# Designing a Kelvin-Varley Potentiometer Part 2 of 3 – Kelvin Potentiometer

We have seen in the previous blog how basic resistors, with their variable, adjustable, or tunable forms, can be used to build a voltage divider. Adjustable voltage divider or potentiometers (pots) are used in various functions such as dimmable light switches, audio controls, and more.

In this second part, we go further to get better precision structures in the form of a Kelvin potentiometer, which is a sort of multi-wipers resistor divider. It is not yet the final Kelvin-Varley divider (KVD), but we are one step closer.

Image 1: Kelvin potentiometer structure using a fixed-position wiper

## Kelvin Potentiometer: Tapped String Resistors in Series

The wiper being the weakest element in term of precision and stability, one possible solution is to replace the wiper with fixed contacts by creating a Kelvin potentiometer. The variation is assured by partitioning the original resistance into several equivalent smaller portions put in series, also called tapped string resistors.

If, for example, one needs to get portions of a reference voltage in increments of 20%, we can use a string of five identical resistances and connectors between each of them (fig. 1). What we did is just “digitalize” the positions so that α is limited to six possible values: 0%, 20%, 40%, 60%, 80% and 100%. This eliminates the inaccuracy of the mechanical wiper positioning and instability by replacing it with fixed (and more stable) connections.

Figure 1 – Kelvin potentiometer, or tapped string resistors in series

But is that change sufficient and satisfying? Obviously not. The number of possible values for A is limited by the number of resistors in the string. To get a variability of 1% increments, you would need to put a string of 100 resistors in series. It’s still feasible, but what about a 0.1% or even 0.01% step? You would need 10,000 or 100,000 resistors with that same amount of contact points! There must be a smarter way.

## Improving the Resolution from 10% to 1%

Let’s start with a 10% precision Kelvin voltage divider with a 10-tapped resistors string (fig. 2). This structure allows you to get variable resistance in increments of 10%, but you will not be able to have VW = 67% of Vref, for example.

Figure 2 – 10% taps Kelvin potentiometer

Figure 3 – 10% taps + 1% taps, but with disturbance

The trick is to add another column of 10-tap dividers connected between two consecutive 10% taps. Since the first column spacing is 10% of Vref, the second column will be spaced by 1% at each secondary tap. By summing the initial 10% tap voltage to the second tap, we can obtain a resolution of two digits instead of only one—not just 10% and 20%, but also 11%, 12%, and so forth (fig. 3).

## Isolation Between Resistor Strings

Problem solved? Well, not quite. The second column of resistors is connected in parallel with a resistor in the first column, and this corrupts the 10% ratio initially established—that is, unless the second column string is made by resistors with values much larger than the ones in the first column. We must find a way to connect the second string without affecting the first column (both in total resistance and the resistance between any two taps in the string).

Figure 4 – Isolation buffer

To do this, we can interface buffers between connectors of the first and second strings. Then, we connect the outputs of the two columns in series to get a final output voltage with 1% precision. The buffer can be an op-amp mounted as seen in Fig. 4. A perfect buffer offers infinite impedance on the input and zero impedance on the output. We now have a working voltage divider that offers a selectable resolution with 1% steps without needing 100 resistors (Fig. 5).

Figure 5 – Enhanced Kelvin potentiometer

## Increasing Precision

The precision can be enhanced further by adding a third column connected to the second in the same way as the second was connected to the first. And so on with a fourth column and beyond (Fig. 6).

Figure 6 – Each column of resistors adds another decimal point of precision

VW can be determined with the equation:

VW/VREF = α = 0.xyzw

Thus the example in Fig. 6 achieves a resolution of 10-4 (100 ppm). However, while a string of tapped resistors can improve on the precision and repeatability of using a wiper alone, this solution is still not practical. The isolation buffers on the wipers are active components mainly comprised of amplifiers, like op-amps, which are additional sources of errors, non-linearities and cost.

A smarter solution would achieve such accuracy without the buffers. That is exactly what we’ll develop with the Kelvin-Varley structure in the third part of this series.

Example circuit diagram of a Kelvin potentiometer from MAX5160 and MAX5161

• The AD569 actually included an innovative patent that got around errors caused by offset in the buffer amplifiers. From the datasheet:

"Buffer amplifiers A1 and A2 leap-frog up the first string to pre-
serve monotonicity at the segment boundaries. For example,
when increasing the digital code from 00FFH to 0100H , (the first
segment boundary), A1 remains connected to the same tap on
the first resistor, while A2 jumps over it and is connected to the
tap which becomes the top of the next segment. This design
guarantees monotonicity even if the amplifiers have offset volt-
ages. In fact, amplifier offset only contributes to integral linear-
ity error."

Doug

• Thanks  ! Glad to see ADI had such structure covered in the mid 1980s! In many electronic labs, KV is still present and in use!

• A few of us who were around back in the mid 1980's will recall that Analog Devices introduced the AD569 16 bit DAC (https://www.analog.com/media/en/technical-documentation/data-sheets/AD569.pdf) before 1984 or about 40 years ago. It basically implemented figure 5 above using two 8 bit (256 tap) resistor strings. A major accomplishment  for 1984.

Doug