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I've noticed that the output ground of most power supply are not quite the same as earth ground. The DC is nearly negligible, but there is usually an AC component between output ground and earth ground of magnitude 4-6 times the intended DC voltage (probably attributable to floating inductive spikes -- the voltage differential output may slightly float). Only the best power supplies, say a PC PSU, or linear regulated power supply can have output ground nearly equal to earth.

I haven't tested, but the current probably won't be that large. So why not use a Schottky rectifier or something to clamp the output ground to earth ground?

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The fact that many power supplies have a floating ground is often a feature, rather than a bug!

You want to avoid ground loops and have the ability to connect multiple pieces of equipment without causing lots of current to flow through the connected grounds. Ground isolation via transformers, differential signals, optical, or RF actually is a way to avoid a number of safety and signal issues in interconnected systems. Ground is not magic. It's just a reference point, and a potentially signal-contaminating one if you get confused and think it's the same in two different places. It can be better for the designer / engineer to decide exactly where to join grounds, rather than having the power supply do it for you.

Your measurement here is also potentially flawed: as you say, "the current probably won't be that large," meaning that this is probably a very high impedance floating condition. (High voltage divided by low current equals high impedance.) The mere presence of a voltage difference probably doesn't actually tell you all that much.

If you did want to tie the input and output grounds together, I'm not sure why you'd want to use a diode rather than a wire!

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Most bench power supplies are designed to be floating by default. This allows you to use them either as positive supplies by connecting the negative terminal to ground or as negative supplies by connecting the positive terminal to ground. You don't even need to ground reference it, for instance if you connect it to some circuit that already has a reference.

If you just leave it floating, you are saying "I don't care what the voltage relative to ground is" but the voltage will be set by something. Most of the time this will be provided by capacitive leakage through the main power transformer or intentional capacitance of EMI filters. Since the capacitance is about equal to the live and neutral terminals, you will normally see an open circuit voltage of Vmains/2 (60 VAC in the US). However, the impedance of that capacitor at 60 Hz is so high that even the 10 megaohm impedance of a typical voltmeter will drop it down a bit.

There are transformers designed to avoid this issue. They have a grounded "shield" electrode between the primary and secondary preventing capacitive leakage current. If you need to use a power supply in the true floating configuration and a small leakage current of a few microamps is a problem, then you probably need one, but that is a rare need, and most general purpose power supplies do not have them.

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