Do I need a supply decoupling/bypass cap for the analog switch/mux (say ADG884) if it does not switch often (mostly one time per power up session)?
The use of a decoupling capacitor is recommended but if you decide to use the device without decoupling it will still function, albeit with a few side effects.
The PSRR will be reduced, so if you have a noisy power supply it will add noise onto you signal.
Also, when switching the input buffer can take a lot of current from VDD but due to fact that you are not switching a lot may not be a big issue for you.
So you need to decide if you can live with these side effects in your application.
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