                 - 
                                                 
                                                   a 
                                                   12 
                                                 
                                               
                                               ) 
                                             
                                             ⁢ 
                                             
                                               Z 
                                               
                                                 - 
                                                 1 
                                               
                                             
                                           
                                           + 
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               
                                                 a 
                                                 12 
                                               
                                             
                                             ) 
                                           
                                           ⁢ 
                                           
                                             Z 
                                             
                                               - 
                                               2 
                                             
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               2 
                               · 
                               
                                 Vr 
                                 1 
                               
                               · 
                               
                                 a 
                                 0 
                               
                               · 
                               
                                 Z 
                                 
                                   - 
                                   2 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   11 
                 
               
             
             
               
                 
                   
                     
                       
                         
                             
                         
                         ⁢ 
                         
                           
                             Y 
                             2 
                           
                           ≅ 
                             
                           ⁢ 
                           
                             
                               
                                 
                                   Q 
                                   1 
                                 
                                 · 
                                 2 
                                 · 
                                 
                                   Vr 
                                   2 
                                 
                               
                               
                                 2 
                                 · 
                                 
                                   Vr 
                                   2 
                                 
                               
                             
                             + 
                             
                               
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       Z 
                                       
                                         - 
                                         1 
                                       
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   
                                     Q 
                                     2 
                                   
                                   · 
                                   2 
                                   · 
                                   
                                     Vr 
                                     2 
                                   
                                 
                               
                               
                                 
                                   2 
                                   · 
                                   
                                     Vr 
                                     2 
                                   
                                   · 
                                   a 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   21 
                                   · 
                                   
                                     Z 
                                     
                                       - 
                                       1 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             Q 
                             1 
                           
                           + 
                           
                             
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     Z 
                                     
                                       - 
                                       1 
                                     
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 Q 
                                 2 
                               
                             
                             
                               
                                 2 
                                 · 
                                 Vr 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 2 
                                 · 
                                 a 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 21 
                                 · 
                                 
                                   Z 
                                   
                                     - 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   12 
                 
               
             
           
         
       
     
     when it is assumed that the values of Vr 2  and a 0  are set to satisfy Vr 2 =Vr 1 ·a 0 /a 11 , as in the case with Expression 3, Expression 13 shown below is given: 
     
       
         
           
             
               
                 
                   
                     Y 
                     1 
                   
                   ≅ 
                   
                     
                       Ain 
                       
                         2 
                         · 
                         
                           Vr 
                           1 
                         
                       
                     
                     + 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 Z 
                                 
                                   - 
                                   1 
                                 
                               
                             
                             ) 
                           
                           2 
                         
                         ⁢ 
                         
                           Q 
                           1 
                         
                       
                       
                         [ 
                         
                           
                             
                               
                                 1 
                                 - 
                                 
                                   
                                     ( 
                                     
                                       2 
                                       - 
                                       
                                         a 
                                         12 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     Z 
                                     
                                       - 
                                       1 
                                     
                                   
                                 
                                 + 
                               
                             
                           
                           
                             
                               
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     
                                       a 
                                       11 
                                     
                                     - 
                                     
                                       a 
                                       12 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   Z 
                                   
                                     - 
                                     2 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   13 
                 
               
             
           
         
       
     
     Accordingly, the output Dout of the cascaded delta sigma modulator can be given by Expression 14 shown below: 
     
       
         
           
             
               
                 
                   Dout 
                   = 
                   
                     
                       Ain 
                       
                         2 
                         · 
                         
                           Vr 
                           1 
                         
                       
                     
                     + 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 Z 
                                 
                                   - 
                                   1 
                                 
                               
                             
                             ) 
                           
                           3 
                         
                         ⁢ 
                         
                           Q 
                           2 
                         
                       
                       
                         
                           
                             
                               
                                 2 
                                 · 
                                 Vr 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 2 
                                 · 
                                 a 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 21 
                                 · 
                               
                             
                           
                         
                         
                           
                             
                               
                                 Z 
                                 
                                   - 
                                   1 
                                 
                               
                               ⁡ 
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         1 
                                         - 
                                         
                                           
                                             ( 
                                             
                                               2 
                                               - 
                                               
                                                 a 
                                                 12 
                                               
                                             
                                             ) 
                                           
                                           ⁢ 
                                           
                                             Z 
                                             
                                               - 
                                               1 
                                             
                                           
                                         
                                         + 
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           ( 
                                           
                                             1 
                                             + 
                                             
                                               a 
                                               11 
                                             
                                             - 
                                             
                                               a 
                                               12 
                                             
                                           
                                           ) 
                                         
                                         ⁢ 
                                         
                                           Z 
                                           
                                             - 
                                             2 
                                           
                                         
                                       
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   14 
                 
               
             
           
         
       
     
     From the foregoing result, it can be seen that, by comprising the first power source terminal  801  connected to the first integration circuit  210  and the second power source terminal  802  connected to the second integration circuit  211  and the third integration circuit  310  in the same manner as in the first embodiment, the settings of, e.g., VDD 1 =3.3 V and VDD 2 =1.8 V or 1.6 V are allowed, and a delta sigma modulator which allows a reduction in power consumption without degrading the SNR can be implemented. 
     The cascaded delta sigma modulator shown in the fifth embodiment of the present invention can be constructed to have a three or more stage configuration. 
     Next, a delta sigma modulator according to a sixth embodiment of the present invention will be shown using  FIG. 11 . The circuit is obtained by partly changing a voltage applied to the delta sigma modulator of  FIG. 2 . Specifically, although the first feedback reference voltage is generated based on the voltage Vr 1  and the second feedback reference voltage is generated based on the voltage Vr 2  in the delta sigma modulator of  FIG. 1 , both of the first and second feedback voltages may be generated based on the voltage Vr 1 . In this case, the same effect as obtained in the first embodiment can also be obtained. 
     The circuit structure when both of the first and second feedback reference voltages are generated based on the voltage Vr 1  in the manner mentioned above is shown in  FIG. 11 . The difference between  FIG. 11  and  FIG. 2  is that the voltage applied to one end of each of the switches  165  and  172  is changed from the voltage Vr 2  to the voltage Vr 1 . 
     However, even though both of the first and second feedback reference voltages are generated based on the voltage Vr 1 , the voltage Vr 2  does not become unnecessary. The reason for this is that the voltage Vr 2  is needed to determine the operation point of the second integration circuit  201 , so that the voltage Vr 2  is applied with respect thereto, in the same manner as in  FIG. 2 . 
     Next, a description will be given to a variation of a method of applying the power source voltage as a seventh embodiment of the present invention with reference to  FIGS. 12A to 12D . 
       FIG. 12A  shows apart of the circuit of  FIG. 5 . The drawing shows the structure in which the first integration circuit  210  is supplied with the power source voltage VDD 1  from the power source terminal  801 , and the second integration circuit  211 , the quantizer  302 , and the delayer  9  are each supplied with the power source voltage VDD 2  from the power source terminal  802 . However, as shown in  FIG. 12B , the integration circuit  211 , the adder/subtractor  204 , the amplifier  222 , and the DA converter  231  are composed of, e.g., the operational amplifier  107 , the capacitors C 21  to C 24 , the switches  161  to  172 , and the buffers  105  and  108 , and it is not necessary to supply the power source voltage VDD 2  to all of the components. In the example of  FIG. 12B , the operational amplifier  107  is supplied with the power source voltage VDD 1 , and the drive circuit for the switches  162  to  172  and the operational amplifier  202  composing the quantizer are each supplied with the power source voltage VDD 2 . However, the structure may also be adopted in which the drive circuit for the switches  161  to  172  is supplied with the power source voltage VDD 1 , and the operational amplifier  107  is supplied with the power source voltage VDD 2  in a manner converse to that used in the example of  FIG. 12B .  FIG. 12C  shows an example of the buffer (drive circuit) supplied with the power source voltage VDD 2  and  FIG. 12D  shows a specific example of the switch driven by the buffer of  FIG. 12C . 
     The operational amplifier  202  composing the quantizer  202  may also be supplied with either the voltage VDD 2  or the voltage VDD 1 . 
     In short, the effect of a reduction in power consumption can be attained without degrading the SNR, provided that the voltage supplied to at least one of the operational amplifier  107 , the buffers  105  and  108  each as the drive circuit, and the operational amplifier  202  composing the quantizer is the voltage VDD 2  which is lower than the voltage VDD 1 . When the structure is adopted in which the voltage VDD 2  is supplied to all of the components mentioned above, the maximum effect is attained. 
     The delta sigma modulator of the present invention shown in  FIGS. 1 ,  5 ,  6 ,  9 , and  10  can be used also in a delta sigma modulator having a multiple order configuration. Moreover, the quantizer and the DA converter can also be used with a two or more bit signal. Furthermore, three or more different power source voltages may also be supplied by increasing the number of the power source terminals to three or more. 
     INDUSTRIAL APPLICABILITY 
     The delta sigma modulator according to the present invention has the effect of allowing a reduction in power consumption without degrading the SNR, and is useful as an A/D conversion circuit for digital audio equipment or the like.