**Varistor V-I characteristic forms of representation**

When selecting metal oxide varistors for specific applications, it is often convenient to use a mathematical representation of the V-I characteristics of the varistors being considered. Generally, a suitable approximation to the V-I behavior of a varistor can be accomplished by use of a power function, an equation of the form

where

*I*is the current through the varistor,

*K*is the ceramic constant (depending on varistor type),

*V*is the voltage across the varistor, and

*α*is the nonlinearity exponent (measure of nonlinearity of curve).

Another possible interpretation of the physical principle underlying these curves is that of a voltage-dependent resistance value, particularly its rapid change at a predetermined voltage. This phenomenon is the basis of the CTVS protection principle. The resistance is given by

The relations given by equations 1 and 2 can be more clearly shown using a log-log scale, since power functions then appear as straight lines:

This result of the above simplification is shown graphically in figure 1.

Another advantage of the log-log format is the possibility of showing the wide range of the V-I curve (more than ten powers of 10). It should be noted that the simplified equations 1 to 4 cannot cover the downturn and upturn regions.

**Determining the nonlinearity exponent α for varistor V-I characteristic**

Two pairs of voltage-current values (V_{1},I_{1)} and (V_{2},I_{2}) can read from the V-I characteristic of the varistor and inserted into equation 3. Solving for *α* then gives

**Real varistor V-I characteristic and ohmic resistance**

Figure 2 shows a typical V-I characteristic. The downturn and upturn regions are easy to make out.

Normally α is determined according to equation 5 from the pairs of values for 1 A and 1 mA of the V-I characteristic. For Figure 2 this gives

The V-I curve of Figure 2 is virtually a straight line between 10

^{-4}and 10

^{3}A, so it is described over a wide range to a good approximation by equation 3. The downturn and upturn regions may be adapted by inserting correction terms in equation 3.

Figure 3 is derived from Figure 2 and shows the change in static resistance *R = V/I* for a given varistor. The resistance is greater than 1 MΩ in the range of the permissible operating voltage, whereas it can drop by as many as ten powers of 10 in case of overvoltage.

**Varistor V-I curve tolerance band**

The real V-I characteristic of individual varistors is subject to a certain deviation, which is primarily due to minor fluctuations in manufacturing and assembly process parameters. For varistors of a certain kind, V-I curves are required to lie entirely within a well-defined tolerance band. The real V-I characteristic of individual varistors is subject to a certain deviation, which is primarily due to minor fluctuations in manufacturing and assembly process parameters.

Varistors are operated under one of two conditions: If the circuit is operated at normal operating voltage, the varistor will be highly resistant. In an overvoltage event, it will be highly conductive. These conditions involve two different segments of the V-I curve (see figure 2):

- Left-hand part of curve (< 1 mA): This part of the curve refers to the “high-resistance” mode, where circuit designers may generally want to know about the largest possible leakage current at given operating voltage. Therefore the lower limit of the tolerance band is shown.
- Right-hand part of the curve (> 1 mA): This segment covers the “low-resistance” mode in an overvoltage event, where the circuit designer’s primary concern is the worst-case voltage drop across the varistor. Therefore the upper limit of the tolerance band is shown.

The 1 mA “dividing line” between the two segments does not really have any electrophysical significance but it is generally used as a standard reference.

V-I characteristic 1 in figure 4 shows the mean value of the tolerance band between the limits indicated by dashed lines. The mean at 1 mA represents the varistor voltage, in this case 22 V. The tolerance K defined as ± 10% refers to this value, so at this point the tolerance band ranges from 19.8 to 24.2 V.

**Varistor leakage current at operating voltage**

A maximum permissibe operating voltage of 18 V_{DC} is given for the varistor corresponding to figure 4. Depending on where the varistor is in the tolerance band (figure 4), one can derive a leakage current between 6 · 10^{–6} A and 2 · 10^{–4} A (figure 4, region 2). If the varistor is operated at a lower voltage, the figure for the maximum possible leakage current also drops (e.g. to max. 2 · 10^{–6} A at 10 V_{DC}).

In the worst case, the peak value of the maximum permissible AC operating voltage will result in an ohmic peak leakage current of 1 mA (see figure, 4 point 3).

**For more information, please read:**

Terms and Descriptions - Varistors

Varistor Operation - Derating, Temperature, Overload

Overvotage Protection with Varistors