Abstract:
In a high-pass (mirrored) integrator structure that employs chopper modulation, the input and output of the mirrored integrator are connected to the input and output ports of the operational amplifier, bypassing the chopper stabilization modulators. The mirrored integrator can be used in sigma-delta analog-to-digital converters.

Description:
REFERENCE TO RELATED APPLICATIONS 
   The present application claims the benefit of U.S. Provisional Application No. 60/462,712, filed Apr. 15, 2003. Related concepts are disclosed in U.S. Pat. No. 6,707,409, issued Mar. 16, 2004. The disclosures of the above-cited &#39;712 provisional application and &#39;409 patent are hereby incorporated by reference in their entireties into the present disclosure. 

   FIELD OF THE INVENTION 
   The present invention is directed to a high-pass filter and more particularly to a switched-capacitor high-pass filter implemented as a mirrored integrator for use in an analog-to-digital converter (ADC). 
   DESCRIPTION OF RELATED ART 
   An overview of the related art will now be provided. Reference numerals in brackets refer to references that will be listed at the end of this section. 
   Signal processing circuits that operate on signals that have been converted to a band near the Nyquist frequency promise to enable new capabilities as well as to offer performance enhancements in existing applications. An example of a circuit enabling new capabilities is a design for a two-path bandpass ΣΔ (sigma-delta) modulator proposed in [1]. In this design, an input IF signal is sampled at a rate four times the input signal carrier frequency. The signal samples are then interleaved between two channel paths at a rate equal to half of the sampling frequency. This results in a shift of the input signal carrier frequency in both channels to the single channel Nyquist frequency (f s,path /2). Each channel is provided a separate high-pass ΣΔ modulator that performs A/D conversion. Thus, the high-pass ΣΔ modulators operate at half of the overall band-pass ΣΔ modulator speed, relaxing the speed requirement placed on analog circuits. Following A/D conversion and downsampling, the outputs of the channels are the in-phase and quadrature components of the baseband IF input signal. This circuit enables direct A/D conversion of intermediate frequency (IF) input signals without prior demodulation, which makes this design very attractive for application in the IF stage of communications systems. 
   An example of an enhancement to a familiar application offered by Nyquist band processing is the high-pass ΣΔ modulator used to digitize low-pass analog signals. A low-pass input signal is modulated with a square wave carrier to shift the input signal to the Nyquist frequency of the ΣΔ modulator, which contains a high-pass filter (mirrored integrator, or MI). The use of a highpass ΣΔ modulator to convert low-pass analog signals results in attenuated 1/f noise (similar to the chopper stabilization method, or CHS), attenuated distortion caused by DAC nonlinearities (cancellation of even-order nonlinearities), attenuated distortion from the limited voltage swing of the loop filters, and reduction of the distortion caused by quantizer clipping. In the design of a high-pass ΣΔ modulator a high-pass filter is used inside the modulator feedback loop. The filter must perform a mirrored integration; i.e., it must have infinite gain at the Nyquist frequency and finite gain at DC. 
   The signal transfer function of the MI (mirrored integrator) is shown in  FIGS. 1A and 1B , where functional block diagrams and transfer functions of both delayed and non-delayed MI&#39;s, respectively, are presented. In both of the mirrored integrators, an input x[n] is received at an input  102  and applied to a subtractor  104  and thence to a circuit which includes a delay element  106  and a feedback loop  108 . The resulting signal y[n] is output at an output  110 . The two integrators differ in whether the delay element is located in the feedback loop or in the other arm of the circuit, which in turn affects the output as a function of the input. The mirrored integrator  100 A of  FIG. 1A  outputs an output 
               Y   ⁡     (   z   )       =         z     -   1         1   +     z     -   1           ⁢     X   ⁡     (   z   )           ,         
while the mirrored integrator  100 B of  FIG. 1B  outputs an output
 
   
     
       
         
           
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   The CHS method together with auto-zeroing and correlated double sampling is well-established method for dealing with amplifier imperfections, [2]. The CHS method was developed first by E. A. Goldberg in 1948. 
   The basic principle is shown in  FIG. 2 . The process starts with an input signal V in (jf). At step  202 , the input signal V in (jf) is multiplied by a carrier or chopper stabilization modulating signal CS 1 (t) having a chopper frequency T chop . As a result of the multiplication, replicas appear at odd multiples of T chop . The result is supplied to an amplifier, which has the effect of adding an offset and noise (primarily at low frequencies) V os +V n  in step  204  and then amplifying the sum in step  206 . In step  208 , the amplified signal is demodulated by multiplying it by a chopper signal CS 2 (t), which is like CS 1 (t) except for having a time offset Δt. The result is an output signal V out (jf). 
   After the CHS is performed, the output signal V out (jf) is low-pass filtered in order to attenuate ripples of the chopper frequency. The resulting signal at baseband is an amplified input signal with no low-frequency degradations (1/f noise and DC offset) caused by the filter. 
   Following the basic principle described above, CHS has been applied to the fully differential SC integrator by introducing chopper modulators at both the front and rear end of the amplifier, as shown in  FIG. 3  and proposed in [3]. As shown in  FIG. 3 , the integrator  300  includes input terminals  302 ,  304  to receive a reference voltage V ref [n] and input terminals  306 ,  308  to receive an input voltage V in [n]. The circuit further includes switches  310 , capacitors  312  having a capacitance C 1 , ground terminals  314 , an opamp (operational amplifier)  316 , feedback loops  318  with capacitors  320  having a capacitance C 2 , and output terminals  322 ,  324  for outputting an ouput voltage V out [n]. The opamp has a non-inverted input port  332 , an inverted input port  334 , a non-inverted output port  326 , and an inverted output port  328 . The switches  310  are switched in accordance with switching phases Φ 1  and Φ 2 , a sampling phase Φ s , and an integration phase Φ t , all of which are shown in  FIG. 5 . As shown in  FIG. 5 , Φ s , and Φ t  have a first period and are inversions of each other, while Φ 1  and Φ 2  have a second period which is double the first period and are inversions of each other. At the output ports  326 ,  328  of the opamp  316 , the switches  310  define two Φ 1 /Φ 2  switching pairs  330 . The same is true at the input ports  332 ,  334  of the opamp  316 . 
   Each pair of switching pairs  330  defines a chopper stabilization modulator  336 , so that there is one chopper stabilization modulator  336  connected to the input ports  332 ,  334  and that there is another chopper stabilization modulator  336  connected to the output ports  326 ,  328 . The switching phases Φ 1  and Φ 2 , in accordance to  FIG. 5 , define a chopper stabilization modulating signal, which is a periodic sequence of +1&#39;s and −1&#39;s with frequency equal to half the sampling frequency. The configuration of the integrator  300  defines an input circuit  338  and an output circuit  340 . The significance of the input and output circuits will be explained below with reference to  FIGS. 4 and 6 . 
   A chopper frequency of f s /2 has been shown to be most effective because it shifts the opamp&#39;s imperfections farthest away from the signal band. The resulting opamp noise difference equation is given in Eq. (1), where e opamp (n) represents the opamp noise and DC offset.
 
 V   out ( n )=(−1) n ( e   opamp ( n )+ e   opamp ( n− 1))  (1)
 
Thus, the opamp noise is low-pass filtered and modulated to Nyquist frequency out of the input signal band.
 
   One particular utility for mirrored integrators is in the ΣΔ analog to digital converter of the above-cited &#39;409 patent. As taught in that patent, both delayed and non-delayed MI&#39;s can be used. 
   However, existing mirrored integrator designs suffer from more noise than is desirable. If noise were reduced, a variety of advantages would result, from smaller circuit design to greater dynamic range. 
   The references identified by numbers in brackets are the following:
     [1] A. K. Ong, “Bandpass Analog-to-Digital Conversion for Wireless Applications”, PhD dissertation, Stanford University, Stanford, Calif., September 1998.   [2] C. C. Enz, G. C. Temes, “Circuit Techniques for Reducing the Effects of Op-Amp Imperfections: Autozeroing, Correlated Double Sampling, and Chopper Stabilization”,  Proc. of the IEEE , Vol. 84, No. 11, November 1996.   [3] K. C. Hsieh, P. R. Gray, D. Senderowicz, and D. G. Messerschmitt “A Low-Noise Chopper-Stabilized Differential Switched-Capacitor Filtering Technique”  IEEE Journal on Solid - state Circuits , Vol. SC-16, No. 6, December 1981.   [4] S. Bazarjani, W. M. Snelgrove, “A 160-MHz Fourth-Order Double-Sampled SC Bandpass Sigma-Delta Modulator”,  IEEE Trans. on Circuits and Syst. II , vol. 45, pp. 547–555, May 1998.   

   SUMMARY OF THE INVENTION 
   It is therefore an object of the invention to provide a mirrored integrator with improved noise characteristics. 
   To achieve the above and other objects, the present invention is directed to a fully differential switched-capacitor MI that will be useful for Nyquist band signal processing applications such as those described above. The present invention also uses CHS methods to obtain noise shaping properties of the MI that are comparable in magnitude, but complementary in frequency dependence, to the noise shaping of conventional integrators in which CHS methods are employed. 
   A new family of fully differential SC highpass filters (MI) with various delays has been proposed and analyzed. It was shown that the new MI design will be lower in noise than a comparable high-pass filter design proposed in [1]; the present invention treats the operational amplifier noise in the same manner as a fully differential SC chopper stabilized low-pass integrator. 
   Although the contribution of switch noise in the new design is reduced only by a factor of 2, the reduction of the operational amplifier noise is much larger. In the unit-delay MI the opamp noise contribution at the Nyquist frequency goes to zero, and in the other two members of the MI filter family the opamp noise power is reduced by a factor of 16 at the Nyquist frequency compared to the previous design, [1]. 
   A mirrored integrator is a specific case of the present invention, namely, in which the chopper stabilization modulating signal is the alternating sequence +1, −1, +1, −1, . . . However, the chopper stabilization modulating signal can be anything, for example, a random sequence of +1&#39;s and −1&#39;s. An example of another integrator within the scope of the present invention is a spread-spectrum integrator, in which the modulator is any random or pseudo-random sequence of +1&#39;s and −1&#39;s. A specific type of spread-spectrum integrator is a blue-noise integrator, in which the modulator signal is a blue-noise random or pseudo-random sequence. The use of blue noise, which has a deficiency of low-frequency spectral power, is known in other arts; however, its use in the context of the present invention is considered to be novel. 
   When used in ΣΔ analog to digital converters, the present invention offers the following advantages over the prior art:
         Improved dynamic range, because higher order DAC will be allowed and a dramatic reduction in 1/f noise. The 1/f noise in typical CMOS circuits is typically below 500 kHz, which is attenuated by the high-pass filter in our design.   Reduced offset error and drift.   Dramatically lower power consumption per bit, allowing the design tradeoff of oversampling ratio for resolution.   Smaller size circuits because smaller input transistors can be used, because of the noise reduction features of the design.   Reduced analog noise.   Reduced operational amplifier analog noise (thermal+1/f).   Suppression of DAC nonlinearity.   Improved attenuation of the DAC&#39;s DC offset.   Improved stability of the Mirrored integrator to clipping of the output voltage, as compared to the integrator element of a conventional Sigma-delta design.       

   The present invention can be used in an ADC like that of the above-cited &#39;409 patent. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A preferred embodiment of the present invention and variations thereon will be disclosed with reference to the drawings, in which: 
       FIGS. 1A and 1B  are block diagrams showing the signal transfer functions of a delayed and a non-delayed MI, respectively; 
       FIG. 2  shows the chopper stabilization principle according to the prior art; 
       FIG. 3  is a circuit diagram showing a fully differential chopper stabilized integrator according to the prior art; 
       FIG. 4  is a circuit diagram showing a fully differential sample-delayed mirror integrator according to the preferred embodiment; 
       FIG. 5  is a graph of the timing sequence used in several variations of the preferred embodiment; 
       FIG. 6  shows a circuit diagram of a fully differential non-delayed MI according to the preferred embodiment; 
       FIGS. 7A and 7B  are a circuit diagram of a MOS switch and a block diagram of a noise model for the MOS switch, respectively; 
       FIG. 8  is a block diagram of a noise model used to estimate opamp noise; 
       FIG. 9  is a block diagram of the 1 st  order ΣΔ analog to digital converter using the mirrored integrator of the preferred embodiment; 
       FIG. 10  shows a circuit diagram of a fully differential multiple-input sample-delayed mirror integrator according to the preferred embodiment; 
       FIGS. 11A–11D  show timing diagrams for: a) the sampling phase of the clock, b) a periodic chopper signal with frequency equal to one-half the sampling frequency, c) a pseudo-random chopper signal, and d) a pseudo-random chopper signal with blue-noise spectral properties, respectively; and 
       FIGS. 12A and 12B  show a) a spectrum of a pseudo-random chopper sequence, and b) a spectrum of the pseudo-random blue-noise sequence, respectively. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
   A preferred embodiment of the present invention and modifications thereon will be disclosed in detail with reference to the drawings, in which like reference numerals refer to like elements or steps throughout. 
   A fully differential, sample-delayed SC high-pass filter according to the preferred embodiment is shown in  FIG. 4 . As will be explained below, the high-pass filter  400  of  FIG. 4  can be implemented as a fully differential sample-delayed or half-sample-delayed filter. 
   Comparing the high-pass filter  400  in  FIG. 4  to the low-pass filter  300  shown in  FIG. 3 , we note that in the high-pass filter  400 , the input circuit  438  and the output circuit  440  are connected directly to the opamp&#39;s input and output ports  326 ,  328 ,  332 ,  334 , as opposed to the low-pass filter  300  of  FIG. 3 , in which the input and output are taken through the switching pairs (the Φ 1  and Φ 2  pairs)  330 . When the output signal is taken at the end of the sampling phase Φ s , and with the timing sequence shown in  FIG. 5 , the configuration of the filter  400  results in a sample-delayed filter having the signal transfer function (STF) given by Eq. (2). 
                     V     o   ⁢           ⁢   u   ⁢           ⁢   t       ⁡     (     z     -   1       )       =         C   1       C   2       ⁢       z     -   1         1   +     z     -   1           ⁢     (         V   in     ⁡     (     z     -   1       )       +       V     r   ⁢           ⁢   e   ⁢           ⁢   f       ⁡     (     z     -   1       )         )               (   2   )               
This signal transfer function represents a sample-delayed MI, with infinite gain at the Nyquist frequency and a gain of C 1 /2C 2  at DC.
 
   In higher order ΣΔ modulators, it is almost always required to have integrators with different delays. Therefore, a complete set of MI filters with various delays has been designed. In  FIG. 4 , when the output signal is taken at the end of the integration phase Φ t , resulting in z −0.5  delay in the output with respect to the input signal samples, the half-sample-delayed MI design is obtained. This design results in the STF shown in Eq. (3). 
   
     
       
         
           
             
               
                 
                   
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   In order to obtain a non-delayed MI, the input and reference signals must be interchanged. The non-delayed SC MI is shown in  FIG. 6 . In the non-delayed SC MI  600 , the input and output signal samples are taken at the end of integration phase Φ t . Thus, the input circuit  638  and the output circuit  640  are modified from those of  FIG. 4 . This configuration results in STF given in Eq. (4). 
   
     
       
         
           
             
               
                 
                   
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   We will now present a model and make an estimate of the noise magnitude of the MI. We show that the noise of the MI filter design will be significantly lower than the noise of the previously proposed high-pass integrator, [1]. Switched-capacitor filters introduce noise that arises from two statistically independent sources: the noise generated by the switches and the operational amplifier noise. In the following we discuss the switch noise and opamp noise in greater detail. 
   Switch noise will now be discussed. There are three independent noise mechanisms associated with MOS switches: thermal noise, flicker (1/f) noise, and shot noise. Shot and flicker noise can be neglected because on average the currents flowing through the filter&#39;s switches are equal to zero. Thus, the thermal noise of the switches is the remaining source of fluctuations that could potentially degrade the filter&#39;s performance. The source of the thermal noise in MOS switches is the nonzero resistance of the MOS channel. 
   In order to estimate the switch noise contributed by the MOS switches, the sample- and hold circuit model has been used, as shown in  FIGS. 7A and 7B .  FIG. 7A  shows a sample-and-hold circuit  700  having a MOS transistor (switch)  702  and a capacitor  704  with a capacitance C s    FIG. 7B  shows a block diagram of a noise model  700 ′ for the switch  700  when the switch is on. The noise model  700 ′ has a zero-mean noise sample  706  with a mean square noise power {overscore (e R   2 )} and a noiseless resistor  708  representing the MOS channel resistance of the transistor  702  when the transistor is on. The power spectral density of thermal noise generated in the MOS-switch channel is given by Eq. (5). 
                     S   thermal     ⁡     (   f   )       =     4   ⁢   k   ⁢           ⁢   T   ⁢           ⁢       R     o   ⁢           ⁢   n       ⁡     [       V   2     Hz     ]                 (   5   )               
where k is Boltzmann&#39;s constant, T is the absolute temperature, and R on  is the MOS channel resistance.
 
   By examining  FIG. 7B , one sees that the noise source undergoes single-pole low-pass filtering. The resulting total noise power is given by Eq. (6). 
   
     
       
         
           
             
               
                 
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   If we assume that R on ˜100 Ohm and C s ˜1 pF, the −3 dB frequency of the equivalent low-pass filter is near 7 GHz. At the same time, the highest achievable sampling frequency in modern CMOS ΣΔ modulators is on the order of 80 MHz [4]. Thus, the switch thermal noise appears as white noise in the sampling bandwidth [−f s /2, f s /2] with noise power spectral density given in Eq. (7). 
   
     
       
         
           
             
               
                 
                   
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   Now we may calculate the noise contributions of the switches to the filter&#39;s total input referred noise. The capacitors  312  C 1  and  320  C 2  ( FIG. 4 ) add switch noise directly to the input and output signal, respectively. Thus, when referred to the input, the noise power generated at a capacitor  312  C 1  is not changed, and the noise at a capacitor  320  C 2  is shaped by the filter&#39;s transfer function (1/|H M1 (f)|) 2 . The total input referred power spectral density of the filter&#39;s switch noise is therefore given by Eq. (8). 
   
     
       
         
           
             
               
                 
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   Comparing Eq. (8) to the input referred switch noise of the design given in [1], we see that the switch noise sampled at C 1  contributes the same to the overall noise in both designs. However, in our design the switch noise sampled at C 2  makes a significantly smaller contribution to the noise near the Nyquist frequency in comparison to the design in [1] and is negligible compared to the noise sampled at C 1 . The resulting total switch noise power is given in Eq. (9). 
   
     
       
         
           
             
               
                 
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                   switch_total 
                   2 
                 
                 = 
                 
                   
                     
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   The conclusion of the foregoing analysis is that the total input referred switch noise power in the MI design is one-half that of the design given in [1]. 
   We proceed with an estimate of the amplifier noise contribution to the filter&#39;s noise for each of the high-pass filters with different delays. We will assume that, as shown in the noise model  800  of  FIG. 8 , both the input signal and the reference signal are equal to zero, and that the opamp&#39;s noise is symmetrically divided between noise sources  802  and  804  the inverting and non-inverting opamp inputs. Dividing the opamp noise into two symmetrical correlated noise sources does not cause loss of generality but is a convenient method to perform noise analysis. 
   In  FIG. 8 , e[n] represents the opamp noise sample at time instance n. The opamp noise is the sum of a thermal noise term, which is flat over the entire frequency range, and 1/f noise that is dominant at lower frequencies. 
   In a sample-delayed MI design, where the output samples are taken during the sampling phase, the opamp noise transfer function is given in Eq. (10). 
                     H   e     ⁡     (   z   )       =         V   ⁡     (   z   )         E   ⁡     (   z   )         =     -       1   +         C   1       C   2       ⁢     z     -   0.5         +     z     -   1           1   +     z     -   1                       (   10   )               
The input referred opamp noise is given in Eq. (11).
 
   
     
       
         
           
             
               
                 
                   
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                     · 
                     
                       E 
                       ⁡ 
                       
                         ( 
                         z 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 11 
                 ) 
               
             
           
         
       
     
   
   If we evaluate the transfer function H in (z) along the unit circle in the z-plane, and assume that the opamp noise sample values at various delays (1, z −0.5  and z −1 ) are uncorrelated, the resulting frequency transfer function H in (jω) is given by Eq. (12).
 
 H   in ( j ω)=−(1+exp(− j ω))  (12)
 
   From Eq. (12) it can be seen that the input referred amplifier noise in the MI undergoes low-pass filtering; the DC component is amplified by a factor of 2, and the highest frequency component, ω=π, is attenuated to zero. This is contrasted to the design of the high-pass filter proposed in [1] in which the input referred amplifier noise undergoes differentiation, i.e., it is multiplied by (1−exp(jω)). Thus, unlike the design proposed in [1] in which the amplifier noise near the Nyquist frequency is amplified by a factor of 4, the new MI design reduces the noise power at the Nyquist frequency to zero. Furthermore, Eq. (12) shows that the new high-pass filter design reduces the contribution to the amplifier noise in much the same manner as the SC integrator design employing the CHS method, which was one of the goals of our design. 
   In a half-sample-delayed MI design, the opamp noise transfer function is given by Eq. (13). 
                     H   e     ⁡     (   z   )       =         V   ⁡     (   z   )         E   ⁡     (   z   )         =     -       1   +       C   1       C   2       +     z     -   1           1   +     z     -   1                       (   13   )               
The input referred opamp noise is given by Eq. (14).
 
   
     
       
         
           
             
               
                 
                   
                     E 
                     in 
                   
                   ⁡ 
                   
                     ( 
                     z 
                     ) 
                   
                 
                 = 
                 
                   
                     
                       
                         H 
                         in 
                       
                       ⁡ 
                       
                         ( 
                         z 
                         ) 
                       
                     
                     · 
                     
                       E 
                       ⁡ 
                       
                         ( 
                         z 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       - 
                       
                         ( 
                         
                           1 
                           + 
                           
                             
                               C 
                               1 
                             
                             
                               C 
                               2 
                             
                           
                           + 
                           
                             z 
                             
                               - 
                               1 
                             
                           
                         
                         ) 
                       
                     
                     · 
                     
                       E 
                       ⁡ 
                       
                         ( 
                         z 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 14 
                 ) 
               
             
           
         
       
     
   
   From Eq. (14) it can be seen that the input referred amplifier noise undergoes low-pass filtering, similar to the sample-delayed high-pass filter. However the half-sample delayed high pass filter does not completely attenuate the Nyquist frequency to zero, but rather it has a power gain of (C 1 /C 2 ) 2  at the Nyquist frequency. In most ΣΔ applications with half-sample delayed filters, the optimal value for (C 1 /C 2 ) is ½ resulting in power gain of ¼ at the Nyquist frequency. 
   With regard to a non-delayed MI design, we can state that in both the half-sample delayed and non-delayed designs the amplifier noise “sees” the same structure looking toward the front-end (input) of the circuit. Therefore, the nondelayed design has the same noise shaping properties as the half-sample delayed design. 
   In all MI designs, the opamp 1/f noise remains near DC, far from the signal band and thus it may be neglected. 
   As noted above, the mirrored integrator  400  or  600  (non-delayed, half-sample delayed, or sample-delayed) can be used in a ΣΔ analog-to-digital converter such as that of the above-cited &#39;409 patent. That patent teaches both single-stage and multiple-stage ADC&#39;s, and the mirrored integrator  400  or  600  can be used in either. 
   An illustrative example will be given with reference to  FIG. 9 , which is based on  FIG. 2A  of the &#39;409 patent. In the ADC  900 , an analog signal received at an input  902  is applied to a multiplier  904 . A chopper signal generator  906 , under control of a sampling clock  908 , produces a chopper signal having a frequency that is equal to one-half of the sampling frequency, i.e., equal to the frequency of Φ 1  or Φ 2 . The chopper signal is a square wave alternating between +1 and −1 and is also applied to the multiplier  904 . The product is applied to an adder  910 , where a feedback signal (to be described later) is added to the product output from the multiplier  904 . The resulting signal is integrated in a mirrored integrator  400  or  600 , and the resulting integrated output is applied to a quantizer  912  to produce a digital number representing a level of the integrated output. The digital number output by the quantizer  912  is applied to a digital-to-analog converter (DAC)  914  to provide the feedback signal noted above. The digital number output by the quantizer  912  is also applied to a digital high-pass FIR filter  916 , where it is high-pass-filtered, and to a downsampler  918 , where it is downsampled. The resulting digital signal is output at an output  920 . 
   The mirrored integrator can be designed to support multiple input signals, as shown in  FIG. 10 . In the mirrored integrator  1000  of  FIG. 10 , each input signal V in   (k) (n), k=1, 2, . . . N, along with associated reference signal V ref   (k) (n), is provided with its own input circuit  438 ( 1 ),  438 ( 2 ), . . .  438 (N). The input circuits may have different sampling capacitance C 1   (k) , thus allowing different gains, given by C 1   (k) /C 2 , for different input signals. The input signals and their reference signals, either all of them or just some of them, can be interchanged in order to provide different delay designs (sample-delayed, half-sample-delayed, and non-delayed design). 
   While a preferred embodiment of the present invention and various modifications thereof have been set forth above, those skilled in the art who have reviewed the present disclosure will readily appreciate that other embodiments can be realized within the scope of the invention. For example, teachings of numerical values are illustrative rather than limiting, as are teachings of specific circuit elements. Also, a modulator or converter as recited in the claims could be implemented in any of several ways, including a single chip, discrete elements, a programmed computing device, or optical computing. 
   Moreover, as noted above, the chopper stabilization modulating signal can be any appropriate signal, including a random or pseudo-random signal, to provide a blue-noise integrator or another suitable integrator. When the chopper stabilization modulating signal is a periodic signal as shown in  FIG. 11B , and it is applied to integrators  400  and  600 , the circuit performs mirrored integration, as explained above. However, when the chopper stabilization modulating signal is a random or pseudo-random sequence and it is applied to integrators  400  and  600 , the circuit performs a spread-spectrum integration. An example of such a random sequence is shown in  FIG. 11C  with its spectrum shown in  FIG. 12A . In order to describe the spread-spectrum integration we recall that the integrator is a filter that amplifies a DC input signal with an infinite gain, which corresponds to a constant chopper modulating signal. Also, the mirrored integrator is a filter that amplifies, with an infinite gain, an input signal at the frequency of the periodic chopper modulating signal (the alternating sequence) at Nyquist frequency. Accordingly, we define a spread-spectrum integrator as a filter that amplifies an input signal that is coherent with the random chopper modulating signal, with an infinite gain. Thus, the spread-spectrum integrator effectively integrates an input signal that has undergone a spread of its spectrum. The spread-spectrum approach has been proven to increase the signal-to-noise ratio in digital communications. However, if the random chopper modulating sequence is white, it is likely that the power of low-frequency non-idealities such as 1/f noise, DC offset and offset drift would leak into the input signal band. Thus, in order to attenuate low-frequency non-idealities, the chopper stabilization modulating random sequence may have a deficiency of low-frequency spectral power (blue-noise). An example of the blue-noise chopper sequence is shown in  FIG. 11D  with its spectrum shown in  FIG. 12B . The resulting blue-noise integrator has advantages of both the mirrored and spread-spectrum integrators. In the blue-noise integrator, an input signal would be shifted to the Nyquist frequency allowing attenuation of the low-frequency non-idealities, similar to mirrored integration, and also it would undergo a spectrum spread, thus accommodating signal-to-noise ratio increase as in spread-spectrum integration. 
   Furthermore, the integrator of the present invention has a wide range of uses beyond that shown in  FIG. 9 , which is intended as illustrative rather than limiting. Therefore, the present invention should be construed as limited only by the appended claims.