# Designing a Kelvin-Varley Potentiometer Part 1 of 3 – Resistors in Voltage Divider

There is a lot of potential in a potentiometer! This measuring instrument, also called a pot or electronic pot, uses a resistor with three terminals to form an adjustable voltage divider. It can be used in light switch dimmers, audio volume controls, fan speed controls, or even joysticks. The potentiometer’s defining feature is the wiper, which sweeps across the resistive element to produce the desired resistance.

In the next three blog posts, we will be designing a Kelvin-Varley potentiometer, which effectively serves as a digital-to-analog converter (DAC) suitable for high-precision laboratory applications. Let’s begin by reviewing resistors and see how they can be used as a voltage divider.

Resistance is Not Futile

Resistors are used in practically every circuit: oscillators, amplifiers, data converters, interfaces, RF transceivers, filters. Their roles are limitless: overcurrent protection, current setting, biasing for transistors, timer etc. Typical examples are current setting for LED (figure 1), gain setting for amplifier (figure 2), or current sensor for power metering system (figure 3).

Resistors come in many shapes and sizes (fig. 4). They can be made of metal or carbon, sold as wiring or sheets, or defined by values: resistance, precision, or the power they can carry (P = RI² or P = V²/R).

Figure 4 – A non-comprehensive collection of resistor types.

Resistance and Ohm’s Law

Resistance, symbol R and unit Ohm (Ω) (figure 5), is the simplest passive element one can find in electronics. It can be seen as the materialization of the linear behavior between I and V (figure 6): voltage across a resistance is proportional to the current passing through it. And the proportional coefficient defines the resistance as visible in the IV characteristics (figure 7).

Resistors in a Basic Voltage Divider

Some applications may call for resistances that are variable or adjustable. There are resistors for which the values can be changed, either by hand or with a tool. Others are fabricated to vary in response to physical parameters like temperature, light, pressure, etc.

When an intermediate voltage (α.Vref) must be derived from a source, it can be obtained via two resistors forming a voltage splitter circuit (figure 8). Multiple different voltages can be obtained by building several simple dividers or by putting multiple resistors in series.

Voltage Dividers as Potentiometers

Potentiometers are electronic devices that can give a portion of a voltage by moving their wiper (W) between the other two terminals of the resistor, A and B. When one measures Vout from the wiper position of a variable or tunable resistor, it creates a potentiometer or voltage divider. Potentiometers with their wiper positions are the compact forms of the voltage divider function. They can take many forms depending on desired precision, values, and power levels (figures 8 and 9).

Figure 10 - Electrical resistors

Such a potentiometer can be modelized by two smaller resistances in series R1 and R2 separated by the wiper position W (figure 12). The position determines the portion of those two resistors we call α, a value between 0% and 100%. This can be represented by the following equation:

P = R1 + R2
with R1 = α.P and R2 = (1-α).P

Figure 11 – Potentiometer with wiper, shown on the right in a fragmented view.

Limitations of the Voltage Divider Potentiometer

By connecting a reference voltage Vref on the two potentiometer terminals A and B, we collect a partial voltage (VW = α.Vref) that is proportional to the wiper position W (figure 13). This functionality is wanted in many cases, especially for electronic lab equipment where calibration is critical.

Figure 12 – Potentiometer with analog wiper

By varying α, one can theoretically obtain an infinite set of values between 0 and Vref. However, limits come very rapidly: the wiper is often a pure mechanical structure (spring, cursor contact) and the potentiometer resistance tolerance, sensitivity to ambient conditions, and non-linearities offer precision not better than few percentage points. That’s not even accounting for fast degradation with time and usage intensity.

The well-known two-resistor structure can often be found where portions of a reference voltage are required, and it has its uses. However, the instabilities caused by the mechanical wiper limit its use in many circuits requiring higher precision. The next post will explore how we can achieve greater precision with a Kelvin potentiometer. Finally, in the third post, we will see how to develop a Kelvin-Varley potentiometer suitable for the most demanding precision laboratory applications.