What signal conditioning circuit could possibly be easier or more straightforward to design than a dual-channel dc amplifier with a common tracking-gain control? Of course, the obvious way to realize this trivial function is by simply wiring up two identical amplifier channels and controlling the gain of each with matching sections of a dual-element, ganged potentiometer.
Unfortunately, a definite rub lurks in this apparent solution. Ganged pots, particularly the precision multiturn variety, are pricey and often hard-to-find, long-lead-time specialty components. This circuit offers an alternative. It avoids the liabilities of dual pots by controlling the gain of both channels with just one ordinary single-section pot, P (see the figure).
The scheme hinges on the arrangement of P with its wiper terminal grounded. This setup creates two mechanically linked but electrically independent variable resistances: KR and (1 - K)R. K's value represents P's wiper's position. Therefore, it goes from 0 to 1 as P is rotated from full counterclockwise (zero gain) to full clockwise (maximum gain). R is P's total element resistance. The net result for both op amps A1 and A3 is a transfer function linear in K:
VOUT/VIN = K(1 + RG/R) = KG
With the example component values shown, G = 11. Yet virtually any gain factor greater than unity can be accommodated by a suitable selection of resistors and op amps.
Why this formula applies to A1 is easy enough to see. Positive feedback from A1's output to P's CCW terminal results in constant current drive to the pot, given by I = V1/R. Therefore, the signal at A1's noninverting input is equal to I x K x R = (V1/R) x K x R = K x V1. This voltage is boosted by A1's noninverting gain of G = 1 + RG/R to produce overall gain as a function of K given by VOUT/VIN = KG.
The story behind A3's operation is a bit more tangled. Surrounding A2 and P's CW terminal is a topology that produces a signal of V2(1 - K)(1 + R/RG) at A2's output. After attenuation by A3's feedback network to V2(1 - K), this voltage appears at A3's inverting input. So the differential voltage seen by A3 is V2 - V2(1 - K) = V2 x K. When amplified by A3's gain of (1 + RG/R) = G, this voltage becomes V2 x K x G. A3's gain, accordingly, is equal to KG, just like A1's.
For applications that are particularly sensitive to a non-zero gain error at K = 0, an optional null-trimmer (RZ) may be used to accommodate tolerances in the various resistance ratios. This ensures that A1's and A3's gains will simultaneously vanish when P hits its full CCW rotation.
Component selection criteria for potentiometer P include a low resistance-element temperature coefficient (for good gain stability) and a low wiper resistance (for low interchannel crosstalk). Fortunately, potentiometers possessing the quality (and price points) sufficient that make all of this trouble worthwhile generally have excellent characteristics for these two design parameters.
Application of this circuit to manual gain control in stereo/audio and similar contexts where P is a mechanical pot is obvious. But the idea also has utility when P is an electronic digitally controlled potentiometer like the Xicor X9xxx series. For example, P might form the basis of an automatic gain-control loop in applications like an ALC for stereo/audio recording. To provide ALC loop feedback, one channel's signal magnitude, or the sum or the greater of both channels' average signal magnitudes would be compared to a setpoint. The signal would drive both channels to the same tracking/balanced gain.
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