With most
'scopes one side of the input is grounded [...]
Ah. That's the part I was
missing! I (naively :-) assumed that the
'scope's whole input amplifier would be 'floating', and the input
signal would be taken as referenced to the 'ground' on the probe,
which could itself be floating.
That amounts to a differential (rather than single-ended) input, and I
would consider that the _right_ way to do it. But, of course, that
costs, and single-ended is plenty good enough for most purposes, so
that's what most scopes do. :-(
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