Many designers are unaware that resistors have a voltage coefficient of resistance (VCR) and a temperature coefficient of resistance (TCR). This is understandable because in low voltage and low resistance applications, the voltage effect is small and can be well masked by temperature effects. However, in circuits using high resistance and/or high voltage (HV), the variation of resistance with voltage may be a major issue. These circuits are used in applications such as high-voltage power supplies, transimpedance amplifiers (TIA), high-voltage LED lighting, and pulse communication systems. Designers of such circuits need to understand the principles and effects of VCR, as well as how to mitigate its impact.
This article first provides an overview of what VCR is and its impact on circuit design. Then, using Stackpole's low VCR resistor as an example, it explains how to select and apply such devices to minimize the impact of VCR and ensure accurate and reliable operation of critical circuits.
What is VCR?
The VCR of a resistor can be defined as the relationship between the resistance value and the applied voltage that varies proportionally. Its measurement unit is usually one millionth per volt (ppm/V) and can be calculated using the following formula:
Formula 1
among which
R ₁ is the resistance value at the reference voltage (V ₁), measured in ohms (Ω)
R ₂ is the resistance value (in ohms) at the test voltage (V ₂).
V ₁ is the reference voltage
V ₂ is the test voltage
VCR can be positive or negative. A positive VCR indicates that as the voltage on the resistor increases, the resistance will also increase; Negative VCR indicates a decrease in resistance.
A typical high-voltage chip resistor with VCR ranging from 200 ppm/V to 300 ppm/V will experience a 20% to 30% change in resistance when the applied voltage changes by 1000 V. If a resistor with VCR ranging from 25 ppm/V to 50 ppm/V is selected, the resistance change will decrease to 2.5 to 5% under the same 1000 V variation.
The standard test method for measuring VCR should follow MIL-STD-202G 309 method. This standard specifies a unified method for testing electronic components, specifying that the standard test voltage is equal to the specified maximum operating voltage, and the reference voltage level is 10% of the maximum operating voltage.
How to minimize VCR
By selecting appropriate designs and materials, VCR can be minimized to the greatest extent possible. Due to the fact that low VCR resistance materials can improve VCR but also increase TCR, thereby reducing temperature stability, engineering compromises are needed when selecting resistance materials. Choosing low resistance ink can also improve the VCR, but it will limit the maximum achievable resistance. Careful selection of the type and usage of resistive ink can optimize VCR.
Laser trimming can also have an impact on VCR. The resistance value generated by unrepaired resistors usually differs from the expected value by 5 to 20%. Laser trimming is used to adjust the resistance value to a smaller tolerance range, such as 1%. The laser trimming process can generate microcracks, leading to local unexpected impedance changes, thereby increasing VCR and causing VCR degradation (Figure 1).