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When is a flyback diode necessary?

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However the reverse voltage rating should be looked at closely as the fly back pulse can reach 4X the coil voltage rating.
That's not true, with the diode in place the maximum voltage will be the forward voltage of the diode.

The diode only has to be rated to the same voltage as the maximum power supply voltage.

Although it doesn't matter here, you can speed the turn off time by including a resistor of the same value as the coil's resistance in series with the diode. This helps to prolong the life of relays as the contacts will open faster and arc less.
 
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