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keep in mind that inrush current is pretty fast so you need a current probe with sufficient bandwidth.
transient protection needs to be measured in such a way that if the system fails to self protect, then your test method is not allowed to deliver desctructive energy.
for example, if you were measuring transient overvoltage, it would be good if you could apply a transient voltage yourself with known duration and then see if protective circuit works. if it does not work it is a good thing that you have applied a known duration transient.. the duration is obviously one that would be short enough not to cause damage. transient voltage can be created by charging inductors and then open circuit, you can charge a capactor and then close a contactor to have it appear in circuit.
in H-bridge, where shoot-through is a concern, you would command a mosfet ON for only 10us. the shoot-through protection circuit would have to self protect in less tine than that.. if it fails to protect, good thing your command signal was only 10uS!
I am not sure that a current transformer would work without calibrating it first. The reason is that the voltage from it works on the Di/Dt for a 50 or 60 HZ sinewave. If you apply a step current waveform then the voltage spike it produces will be a function of the rise time as well as the current amplitude. With current inrush measurements on the mains the test has to be done many times (10?) to make sure that you are close to capturing the worst result.
A good quality current transformer will transform primary current into secondary current with the same waveform.
The only thing you have to take care is not to charge the transformer with DC current so it gets in saturation.
A sine wavefrom at the input will produce a sine waveform at the output.
A triangle wavefrom at the input will produce a triangle waveform at the output.
A square wavefrom at the input will produce a square waveform at the output.
Inside the transformer there is
1) an integration: from primary current to magnetic field
2) an differentiation: from magnetic field to secondary current. (here you loose the DC current)