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 RT and RB (center figure) with
The pot terminals between R are shown connected to voltage sources at top, VT, and bottom, VB. (If the top and bottom terminals are connected to voltages in series with resistances, add the respective resistances to RT and RB.) The pot output terminal is loaded by resistance RL. The open-circuit (RL →
) divider transfer function is
where the voltage across the pot is
The pot resistance at the wiper port is the parallel combination of the two resistances;
with maximum RW = R/4. The wiper voltage without RL by superposition is thus
As T varies, VW varies with it linearly, where T is the rate of change (slope) of VW and VB is the offset.
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, VW, in series with the equivalent wiper resistance, RW, as shown in the figure above on the right. Solving this simple divider circuit for output voltage, VO, as a ratio of VW,
To unclutter the design formulas, let RL be some fraction or multiple, α, the loading factor of R;
Then substituting for RL ,
This voltage-divider transfer function is that of the loaded voltage normalized to the open-circuit pot divider voltage. Ideally, with no loading, VO = VW . As loading increases, the loaded-divider ratio decreases. As a function of T, the wiper position, it shows the extent to which VO departs from the ideal linear case of VW. Some curves of VO/VW as a function of T and loading parameter α are shown in the graph below, where
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 (RL = RW),
is about 20 %. For α = 2.5, it is about 9 % and for α = 25, is close to 1 %. The formula evaluated at maximum error, or T = 1/2, is
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 VO/VW of T, setting it equal to zero, and solving for T at which the minimum value occurs:
In conclusion, digipots with 250 positions (≈ 8 bits of resolution) require that RL be greater than 64 times the pot R value for less than one bit of error. For 10-turn analog pots with linear readouts having about 3 decades of resolution, loading should not exceed 256 x R for one bit of error. For single-turn analog pots, a loading of 25 x R will keep the error within a percent. Therefore, loading of a 10 kΩ pot must be no more than 250 kΩ for < 1 % compression error, 25 kΩ for < 10 %, and 10 kΩ for < 20 % error.