Abstract:
An analog multiplier circuit utilizes a dual feedback structure, in which two multiplier core sections can be progressively enabled or disabled to varying degrees, thereby providing variable gain while maintaining constant bandwidth. The multipliers are preferably controlled by a pair of ratiometric gain control signals in a manner that provides very accurate end-point gain. A summing device combines the outputs from the multipliers to generate a final output signal that is buffered and fed back to the multipliers through two separate feedback paths. The circuit can operate as a video keyer that linearly selects between two input signals applied to the multipliers. Alternatively, the circuit can be operated as a variable gain amplifier (two quadrant multiplier) when one of the two inputs is not used. Each of the multipliers is preferably implemented with sets of differential transistor pairs having complementary symmetry and a Class AB current conveyor input. The outputs of the multipliers can be coupled to a transimpedance node through current mirrors, thereby providing push-pull drive that is free of slew-rate limitations.

Description:
BACKGROUND 
     A prior art analog multiplier is shown in block diagram form in FIG.  1  and in more detailed schematic form in FIG.  2 . Referring to FIG. 1, the circuit includes a translinear multiplier core  10  which is driven by two identical input amplifiers  12  and  14 . The input amplifiers are transconductance (gm) stages which convert the input voltages V X  and V Y  into currents I X  and I Y . The multiplier core generates an output current I OUT  proportional to the product of V X  and V Y  divided by a scale factor SF:                I   OUT     =     (         V   X          V   Y       SF     )             (     Eq   .              1     )                                
     Referring FIG. 2, the translinear multiplier core is implemented as a pair of emitter-coupled transistors Q 3 , Q 4  which are preceded by a classic arrangement of pre-distortion diodes Q 1  and Q 2  that predistort the X input signal so as to compensate for the hyperbolic tangent (tanh) characteristic of the emitter-coupled pair, thereby extending the linear input range. For simplicity, the input amplifiers  12  and  14  are not shown in FIG.  2 . Instead, the “X” input is shown generically as (1−X)I X  and (1+X)I X , where X is a modulation factor that varies between −1 and +1. The “Y” input is shown as the current (1−Y)I Y , where Y varies between −1 and +1. 
     The circuit shown in FIGS. 1 and 2 suffers from several sources of error. Although these errors have been analyzed in detail in B. Gilbert, “A Precise four-quadrant multiplier with subnanosecond response,”  IEEE J. Solid State Circuits , vol. SC-3, pp. 365-373, December 1968, a few will be summarized here. First, any mismatch in the emitter area ratios of Q 1  through Q 4  causes even-order distortion. More specifically, if A 1  through A 4  are the emitter areas of Q 1  through Q 4 , respectively, then there is no distortion in the ideal case where:                    A   1       A   2       ·       A   4       A   3         =   1           (     Eq   .              2     )                                
     Any inaccuracy in area the area ratios, however, causes even-order distortion as shown in FIG.  3 . The solid line in FIG. 3 illustrates the ideal output characteristic of I OUT  for a given value of Y, as X is swept from −1 to +1, whereas the broken line shows the actual output characteristic when there is a mismatch in the emitter area ratios. 
     An additional source of error is the ohmic resistance associated with transistors Q 3  and Q 4 . This introduces odd-order distortion as shown in FIG. 4, where the solid line shows the ideal output characteristic, and the broken line shows the actual output characteristic caused by the ohmic resistances of the transistors. 
     Another source of error is the distortion introduced by the gm stages used to convert the input voltages to currents. FIG. 5 illustrates a typical gm stage used to generate the input currents to the translinear multiplier. The circuit of FIG. 5 is shown configured to generate the (1−Y)I Y  input to the translinear multiplier (the (1+Y)I Y  output from Q 6  is diverted to ground), but an identical circuit could also be used generate the “X” inputs as well. Curves  13 ,  15  and  17  in FIG. 6 illustrate the incremental gain of this gm stage for increasing values of the emitter resistor R Y , respectively. From FIG. 6, it is apparent that the curvature of the incremental gain near the gain axis can be reduced, and therefore, the linearity improved, by increasing the value of R Y . However, this also reduces the sensitivity of the gm stage and introduces a noise penalty because R Y  is a significant noise generator. Moreover, the non-linearity of this stage is never completely eliminated. 
     A well-known technique for reducing the distortion of a circuit element is to close a negative feedback path around the element. A prior art circuit that attempts to use feedback in the context of a multiplier is shown in block diagram form in FIG.  7  and in more detailed schematic form in FIG.  8 . Referring to FIG. 7, a third input amplifier  16  for receiving a “Z” input has been added to the circuit of FIG. 1. A high gain amplifier  18  nulls the output from the multiplier core and the output from the Z amplifier (attenuated by network  19 ) to produce the final output signal V OUT . The output signal is fed back to the Z amplifier through a feedback path including resistors R 1  and R 2 . 
     Because the X, Y, and Z input amplifiers  12 ,  14 , and  16  are identical, the circuit of FIGS. 7 and 8 reduces the distortion introduced by the X and Y amplifiers. This circuit does not, however, reduce the distortion introduced by the multiplier core because the feedback path is not closed around the multiplier core. If the final output signal V OUT  is fed back to the Y input amplifier in an effort to close the feedback loop around the multiplier core as shown in FIG. 9, the circuit ceases to function as a multiplier. Instead, it behaves as a divider with the Z input providing the numerator and the X input providing the denominator:                V   OUT     =       SF   ·     (       V     X   +       -     V     X   -         )         (       V     Z   -       -     V     Z   +         )               (     Eq   .              3     )                                
     A further problem with such a feedback arrangement is that the bandwidth is now proportional to the magnitude of the denominator as shown in FIG.  10 . That is, bandwidth is obtained at the expense of gain, as is well-known when utilizing negative feedback. 
     Another aspect of the multiplier circuits described above is that the gain is only well-defined at the minimum end of the gain range, but the maximum gain is not defined. That is, when the Y input is zero, the output is zero for any value of the X input, but as the Y input increases, the gain continues to increase indefinitely. There are applications, however, where a well-defined maximum gain is useful, as for example, with a video keyer. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a prior art multiplier. 
     FIG. 2 is a schematic diagram showing more details of the multiplier of FIG.  1 . 
     FIGS. 3 and 4 illustrate the effects of even and odd-order distortion in the circuit of FIGS. 1 and 2. 
     FIG. 5 is a schematic diagram of a prior art transconductance (gm) input stage used with the circuit of FIGS. 1 and 2. 
     FIG. 6 illustrates the incremental gain of the gm stage of FIG. 5 for several different values of emitter resistor. 
     FIG. 7 is a block diagram of another prior art multiplier. 
     FIG. 8 is a schematic diagram showing more details of the multiplier of FIG.  7 . 
     FIG. 9 is a block diagram show in the circuit of FIG. 7 reconfigured as a divider. 
     FIG. 10 illustrates the frequency response of the circuit of FIG.  9 . 
     FIG. 11 is a block diagram of a circuit in accordance with the present invention. 
     FIG. 12 illustrates the frequency response of the circuit of FIG.  11 . 
     FIG. 13 is a schematic diagram of another embodiment of a circuit in accordance with the present invention. 
     FIG. 14 is a schematic diagram of another embodiment of a circuit in accordance with the present invention. 
     FIGS. 15 and 16 are a schematic diagram of a gain control circuit in accordance with the present invention. 
    
    
     DETAILED DESCRIPTION 
     The present invention utilizes dual feedback multipliers to achieve various benefits including constant loop bandwidth, improved linearity, and precise end-point gain, depending on the actual implementation. The present invention, however, is not limited to any specific embodiment, and it should be apparent that, although the principles of the present invention will be described with reference to the example embodiments illustrated below, the present invention can be modified in arrangement and detail without departing from such principles. 
     FIG. 11 is a block diagram of an embodiment of a circuit in accordance with the present invention. The circuit of FIG. 11 includes two multiplier cells  20  and  22 , each having an output connected to a summing device  24 . The output from the summing device is applied to a high-gain amplifier  26  to generate the output signal V OUT . V OUT  is attenuated by the factor β and fed back to the inverting inputs of both multipliers as V F . The factor β is determined by the values of resistors R 3  and R 4  which form the feedback network. Separate feedback networks can be coupled between V OUT  and the V F  inputs of multiplier cells  20  and  22  to independently set the overall gain of each part of the system. A gain control signal X, which varies between a normalized range of one and zero, is applied to the first multiplier. A complementary signal 1−X is applied to the other multiplier. 
     The output from the first multiplier is X(V A −V F ), and the output from the second multiplier is (1−X)(V B −V F ). Assuming the amplifier  26  has a very high gain of −A 0 , the output signal V OUT  is given by:                V   OUT     =         A   0       1   +     β                   A   0                [       X                   V   A       -       (     1   -   X     )          V   B         ]               (     Eq   .              4     )                                
     where                  A   0       1   +     β                   A   0           →   1           (     Eq   .              5     )                                
     as A0→∞. Thus, the output is V A  when X=0, and the output is V B  when X=1. The gain can also be made very accurate in all cases, but especially so when one of the channels is fully selected—that is, when X is one or zero. The endpoint gain of the system is determined solely by the attenuation of the feedback paths. When one of the multipliers is filly on and the other is fully off, the gain of the active channel is defined by the feedback path because the multiplier that is fully on behaves as a differencing stage that simply responds to the difference between the input signal V A  and the feedback signal V F . Therefore, it is possible to achieve very accurate endpoint gain. 
     Another advantage of the circuit of FIG. 11 is that it provides constant bandwidth as shown in FIG.  12 . This is in contrast to the circuit of FIG. 9 in which the bandwidth depends on the value of the gain control signal X. With the circuit of FIG. 11, however, the weak feedback in the channel having a lower gain control signal is balanced by the stronger feedback in the other channel which has a higher gain control signal. Therefore, the overall loop gain and bandwidth remains constant. 
     If two separate input signals are applied to the V A  and V B  inputs, the circuit of FIG. 11 can operate as a keyer. For example, if two video signals are applied as the V A  and V B  and, the output signal V OUT  fades from one signal to the other as X is varied from zero to one. Alternatively, one of the inputs can be AC grounded, in which case the system functions as a variable gain amplifier (VGA) having constant loop gain and bandwidth. 
     FIG. 13 illustrates a more detailed embodiment of a circuit in accordance with the present invention. In the system of FIG. 13, the multiplier cores are formed from differential pairs of emitter-coupled transistors Q 1 , Q 2  and Q 3 , Q 4 , respectively. The multiplier cores Q 1 , Q 2  and Q 3 , Q 4  are driven by transconductance (gm) cells  28  and  30 , respectively. The differential pairs are connected in anti-phase, wherein one transistor in each pair is diverted to the positive power supply V P . Since the outputs from the multipliers are currents, the summing device can be implemented as a simple wire connection at node N 1 . Although not shown in FIG. 13, some type of load would be necessary to provide the current through Q 1  and Q 4 . Rather than utilizing separate gain control signals for each multiplier, a single gain control signal V X  is applied to the bases of both differential pairs. Since the outputs are added in anti-phase, the result is the same as if complementary gain control signals where applied to the two separate multipliers. 
     It is preferable for the gm cells have low distortion because when channel A is operating at low gain, there is very little feedback through that channel, so the distortion (in channel A) is determined primarily by the distortion of the gm cell in the A channel. 
     FIG. 14 shows a preferred embodiment of a circuit in accordance with the present invention. As with the circuit of FIG. 13, the circuit of FIG. 14 includes two multipliers that are serviced by two separate feedback paths. However, each of the multipliers in FIG. 14 includes a second, complementary multiplier core. Moreover, the multiplier cores are driven by current conveyors rather than gm cells. Specifically, the first multiplier in FIG. 14 includes a first multiplier core Q 1 , Q 2  and a second core Q 5 , Q 6  of the opposite polarity. Transistors Q 9  through Q 12  form a class AB current conveyor which is coupled between the common emitter nodes of the two multiplier cores. Transistors Q 11  and Q 12  are diode-connected and biased by currents I 1  and I 2 , respectively. Since the emitters of Q 11  and Q 12  are connected to ground at node N 1 , node NA behaves as a virtual ground, and Q 9  and Q 10  convey any input current at node NA to the common emitter nodes of cores Q 1 , Q 2  and Q 5 , Q 6 . 
     The second multiplier is identical to the first and includes first and second multiplier cores Q 3 , Q 4  and Q 7 , Q 8 , a current conveyor formed from Q 13  through Q 16 , and current sources I 3 , and I 4 . 
     The current conveyors in the first and second multipliers preferably include emitter degeneration resistors R 1  through R 8  which improve the linearity of the system as described in more detail below. Complementary gain control signals V XL  and V XU  are applied to the upper and lower cores as described below. The outputs of the NPN multiplier cores Q 1 , Q 2  and Q 3 , Q 4  are combined in anti-phase with one of the currents being diverted to the positive power supply V P , and the other driving a current mirror Q 17 , Q 18 . Likewise, the outputs of the PNP cores Q 5 , Q 6  and Q 7 , Q 8  are combined in anti-phase with one of the currents being diverted to the negative power supply V N , and the other driving current mirror Q 19 , Q 20 . The outputs from the current mirrors are combined at a high impedance summing node N 3  which is buffered by a unity gain amplifier  26  to provide the final output signal V OUT . The unity gain frequency is set by a compensation capacitor C 1  coupled between node N 3  and ground. Alternatively, cascode transistors could be used instead of the current mirrors. 
     Resistor R 9  forms a first feedback path from V OUT  to node NA, while R 10  forms the second feedback path from V OUT  to node NB. For RF applications, the inputs are preferably compatible with 50 ohm systems. By applying the V A  and V B  inputs to nodes NA and NB through resistors R 11  and R 12 , respectively, the resistors can be sized to provide 50 ohm inputs. By judicious selection of resistors R 1  through R 12 , third-order harmonic distortion in the current conveyors can be cancelled completely, while at the same time, the input impedance can be set to the desired value. 
     Turning first to the linearity issue, the third-order harmonic distortion of the current conveyor is cancelled when the resistances of R 1  through R 4  are approximately one-half the incremental resistance r e  of their corresponding transistors. The incremental resistance of a BJT transistor is given by r e =V T /I C  where V T  is the thermal voltage (V T ≈26 mV at 300° K) and I C  is the quiescent value of the collector current through the transistor. Thus, if Q 11  and Q 12  have a collector current of about 500μA, r e  is about 50 ohms, and R 3  and R 4  should be about 25 ohms. Transistors Q 9  and Q 10  preferably have twice the emitter areas of Q 11  and Q 12 , so their collector currents are about 1mA, and r e  is about 25 ohms. Thus, R 1  and R 2  should be about 12 ohms. 
     Turning next to the input impedance, if the feedback system had infinite gain, node NA would be a perfect virtual ground, and the input impedance could be set by simply setting R 1  to 50 ohms. However, the gain at high frequencies, which is set by the capacitor C 1  at node N 3 , is not infinite, so the resistances of R 1 , R 2 , and R 11  must be considered as well. Values of 45 ohms and 180 ohms for R 9  and R 11 , respectively, have been found to yield good results. 
     One advantage of the circuit of FIG. 13 is that it utilizes current mode feedback. Feedback is generally difficult to utilize at high frequencies because parasitic capacitances cause undesirable phase shift in voltage signals around the loop. In the circuit of FIG. 14, the only voltage mode signal is V OUT  which is immediately converted back into a current signal when fed back to nodes NA and NB. Thus, feedback can still be utilized at very high frequencies. 
     A further advantage of the circuit of FIG. 14 is that the complementary arrangement provides very high on-demand current to node N 3 , thereby eliminating slew rate limitations. A further benefit of the complementary arrangement is that, in principle, there is no limit to the amount of input current that can be applied because the current mirrors will continue to absorb the input current without causing the system to become nonlinear. 
     As with the circuits of FIGS. 11 and 13, the use of dual multipliers and dual feedback paths in the circuit of FIG. 14 allows one of the feedback paths to balance any deficit in the other feedback path, thereby providing constant loop gain. 
     FIGS. 15 and 16 illustrate a gain control circuit suitable for use with the circuit of FIG.  14 . The circuit of FIGS. 15 and 16 receives a single-ended gain control signal V G  and generates the two differential gain control signals V XU  and V XL  which drive the upper and lower multiplier cores, respectively. It provides linear-in-dB gain control, and it is also capable of imparting a temperature dependency to V XU  and V XL  to compensate for the temperature dependency of the multiplier cores. 
     Referring to FIG. 15, differential pair Q 21 , Q 22  is biased by a temperature stable current I Z ; that is, I Z  has a zero temperature coefficient. Differential pair Q 23 , Q 24  is biased by a current I P  that is proportional to absolute temperature (PTAT). The bases of Q 22  and Q 23  are connected together at node N 5  which receives an anchor voltage V R , while the bases of Q 21  and Q 24  are connected together at node N 4  and driven by operational amplifier (op amp)  32  which receives the gain control signal V G  at its noninverting input. The collector of Q 22  is grounded, and the collector of Q 21  is coupled to a resistor R 0  which generates the inverting input to the op amp  32 . Op amp  32  generates a voltage V GB  between N 4  and N 5  so as to maintain the voltage across R 0  at the same voltage as the gain control signal V G  The voltage V GB  is also applied to Q 23 , Q 24  which generates a pair of currents I GU  and I GD  which are proportional to absolute temperature. At this point, it would be possible to apply I GU  and I GD  to a pair of diode-connected transistors to generate the differential voltage V XL  which could be used to drive the lower multiplier cores Q 5 , Q 6  and Q 7 , Q 8  in FIG. 14, thereby providing linear gain control. However, the circuit of FIGS. 15 and 16 includes additional circuitry to provide linear-in-dB gain control in an accurate ratiometric manner. 
     The current I GD  is applied to an exponential generator including Q 27 -Q 30  and R 17 -R 18  which is similar in operation to that described in U.S. Pat. No. 5,572,166 titled Linear-in-Decibel Variable Gain Amplifier by the same inventor as the present invention. The current XI X  generated at the collector of Q 30  is PTAT and linear-in-dB with respect to V G . By including the additional transistor Q 31 , the exponential generator also functions as part of a ratiometric current generator similar to those described in U.S. patent application Ser. No. 09/466,050, filed Dec. 17, 1999 entitled “Interpolator Having Dual Transistor Ranks and Ratiometric Control” by the same inventor as the present application and which is incorporated by reference. That is, Q 31  and Q 32  split the current I 8  in a ratio that varies in response to V G . Transistor Q 35  forms a current mirror with Q 32  and generates the complementary current (1−X)I X . 
     Transistors Q 28  and Q 29  provide beta compensation for the exponential generator, while Q 33  and Q 34  provide beta compensation for the Q 32 , Q 35  current mirror. The current I GU  could simply be diverted to ground, but to improve accuracy, Q 25 , Q 26 , R 20 , R 21 , and I 5  are arranged in a similar manner to the corresponding components in the exponential generator so that collector voltages of Q 23  and Q 24  are equal. 
     The gain control signals V XL + and V XL − for the lower multiplier cores can now be taken directly from the bases of Q 35  and Q 30 , respectively, with capacitors C 4  and C 5  providing a very low impedance high frequency path. The gain control signals V XL + and V XL − are temperature compensated, ratiometric, and linear-in-dB with respect to V G . Thus, the circuit of FIG. 15 combines several useful functions to provide accurate control of the lower multiplier cores from a single gain control signal V G . 
     To drive the upper multiplier cores in FIG. 14, the circuit of FIG. 16 utilizes the ratiometric currents XI X  and (1−X)I X  from the circuit of FIG. 15 to generate the upper gain control signals V XU + and V XU −. Diode connected transistors Q 42  and Q 43  and current source I 9  provide an anchor voltage at node N 6  for grounded base transistors Q 40  and Q 41 . Since the bases of Q 40  and Q 41  are connected together, they generate a ΔV BE  signal V XU  that depends on the difference between the currents XI X  and (1−X)I X  which are provided by Q 36  and Q 37  with the help of beta compensation transistors Q 38  and Q 39 . Capacitors C 2  and C 3  provide firm AC grounds at V XU + and V XU −. 
     Having described and illustrated the principles of the invention in a preferred embodiment thereof, it should be apparent that the invention can be modified in arrangement and detail without departing from such principles. For example, certain signals in the embodiments described above are illustrated as voltages or currents. However, the present invention is not limited to specific voltage or current mode signals. As a further example, the circuit of FIG. 14 is operated from positive and negative supplies V P  and V N  with the nodes N 1  and N 2  connected to system ground. Alternatively, the circuit could be operated from a single supply voltage with nodes N 1  and N 2  held at a midpoint reference. 
     Although the gain control signals are preferably ratiometric (e.g., X and 1 −X), the present invention is not limited to circuits that utilize ratiometric gain control signals. Furthermore, the multiplier cores shown in FIGS. 13 and 14 are differential pairs, but other types of multipliers are contemplated by the present invention. The manner in which the multiplier cores are driven can also be modified. For Example, in the circuits of FIGS. 13 and 14, the gain control signals are applied to the bases of the differential pairs, while the input and feedback signals are used to control the bias current through the pair. However, the signals could be applied in the opposite manner. 
     Some of the many other modifications that are contemplated by the present invention are as follows: CMOS or other devices can be utilized instead of the BJT transistors illustrated above; input stages other than gm cells or current conveyers can be used; the feedback paths can any type of generalized feedback network rather than simple resistors or wire connections; the buffer amplifier can be realized with any amount of gain, and in some applications it might be possible to eliminate it completely. 
     I claim all modifications and variations coming within the spirit and scope of the following claims.