Patent Publication Number: US-6222418-B1

Title: Feed-forward compensation scheme for feedback circuits

Description:
TECHNICAL FIELD 
     This invention is related to an improved negative feedback op-amp circuit, such as a high performance integrator having an op-amp with low conductance for use in integrated circuits. 
     BACKGROUND OF THE INVENTION 
     Operational amplifiers in negative feedback arrangements are common circuit elements in analog integrated circuits. An ideal integrator circuit has infinite DC gain and a constant phase of −90°. However, due to non-idealities, these circuits have a finite gain and a phase shift which is different from −90° (henceforth called phase error). In particular, parasitic input and output capacitances introduce a extra poles in the transfer equation which produces unacceptable phase errors if the pole is too close to the unity gain frequency of the integrator. 
     This problem becomes particularly acute for high frequency applications which are implemented using MOS technologies. This is because the op-amps built using these technologies are usually single-stage circuits that are built with MOSFETS which have a limited transconductance. This limitation reduces the frequency of the parasitic pole. 
     A conventional feedback circuit is illustrated in FIGS. 1 a  and  1   b . The circuit  10  comprises an operational amplifier  12  having trans-conductance g m  and a transconductance amplifier  14  having trans-conductance G m . Ideally, the transconductance amplifier  14  sources (or sinks) an output current equal to G m V in . A transconductance amplifier  14  is used instead of the more conventional resistor to ensure adequate DC gains for the integrator, which is the cascaded gains of the transconductor and the opamp. A feedback impedance  16  of magnitude Y is connected between the inputs and outputs of the op-amp  12 . Also illustrated are the parasitic input and output capacitances C pi    18  and C po    20 , respectively. 
     The frequency domain transfer function for this circuit  10  can be written as:                  H   I          (   s   )       ≈       [     1     s        (     Y   /     G   m       )         ]          [       1   -     s        (     Y     g   m       )           1   +     s        (         C   po     +     C   pi         g   m       )           ]               (     Equ   .              1     )                         
     The first term in the equation represents the transfer function for an ideal op-amp  12 . The second term is a result of the non-ideal input and output capacitances combined with a non-infinite g m . Because of the difference in sign between the numerator and denominator of the non-ideal equation component and the non-infinite g m , the phase error terms of the pole and zero do not cancel and a net negative phase error is produced. The lower the value of g m , the more significant the error introduced by these terms, and thus the more significant the impact of the pole/zero on the performance of this circuit and other circuits which include a similar feedback circuit design. 
     Because of the feedback loop, the op-amp  12  must generate the same current as provided by the transconductance amplifier  14 . In addition, opamp  12  must also generate current to account for the current drawn by the parasitic capacitances. With reference to the current flows illustrated in FIG. 1 b , the op-amp  12  must source an output current I O =I F +I PO , where I PO  is the current flow through the parasitic output capacitance C PO    20 . Further, there is also an induced voltage V PI , at the input to the op-amp  12 , which produces an additional current I PI . Thus, I F =G m V IN +I PI . In other words, some of the output current is “stolen” to supply the parasitic input and output capacitances, This difference results in detriments, such as phase error, which impact the performance of the circuit. 
     Various techniques have been employed to reduce the errors caused by these non-idealities. In one variation, a resistance is introduced in series with the feedback impedance  16 . This provides some improvement at low frequencies, but is not particularly effective in high frequency situations. Alternative configurations make use of error detection devices which measure the output of the op-amp and adjust various circuit parameters by means of a control signal to compensate for the unwanted phase-shift. However, this technique can be cumbersome and requires relatively complex error detection and adaptive circuitry. 
     One particular solution for the case when the feedback impedance is a capacitor used for the purpose of Miller-compensating a transconductance stage has been implemented using a Multipath Miller Cancellation technique, such as described in U.S. Pat. No. 5,485,121 and discussed in R. Eschauzier and J. Huijsing, “An Operational Amplifier with Miller-Zero cancelation for RHP zero removal”, ESSCIRC&#39;93, European Solid-state Circuits Conference 1993, pp.122-125. This technique provides a parallel current path which is configured to bypass the Miller-compensated transductance stage and provide a current which compensates for the current directly passing through the Miller capacitor. However, the solution presented is restricted to Miller-compensated amplifiers and does not generally address the problems created by non-ideal amplifiers in negative feedback configurations with non-capacitive impedances. 
     An alternative solution is to introduce a unity-gain buffer  22  in the feedback loop between the output of the op-amp  12  and the impedance  16 , such as shown in FIG. 1 c . The purpose of the buffer  22  is to supply the feedback current G m V IN  instead of the op-amp  22  and thereby avoid introducing a voltage differential at the input of the op-amp  12  which results in a current drain into the parasitic input capacitance. However, the buffer  22  has a finite output impedance R O    24 . Thus, the transfer function of this circuit is:                  V   O       V   I       =       (     -       G   m     Y       )          (     1   -     YR   O       )               (     Equ   .              2     )                         
     The first term in Equation 2 is the ideal behavior. The second term represents the error which results from the non-ideality of the buffer  22 . In particular, the current G m V IN  produced by buffer  22  is forced to flow through the output impedance R O    24  as well as the feedback impedance  16 . Thus, there is a voltage drop in the feedback path which degrades the performance of the circuit. Although the buffer  22  could be designed to have a very small output impedance, such a buffer would require substantially more power than is generally available for high-frequency, low power devices. 
     Accordingly, it would be advantageous to provide a generalized op-amp feedback circuit structure with compensation for input and output capacitances. 
     It would also be advantageous to provide an improved unity-gain buffered feedback circuit with compensation for the output resistance of the feedback buffer. 
     SUMMARY OF THE INVENTION 
     According to a first aspect of the invention, a feed-forward compensated negative feedback circuit is provided which comprises an operational amplifier with a conductance gm and having an inverting and a non-inverting input and an output. A non-capacitive impedance element is connected between the output of the operational amplifier and its inverting input to form a negative feedback loop. The inverting input of the op-amp is driven with a first transconductance amplifier having conductance Gm and which produces an output current proportional to an input voltage. A feed-forward transconductance amplifier with a conductance substantially equal to Gm receives the input voltage and produces an inverted output current proportional to the input voltage. The feed-forward current is injected at the output of the operational amplifier. By providing at the output of the op-amp the amount of current it would be required to carry over the feedback loop, a voltage differential at the op-amp inputs is avoided, thus eliminating parasitic current flows across the parasitic input capacitance and thereby improving the circuits overall performance. 
     In a second embodiment of the invention, the feed-forward current is injected into a unity-gain buffered feedback circuit at a point between the impedance element and the unity-gain feedback buffer. By providing the feedback current from an external source, the buffer does not need to source any current through the impedance element, thus eliminating any drop in the buffer&#39;s output impedance since no current needs to flow through it. Preferably, in both embodiments, the transconductance amplifiers are substantially identical to each other. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing and other features of the present invention will be more readily apparent from the following detailed description and drawings of illustrative embodiments of the invention in which: 
     FIG. 1 a  is a schematic diagram of a conventional op-amp feedback circuit; 
     FIG. 1 b  is a schematic diagram illustrating the current flows in the circuit of FIG. 1 a;    
     FIG. 1 c  is a schematic diagram of conventional unity-gain buffered feedback circuit; 
     FIG. 2 is a schematic diagram of a feed-forward compensated negative feedback circuit according to a first embodiment of the invention; and 
     FIG. 3 is a schematic diagram of a feed-forward compensated negative feedback circuit according to a second embodiment of the invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Turning to FIG. 2, there is shown a schematic diagram of a feed-forward compensated negative feedback circuit according to a first embodiment of the invention. The circuit includes an operational amplifier  12  with conductance g m  and having an inverting and a non-inverting input and an output. An impedance element  16 , preferably a non-capacitive impedance, is connected between the output of the operational amplifier  12  and its inverting input. A first transconductance amplifier  14  with conductance G m  receives an input signal Vin and has an output connected to the inverting input of the op-amp  12 , which output sources or sinks a current of G m V IN . The parasitic input and output capacitances of the op-amp  12 , C pi    18  and C po    20 , respectively, are also illustrated. 
     According to the invention, a feed-forward transconductance amplifier  30  is provided which provides some, and preferably all of the feedback current which otherwise would have to be supplied by the op-amp  12 . As can be appreciated, the current sourced or sunk by transconductance amplifier  14  is equivalent to the ideal feedback current. This feedback current can be duplicated by configuring the feed-forward transconductance amplifier  30  to be substantially equivalent to transconductance amplifier  14 . 
     By injecting the required feedback current into the feedback loop, i.e., at the output of the op-amp  12 , the op-amp  12  does not need to supply or sink the feedback current. Provided that the output impedance is negligible, the op-amp does not need to source or sink any current (since the feedback current is supplied externally) and thus, the op-amp  12  is forced into a state where the input voltage differential is zero. Because the inputs of the op-amp are necessarily at the same voltage, no parasitic currents are generated across the parasitic input capacitance C pi . As a result, the circuit behaves as an ideal circuit having a transfer function V O /V I =−G m /Y, which is independent of the value of the input capacitance. 
     For a non-negligible output impedance, such as capacitance C po , the circuit performance is still significantly better than without the feed-forward current. Because the feedback current is supplied by the feed-forward transconductance amplifier  30 , the only current which must be source or sunk by the op-amp  12  is that which flows through the output impedance. Mathematically, the resulting feed-forward transfer function can be written as:                  H   FFI          (   s   )       ≈       [     1     s        (     Y   /     G   m       )         ]          [       1   -     s        (       C   pi       g   m       )           1   +     s        (         C   po     +     C   pi         g   m       )           ]               (     Equ   .              3     )                         
     If C po  is small and g m  is large, the error term approaches one, resulting in an ideal transfer function. (This result should be compared to the circuit of FIG.  1  and Equ. 1, where the error term does not cancel). 
     In a preferred embodiment, the op-amp  12  is a simple high-speed operational transconductance amplifier having a transconductance g m  which is substantially larger than the G m  of the input transconductance amplifiers  14 . Most preferably, g m  is at least 10-times greater than G m . 
     Turning to FIG. 3, there is shown is a schematic diagram of a feed-forward compensated negative feedback circuit according to a second embodiment of the invention. The circuit includes an operational amplifier  12  with trans-conductance g m , a negative feedback impedance  16  and a transconductance amplifier  14  with trans-conductance G m  connected to the input of the op-amp  18  as shown. A unity gain buffer  22  having output impedance R O    24  is connected between the output of the op-amp  12  and the impedance  16 . In conventional circuits, such a buffer may be introduced into the feedback loop to generate the feedback current such that the op-amp  12  does not need to generate it. However, when current flows, there is a voltage drop across the output impedance R O    24 , degrading the performance of the circuit. 
     To address this problem, the output of a feed-forward transconductance amplifier  30 , having a conductance substantially equal to G m  and receiving the same input signal as transconductance amplifier  14  is connected between the unity-gain buffer  22  and the impedance element  16 . Because the transconductance amplifiers  14  and  30  are substantially equal to each other and receive the same input, the current sourced or sunk by the feed-forward amplifier  30  equals the current sunk or sourced by the input transconductance amplifier  14 . As a result, the buffer  22  does not need to supply any current through the feedback impedance  16  and thus, there is no voltage drop across the output impedance  24  of the buffer  22 . 
     Ignoring any output impedance associated with the op-amp, the transfer function for the circuit of FIG. 3 can be written as:                  V   O       V   I       =     (     -       G   m     Y       )             (     Equ   .              4     )                         
     In other words, the addition of thefeed-forward current in the feedback path relieves the feedback buffer of the need to supply any current exceeding parasitic losses. Removing the buffer would result in a circuit similar to that in FIG.  2 . However, the addition of the buffer, as supplemented by the use of the injected feed-forward current, advantageously turns the feed-back path into a unidirectional path. As a result, 1−s term in the numerator of Equ. 1 is cancelled when the feed-forward transconductance and input transconductance are equal. Adding the buffer by itself does improve the circuit but requires additional power. Using the feedfoward technique described herein, where a feed forward current is injected at output of the feedback buffer, the feedback buffer does not need to supply the feedback buffer, but instead can simply serve as a unidirectional gateway. As a result, the buffer can be made smaller, thus providing an overall power advantage when compared to circuits which include the buffer but not feedforward. 
     As in the circuit of FIG. 2, in a preferred embodiment of the circuit of FIG. 3, the op-amp  12  is a simple high-speed operational transconductance amplifier having a transconductance g m  which is substantially larger than the G m  of the input transconductance amplifiers  14 . Most preferably, g m  is at least 10-times greater than G m . While a variety of impedances can be used in the feedback impedance  16  in the circuit of FIG. 3, in a particular embodiment, the impedance  16  is a capacitor. 
     While the invention has been particularly shown and described with reference to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in formn and details may be made therein without departing from the spirit and scope of the invention.