Kelvin-Varley divider

The Kelvin-Varley voltage divider, named after its inventors William Thomson, 1st Baron Kelvin and Cromwell Fleetwood Varley, is an electronic circuit used to divide voltages, i.e. to generate an output voltage as a precision ratio of an input voltage, with several decades of resolution. In effect, the Kelvin–Varley divider is an electromechanical precision digital-to-analog converter.

The circuit is used for precision voltage measurements in calibration and metrology laboratories. It can achieve resolution, accuracy and linearity of 0.1 ppm (1 in 10 million).

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. Let the value of each resistor in the i-th stage be R_i Ω. For a decade stage, there will be eleven resistors. Two of those resistors will be bridged by the following stage, and the following stage is designed to have an input impedance of 2 R_i. That design choice makes the effective resistance of the bridged portion to be R_i. The resulting input impedance of the i-th stage will be 10 R_i.

In the simple Kelvin-Varley decade design, the resistance of each stage decreases by a factor of 5: R_i+1 = R_i / 5. The first stage might use 10 kΩ resistors, the second stage 2 kΩ, the third stage 400 Ω, the fourth stage 80 Ω, and the fifth stage 16 Ω.

The full precision of the circuit can only be realized with no output current flowing, since the output's effective source resistance is variable. Kelvin–Varley dividers are therefore usually applied in conjunction with a null detector to compare their output voltage against a known voltage standard, e.g. a Weston cell (which must also be used without drawing current from it).

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