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I'll leave my specific circuit out of this for a more broad question:

What criteria does one use when deciding whether to use a Zener diode or a transient voltage suppressor, for overvoltage protection on a particular application? Also when would one use a bidirectional TVS?

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    \$\begingroup\$ One use for bidirectional TVS is when you need to protect a bus. For example in RS-485 you have maximum voltage between data lines and you'd use bidirectional TVS between the lines in order to protect the receiver. \$\endgroup\$ – AndrejaKo Dec 4 '12 at 22:11
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The characteristics of TVS diodes are similar to those of zener diodes. However, the TVS diodes are specifically designed, characterized and tested for transient voltage suppression. Zener diodes are designed towards voltage regulation.

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The primary tradeoff is the thermal management or derating features that must be considered in these combined dual roles. If a TVS device is also used as a Zener for continuous voltage regulation, the device would then be operating with sustained power dissipation where internal p-n junction temperatures are driven well above ambient from its own thermal resistance junction to ambient RθJA. That type of operating condition will reduce P(PP) capabilities.

"Zeners and TVSs have different design considerations and are also tested differently for their primary operating features. As a result, careful consideration in selection for overall optimum performance and thermal management considerations are required for each.
Only under judiciously chosen operating conditions can they be combined with careful
consideration and also optimally accompanied by special device testing.
" Says Kent Walters in his MicroNote 134 application note. (1)

You can have a quick read of his application note if you wish to know more.

(1). MicroNote 134

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The difference between the TVS and Zener diodes is construction. A Zener diode is primarily designed to handle steady state power. The Zener functions as a voltage regulator (shunt style) or voltage reference in a power supply system. While electrically similar, the TVS unit has a different construction and is designed to absorb large amounts of energy (joules) in a very short period of time (milliseconds).

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