Electronic – Is this pulse transformer in saturation

If you were really applying 230V there would be a fire - you are more likely to be applying a current through the CT that is sourced from an AC voltage and that voltage happens to be 230V.

So the real issue is how much current is the primary being fed. It's the primary current, and the core material that determine saturation. If you know the exact specification of the core materials and you had the appropriate manufacturer's data you can calculate this but where does this get you? If you do a test by injecting current (as you appear to be doing) then use this data.

I'll also point out that putting the recommended burden resistor on the secondary will significantly reduce the point at which the CT core saturates. You should have a burden resistor normally so I can't understand why you are testing without one. For instance, if the primary inductance (a single turn) is (say) 10 uH, this will have an impedance of about 3 milli ohms if the AC is 50 Hz. This impedance is "shunted" by the secondary burden resistor (referred to the primary) and reduces the current thru the primary magnetizing inductance by diverting current thru the secondary - if the burden resistance is (say) 100 ohms it will appear on the primary side as a resistance of: -

\$\dfrac{100\space\Omega}{(turns\space ratio)^2}\$ = 16 micro ohms

Clearly this is a lot smaller than the impedance of the primary single turn and duly reduces magnetization current which, in turn, reduces the point at which the core saturates.

No matter how you look at it you are pumping DC into the transformer primary. The FET's source is going to be wanting to produce a square wave from 0V to +12V and the transformer will want a primary waveform that has an average value of zero volts. Somewhere along the line you might be getting saturation because you are not "resetting" the flux in the core. In other words residual flux left from one switching cycle gets built on by the next cycle and the transformer is said to be "walking into saturation".

Get this bit right then start to worry about the secondary because unless you drive the primary correctly you will be fighting a losing battle.