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Usually we build Class I equipment, i.e. with a ground lead. For EMC purposes we use an input filter (commercially bought).

For reference a typical filter is made in this way (source electronics weekly) Typical filter

The idea is to shunt the noise with C1-C2 (X capacitors) and draining it to ground with Y-capacitors (C3 and C4). The magnetic parts also help filtering noise at different frequency. Also the power supply has it’s own filtering stage needing a ground connection (only FG)

For various reasons (included people who don’t have a ground terminal in their sockets!) we need to convert to Class II (double insulation), and that’s a pain in itself.

However the bigger issue is that Class II equipment cannot have a ground lead, for safety (for fixed installations you can have a functional ground for this exact purpose but this is not the case). So now the filter has nowhere to dump the noise. It would somewhat work (all the inductive parts and C1/C2 are still effective) but without C3/C4 it’s not at it’s full potential (also: the input plug is embedded and has a ground lead which is forbidden.

There are groundless input filters (for medical use) but they are less effective and quite expensive. Also there’s still the issue of the power supply (which probably has the same topology inside).

What’s the recommended way to filter the mains supply without ground? should I simply put ‘more’ LC filtering action between the line or is there some other technique?