## Voltage Dividers

#### Resistors, Capacitors, RC combinations

A general method for measuring high voltages is to use a voltage divider composed of two impedances in series. The ratio of impedance is such that the voltage across one of the elements is some convenient fraction (like 1/1000) of the voltage across the combination.

[figure here]

To make the power consumption of the divider as low as possible, the impedances are quite large: 10's of Gigaohm (1e9 ohms) might be used for measuring megavolt level signals (resulting in a current of a few tens of microamps). In an ideal world, the impedances would be pure resistors. The physically large size and the high impedances of high voltage equipment means that parasitic inductances and capacitances  can be significant. Even at 60 Hz, a 10pF parasitic C has an impedance of 260 Megohm. 10 pF is roughly the capacitance of a 10 cm radius sphere (8" diameter). If the resistor string is 2 meters long, it's inductance is probably several microhenries, not particularly significant at power line frequencies, but a signficant concern at the higher frequencies encountered in fast impulse work. Measuring voltages or potentials with any AC component is greatly affected by these parasitic reactances, and much of high quality divider design goes to minimizing or compensating their effect.

[figure here]

For making AC measurements, purely capacitive dividers are popular. A fairly small capacitor forms the upper arm of the divider, and a larger, lower voltage capacitor forms the bottom. High pressure gas capacitors are popular for the high voltage arm. A high pressure gas capacitor can provide a reasonable capacitance with a high voltage rating in a physically small package, which is important for measurements on fast transients.

#### Thermal effects

Small as the current is through most high value resistive dividers, it may consititute a significant amount of power, which goes into heating yup the resistive elements. This heating will cause a change in the value of the resistor, changing the overall ratio of the divider.

Classic standards work, as reported in Craggs & Meek, used maganin resistors. Manganin has an extremely low temperature coefficient of resistance (1.5 ppm/deg C) (see Resistance Wire Table) compared to Nichrome ( 13 ppm) or Copper ( ppm).

Immersing the entire resistive divider in oil or rapidly circulating dielectric gas (e.g. SF6 or dry air) also ensures that all components are at the same temperature, so that, while the absolute values might change, the ratios will remain constant, for DC at least. Resistance value changes will change the parasitic RC time constants, changing the frequency response.

#### Voltage Coefficient of Resistance

Some resistive materials show a change in the resistivity as a function of the impressed electric field strength. This would manifest itself as a change in the resistance as the voltage changes. A long string of individual resistors, each run at a relatively low voltage, should not show this effect.

#### Safety Considerations

In the classic series resistor method for measuring voltage, the high value resistor string is in series with a sensistive current measuring meter (typically a d'Arsonval meter). If the resistor were to fail shorted, or flash over, the high voltage would appear across the meter, possibly producing a personnel safety hazard, as well as destroying the meter. A simple safety precaution is a spark gap across the meter, set for a kilovolt or so, that will arc over in case of a series resistor failure.

Another means is to measure current through the high value resistor by measuring the voltage across a resistor with a high impedance meter.

Good, reliable ground connections for the low end of the divider are essential. Consider the circuit shown below:

[figure here]

If the ground connection at A is broken, the full high voltage will appear on the measuring device, limited by the inevitable internal arcing or failure. Fortunately, the power will most likely be limited by the high series resistance of the divider.

Physical construction of voltage dividers

Copyright 1998, Jim Lux / vdiv.htm / 8 March 1998 / Back to HV Home / Back to home page / Mail to Jim