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It is important to choose a low VCR value for high voltage resistors used in precision applications. These include measurement systems, divider circuits, power supply control circuits and high stability power supplies.

In this post, we define VCR and discuss the various issues caused by a high VCR in precision applications. VCR is a complex issue regardless of the resistor technology and there are no simple solutions. We cover the most common methods thick film resistor manufacturers use to try to limit the impact of VCR in high voltage applications.

What is VCR?

Voltage Coefficient of Resistance (VCR) is defined as the change in resistance of a resistor device with respect to a given change in the applied voltage over a specified voltage range.

VCR is measured in parts per million per volt. For high-value resistors, the higher the VCR value the higher the decrease in resistance for a given voltage increase.

VCR is generally negative for 10 KOhm (and above) resistor inks, but positive for ink values of 1 KOhms and below. It is predictable for steady-state voltages. This applies regardless of the voltage range.

VCR is an issue when there is a voltage change over time (dV/dt). The faster the voltage changes, and the larger the voltage changes are, the larger the VCR effect

For high voltage thick film resistor devices VCR can range from 5ppm for precision devices to low hundreds of parts per million depending. The VCR depends on the construction (see below) and the application.

However, VCR specific data is rarely available on manufacturers datasheets. If it is available it is given in respect to very limited and precise conditions. VCR is either not measured or only measured on a very limited set of devices.

VCR Issues In Specialist Applications

A perfect resistor will not vary in resistance with any change in operating voltage. Unfortunately, the perfect resistor does not exist.

During the thick film high voltage resistor manufacturing process a resistive film is printed onto a substrate. The assembly is then subjected to a high-temperature firing process. During firing metal oxides spheres within the film combine to form the resistor track. A glassy frit melts to hold the resistor material in place.

The quantity and proximity of the metal oxide spheres determine the resistance. As voltage is increased new conductive paths through the oxide spheres and glass frit can form and reduce the resistance.

In many applications, a change in resistance measured in parts per million per volt is not a concern. But in high voltage applications where resistor stability is important VCR must be minimised.

A Low VCR – Potential Solutions

The selection of resistor materials is part of the solution. VCR is material specific and a trade-off is required between the various parameters of the resistor material. The lower the resistivity, the lower the VCR. To minimise VCR It is important to select a termination material that closely matches the material in the resistor track.

Long resistors elements reduce the voltage stress per unit length. VCR values drop sharply for long resistor tracks but there are trade-offs in performance to consider. Long resistor elements tend to increase TCR.

A serpentine pattern is often used to maximise resistor track length but this limits the track width. This, in turn, limits the maximum power handling capability of the resistor device. A level of compromise is required. Some system manufacturers use experimentation to determine the optimal resistance for their application, but even with this approach, there are trade-offs.

It is possible to trim resistors in order to compensate for the VCR drop at a specific high voltage. This approach is predictable from batch to batch, but it only works for specific steady-state operational voltages.

There is lots to consider. A low VCR for high voltage resistors in precision applications is a key consideration. However, too much focus on a single parameter can be detrimental to the overall performance of the resistor device. It is often best to consult a specialist thick film resistor manufacturer when selecting a high voltage resistor for precision applications.