Here is a way to tell when your transfomer is saturating.
You put a resistor in the leg of the primary and put a scope across the resistor. You will be looking at the magnetizing current waveform across the resistor.
When your peak exciting current, B, is twice the average exciting current, A, saturation occurs.
This chart is for a square wave.
I also measured the input signal with an average reading voltmeter, not true rms, as recomended by Mike over at Magnequest.
Here is a transformer hitting the wall at 40 hertz with a sine wave.
The lower wave is the mag curent, upper is input to primary.
14.8 volt peak to peak saturates the x-former. Avg reading was 6.22 vac.
Here it is at 20 hertz.
Notice that the saturation voltage decreased to 7.40 volts peak to peak.
This is due to the lower frequency. The transformer saturates easier at the lower frequency. Avg. reading 2.77 vac.
Here is the same transformer getting smacked by a 40 hertz square wave.
The scope reading is wrong, there is actually a 11.4 volt peak to peak square wave being input.. Avg. reading was 4.42 vac.
The square wave saturates the transformer a little more easily.
Here is the square wave at 20 hertz:
The input voltage required to saturate the x-former dropped from 11.4 to 7.20 volts peak to peak, avg was 2.32 vac.
Just some more tidbits to file under your "useless information" directory!
Party on, Garth!