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There are lots of questions about "traditional" low-side current sensing using a shunt resistor.

Most discussions and papers mention the drawback of "ground disturbance" introduced by the measurement principle (dropping voltage across the sense resistor).

Why is that usually a problem? Assuming that the sense resistor is only a resistance (neglecting parasitic inductance) and assuming the voltage drop is low enough to not brown out the circuit, the "circuit under test" will not see any influence from outside?

Am I right in the assumption, that ground disturbance is only a topic if the circuit under test is somehow interfaced to other circuit parts that assume a common ground to the circuit under test (e.g. some digital interface such as SPI)?

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The problem is with the fact, that the ground itself is not absolute, as in it is affected by all the AC surroundings. If you ensure controlled environment (return paths of all your AC signals never cross paths with your measurement path (including whole digitizing section) AND clean return path of your sense resistor AND it in itself does not act as an antenna) then yes, your assumption is correct.

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The voltage disturbance is often the lesser of two evils. The introduction of impedance, even if it is milliohms can be detrimental to good grounding of sensitive or precision circuits.

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