he article title is not a spelling test, but an attempt to explain the properties of the neglected varistor resistance parameter, R. Resistance, in this case, is the varistor voltage at a point in the V-I characteristic divided by the varistor current at that point.
A nominal 275 V rms, 14 mm diameter varistor will be used as an example. Manufacturers usually provide a single V-I graph of all the varistor characteristics of a given type. Figure 1 shows the extracted characteristic for a nominal 275 V rms varistor of 14 mm diameter. The characteristic 20% upward step at 1 mA is when the curve changes from the lowest component voltage to the highest component voltage. To form a single curve for the highest voltage component, the curve below 1 mA needs to be lifted by the value of the step. The characteristic normally ends at the rated single 8/20 impulse peak current level.
Turning Figure 1 into a line of data points involved several steps. An enlarged Figure 1 was printed and voltage values taken at the current vertical grid lines. Using a logarithmic reference, such logarithmic graph paper or the slider of a slide rule, enabled accurate measurement of the voltage values. Figure 1 shows a step increase of about 20% in the characteristic at 1 mA as the characteristic changes from minimum voltage (384 V @ 1 mA) characteristic to maximum voltage characteristic (474 V @ 1 mA).
Varistor V-I curves depend on the test current waveform used, a classic case of “It ain’t what you do it’s the way that you do it.” Figure 3 shows the effects of DC, AC, pulse and impulse currents on the shape of the V-I characteristic. At low currents DC is a continuous condition whereas the AC current value will vary over the AC voltage cycle. At high currents the voltage will have a dependence on the impulse rate of current rise. At a given peak current for 1/5, 4/10 and 8/20 impulses, the 1/5 impulse will have the fastest di/dt and, as a result, the highest voltage. These effects need to be born in mind when working from the manufacturers published V-I curves.
Using curve-fitting software resulted in the more complex equation of r = 5.793×(i)^-0.5 + (595.5 + 18×LN(i))/i – 1/(1.953E-7 + 871×((i)^2)), which reduces the maximum error to 1%. One needs to be careful in using such software as outside the data current range some crazy results may occur that causes circuit simulations to fail. The fit quality of this equation (multiplied by current) to the data point set is shown in Figure 7.
In testing a varistor with a 1.2/50-8/20 generator, the varistor voltage will reduce the delivered current. Using the 275 V rms varistor with a 1.2/50-8/20 generator set to 2.5 kV and 4.0 kV results in peak currents of 720 A and 1.4 kA. According to the data sheet maximum peak current derating characteristic, the rated number of impulses at these peak current levels are 80 and 50.
voltage dependent resistor (VDR)
component, whose conductance, at a given temperature range, increases rapidly with voltage within a given current range.
- I is the current flowing through the varistor;
- U is the voltage applied across the varistor;
- β is the non-linearity current index (see 3.4);
- γ is the non-linearity voltage index (see 3.5);
- A and C are constants
Figure 11 shows that the varistor accumulates energy in two steps; in the positive polarity the step is 107 J and in the negative polarity a further 10 J is added making 117 J in total.
This has been a simple example; the real benefit of an accurate varistor model is when more complex circuits are analyzed. For example, the addition of two more varistors in parallel with the single varistor of Figure 9. When three similar varistors are connected in parallel the lowest voltage one will take most current, set in this case to the maximum single 8/20 rated current of 6.0 kA. Table 2 shows what the individual peak currents and energies would be for three varistors that have the highest, nominal and lowest voltages of a selection. An alternative analytical approach would be to work to a maximum energy criterion as the lowest voltage varistor would develop less energy than the highest voltage varistor at the same rated peak current.