Kelvin–Varley Divider

Kelvin-Varley Voltage Divider, named after its inventors William Thomson, 1st Baron Kelvin and Cromwell Fleetwood Varley, is an electronic circuit used to generate an output voltage as a precision ratio of an input voltage, with several decades of resolution.

The Kelvin Varley Voltage Divider may be thought of as being equivalent to a digital potentiometer, except that it has an additional, variable resistance in series with the wiper arm (see the circuit model figure below).

In effect, the Kelvin–Varley divider is an electromechanical precision digital-to-analog converter, and it is used for precision voltage measurements in calibration and metrology laboratories. It can achieve resolution, accuracy and linearity of 0.1 ppm. 

The conventional voltage divider - Kelvin divider - uses a tapped string of resistors connected in series. The fundamental disadvantage of this architecture is that resolution of 1 part in 1000 would require 1000 precision resistors.

To overcome this limitation, the Kelvin–Varley divider uses an iterated scheme whereby cascaded stages consisting of eleven precision resistors provide one decade of resolution per stage.

Cascading three stages, for example, therefore permits any division ratio from 0 to 1 in increments of 0.001 to be selected. Each stage of a Kelvin–Varley divider consists of a tapped string of equal value resistors. See Wikipedia ↗

In practice, if you want 10 steps you need 11 resistors. But by placing a second resistor divider of 11 resistors over two resistors of the tap of choice of the first, you can divide that step into 10 steps again. 

So you already have a resolution of 100 steps with 22 resistors. In essence, you can continue like this infinitely and make incredibly small but also very precise steps. The last string is, what is called, a normal Kelvin Divider.

Below is the basic circuit of a 4-Decade Kevin-Varley Voltage Divider (click on image to enlarge).

Note that in a typical KVD design, each stage provides a decade of resolution and requires only 11 precision resistors. Cascading 3 stages permits any division ratio from 0 to 1 in increments of 0.001 (i.e. resolution of 1 part in 1000).

Now see the three-terminal, Kelvin-Varley Voltage Divider KVD-500 with thumbwheel switches suitable for use in voltage and current dividers for calibration and linearity testing.

Well, comments and corrections to our understanding are always welcome. See you soon!