so you think current of 12v dc littleAbout the transformer. It sounds as though you are driving the 12 volt winding of a 220V to 12V step-down transformer.
12 VAC is 33.8 V P-P but you need more than that.
Both windings of your transformer have resistance and the winding that is being driven will have to supply magnetizing current (this is current that results from driving an inductor with AC) and some core losses, and this will result in a voltage drop within the driven winding. Further, if you load the un-driven winding there will be an additional voltage drop in that winding.
If you go to a higher frequency the magnetizing current will get smaller quickly. If you go to too high of a frequency other losses start to take over, so for a given transformer and a given waveform there is an optimum frequency.
A product that I am designing generates 230 VAC (sine) waveforms that are loaded very lightly, but even at that I have to drive the 5 volt windings of a little 1.1 VA transformer with 19.7 V P-P.
The yellow trace in the picture below shows the magnetizing current waveform in a 1.5 VA transformer I tested. The vertical scales are 200 am/div for magnetizing current (yellow) on a 6 volt winding and 100 volts/division for the 220 VAC winging (blue). Notice that the magnetizing current is 1.4 amps P-P.
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