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OK I feel very stupid for asking this but real-life analog anything is not my area, real life power supplies doubly so. CM noise on a power supply is noise common to +V and the supply "ground" relative to... earth? Why does that matter for a voltage supply. If I probe it on my bench meter its earthed and the CM noise is gone(??) and if I use a hand held meter the meter floats with the CM noise ya?
You're not entirely wrong, as a common-mode voltage, it isn't too big a deal. At the power supply terminals may be the point that you can say "we have a DC level of X, plus a differential mode noise of Y and common mode noise of Z", in a totally symmetrical circuit with very high impedance between each V+ and 0V wrt earth, it will stay quite symmetrical and you could have the same DC+[DM+CM noise] at the load input and the rest of the circuit. The DM noise stays easily filtered and
can be quite well filtered still, some may leach through to your outputs, but that's still tolerable or manageable by design - 'not a big deal'/'fun challenge'. The multimeter in reality isn't
completely isolated and it will have some capacitance to earth and other "things"; the power supply's wires similarly so and won't have totally symmetrical impedance. (I'm making a bit of a logical jump here between treating CM as voltage and current) So for CM noise, it will find its way through the circuit and to a return path it like the look of, if its entirely symmetrical, the voltages cancel: but in reality, it isn't and they don't.
So I don't mean to say that the CM noise will definitely be an issue, but it has the potential to be an utter nightmare. Good decoupling, filtering, and filtering of outputs will help the CM noise if it infects your DM signal... but the CM noise has a strange ability to uncover any weaknesses there, so it can appear as a problem when you least expect it. When it comes to PSUs, if it's part of a "system" that specific requirements for size and weight, then yeah, it's worth the fuss of SMPS, but for bench test items, I personally go for the less trouble option. Though I'm sure many people will jump in and say "I used This PSU with This circuit and it was totally fine": I'm just skeptical, especially with such a broad range of PSU 'quality levels' and permutations of filters and construction methods.
I'm not sure if I explained that very well, so I
might draw a diagram if I get a moment later on. In conclusion, SMPSs are a tameable beast, linear are much more docile, but each one will bite your hand off when it's hungry (analogy broke down there).