Consider the need to vary two voltages, V1 and V2, by an equal percentage of their ranges (V1_{MAX }- V1_{MIN}) and (V2_{MAX }- V2_{MIN}), with V1_{MAX}, V1_{MIN}, V2_{MAX}, and V2_{MIN} independent of each other. The first idea that comes to mind is to use ganged potentiometers *(Fig. 1)*. However, ganged potentiometers are notorious for producing tracking errors as high as 5%. Here's a simple method that uses a single potentiometer to generate two or more tracking voltages with an accuracy of better than 0.5% of range *(Fig. 2)*.

The circuit around IC1a is a square-wave oscillator. Triangular waves across C1 are applied to comparator IC1b. Potentiometer P1 varies the duty cycle of the pulses at the comparator output from 0% to 100%. Transistor Q1 and the multiplexer switch IC2 convert the comparator output into pulses with well defined edges. These pulses are applied to the digital control inputs of the analog multiplexer that receives V1_{MAX}, V1_{MIN}, V2_{MAX}, and V2_{MIN} as the analog inputs. The multiplexer outputs, which are integrated by components R7-C2 and R8-C3, are buffered by IC1c and IC1d.

When P1 varies the duty cycle from η 1 to η 2, the following changes in V1 and V2 occur:

V1 = (η 1 - η 2)(V1_{MAX }- V1_{MIN})

V2 = (η 1 - η 2)(V2_{MAX }- V2_{MIN})

The oscillator's frequency is optimized to be about 5 kHz. This frequency is high enough to produce negligible ripple in the integrator output. At the same time, the frequency is low enough to ensure that rise and fall times of the pulses are negligible compared to the pulse repetition period. Note that capacitors C2 and C3 must be low-leakage types. This idea can be extended to generate more tracking voltages by using additional multiplexer switches, integrators, and buffers.