It doesn't have to add much, although if you can get away with a shunt of a few hundred [μ][Ω] then it 'might' be achieveable. That's a small signal if it's a noisy environment though! The following is the spec for a good quality electrolytic:
250V DC, 6800uF, 43.5A @ 40[°]C, ESR = 20m[Ω] @100Hz, ESR = 12m[Ω] @100kHz, ESL = 16nH
I suppose you might get away with using a part of the interconnecting wiring or PCB trace as a shunt. A PCB trace should be of a known thickness so it should be very easy to determine a convenient length to act as shunt.
Rogowski coils are readily available, but it's simple to wind your own too. Any bit of flexible tubing will do as a former providing it can be wound with fine magnet wire. The inner bore provides a return path so both ends of the coil are conveniently placed together for connection to the outside world. The governing equations are readily available - I ain't fighting TGML to post them here, ha-ha - but the trick (if there is one) is usually the integrator design, making sure that it is behaving correctly at the frequencies of interest. For precision work I'm told it is possible to add compensating networks to the coil to get a response accurate down into the handful of PPM level - the guy who owns
Ro-Coil has done some pretty specialised stuff and is very knowledgable about the subject, and he's been kind enough to improve my understanding of these transducers.
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If we learn from our mistakes I'm getting a great education!