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Case: I design a pcb with a microprocessor and a adc (I'll leave out the details).

Is this correct: The digital ground and the analog ground should be connected, but by a small passage.

Next question: If the pcb have hole's for mounting to a metal chassis, should the skrew's then be grounded to the pcb analog/digital ground and to the chassis? Wouldn't that be a better protection?

Or should the analog and digital ground not be connected to the chassis. Instead I should design a "chassis ground" surrounding the digital/analog ground.

Or should the analog/digital just be on the pcb and not connected to the chassis nor should the be any chassis ground either.

Kind Regards

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The digital ground and the analog ground should be connected, but by a small passage.

Yes this is correct. All you need between the two is a single point of reference. Best practice in most applications is a star ground, i.e. connect the digital ground plane to the power source's ground connection and the analog ground plane to the same physical point. The small passage should be capable of handling any current that could potentially flow through it.

If the pcb have hole's for mounting to a metal chassis, should the skrew's then be grounded to the pcb analog/digital ground and to the chassis? Wouldn't that be a better protection?

This depends on the application. In some applications, such as underwater, the chassis should be electrically isolated from any charge storage element to reduce oxydization. If you want to electrically connect the chassis connect it to earth ground if the application allows.

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