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Selecting a low VCR (Voltage Coefficient of Resistance) value is crucial when choosing high voltage resistors for 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 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. It 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.

Voltage Coefficient of Resistance becomes an issue when voltage changes over time (dV/dt). The faster the voltage changes, the larger the VCR effect and the larger the voltage changes. For high voltage thick film resistor devices VCR can range from 5ppm for precision devices to low hundreds of parts per million depending on the resistor construction (see below) and the application.

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

VCR Issues In Specialist Applications

VCR as it is inherent in the materials used and also depends largely on the high voltage resistor application. A perfect resistor will not vary in resistance with any change in operating voltage. Unfortunately, the perfect resistor does not exist. 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 critical, it is important to minimise VCR.

During the thick film high voltage resistor manufacturing process, a resistive film is printed onto a substrate. The assembly is then fired at a high temperature. 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 increases, new conductive paths through the oxide spheres and glass frit can form and reduce the resistance.

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 resistor elements reduce the voltage stress per unit length. VCR values drop sharply for long resistor tracks, depending on the resistor value and materials, but there are trade-offs in performance to consider. Theoretically the longer the resistor, the less voltage stress and therefore the less VCR, but long resistors also give higher TCR and VCR and TCR oppose each other.

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 to compensate for the VCR drop at a specific high voltage. This approach is predictable from batch to batch, but only works for specific steady-state voltages. Manufacturers of application specific low TCR resistors measure each resistor for VCR over a very small temperature range. When the resistors operate outside this range the VCR is no longer valid.

However, too much focus on a single parameter can be detrimental to the performance of the resistor device.  It is often best to consult a specialist resistor manufacturer when selecting a thick film high voltage resistor for precision applications.