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I'm taking a course on semiconductor physics and another on something like "usage of electronic devices". On both I've come across the I/V curve on a varistor, this is:

I/V curve of a varistor.

I cannot find the answer to why is there a straight jump when it goes from the maximun leakage current region to the maximun clamping voltage region. Does anyone know the answer?

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The "jump" is in the specifications, it is not real.

They guarantee maximum leakage current and (effectively) the minimum clamping current for a given voltage.

The centre solid black line is the typical performance. Real devices are guaranteed to be somewhere above the red line in voltage up to 1mA, and below the red line in voltage above 1mA.

They are not going to reject a device due to performance if it leaks less than the upper dotted line, nor will they reject it if clamps better than the lower dotted line.

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