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I'm using an AC/DC switching supply (Meanwell PD-45) with the following schematics:

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The Frame Ground (FG) is connected to the metal chassis of my device with a screw. The output of the switching supply is used to power a PCB. Therefore, +5V and COM are connected to the PCB. But the ground of the PCB is in itself also connected to the metal chassis via the mounting screws. Therefore, COM and FG are connected. Is this a good practice? Should the PCBs be kept floating with COM only?

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Shorting the earth and DC ground (i.e. making the output earth-referenced or ground-referenced) is a common practice (e.g. PC ATX PSUs or industrial applications where VFDs, PLCs, etc are used). It cancels out the common mode noise.

But you MUST make sure the FG (and chassis) is connected properly to the earth ground (PE: protective earth). Because it's a safety requirement i.e. in case of a wiring issue such as live wire gets loose and touches to the metal chassis it should provide the shortest and safest path to the ground (PE) so the user doesn't get shocked and the breaker trips.

But the grounding scheme (on both PSU and target/load PCBs) should be done properly or else there can be ground loops which may cause problems on analog or sensitive digital communications, if there's any.

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Yes, that's a common setup. The user may touch the chassis at any time, and may also touch connectors, and there should only be a minimal voltage between those.

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