Yes, something like this can be used. The following shall yield an estimation of expected error.

First some basics:

If you use a Rogowski coil or a current transformer (CT) you get an equivalent circuit like that:



By 'CT' I mean something like a Rogowski coil, but which is wound on a core of relevant µ. In the following we want to assume, that 'Ri' can be ignored..
Rogowski coil and CT show very different inductivities, which is the reason, why the one is connected to a high ohmic load, while the other needs a low ohmic one. But there's some other difference: Signal coming from a Rogowski coil, which should be connected to a high ohmic load must go through an additional integrator, while the CT does not need such one. Look at the following to see why the both are so different:

Welding current, which is to be measured, produces a magnetic flux density of



k contains µ, for instance.

Coil, which is hit by 'B(t)' produces a voltage of



'n' is the number of windings of coil and 'A' is cross section of core (either showing relevant µ or µ=1).

On the other hand, if a current is flowing through the coil, then following relation is valid:



'UL(t)' is voltage drop across L and 'IL(t)' is current through L.

Now consider two special cases,

1. RL is extremely low, means 'short circuit' case:

Then, US(t) is:



2. RL is extremely high, means 'open circuit' case:

Then, US(t) = Uind(t) of course, because no current is flowing through L. In this case US(t) is not proportional to IW(t) but to its time derivative. So, we have to additionally integrate US(t):



Which of both cases should be used?

Well, in the case of Rogowski coil where µ=1, inductivity of L is rather low. In this case RL should not be low, as it's rather difficult to find a such low RL, that it will not cause too much error. In the case of Rogowsky coil a rather high ohmic load is preferred and an additional integrator is needed.

In the case of current transformer, just the opposite is valid: L can be rather high, due to relevant µ of core. In this case it's rather difficult to find a such high RL, that it will not cause too much error. Keep in mind, that impedance of L increases with increasing frequency. So, what might work with 50Hz mains frequency will tend to cause errors if you are interested in harmonics. In the case of CT a rather low ohmic load is preferred and no additional integrator is needed.

What's the advantage of using these two special cases?
Any other configuration would introduce relevant frequency dependency of US(t), which would be very unsuited. By using either 'quasi short circuit' or 'quasi open circuit' configuration, on the other hand, frequency dependency is mostly negligible for a wide range of frequencies.

Now to your question: What is the error of introduced poti?
Introducing a RL which is not ideal, means which is not infinite or negligible both results in a loss of signal. Means, only a certain portion of signal is available. If you think in the frequency domain (if you assume sinus functions), then only the fraction



is available. You see from this relation, that the error depends on frequency. So, any connected RL introduces a frequency dependent signal divider.

I think you should determine the inductance L of your self fabricated Rogowski coil to find out what sort of load impedance RL is suited.

Good luck,
Kai