Electronic Design

# Negative Resistance Nulls Potentiometer's Wiper Resistance

While almost always called "potentiometers" (which are technically defined as three-terminal variable voltage dividers), many "pots" actually end up being used as variable resistors (rheostats) instead. When used as a variable resistor, all pots—whether electromechanical or electronic—suffer from the parasitic error of "wiper resistance."

In electromechanical pots, wiper resistance arises because the point of contact between the wiper and the resistance element inevitably makes an undesirable nonzero contribution ("RW" in the figure) to the total resistance. The effective resistance of the pot can therefore never be adjusted to zero, but instead has a minimum value of RW. Any nonzero wiper current (IW) therefore produces a parasitic nonzero wiper voltage: VW = IWRW. A similar effect plagues electronic (i.e., digitally controlled) potentiometers (DCPs). DCPs escape the contact-resistance problems of the mechanical pot but must contend instead with the relatively large RON resistances (usually tens of ohms) of the FET switches in the multiplexed resistor array that substitute for the mechanical pot's wiper. For these DCPs, VW = IWRON.

An earlier IFD ("Active Cancellation of Potentiometer Wiper Resistance," Electronic Design, June 14, 1999, p. 104) presented one idea for active cancellation of wiper resistance. Although effective when it can be used, the method suggested in "Active..." requires that one termination of the pot resistance element be available as a VW sense point. It is therefore not available for use by the application circuit. This requirement makes the "Active..." approach incompatible with applications in which both ends of the resistance element are needed.

By contrast, the wiper-resistance cancellation method presented here doesn't suffer from this limitation (see the figure). This leaves both terminals of the resistance element available for use in the application circuit. This idea assumes that RW can be approximated by a separate cancellation resistor RC. To the extent this assumption is correct and RC = RW, then IC = -IW and the voltage developed at the noninverting op-amp input = VC = ICRC = -IWRW.

If ideal operation of the op amp can be assumed (i.e., negligible offset and gain errors), then VC will appear at both op-amp inputs, driving the right-hand end of RW to VC. This, in turn, will pull the left-hand end of RW to VW — VC = VW — VW = 0, thus canceling the effects of RW.

Of course, there's no such thing as a "free lunch," and the RW cancellation effect will be no better than the accuracy of the ap-proximation RC = RW. In some cases, trickery can be employed to improve the guess for the value of RC. For example, if the pot to be compensated is one element of a multisection DCP integrated circuit in which one of the elements can be dedicated for duty as an RC (RW = RON) reference, then the accuracy of the RC/RW compensation may be very good indeed. This effect is due to the inherently good tracking of elements in most monolithic chips. However, in other scenarios (e.g., mechanical pots and digital pots in which no internal RC reference is available), the compensation may be less accurate and the cancellation will therefore be less than perfect. Nevertheless, a useful improvement in accuracy in the relationship of resistance-to-pot-setting may still be attainable.