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What does Transient Protection mean?

I'm looking at a datasheet that explains transformerless PSU's, and there is an example schematic that shows a varistor or MOV that provides transient protection (VR1 below). There is no description in the datasheet that explains what this is or how the VR protects against it.

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It's taken from Microchip application note AN954, page 10.

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Varistors are variable resistors whose resistance will sharply drop when the applied voltage is higher than the threshold voltage.

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In the given circuit the varistor is placed parallel to the mains voltage. I may be rated at 275V, like Littelfuse's V275LA10CP for a 230V supply. The datasheet says that it will draw 1mA at minimum 389V, so during normal operation the current will be negligible. If there's a voltage peak of minimum 710V on the mains however, the resistance will drop and the varistor will draw a considerable current (datasheet says up to 25A), so that the energy of the peak will be absorbed by the varistor, and that there's no damage to the circuit.
The energy a varistor can absorb is limited, mainly by its size, but in general they can only handle short peaks.

Selecting varistors is not easy. The curve isn't very sharp, and you can't expect to have zero leakage current at 300V and full clamping at 310V. There's a trade-off between leakage (1mA in the example) and the height of the clamping voltage (710V in the example).

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Whenever the mains take an excursion too far outside the normal limits, the MOV conducts and absorbs some energy in an effort to keep the voltage down, at least within the equipment in which it is located. Mains power can be rather uneven, especially if you are near a lot of loads that switch in and out, for example, if you share a drop with a public laundromat. MOVs can only absorb a finite amount of energy before they essentially become useless open circuits, so any that have been on-line for some time are apt to be spent; ones in rougher neighborhoods more quickly.

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