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Posted on 07 April 2019

Selection Guide - Varistors

 

 

Choosing a varistor involves three main steps:

  1. Select varistors that are suitable for the operating voltage.
  2. Determine the varistor that is most suitable for the intended application in terms of:

    a) surge current
    b) energy absorption
    c) average power dissipation

    (for a and b also estimating the number of repetitions)

  3. Determine the maximum possible voltage rise on the selected varistor in case of overvoltage and compare this to the electric strength of the component or circuit that is to be protected.

To ensure proper identification of circuit and varistor data, the following distinction is made:

  • Maximum possible loading of varistor that is determined by the electrical specifications of the intended location.
  • Maximum permissible loading of varistor that is given by its surge current and absorption capability.

(note: maximum permissible quantities will be signified by a *)

So the following will always apply:
i* ≤ imax
W* ≤ Wmax
P* ≤ Pmax

Operating voltage

Maximum permissible AC and DC operating voltages are stated in the product tables for all varistors. To obtain as low a protection level as possible, varistors must be selected whose maximum permissible operating voltage equals or minimally exceeds the operating voltage of the application.
Nonsinusoidal AC voltages are compared with the maximum permissible DC operating voltages so that the peak or amplitude of the applied voltage does not exceed the maximum permissible DC voltage.

Note:
Of course, you may also select any varistor with a higher permissible operating voltage. This procedure is used, for example, when it is more important to have an extremely low leakage current than the lowest possible protection level. In addition, the service life of the varistor is increased. Also the type for the highest operating voltage may be selected to reduce the number of types being used for different voltages.

Surge current

Definition of the maximum possible operating voltage in the previous step will have narrowed down the choice of an optimum varistor to the models of a voltage class (e.g. those whose designation ends in 275 for 230 V + 10% = 253 V). Then you check, with reference to the conditions of the application, what kind of load the varistor can be subjected to. Determining the load on the varistor when limiting overvoltage means that one must know the surge current that is to be handled.

Predefined surge current

Often the surge current is predefined in specifications. After transformation into an equivalent rectangular wave, the suitable varistor type can be selected by the derating curves.

Predefined voltage or network

If the voltage or a network is predefined, the surge current can be determined in one of the following ways:

Linear scale load line
Figure 1. Load line on a linear scale

 

Simulation

Using the PSpice simulation models of the varistors, the surge current, waveform, and energy content can be calculated without difficulty. In these models, the maximum surge current is deduced for the lower limit of the tolerance band, i.e. setting TOL = –10.

Test circuit

The amplitude and waveform of the surge current can be determined with the aid of a test circuit. The dynamic processes for overvoltages require adapted measuring procedures.

Graphical method

As shown below, the overvoltage can be drawn into the V/I characteristic curve fields as a load line (open circuit voltage, short circuit current). At the intersection of this “load line” with the varistor curve selected to suit the operating voltage, the maximum protection level and the corresponding surge current can be read off. The waveform and thus the energy content cannot be determined by this method.  Since the V/I characteristic curves are drawn in a log-log representation, the “load line” in figure 2 is distorted to a curve.

V-I characteristic curves

Figure 2. V/I characteristic curves with the load line drawn for a surge current amplitude 4 kV with Zsource = 2 W

Mathematic approximation

The surge current is determined solely from the source impedance of the surge voltage (Vs). By subtracting the voltage drop across the varistor (from the V/I curve) one can approximate the maximum surge current with the following equation:

\begin{equation}i^* = \frac{V_{S} - V_{VAR}}{Z_{SOURCE}}\end{equation}

where Vs is the surge voltage, VVAR is the voltage drop accross the varistor, and ZSOURCE is the voltage-independent impedence of the voltage source

Switching off inductive loads

If the transient problems are caused by switching off an inductor, the “surge current” can be estimated as follows:

The current through an inductance cannot change abruptly, so, when switching off, a current of the order of the operating current must flow across the varistor as an initial value and then decay following an exponential function. The path taken by the current during this time is referred to as a flywheel circuit. The time constant τ = L/R  that can be calculated from the inductance and the resistance of the flywheel circuit (including varistor resistance) shows how long the current requires to return to the 1/e part (approx. 37%) of its original value. According to theory, τ is also the time that the flywheel current must continue to flow at constant magnitude to transport the same charge as the decaying current. So the amplitude of the “surge current” is known, and its duration is approximately τ (figure 3).

The value of τ depends on the value of the inductance and the resistances of the flywheel circuit, generally therefore on the resistance of the coil and the varistor. The latter is, by definition, dependent on voltage and thus also current and so, for a given current, it has to be calculated from the voltage drop across the varistor (V/I characteristic).

\begin{equation}\tau\approx\frac{L}{R_{Cu}+R_{VAR}}\end{equation}

  where L is the inductance, RCu is the coil resistance, and RVAR is the varistor resistance at operating current.

RVAR increases as current decreases. Therefore, τ is not constant either during a decay process. This dependence can, however, be ignored in such a calculation. For comparison with the derating curves of the current, one can assume that τ =  tr, where tr is the amount of time that energy is applied to the varistor.

Figure 3. Time constant of flywheel circuit

 

Comparison: determined surge current / derating curve

The maximum permissible surge current of the varistor depends on the duration of current flow and the required number of repetitions. Taking these two parameters, maximum permissible surge current can be read from the derating curves. This value is compared to the maximum possible surge currents in the intended electrical environment of the varistor. From the derating curves, one can obtain maximum figures for rectangular surge current waves.

For correct comparison with these maximum permissible values, the real surge current wave (any shape) has to be converted into an equivalent rectangular wave. This is best done graphically by the “rectangle method” illustrated in figure 4. Keeping the maximum value, you can change the surge current wave into a rectangle of the same area. t*r is then the duration of the equivalent rectangular wave and is identical to the “pulse width” in the derating curves. (The period T* is needed to calculate the average power dissipation resulting from periodic application of energy.)

Rectangle method
Figure 4. Rectangle method

 

If the pulse load is known, then tr can be calculated using the following equation:

\begin{equation}t^*_r = \frac{\int i^*dt}{\hat{i}^*}\end{equation}

(see figure 4)

The duration of surge current waves is frequently specified using the 50% value of the trailing edge. The decay pattern of such waves can be represented by an exponential function.

According to figure 5 and the equation derived from this, 

\begin{equation} \frac{ t_{37\%}}{ t_{50\%}}= \frac{\ ln 0.37 }{\ ln 0.50 }= \frac{-0.994}{-0.693}=\frac{ \tau }{T_r}\end{equation}

the “equivalent rectangular wave” for such processes is found to be t*r = 1.43 Tr.

Equivalent rectangular wave
Figure 5. Equivalent rectangular wave of an e-function

 

Energy absorption

When a surge current flows across the varistor, there will be absorption of energy. The amount of energy to be absorbed by the varistor can generally be calculated using

\begin{equation} W= \int_{t_0}^{t_1} v(t)i(t)\,dt.\end{equation}

Calculation method

Often the energy absorption can be read directly from a storage oscilloscope or can be calculated from the voltage/current curve using numerical methods.

Simulation

Determination of the energy absorption by simulation (PSpice) is even more convenient.

Graphic method

This can be also solved graphically with sufficient accuracy by using the rectangle method. i* (t) is converted as in figure 4 and multiplied by the highest voltage appearing on the varistor according to :

\begin{equation} W^*=\hat{v}^*\hat{i}^*t^*_r\end{equation}

where v* can either be derived from the V/I characteristic as the value matching, or likewise be determined with the aid of an oscilloscope as the maximum voltage drop across the varistor.

Switching off inductive loads

If transients are caused by interrupting the current supply of an inductor, the worst-case principle can be applied to calculate the necessary energy absorption of a varistor. The energy to be absorbed by the varistor cannot be greater than that stored in the inductor:

\begin{equation} W^*=\frac{1}{2}Li^{*2}\end{equation}

where L is the inductance.

This calculation will always include a safety margin because of losses in other components.

Comparison: determined energy input / maximum permissible energy absorption

To check the selection requirement W* ≤ Wmax, you have to determine the maximum permissible energy absorption for the intended varistor. This can be calculated as a function of the time the energy is applied (tr) and the number of repetitions from the derating curves:

\begin{equation} W_{max}=v_{max}i_{max}t_{r\max}\end{equation}

vmax is derived from the V/I characteristic of the intended varistor type for the surge current imax while tr max can be taken as being the same as t*r since Wmax is to be calculated for the given time of
current flow.

 Average power dissipation

The actual power dissipation of a varistor is composed of the basic dissipation P0 caused by the operating voltage and, possibly, the average of periodic energy absorption. If metal oxide varistors are chosen from the product tables in agreement with the maximum permissible operating voltages, P0 will be negligible. Periodic energy absorption produces an average power dissipation of:

\begin{equation} P^*=\frac{W^*}{T^*}=\frac{v^*i^*t^*_r}{T^*}\end{equation}

W* takes the value of a single absorption of energy.
T* is the period of figure 4.

By solving this equation for T* it is possible to calculate the minimum time that must elapse before energy is applied again without exceeding the maximum permissible average power dissipation of the varistor:

\begin{equation}T_{min}=\frac{W^*}{P_{max}}\end{equation}

Note:
Metal oxide varistors are not to be “operated” at Pmax. They are not suitable for “static” power dissipation, e.g. voltage stabilization. There are other kinds of components, like zener diodes, designed primarily for this kind of application, but with much lower surge current handling capability.

Maximum protection level

The maximum possible voltage rise in the event of a surge current is checked with the aid of the V/I curves or PSpice models. This figure can be read directly from the curve for a given surge current (for worst-case varistor tolerances). If the voltage value thus obtained is higher than acceptable, the following possibilities may assist in reducing the protection level:

  • Choose a type with a larger disk diameter

The protection level is lower for the same surge current because the current density is reduced.

  • Better matching to the operating voltage by series connection

 

For more information, please read:

Terms and Descriptions - Varistors

Calculation Example: Switching of Inductive Loads

PSpice Simulation Model

Overvoltage Protection with Varistors

 

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