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I have an oscilloscope and power supply which have a common ground-reference (I think that is the correct wording? Neither of them are isolated/battery-operated/floating). Is it typically the case that use of the oscilloscope probe's ground connector will result in a current loop?

In essence, should I always be using something like a differential probe (or similar differential functions) in this configuration?

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Ground loops are important and safety is always a major consideration BUT from a technical point of view, use of the ground AT the probe tip is essential in many circuits.

The oscilloscope "sees" a voltage between probe tip and some reference point.
If the reference point is the probe-ground the ground lead can be connected very close to the point under measurement at a point where "ground" is meaningful for the signal concerned.

If the circuit is operating at say 100 MHz and involves other than perfect infinite ground planes then local ground for a signal may be quite different in potential than the "ground" level on the oscilloscope itself. Failure to use probe ground will often produce a signal that would be ideal for use as a source of random numbers.

So, for technical reasons, in complex situations, use of a probe ground connected AT the point of relevance is utterly essential. Safety and ground loop and other considerations are not made any less important by this need, but must be worked out AFTER the technical ground point requirement is met.

Achieving anything worthwhile was never meant to be easy :-)

How real men (and women) do it - a picture from a Jim Williams application note:

enter image description here

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A ground loop, as the name says, must be a complete circle. You won't get a loop without ground being connected from your device under test (DUT) via your PE connectors in the power installations to your scope's case and back to the DUT via the probe's ground clip.

If this is a problem, it is o.k. to float your DUT, using an safety transformer. Differential probes are also a good choice.

Do not float your scope! It is important that your scope be grounded! Otherwise, your scope's case may float on a high voltage and you may not notice.

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