It can be shown that output signal of an integrator driven by a Rogowski coil is proportional to 1/RC, where R and C are the parts of integrator.
But when giving a sine to input of an integrator, output will be proportional to 1/wRC. So, when wanting to calibrate an integrator by the help of a sine, then w = 2*pi*f, must be known very accurately.

Why not using a quartz stabilized sine generator then, like the following one?





A 32768Hz quartz in combination with CD4060 is used to produce a 256Hz square wave. Amplitude of this square wave is divided by ten by the 39k and 3k9 resistors. 10µF electrolytic removes DC component. The first OPamp of TL084 is part of a third order Butterworth low pass filter yielding a corner frequency of about 260Hz. The reason why here is not used a different order low pass filter is, that the first stage of third order filter is a passive one, allowing to remove the sharp edges of square wave coming from CD4060. An active low pass filter would have problems with the sharp edges. Due to unavoidable imperfections of HF performance of TL084 the edges would appear at output nearly unsuppressed.

After the first two OPamps, which form the third order Butterworth low pass filter an additional fourth order Butterworth low pass filter follows, producing a sine of very low distortion: Only the fundamental of square wave is passed, all the harmonics are suppressed.

At output of the fourth OPamp, a sine with an amplitude of about 2.5V can be observed. The following poti and TL051 allows to adjust amplitude within a range of 0...10V.
Directly at output a 1µF cap can be seen. This cap is needed to remove even the least amount of offset voltage. Prahlads integrator amplifies DC components by a factor of 100. So, any offset voltage from the sine generator would cause huge errors!

Directly at output of sine generator the signal also goes to a peak detector allowing to measure the amplitude of sine fed to input of integrator. Here also a 1µF cap is used to isolate the integrator fom input bias current of first OPamp of TL052A.
Connect the output of peak detector to a good DVM (digital voltage meter) having a high input impedance.

Why a 256Hz sine?
To keep the noise at minimum a 32.768kHz quartz is used. So, the frequency of sine is crooked 'by design'.
As the welding current is phase angle controlled it contains 50Hz and lots of harmonics. So, chosing a frequency in the 100Hz range is a good idea.
256Hz was choosen, because it's a good compromise between signal height at output of integrator and settling time of peak detector. At 256Hz the integrator shows a 'gain' of 1 / 2 * pi * 256 * 47k * 47e-9 = 0.28, so a rather high sine amplitude at input is needed to produce a sufficient high signal at output. This dratsically reduces the influence of offset voltage errors at the peak detector and guarantees very precise results.

To calibrate the integrator do the following:
First, adjust the offset at output of integrator to zero, with grounded input.
Then, connect sine generator output to input of integrator and adjust amplitude to about 10.00V, or whatever you need. Look what the microcontroller outputs and adjust the total gain of signal chain by the help of according gain trimmer to wished value. This procedure will include the whole signal chain, not only the integration cap and reference voltage but also the ADC!

You can also adjust additional offset voltage of signal chain: Adjust the poti to a much much smaller amplitude of sine. Look what the microcontroller outputs and adjust total gain of signal chain by according offset trimmer to wished value. Afterwards repeat the above gain trimmer adjustment.

Kai