# Don’t forget the voltage coefficient of your resistors

**One of the lesser known parameters of a resistor, its voltage coefficient, is normally so minimal that it can safely be ignored. However in precision high voltage applications this error can become significant, writes Ian Moore**

Voltage coefficient, measured in ppm/V, is negative for most materials. Voltage coefficient is generally measured between 10% and full rated voltage.

Voltage coefficient (VC) is usually experienced with film resistors as the electrostatic field generated by the voltage tends to align polarised molecules in the resistance film, much in the same way as a capacitor dielectric.

Wirewound resistors or metal foil resistors tend not to suffer in the same way as their resistance elements are in a much stronger chemical structure. However these technologies tend not to go beyond 1M, and most high voltage applications need to go well beyond this resistance range.

VCs for high voltage resistors vary from immeasurable to over – 10ppm/V for some film resistors. A VC of -10ppm/V is equivalent to 0.001%/V or –1%/kV. This is unsatisfactory for precision applications where total error is maintained below 1%.

For precision requirements the voltage coefficient should not exceed -1 ppm/V ( -0.1%/kV). VC varies in direct proportion to the resistance value with a constant physical size, and resistance pattern, and varies in inverse portion for a constant value with increasing physical size.

In reality the VC will vary for every resistance value for a given resistor model. This is why you should be wary of high voltage resistor specification sheets that specify a single voltage co-efficient. The reason you should be wary is that unless this specification says it is the worst case VC for a given model, then it is usually the best VC for that model. This means that the VC of other resistance values in the series is probably worse or much worse.

The only way to be sure is to find out the VC for the given resistance value you need to use.

Most good resistor manufacturers will have data on the VC of their high voltage resistors, especially when these are designed to be used in precision voltage applications.

Many high voltage resistors are used in high voltage divider networks or sets, and this leads to another important parameter: ratio voltage coefficient (ratio VC).

This is the difference in VC effect between two or more resistors. With a high voltage divider the tap resistor seldom has more than I0V across it. With a VC of as much as 10ppm/V, the VC effect is to reduce the value of the tap resistor by 100ppm or only 0.01%.

Since the VC of the tap resistor is normally less than 10ppm/V the effect on the tap resistor can be ignored in most applications.

High voltage dividers can be separated into two basic categories for the discussion of VC effects; firstly where the input voltage to the divider remains reasonably fixed with variations generally less than 2%, and secondly where the input voltage varies over a wide range.

With fixed input dividers, the effect of the voltage coefficient is to reduce the value of the high voltage resistor by an amount equal to the product of the voltage coefficient and the applied voltage. This can increase the tap voltage above the ideal value.

This can be compensated for by varying the value of the high and/or low resistors. The amount of compensation is equivalent to the VC effect expressed as a percentage.

Where the VC effect is a significant part of the desired ratio tolerance, it is essential that the absolute tolerance specification of the divider resistors is wide enough to allow this compensation.

With wide input voltage variations, the VC has a more significant effect. Consider the case of a divider where the input voltage varies from 2kV to 8kV; a 6kV range. If the VC of the high voltage resistor is only 1ppm/V the ratio will vary by 0.6% over the range of operation.

While this may be satisfactory for some applications, it is unacceptable in applications that stipulate a 1% ratio tolerance which may also include the effects of TC over the operating range.

It is apparent in this second case that the VC must be reduced to keep its contribution to total performance within acceptable limits.

Ways of achieving this include the selection of a large physical size for the high voltage resistor or by using several elements in the high voltage section. The latter course of action may be implemented by putting two similar resistors in series with a VC of 0.5ppm/V each. The effective VC will then be only 0.25ppm/V.

In general, the VC of a series string of equal value resistors of a specified model can be approximated by dividing the individual resistor VC by the number of devices.

When measuring VC you have to be very careful to ensure that the voltage across the resistor does not lead to self-heating, which could confuse the measurement.

When working on a precision high voltage design check the VC of the resistance value you intend to use, it could save a great deal of time.

*Ian Moore is sales and marketing director at Rhopoint Components*

**Tags:**design, Passive, power, resistors