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Could you monitor current using a low value R and then just do the math?
For example, let's say you had 200mA flowing into a load. You could add a series 1Ω, and then the voltage drop would be
V = IR = 200mA*(1) = 200mV
When you see 200mV on your meter, you'd know you have 200mA flowing.
But, since you want a waveform on the scope, is there a math function on the scope? You could place Input A on the hgh side of R, Input B on the low side of R, and then display the difference voltage of the two, vA-vB, the voltage drop across R. This would give you a trace that changed with current draw. Still you wouldn't see amps, but you could just read the voltage as amps.
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