Both analog potentiometers and digipots have output or wiper terminals that drive load resistances. How does potentiometer loading affect output linearity? How light must the loading be to achieve a desired linearity? This article addresses these questions.

The circuit of either an analog potentiometer (or *pot*, for short) or a digipot is basically the same, as shown below (left figure) using an analog pot symbol. The analog pot voltage-divider attenuation, *T*, is varied mechanically while the digipot receives a digital input value that selects where in the pot resistance the output terminal - the digital wiper - is to be attached, using many analog switches for selection.

The wiper of the pot - the arrow in the symbol - moves across a constant resistance between the top and bottom terminals, the pot resistance value of *R*. Moving the wiper causes the divider to change *T* by apportioning *R* among *R _{T}* and

The pot terminals between *R* are shown connected to voltage sources at top, *V _{T}*, and bottom,

where the voltage across the pot is

The pot resistance at the wiper port is the parallel combination of the two resistances;

with maximum *R _{W}* =

As *T* varies, *V _{W}* varies with it linearly, where

Now consider the case where the pot is loaded. Then the circuit can be Thevenized so that the pot wiper port is made equivalent to an open-circuit voltage source, *V _{W}*, in series with the equivalent wiper resistance,

To unclutter the design formulas, let *R _{L}* be some fraction or multiple,

Then substituting for *R _{L}* ,

This voltage-divider transfer function is that of the loaded voltage normalized to the open-circuit pot divider voltage. Ideally, with no loading, *V _{O}* =

Two observations can be made of this graph. First, the curves compress to a lower than ideal value, with maximum departure at midscale, *T* = 1/2. Second, as loading increases, the compression flattens, with steeper sides at the extremes of the pot range, and closer to constant in the midrange. *Compression error* is

For *α* = 1 (*R _{L}* =

Then maximum compression error is

Thus, to achieve a given maximum error as expressed by compression, and in bits, the following table gives some values, where the conversion of ε to number of bits, *n*, of accuracy is

Then for *n* bits of maximum error,

The maximum error at *T* = 1/2 can be verified by taking the derivative of *V _{O}*/

In conclusion, digipots with 250 positions (≈ 8 bits of resolution) require that *R _{L}* be greater than 64 times the pot

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