This looks pretty good!



Don't confuse 'fc' with 'corner frequency'. Here it means 'center frequency'.
If you apply a sine signal to input of above integrator, then after integration the term 1/w appears, which is to be multiplied by 1/(R1 x C1). Means, Vout is proportional to 1/(w x R1 x C1), or, differently spoken, Vout is inversely proportional to 'f'.
In opposition to the performance of a RC filter you will not see something like a 'corner frequency' with above shown integrator, because if you draw a plot of Vout versus frequency there will not be any plateau.
But you will find a certain frequency, where the sine signal at output (concretely spoken the cosine signal) shows the same amplitude as the sine signal at input. This frequency is called 'center frequency' and its value is as stated in the picture.

But please remember, that your application totally differs from the situation above, because you don't apply a sine signal to input of integrator, but the output signal of your Rogowski coil. And this signal contains the time derivative of welding current. This is something totally different. From the calculation below, you will see, that an integration is needed to recover the welding current from its time derivative. After integrating the Rogowski coil signal there is no further frequency dependency (ideal components assumed, of course):

If your welding current to be measured is Isig(t), then Rogowsky coil gives a signal voltage of Urog(t) = M x dIsig(t) / dt. If you apply this voltage to the input of following integrator



then, assuming having an ideal operational amplifier without showing any input bias current and input offset voltage, at output the signal Uout(t) can be found, according to:



The minus results from the fact, that integrator is built using an inverting circuitry.

Provided that load resistance at output of Rogowski coil is properly choosen, what I discussed in another post, then you get at output of integrator an exact copy of welding current. No further frequency dependency and no corner frequency stuff!

By suited choice of 'R' and 'C' output signal height can be adjusted. But it's always an exact copy of welding current you see at output of integrator (again ideal components assumed)!

Kai