Patent Publication Number: US-7714634-B2

Title: Pseudo-differential active RC integrator

Description:
BACKGROUND 
   1. Field of Invention 
   The technology described relates to integrators and methods of operation of the same. 
   2. Discussion of Related Art 
   Integrators are commonly used in various types of circuits. Timing circuits, charge measurement circuits, and signal processing circuits all may implement one or more integrators. A specific example of a circuit which may implement an integrator is a Sigma Delta Modulator circuit. The Sigma Delta Modulator may include a filter, which can be formed using one or more integrators in an appropriate configuration. 
   Integrators can take a variety of forms depending on the environment in which they are used and the desired operating characteristics. When selecting or designing an integrator for a particular application, a circuit designer may consider factors such as power consumption, linearity, size, ease of processing, and compatibility with surrounding circuitry. Thus, while a given integrator design may be beneficial in some settings, it may have significant drawbacks in other settings. 
   One example of a known integrator design is the fully-differential integrator.  FIGS. 1A and 1B  illustrate an example of an inverting fully-differential active RC integrator  100 , shown in schematic and a more detailed representation, respectively. As shown in  FIG. 1A , the fully-differential integrator  100  is configured to receive a differential input signal having positive and negative components V in+  and V in− , and output a differential output signal having positive and negative components V out+  and V out− . The fully-differential integrator  100  includes an amplifier circuit  102  which has two input terminals, one configured to receive each of the components of the differential input signal V in . The two components of the differential input signal V in  may be provided to the amplifier  102  via respective resistors, R 1  and R 2 . The amplifier provides the differential output signal V out  from two output terminals. Feedback paths are included in the circuit design, and include respective capacitances, illustrated as capacitors, C 1  and C 2 . The fully-differential integrator  100  is referred to as an active RC integrator because of the presence of the resistors coupled with the capacitors, and the use of amplifier  102 . 
     FIG. 1B  shows the fully-differential active RC integrator of  FIG. 1A  in greater detail, and in particular expands on the detail of the amplifier  102  from  FIG. 1A . As shown in  FIG. 1B , the amplifier  102  can be viewed as having two substantially identical branches coupled together at a tail current source I 3 . A first branch of the amplifier  102  includes current source I 1  coupled to NMOS transistor  104   a . The current source I 1  is coupled between a supply voltage level V dd1  and the drain of NMOS transistor  104   a . The drain of NMOS transistor  104   a  is also coupled to capacitor C 2 , and is the point of the circuit from which the output V out−  is taken. 
   Similarly, a second branch of the amplifier includes current source I 2  coupled to NMOS transistor  104   b . The current source I 2  is coupled between a supply voltage level V dd2 , which may be the same as V dd1 , and a drain of NMOS transistor  104   b . The drain of NMOS transistor  104   b  is also coupled to capacitor C 1 , and is the point of the circuit from which the output V out+  is taken. 
   As shown, the first and second branches of the amplifier join at a tail current source I 3 , which could be a transistor. In particular, the source terminals of NMOS transistors  104   a  and  104   b  are coupled to tail current source I 3 . The tail current source I 3  is also coupled to ground. The combination of current sources I 1 -I 3  and the two NMOS transistors  104   a  and  104   b  constitute an operational transconductance amplifier (OTA), outlined by box  102 . 
   Another example of a known integrator design is illustrated in  FIG. 2 . The pseudo-differential active RC integrator  200  is similar to the fully-differential active RC integrator  100  of  FIG. 1B , except that the tail current source I 3  in  FIG. 1B  is removed. The source terminals of NMOS transistors  204   a  and  204   b  are therefore coupled directly to ground. Since the input common-mode may not coincide with the gate to source voltage, V gs , of transistors  204   a  and  204   b , the pseudo-differential active RC integrator also includes current sources I 4  and I 5  to provide level shifting. Current sources I 4  and I 5  can be implemented as transistors. The current sources I 4  and I 5  are coupled between respective virtual ground nodes,  211   a  and  211   b  (corresponding to the gate terminals of transistors  204   a  and  204   b ) and ground. 
   SUMMARY 
   According to an aspect of the invention, a pseudo-differential active RC integrator with common-mode feedback comprises a first branch configured to receive a first component of a differential input signal and produce a first component of a differential output signal. The first branch comprises a first virtual ground node, and a first transconductor coupled to the first virtual ground node. The pseudo-differential active RC integrator with common-mode feedback further comprises a second branch configured to receive a second component of the differential input signal and produce a second component of the differential output signal. The second branch comprises a second virtual ground node, and a second transconductor coupled to the second virtual ground node. The pseudo-differential active RC integrator with common-mode feedback further comprises a common-mode feedback subcircuit coupled to the first transconductor and the second transconductor and configured to adjust a common-mode output signal of the pseudo-differential active RC integrator. 
   According to another aspect of the invention, a pseudo-differential active RC integrator with common-mode feedback is disclosed. The pseudo differential active RC integrator comprises a first branch configured to receive a first component of a differential input signal and produce a first component of a differential output signal. The first branch comprises a first virtual ground node, a first transconductor coupled to the first virtual ground node, a first resistor, and a first transistor. The first transistor comprises a first terminal configured to receive the first component of the differential input signal via the first resistor, the first terminal of the first transistor defining the first virtual ground node, and a second terminal configured to produce the first component of the differential output signal. The pseudo-differential active RC integrator further comprises a second branch configured to receive a second component of the differential input signal and produce a second component of the differential output signal. The second branch comprises a second virtual ground node, a second transconductor coupled to the second virtual ground node, a second resistor, and a second transistor. The second transistor comprises a first terminal configured to receive the second component of the differential input signal via the second resistor, the first terminal of the second transistor defining the second virtual ground node, and a second terminal configured to produce the second component of the differential output signal. The pseudo-differential active RC integrator further comprises a common-mode feedback subcircuit comprising a first gain stage having an output coupled to the first transconductor, and a second gain stage having an output coupled to the second transconductor. 

   
     BRIEF DESCRIPTION OF DRAWINGS 
     The accompanying drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures is represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing. In the drawings: 
       FIG. 1A  is a high level representation of a conventional inverting fully-differential active RC integrator; 
       FIG. 1B  is a more detailed illustration of the circuit shown in  FIG. 1A ; 
       FIG. 2  is an illustration of a conventional pseudo-differential active RC integrator; 
       FIG. 3  is a graphical representation of the non-linear operation of the circuits illustrated in  FIGS. 1A and 1B ; 
       FIG. 4  is a graphical representation of headroom problems associated with some conventional integrators; 
       FIG. 5  illustrates a pseudo-differential active RC integrator with common-mode feedback according to an embodiment of the present invention; 
       FIG. 6  illustrates a pseudo-differential active RC integrator with common-mode feedback having reset capabilities, in accordance with an embodiment of the present invention; 
       FIG. 7  illustrates a pseudo-differential active RC integrator with common-mode feedback having DC gain enhancement capabilities, in accordance with an embodiment of the present invention; and 
       FIGS. 8A and 8B  illustrate alternative embodiments of a pseudo-differential active RC integrator providing control of the polarity of common-mode feedback, according to some embodiments of the present invention. 
   

   DETAILED DESCRIPTION 
   As mentioned, any given integrator design results in operating characteristics of that integrator which may be unsatisfactory for some applications. Fully-differential active RC integrators are no exception, and include multiple operating characteristics which may make them unsatisfactory for some applications. In particular, conventional fully-differential active RC integrators, such as integrator  100 , demonstrate limited output voltage swing, as well as non-linear behavior, both of which may hinder performance. 
   The limited output voltage swing of fully-differential active RC integrators can be understood by reference to  FIG. 1B . As shown, each branch of the amplifier circuit  102  includes three voltage drops, listed as Δv 1 , Δv 2 , and Δv 3 . In particular, Δv 1  represents the voltage drops across current sources I 1  and I 2 , which are presumed to be approximately equal. The transistors  104   a  and  104   b  give rise to voltage drops Δv 2 , which are also presumed to be approximately equal. The tail current source I 3  causes the voltage drop Δv 3 . Each of the three voltage drops per branch has the effect of limiting the output voltage swing of the differential output signal components V out+  and V out−  by either raising the minimum possible voltage for the output signals or lowering the maximum possible voltage for the output signals. The impact can be appreciated by considering some exemplary numbers. For example, the integrator  100  may be implemented using a 1.6 Volt supply. If the voltage drops Δv 1 , Δv 2 , and Δv 3  are each approximately 0.2 Volts, as an example, the output voltage swing will be reduced by approximately 0.6 Volts. As will be described below, a pseudo-differential active RC integrator may have a smaller reduction (e.g., approximately only a 0.4 Volt reduction as compared to 0.6 Volts) in the possible voltage swing of the differential output signal since the tail current source I 3 , and its associated voltage drop, are removed in the pseudo-differential design. 
   As mentioned above, fully-differential active RC integrators also suffer from non-linear operation, and more particularly from a non-linear transconductance, which can be understood by reference to  FIGS. 1B and 3 . As shown in  FIG. 1B , the two branches of the amplifier  102  carry respective currents, i 1  and i 2 . The relationship between the two currents can be characterized by the quantity Δi=(i 1 −i 2 )/2. The value of Δi depends on the difference between the two components of the input to the OTA  102  (not shown), which can be written as Δv amp . It may be desirable for Δi to be linearly related to Δv amp , or in other words for the circuit to have a linear transconductance. However, as shown in  FIG. 3 , fully-differential active RC integrators do not provide a linear relationship between these two quantities. Rather, curve  304  represents the relationship of Δi as a function of Δv amp , and demonstrates that the fully-differential active RC integrator has a strong third-order non-linearity which may have undesirable effects, such as increasing the noise and distortion of the circuit. 
   The pseudo-differential active RC integrator  200  offers improvements over the operation of a fully-differential active RC integrator. First, removal of the tail current source I 3  and its associated voltage drop Δv 3 , shown in  FIG. 1B , gives the pseudo-differential active RC integrator  200  a larger output voltage swing than the fully-differential active RC integrator  100 . Second, because each branch of the pseudo-differential active RC integrator has mostly second-order non-linearity that cancels out pseudo-differentially, the pseudo-differential active RC integrator has improved linear transconductance behavior, as compared to the strongly non-linear transconductance of the fully-differential version. The improved linear transconductance behavior offers such as reduced circuit noise and distortion. 
   Another characteristic of pseudo-differential active RC integrators to consider is the common-mode signal of the circuit. The common-mode signal of a circuit, such as that shown in  FIG. 2 , is the average of the components of a differential signal. Poor control of the common-mode signal is sometimes associated with headroom problems.  FIG. 4  offers an illustration of the basic concept.  FIG. 4  illustrates the positive and negative components of a differential output signal, V out+  and V out− , as well as a common-mode signal V cm =(V out+ +V out− )/2, as a function of time for three regions of interest,  401 ,  403 , and  405 . The differential signal (i.e., the components V out+  and V out− ) is shown as a sinusoidal signal, and could correspond to an output of a pseudo-differential active RC integrator. The minimum value the signals can take may be limited to a lower boundary voltage V a , the value of which could be determined by the properties of the circuit. For example, referring to  FIG. 1B  and the example of a fully-differential integrator, the value of V a  may be determined in whole or in part by the voltage drops Δv 1 , Δv 2 , and Δv 3 . For example, V a  may be equal to Δv 2 +Δv 3 . Similarly, the maximum value the signals in  FIG. 4  can take may be limited by an upper boundary voltage V b , which, referring to  FIG. 1B  and the example of a fully-differential integrator, may be equal to V dd1 −Δv 1 . 
   As shown, in regions  401  and  405 , the common-mode voltage V cm  is approximately equidistant between the lower and upper boundary voltages V a  and V b , which allows signals V out+  and V out−  to oscillate within the entire voltage range from V a  to V b . By contrast, region  403  illustrates a headroom problem that can lead to erroneous circuit operation. In particular, in region  403  the common-mode voltage V cm  drifts toward the upper boundary voltage V b , and as shown V out−  is clipped by the upper boundary voltage V b , such that V out+  and V out−  do not oscillate within the entire range from V a  to V b . Behavior such as that shown in region  403  can impair accurate circuit operation, and therefore it is desirable to accurately control the common-mode voltage of differential circuits, such as pseudo-differential active RC integrators. 
   According to an aspect of the present invention, a pseudo-differential active RC integrator having common-mode feedback is disclosed. The common-mode feedback component of the circuit provides accurate control of a common-mode signal and therefore makes the circuit operation stable. Various modifications can also be made to the basic circuit design to provide additional functionality, such as the ability to reset each of the differential output signals to a common-mode value, as well as enhancing the DC gain of the integrator. Additional features and benefits will be appreciated in the following discussion. 
     FIG. 5  illustrates one example of a pseudo-differential active RC integrator with common-mode feedback according to an embodiment of the present invention. As shown, the pseudo-differential active RC integrator  500  comprises two branches configured approximately symmetrically about gain stage  506  and capacitor C 5 , discussed further below. A first branch of the pseudo-differential active RC integrator  500  includes current source I 1  coupled to NMOS transistor  504   a . The current source I 1  is coupled between a supply voltage level V dd1  and the drain of NMOS transistor  504   a . The drain of NMOS transistor  504   a  is also coupled to capacitor C 2 , and is the point of the circuit from which the negative component, V out− , of the differential output signal is provided. It will be appreciated that the output signal V out−  could be provided directly from the drain of NMOS transistor  504   a  (as shown) or could be coupled to the drain of NMOS transistor  504   a  through one or more additional components. For example, a cascode configuration could be used to convert the signal from the drain of  504   a  to the desired output signal. Thus, it will be appreciated that the terms “couple,” “coupled,” “coupling,” and any variations thereof as used in this application encompass direct or indirect (i.e., through one or more components) connections. Similarly, a circuit or component described as “providing,” or “producing” a signal is meant to encompass direct provision or production of that signal as well as provision or production of the signal through one or more additional circuits or components. The positive component V in+  of the differential input signal is input to the gate terminal of NMOS transistor  504   a  via resistor R 2 . 
   The first branch further comprises a transconductor  507   a , having a transconductance g m  coupled to the virtual ground node  511   a . The transconductor  507   a  is illustrated as an NMOS transistor, but is not limited in this respect, as any type of transconductor could be used. For example, the transconductor  507   a  could be a PMOS transistor, a bipolar junction transistor (BJT), or any other type of transconductor. Node  511   a  represents a virtual ground node, and corresponds in the illustrated embodiment to the gate terminal of NMOS transistor  504   a . The virtual ground node  511   a  may have an approximately constant voltage having a value sufficient to keep a current through transistor  504   a  approximately equal to I 1 . 
   The second branch of the integrator  500  is substantially the same in design and operation as the first branch, and represents the negative input, V in− , branch. For example, the following components may be substantially the same as each other in configuration and operation: supply voltage levels V dd1  and V dd2  (which may be the same supply voltage); current sources I 1  and I 2 ; capacitors C 1  and C 2 ; transistors  504   a  and  504   b ; resistors R 1  and R 2 ; and transconductors  507   a  and  507   b.    
   As shown, the pseudo-differential active RC integrator  500  includes a common-mode feedback subcircuit for controlling the common-mode output signal of the integrator. The common-mode feedback subcircuit comprises a capacitor C 5  configured in parallel with a gain stage  506 , which may be an amplifier, an OTA, or any other type of gain stage. The gain stage  506  has two inputs, one of which is coupled to receive the common-mode output signal of the integrator (node  509 ), and the second of which is configured to receive a reference signal representing a target value, V cmt , for the common-mode output signal. The common-mode output signal of the integrator is provided at node  509 , and is the average of the two components of the differential output signal, V out+  and V out− . In the non-limiting example of  FIG. 5 , the common-mode output signal is provided to node  509  by providing V out−  from the drain of transistor  504   a  to node  509  through an RC subcircuit comprising resistor R 4  in parallel with capacitor C 4 , while providing V out+  from the drain of transistor  504   b  to node  509  through an RC subcircuit comprising resistor R 3  in parallel with capacitor C 3 . It may be desirable for R 3  and R 4  to have large values, however, the invention is not limited in this respect. 
   The gain stage  506  of the common-mode feedback subcircuit may have an output coupled to the transconductors  507   a  and  507   b , which in turn are coupled to the virtual ground nodes  511   a  and  511   b , respectively. In the embodiment of  FIG. 5 , transconductors  507   a  and  507   b  are transistors, and the output of gain stage  506  is coupled to the gate terminals of the transistors. In this manner, the common-mode output signal is controlled using the transconductors  507   a  and  507   b  coupled to the virtual ground nodes, as can be understood by considering two non-limiting scenarios. 
   In the first scenario, the common-mode output signal, at node  509 , is greater than the target value of the common-mode output signal V cmt . Accordingly, the output of the gain stage  506  decreases, and reduces the current through transistors  507   a  and  507   b , which causes the common-mode output signal to decrease, and drives the common-mode output signal closer to the target value V cmt . 
   In the second scenario, the common-mode output signal at node  509  is less than the target value V cmt . Accordingly, the output of the gain stage  506   a  increases, and increases the current through transistors  507   a  and  507   b , which causes the common-mode output signal to increase, and drives the common-mode output signal closer to the target value V cmt . Thus, as illustrated by the first and second scenarios described, the common-mode feedback subcircuit maintains the value of the common-mode output signal at approximately the target value, and thus enhances the stability of the circuit. 
   It will be appreciated that the groupings of components described in  FIG. 5  (and other figures of this application) are meant for purposes of illustration, and are not limiting. For example, while some components in  FIG. 5  are described as being part of a first or second branch of the pseudo-differential active RC integrator  500 , they may alternatively be described as being part of the common-mode feedback subcircuit, and vice versa. 
   Capacitors C 3  and C 4  in  FIG. 5  may stabilize the common-mode signal in the pseudo-differential active RC integrator  500 . For example, the common-mode operation of pseudo-differential active RC integrator  500  with respect to the common-mode output signal can be analogous to a resonator circuit. Resonator circuits may produce an oscillating, or periodic, output in response to an oscillating input. As is known, one manner of characterizing resonator circuits is by their quality factor, Q, which is a measure of how fast an oscillation decays. If Q is large, the oscillation of the output signal may be accentuated, resulting in ringing of the output signal. 
   In the context of pseudo-differential active RC integrator  500 , it may not be desirable for the common-mode output signal to fluctuate. Rather, it may be desirable for the common-mode output signal to remain approximately constant to avoid problems during circuit operation, such as headroom problems. Capacitors C 3  and C 4  in the pseudo-differential active RC integrator  500  reduce the Q of the resonator with respect to the common-mode output signal, thus providing stable control of the common-mode output signal. 
   The circuits illustrated and discussed thus far can be expanded upon in numerous ways to provide additional functionality. For example, it may be desirable to provide the capability to reset the common-mode output signal to a target value for one or more of the circuits shown. The common-mode output signal may drift during operation of the circuit, so that resetting the value of the common-mode output signal to a target value may enhance stable circuit operation. Other reasons for resetting the common-mode output signal to a target value are also possible, as the aspects of the invention are not limited in this respect. It may also be desirable to provide a circuit with enhanced DC gain. 
     FIG. 6  illustrates a pseudo-differential active RC integrator having common-mode feedback and the capability to reset the common-mode output signal. It should be appreciated that the pseudo-differential active RC integrator  600  in  FIG. 6  is substantially the same as pseudo-differential active RC integrator  500  in  FIG. 5 . For simplicity, components previously described in relation with  FIG. 5  are not described in detail here. As shown, the common-mode feedback sub-circuit of pseudo-differential active RC integrator  600  comprises two gain stages  606   a  and  606   b , each with a respective parallel capacitor C 5  and C 6 . Each gain stage  606   a  and  606   b  comprises an input configured to receive the target value, V cmt , of the common-mode output signal. Each gain stage  606   a  and  606   b  has an output capable of being connected simultaneously to transconductors  507   a  and  507   b , depending on the operation of switch SW 1  configured between the outputs of the two gain stages  606   a  and  606   b.    
   The inclusion of switches SW 1  and SW 2  in the pseudo-differential active RC integrator  600  provides the circuit with at least two distinct operating scenarios. In the first scenario, switch SW 1  and switch SW 2  (which replaces node  509  in  FIG. 5 ) are closed, thus operating as short circuits. Accordingly, the two branches of the pseudo-differential active RC integrator  600  are coupled together and the integrator functions in substantially the same manner as the pseudo-differential active RC integrator  500  of  FIG. 5 . In this scenario, the gain stages  606   a  and  606   b  each comprise an input configured to receive the common-mode output signal of the integrator  600  (at the position of SW 2 ) and provide a combined, amplified output at switch SW 1 , which is provided to the gates of transconductors  507   a  and  507   b . The values of capacitors C 5  and C 6 , as well as the gain values of gain stages  606   a  and  606   b , may be chosen to account for the presence of the two amplifiers  606   a  and  606   b  (as compared to the single amplifier in the common-mode feedback subcircuit of  FIG. 5 ), although the invention is not limited in this respect. As with the pseudo-differential active RC integrator  500  of  FIG. 5 , the pseudo-differential active RC integrator  600  of  FIG. 6  may maintain the output common-mode signal at approximately the target value V cmt  when switches SW 1  and SW 2  are closed. 
   In the second operating scenario for pseudo-differential active RC integrator  600 , the switches SW 1  and SW 2  are open, thus creating two independent single-ended loops. In this scenario, gain stage  606   a  does not receive the common-mode output signal at one of its inputs, but rather receives the output signal of the first branch (i.e., a single component of the differential output signal) of the integrator  600 . The output of gain stage  606   a  is coupled to transconductor  507   a , but not to transconductor  507   b . Thus, the feedback subcircuit of the first branch (comprising gain stage  606   a  and capacitor C 5 ) drives the output signal of the first branch to the target value V cmt . Similarly, gain stage  606   b  does not receive the common-mode output signal at one of its inputs, but rather receives the output signal of the second branch (i.e., a single component of the differential output signal) of the integrator  600 . The output of gain stage  606   b  is coupled to transconductor  507   b , but not transconductor  507   a . Thus, the feedback subcircuit of the second branch (comprising gain stage  606   b  and capacitor C 6 ) drives the output signal of the second branch to the target value V cmt . In this manner, both components of the differential output signal are individually driven to the target value V cmt . Thus, if and when switches SW 1  and SW 2  are closed, the common-mode output signal will have a value approximately equal to the target value V cmt , and thus will have been reset. 
   With reference to  FIG. 6 , it should also be appreciated that the terminology used herein is not limiting. Accordingly,  FIG. 6  could be described as comprising two common-mode feedback subcircuits, with one such subcircuit corresponding to each of the two branches of the integrator  600 . However, integrator  600  could be described equally well as comprising one common-mode feedback subcircuit comprising both gain stages  606   a  and  606   b , and capacitors C 5  and C 6 . The common-mode feedback subcircuit may contain any one or combination of components described herein, as the aspects of the invention are not limited in this respect. 
     FIG. 7  illustrates a variation on the pseudo-differential active RC integrator  600  of  FIG. 6  that provides enhanced DC gain. As shown, the pseudo-differential active RC integrator  700  of  FIG. 7  is substantially the same as the pseudo-differential active RC integrator  600 , with switches SW 1  and SW 2  being replaced by variable resistors R 6  and R 5 , respectively. The variable resistors R 5  and R 6  provide controlled differential feedback, which may move the pole of the pseudo-differential active RC integrator  700 . Proper control of the resistances of variable resistors R 5  and R 6  thus may enable the pole of the integrator  700  to be moved to the origin, such that the integrator  700  may provide an approximately infinite DC gain. 
     FIGS. 8A and 8B  show an alternative implementation of a pseudo-differential active RC integrator with common-mode feedback, according to another aspect of the present invention. The circuits shown in  FIGS. 8A and 8B  enable control of the pole of the integrator. As is known, an ideal integrator has a single pole at the origin. However, in practice, integrators may have a pole that is not located at the origin, but rather is located somewhere else along the real axis. The location of the pole on the real axis may dictate the polarity of the feedback for the integrator, i.e., positive feedback or negative feedback. The circuits shown in  FIGS. 8A and 8B  provide alternative configurations for controlling the polarity of the common-mode feedback. 
   Pseudo-differential active RC integrator  800   a  comprises two swapping circuits,  813   a  and  813   b , which act in combination (and could be referred to as constituting a single swapping circuit). Swapping circuit  813   a  is configured between the output of gain stage  606   a  and the gates of transconductors  507   a  and  507   b , and is configured to receive an input control signal labeled as “swap.” Similarly, swapping circuit  813   b  is configured between the output of gain stage  606   b  and the gates of transconductors  507   a  and  507   b , and is configured to receive the input control signal “swap.” If the pole of the integrator is such that negative feedback is desired, the swapping circuits  813   a  and  813   b  may operate, by input of an appropriate control input signal “swap,” to connect the output of gain stage  606   a  to the gate of transconductor  507   b  and the output of gain stage  606   b  to the gate of transconductor  507   a , while at the same time disconnecting the output of gain stage  606   a  from the gate of transconductor  507   a  and the output of gain stage  606   b  from the gate of transconductor  507   b . Alternately, if the pole of the integrator is such that positive feedback is desired to move the pole closer to the origin, the swapping circuits  813   a  and  813   b  may operate, by input of an appropriate control input signal “swap,” to connect the output of gain stage  606   a  to the gate of transconductor  507   a  and the output of gain stage  606   b  to the gate of transconductor  507   b , while disconnecting the output of gain stage  606   a  from the gate of transconductor  507   b  and the output of gain stage  606   b  from the gate of transconductor  507   a.    
     FIG. 8B  is an alternative embodiment enabling control of the polarity of the common-mode feedback using swapping circuits  813   a  and  813   b . The pseudo-differential active RC integrator  800   b  comprises swapping circuits  813   a  and  813   b  positioned differently from their configuration in pseudo-differential active RC integrator  800   a . In  800   b , swapping circuits  813   a  and  813   b  are configured between the drain of transconductor  507   a  and the drain of transconductor  507   b , and the virtual ground nodes  511   a  and  511   b . The swapping circuit  813   a  may operate to alternately connect the drain of transconductor  507   a  to the virtual ground nodes  511   a  and  511   b , while swapping circuit  813   b  may operate to alternately connect the drain of transconductor  507   b  to the virtual ground nodes  511   b  and  511   a , thus providing control of the polarity of the common-mode feedback. For example, if negative feedback is desired, swapping circuits  813   a  and  813   b  may, by input of appropriate control input signals “swap” (which may be the same for both  813   a  and  813   b , or which may differ), connect the drain of transconductor  507   a  to virtual ground node  511   b  and the drain of transconductor  507   b  to virtual ground node  511   a , while disconnecting the drain of transconductor  507   a  from the virtual ground node  511   a  and the drain of transconductor  507   b  from the virtual ground node  511   b . By contrast, if positive feedback is desired, the swapping circuits  813   a  and  813   b  may operate to connect the drain of transconductor  507   a  to virtual ground node  511   a  and the drain of transconductor  507   b  to virtual ground node  511   b , while disconnecting the drain of transconductor  507   a  from virtual ground node  511   b  and the drain of transconductor  507   b  from virtual ground node  511   a.    
   As will be appreciated, the swapping circuits  813   a  and  813   b  can be implemented in any manner, and the invention is not limited in this respect. For example, the swapping circuits could be implemented as alternate switches. Other implementations of the swapping circuits are also possible. 
   Having thus described several aspects of at least one embodiment of this invention, it is to be appreciated various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and scope of the invention. Accordingly, the foregoing description and drawings are by way of example only. 
   For example, the polarity of the circuits shown is not limiting. While some of the circuits have been shown as comprising NMOS transistors, the invention is not limited in this respect. Rather, it will be appreciated that a similar circuit design and operation could be achieved using PMOS transistors, BJTs, or any other type of transistors. Moreover, while some of the circuits shown have been inverting integrators, it will be appreciated that non-inverting integrators could also be achieved by implementing one or more aspects of the present invention. 
   This invention is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and of being practiced or of being carried out in various ways. Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having,” “containing,” “involving,” and variations thereof herein, is meant to encompass the items listed thereafter and equivalents thereof as well as additional items.