Abstract:
A polyphase filter passes a desired frequency and attenuates an image frequency in many communication systems. The invention is an error correction circuit that compensates the polyphase filter for low open loop gain operational amplifiers. When multiple polyphase filters are used in communication circuits on a single integrated circuit (IC), the open loop gain of the operational amplifiers is limited by the IC&#39;s ability to dissipate power. The error correction circuit reduces the dependency of the polyphase filter performance on the low open loop gain of its operational amplifiers and hence, on temperature and IC process parameters.

Description:
FIELD OF INVENTION 
     The invention is directed towards signal filtering with a polyphase filter, in particular, to provide error reduction in quadrature polyphase filters with low open loop gain operational amplifiers. 
     BACKGROUND 
     Many radio, video and data communication systems need to distinguish between a desired signal and an image signal and to attenuate the image signal relative to the desired signal. A polyphase filter performs this function. 
     For example, a heterodyne receiver with a desired signal of 110 MHz and a local oscillator frequency of 100 MHz generates a desired 10 MHz signal, which is easier to demodulate than the 110 MHz signal that requires difficult to build higher frequency components. However, an image signal of 90 MHz is also converted to an image 10 MHz signal that is not removed from the desired 10 MHz signal by conventional bandpass filters. A quadrature polyphase filter has an asymmetric frequency response resulting from the quadrature phase of its two input signals. It passes or attenuates a signal of the same frequency depending on the phase lag or lead between its two inputs. For instance, a quadrature polyphase filter, with a first and second input current, when driven by a quadrature mixer, will pass the desired signal with the second input current leading the first input current and attenuate the image signal with the second input current lagging the first input current. 
     The polyphase filter has a resonance frequency, at which its response is maximum. One implementation of a quadrature polyphase filter has two damped integrators matched in values and properties, each with an operational amplifier. An ideal polyphase filter has operational amplifiers of sufficiently high open loop gain so that their input voltages are negligibly small compared to their output voltages. As long as the input voltages remain negligibly small, the resonance frequency and the response of an ideal polyphase filter are independent of the input voltages and thus of the open loop gain of the operational amplifiers. 
     When multiple polyphase filters are used in communication circuits on a single integrated circuit (IC), the open loop gain of the operational amplifiers is limited by the IC&#39;s ability to dissipate power. And since the open loop gain of the operational amplifiers varies with IC process parameters and temperature, the polyphase filter&#39;s performance will also be dependent on IC process parameters and temperature. Thus, an undesirable result of the low open loop gain of the operational amplifiers of the polyphase filter is that the resonance frequency and response become dependent on IC process parameters and temperature. 
     SUMMARY 
     The invention is a circuit to provide error correction to polyphase filters with low open loop gain operational amplifiers. The polyphase filter includes a first and second damped integrator, a first and second cross coupling transconductor, and an inverter. The first transconductor is connected between the output of the second damped integrator and the input of the first damped integrator. The inverter is connected to the output of the first damped integrator and has an inverted output. The second transconductor is connected between the inverted output and the input of the second damped integrator. Each damped integrator includes an operational amplifier, a capacitor, and a feedback transconductor. Both the capacitor and the feedback transconductor connect between the inverting input and the output of the operational amplifier. The polyphase filter has a resonance frequency. The embodiments of this invention include error correction circuits for the polyphase filter: voltage based and current based. 
     The voltage based error correction circuit provides a correction voltage in series with each capacitor of the polyphase filter. Each correction voltage has a magnitude approximately equal to the magnitude of the input voltage of the corresponding damped integrator and a phase approximately equal to the phase of the input voltage of the corresponding damped integrator. The response of each damped integrator is corrected by subtracting the correction voltage from the capacitor voltage. 
     The current based error correction circuit provides a correction current to the input of each damped integrator of the polyphase filter. Each correction current has a magnitude proportional to the product of the magnitude of the input voltage, the frequency and the capacitance of the capacitor of the corresponding damped integrator and a phase leading the phase of the input voltage of the corresponding damped integrator by approximately 90°. 
     The correction voltages and currents reduce the dependency of the performance of the polyphase filter on the open loop gain of its operational amplifiers. Thus, the error correction reduces the dependency of the polyphase filter resonance frequency and response on the IC process parameters and temperature. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a polyphase filter. 
     FIG. 2 is a schematic diagram of a damped integrator of FIG. 1 (prior art). 
     FIG. 3 is a schematic diagram of a damped integrator of FIG. 1 in one embodiment of the present invention. 
     FIG. 4 is a schematic diagram of an error correction voltage circuit of FIG.  3 . 
     FIG. 5 is a block diagram of another embodiment of the invention. 
     FIG. 6 is a schematic diagram of one embodiment of an error correction current circuit of FIG.  5 . 
     FIG. 7 is a schematic diagram of another embodiment of an error correction current circuit of FIG.  5 . 
     FIG. 8 is a block diagram of another embodiment of the invention. 
     FIG. 9 is a schematic diagram of an error correction current circuit of FIG.  8 . 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 shows a block diagram of a polyphase filter  10 . The polyphase filter  10  includes a first and second damped integrator  12   x , which are matched, a first and second cross coupling transconductor  14   x , which are matched, and an inverter  16 . The first transconductor  14   1  is connected between the output of the second damped integrator  12   2  and the input of the first damped integrator  12   1 . The inverter  16  is connected to the output of the first damped integrator  12   1  and has an inverted output. The second transconductor  14   2  is connected between the inverted output and the input of the second damped integrator  12   2 . The cross coupling transconductors  14   x  should have a high output impedance so that the input voltages do not affect their output currents. The polyphase filter  10  has a resonance frequency. When driving the polyphase filter by a quadrature mixer, the desired signal may result in the input to the first damped integrator  12   1  leading the input to the second damped integrator  12   2 . Also, the image signal will result in the input to the first damped integrator  12   1  lagging the input to the second damped integrator  12   2 . Thus, the polyphase filter will pass the desired signal and attenuate the image signal. 
     FIG. 2 shows a schematic diagram of one of the damped integrators  12   x  of FIG. 1 according to prior art. The damped integrator  12  includes an operational amplifier  18 , a capacitor  22 , and a feedback transconductor  24 . Both the capacitor  22  and feedback transconductor  24  connect between an inverting input and an output of the operational amplifier  18 . 
     The voltage V cap  across capacitor  22  in FIG. 2 is equal to the vector sum of the operational amplifier output voltage V out  and its input voltage V in : 
     
       
         V cap =V out  +V in   (1) 
       
     
     In an ideal polyphase filter  10 , each operational amplifier  18  has sufficient open loop gain so that the input voltage V in  is negligible compared to the output voltage V out . In this ideal case, V cap =V out  and the value chosen for the transconductance g c  of the cross coupling transconductors  14   x  and the capacitance C of the capacitors  22  determine the resonance frequency fr of the polyphase filter  10 : 
     
       
         f r =g c /(2πC)  (2) 
       
     
     When the open loop gain of each operational amplifier  18  is insufficient to make the input voltage V in  negligible with respect to the output voltage V out , the magnitude and the phase of the capacitor voltage V cap  does not match the magnitude and the phase of output voltage V out . 
     If the phase of the input voltage V in  is in quadrature (±90°) with the phase of the output voltage V out , the phase of the capacitor voltage V cap  differs from the phase of the output voltage V out . Each capacitor  22  requires an extra current to accommodate this phase difference. At the resonance frequency f r , the extra current I e  required by each capacitor  22  is: 
     
       
         I e =2πf r V in C=V in g c   (3) 
       
     
     where g c  is the transconductance of the first and second cross coupling transconductors  14   x . This extra current is supplied by a change in the current of the feedback transconductor  24 . For the feedback transconductor  24  to generate this extra currents I e , the output voltage V out  must change by an error voltage V e  to: 
     
       
         V out =V id ±V e   (4) 
       
     
     where V id  is the output voltage of an ideal operation amplifier with V in =0 and the sign of V e  is determined by whether input voltage V in  leads or lags output voltage V out . 
     The error voltage V e  is: 
     
       
         V e =I e /g f =V in g c /g f   (5) 
       
     
     where g f  is the transconductance of each feedback transconductor  24 . The input voltage V in  can be expressed as: 
     
       
         V in =(V id +V e )/A  (6) 
       
     
     where A is the open loop gain of each operational amplifier  18 . Combining Equations (4), (5), and (6) and expressing P=g c /(Ag f ) for clarity: 
     
       
         V out =V id ±V e =V id (1±(P/(1∓P)))  (7) 
       
     
     To illustrate, when a non-ideal polyphase filter  10  has a cross coupling transconductance of g c =0.1 mS, feedback transcondance of g f =0.01 mS, and operational amplifier  18  open loop gain of A=30, the resulting output voltage is V out =1.5 V id  or 0.75 V id  depending on whether input voltage V in  leads or lags output voltage V out . Thus, the output voltage is in error by a substantial amount. 
     If the phase of input voltage V in  is parallel (0° or 180°) with the phase of the output voltage V out , a mismatch in magnitude results. In this case, there is no source of extra capacitor current having the proper phase, so the mismatch is compensated by a change in resonance frequency f r . The voltage across each capacitor  22  is then V cap =V out ±V in , instead of the output voltage V out  as is the case with V in =0. The sign of V in  is selected based on the 0° or 180° phase of the input voltage V in  with respect to output voltage V out . The resulting changed resonance frequency f i  is: 
     
       
         f i =f r V out /V cap =f r V out /(V out ±V in )=f r /(1±A −1 )  (8) 
       
     
     where A is the open loop gain of each operational amplifier  18 . For example, with an open loop gain of A=33 the changed resonance frequency is f i =0.97 f r  or 1.03 f r  depending on the 0° or 180° phase of the input voltage V in  with respect to output voltage V out . 
     If the phase of input voltage V in  with respect to the output voltage V out  is neither parallel nor in quadrature, both the resonance frequency and the response will be in error and may be analyzed by simple linear superposition. 
     FIG. 3 shows a schematic diagram of one of the damped integrators  12   x  of FIG. 1 according to one embodiment of the invention. The damped integrator  12  includes an operational amplifier  18 , an error correction voltage circuit EC v    20 , a capacitor  22 , and a feedback transconductor  24 . The feedback transconductor  24  connects between an inverting input and an output of the operational amplifier  18 . The error correction voltage circuit EC v    20  and the capacitor  22  are connected in series between the inverting input and output of the operational amplifier  18 . The error correction voltage circuit EC v    20  also receives the inverting input of the operational amplifier  18  and generates a correction voltage. The feedback transconductor  24  should have a high output impedance so that the input voltage V in  does not affect its output current. 
     FIG. 4 shows a schematic diagram of the error correction voltage circuit EC v    20  of FIG.  3 . The error correction voltage circuit EC v    20  is a floating output voltage amplifier  26  with a gain of about one. The error correction voltage circuit EC v    20  has a non-inverting input and two floating output voltage terminals. Since the floating output carries the capacitor current, the serial impedance of the floating output must be negligible compared to the impedance of capacitor  22 . 
     When the open loop gain of each operational amplifier  18  is insufficient to make the input voltage V in  negligible with respect to the output voltage V out , the correction voltage V c  maintains the polyphase filter&#39;s resonance frequency and response the same as the ideal polyphase filter  10 . Each correction voltage V c  has a magnitude and phase approximately equal to the input voltage V in . The error correction voltage circuit EC v    20  subtracts the correction voltage V c  from the capacitor voltage V cap  of Equation (1): 
     
       
         V cap =V out +V in −V c =V out +V in −V in =V out   (9) 
       
     
     Thus, the voltage V cap  across capacitor  22  is equal to output voltage V out  and does not require any extra current regardless of the magnitude and phase of the input voltage. 
     FIG. 5 shows a block diagram of another embodiment of the invention: a polyphase filter  10  having two outputs and two inputs, each input with an error correction current circuit EC 1    30 . The error correction current circuit EC 1    30  receives the input voltage of the corresponding damped integrator  12  and outputs a correction current to the input. Here, the capacitor voltage V cap  and output voltage V out  remain mismatched by the input voltage V in , but the extra current I e  required by the capacitors  22  due to the mismatch is supplied by the error correction current circuits EC 1    30 . 
     FIG. 6 shows a schematic diagram of an embodiment of the error correction current circuit EC 1    30  shown in FIG. 5. A buffer amplifier  32  has a non-inverting input and has an output connected to a transistor  38 . The transistor  38  also receives a direct current sink  34  in parallel with a load capacitor  36 . The transistor  38  has a negligible source resistance compared to the reactance of the load capacitor  36 . The transistor  38  has a correction current output. 
     The buffer amplifier  32  with a voltage gain G B  isolates its non-inverting input from the transistor  38 , the direct current sink  34 , and the load capacitor  36 . The buffer amplifier  32  receives the input voltage V in  and generates an output voltage that is sent to the transistor  38 . The transistor  38  applies this output voltage to the load capacitor  36 . The load capacitor  36  is chosen to have a capacitance C B  that matches the capacitance C of the capacitor  22  divided by the voltage gain G B  of the buffer amplifier  32 . This load capacitance C B  remains proportional to the capacitance C of capacitor  22  over temperature and IC process parameters since it may be formed on the same substrate. The larger the voltage gain G B  of the buffer amplifier  32  is, the smaller the load capacitance C B  can be. This is important for IC fabrication where the larger the capacitance of the load capacitor  36  is, the more substrate area it requires. The transistor  38  generates a correction current output. The correction current I c  can be expressed as: 
     
       
         I c =j(2πfC B )V in G B =j(2πfC/G B )V in G B =j(2πfC)V in   (10) 
       
     
     This correction current has a magnitude proportional to the frequency f of the input signal, which makes it equal to the extra current required by the capacitors  22  at all frequencies f. 
     FIG. 7 shows another embodiment of an error correction current circuit EC 1    30  shown in FIG. 5. A 90° phase shifter  40  receives the input voltage and generates a phase shifted voltage. The phase shifted voltage is received by an error correction transconductor  42 , which generates an error correction current. The transconductance g x  of the error correction transconductor  42  is chosen such that: 
     
       
         g x =2πf r C  (11) 
       
     
     Thus, a correction current from each error correction transconductor  42  is generated having a magnitude that is proportional to the product of the magnitude of the input voltage of the damped integrator  12 , the resonance frequency, and the capacitance C of capacitor  22  of the damped integrator  12 . The phase of the correction current leads the phase of the input voltage by approximately 90°. The correction current I c  can be expressed as: 
     
       
         I c =j(2πf r C)V in   (12) 
       
     
     The error correction current equals the extra current required by the capacitors  22  only at the resonance frequency f r , but is slightly off at frequencies different than the resonance frequency. This error amounts to only about a few percent deviation of the −3 dB bandwidth. 
     FIG. 8 shows another embodiment of the invention: a polyphase filter  10  having a first and second output, a first and second input, a correction inverter  46 , and a first and second error correction current circuit EC 2    44  each generating a correction current. The correction inverter  46  is connected to the second input and has a correction inverted output. The first error correction current circuit EC 2   44  has an input connected to the correction inverted output and outputs a correction current to the first input. The second error correction current circuit EC 2   44  has an input connected to the first input and outputs a correction current to the second input. 
     FIG. 9 shows a schematic diagram of the error correction current circuit EC 2    44  shown in FIG.  8 . The error correction current circuit EC 2    44  is a transconductor  48  with an input and output, having a transconductance according to Equation (11). This embodiment uses the 90° phase difference between the input voltages of the damped integrators  12   x  to generate the 90° phase shift shown in FIG.  7 . The correction inverter  46  ensures proper polarity. The transconductor  48  generates a correction current that has a magnitude proportional to the product of the magnitude of the input voltage from the opposing damped integrator  12 , the resonance frequency, and the capacitance of capacitor  22  of the damped integrator  12  and a phase leading the phase of the input voltage of the corresponding damped integrator  12  by approximately 90°. The correction current is generated according to Equation (12). 
     By supplying the correction voltage or correction current to the corresponding damped integrator  12 , the dependency of the polyphase filter  10  resonance frequency and response on the open loop gain of its operational amplifiers  18  are reduced or eliminated. The error correction reduces the dependency of the performance of the polyphase filter  10  on the IC process parameters and temperature. 
     The present invention is an elegant solution to achieve error correction in a polyphase filter  10 . There are many possible ways to configure and implement these types of error correction. Although voltage based and current based circuits were described, a combination of voltage and current circuits could be implemented. The circuit elements described may be substituted with equivalent devices. For instance, resistors, whose current is also a function of voltage, can replace the transconductors. The polyphase filter may have N inputs and N outputs and the error correction may be implemented for each of the N terminals as described above for N=2. The error correction circuits are particularly useful for polyphase filters formed on a single substrate of an IC, but works equally well for discrete polyphase filters.