Voltage Coefficient of Resistance, VCR

The voltage coefficient of resistance is the amount of resistance change a resistor exhibits with a change in voltage.

Resistance Tutorial Includes:
What is resistance     Ohms Law     Ohmic & Non-Ohmic conductors     Resistance of filament lamp     Resistivity     Resistivity table for common materials     Resistance temperature coefficient     Voltage coefficient of resistance, VCR     Electrical conductivity     Series & parallel resistors     Parallel resistors table    

It is an often forgotten or ignored fact that resistance can change their values with a change in resistance. Like many other electronic components, there can be changes with the voltage applied.

Often the voltage coefficient of resistance, VCR is masked out by the temperature coefficient of resistance - as the voltage increases, so the current increases and hence the power dissipated and this brings a rise in temperature that changes the resistance.

Selection of various types of fixed leaded resistors - these electronic components are used in virtually all electronic circuit designs
Selection of fixed leaded resistors or various types

However, even if the temperature remains constant, resistors will change their resistance marginally, and some more than others.

The resistor voltage coefficient is not a parameter that is widely seen and used. As resistors are seen as being Ohmic electronic components, it is often not realised that the resistance of a resistor can vary with voltage.

While the voltage coefficient of resistance is masked out by the temperature coefficient for most circuit designs, there are some instances where the voltage coefficient of resistance can be of great importance.

What is resistor voltage coefficient

As the name or title of this parameter indicates, it is the change in resistance that is caused by a change in voltage.

it is worth giving a more exact definition of the voltage coefficient of resistance:

Voltage Coefficient of Resistance, VCR, definition:

The voltage coefficient of resistance is defined as as the change in resistance that results from a change in voltage when all other factors that would change the resistance have been removed. This change is often specified in terms of parts per million per volt or sometimes as a percentage change per volt.

The voltage coefficient of resistance formula can be expressed very easily:

VCR = R 2 - R 1 R 1 ( V 2 - V 1 )   10 6

Where:
    VCR = voltage coefficient of resistance in parts per million per volt (ppm/V)
    R1 = resistance at reference voltage
    R2 = resistance at test voltage
    V1 = reference voltage
    V2 = test voltage

Using the voltage coefficient of resistance formula it is very easy to calculate the VCR from test measurements. Simply substituting known values into the formula will give the VCR for the test conditions.

The voltage coefficient of resistance is normally ignored for many basic electronic design and electrical calculations and formulas. This is because VCR is masked out by the temperature coefficient which will cause resistance changes due to increased heat dissipation and temperature rise as the voltage increases. Nevertheless, the voltage coefficient of resistance is important in some electronic circuit designs and other situations.

it is found that the resistance of a resistor changes marginally as a result of only the voltage. The resistance reduces in value slightly in a non-linear fashion.

The changes of resistance with voltage for the resistors occurs because as the voltage increases there are parasitic impedance changes in the resistor.

The issue of these resistance changes with voltage occurs in all resistors to some degree. It occurs for a variety of reasons which include:

  • Microcracks from composite materials or trimming:   It is found that composite materials have a high voltage coefficient of resistance. Also, the manufacture of many resistors, particularly close tolerance ones uses mechanical or laser trimming of the resistive element occurs to provide exactly the right value.

    Both of these aspects can leave junctions and micro-cracks in the material used in the resistor which give rise to parasitic impedance changes with voltage, etc as well as giving some increased noise level.

  • Size and geometry:   The size and geometry of a resistor has an effect on the voltage coefficient of resistance. It is found that increasing the length also increases the level of resistance change.

  • Resistor termination :   Different resistor terminations can have an effect on the VCR.

It is found that most resistors have a negative voltage coefficient of resistance, meaning that the resistance will fall if high level voltages are applied.

However some resistors can exhibit a positive voltage coefficient of resistance.

The voltage coefficient varies with different resistive materials and it is very much higher for materials that have a granular structure. Carbon composition resistors and cermet film resistors are particularly prone to having high levels of voltage coefficient of resistance.

The reason for this is that tunnelling occurs across the microscopic gaps that have been created between conductive particles or areas. The actual prediction of the voltage coefficient can be difficult to predict because it is dependent upon factors including the particle size, the electron emission coefficients of the materials, etc.

End connections can also have an impact on the voltage coefficient of resistance as there are minute cracks and gaps between the materials in the junction.

As might be gathered resistors that use resistance wire, i.e. wire-wound resistors have very low temperature coefficients of resistance.

Wirewound resistor basic construction
Wire wound resistors have a very low voltage coefficient of resistance

Wire wound resistors should be used where a very low temperature coefficient of resistance is required, but this must be balanced against the fact that these resistors are not available in very high values.

Where is voltage coefficient of resistance important

The resistance voltage coefficient may not be particularly important in standard electronic circuit designs where large margins are generally allowable in the resistance of resistors. A logic pull up resistor could work equally well if it was 1kΩ or 10kΩ, and there are many other similar examples.

However where values are critical and voltages rise, then the resistance voltage coefficient can be particularly important.

If a steady voltage is applied to a resistor then the resistance will change as a result of the temperature rise caused by the power dissipated within it, and also as a result of the applied voltage. For most standard electronics designs where a relatively constant voltage is applied, the change in resistance caused by the change in temperature will mask out any changes resulting from the applied voltage.

However, if short pulses are applied to the resistor, the average power dissipation will be very low and the resistance changes will result from the applied voltage. They will also be limited to the time when the voltage is applied.

It is found that if high voltage, short pulses are applied to low value resistors, then the change in resistance can be quite appreciable. This can affect measurements that might need to be mde or the operation of some electronic circuits.



Although the resistor voltage coefficient can be ignored for many everyday electronics design calculations, it needs to be taken into account in some circumstances where it can be a major factor. High voltage circuit designs, where there are large voltage changes can present problems with the VCR in some situations. Understanding what the voltage coefficient of resistance is and how it can affect a circuit, along with looking for this parameter in the data sheets for the relevant electronic components will ensure that the voltage coefficient of resistance does not unduly affect any electronic circuit design.

Ian Poole   Written by Ian Poole .
  Experienced electronics engineer and author.




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