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Zener diodes can conduct current in both directions. Zener’s are designed to have a very precise breakdown voltage, called the zener breakdown or zener voltage. When enough current runs in reverse through the zener, the voltage drop across it will hold steady at the breakdown voltage.
Taking advantage of their breakdown property, Zener diodes are often used to create a known reference voltage at exactly their Zener voltage. They can be used as a voltage regulator for small loads, but they’re not really made to regulate voltage to circuits that will pull significant amounts of current.
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