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You may notice that the transformer of sine wave inverter has 0V - 8V primary to 0V - 220V/240V secondary winding. But for a square wave inverter kit, you require a transformer of 12V - 0V - 12V (Bifiler winding) primary to 0V - 230V secondary winding with a tap at 160/170V (for CCCV SCR/TRIAC charging). So normally it is not possible to use the transformer with square wave inverter kit. I am writing from my practical experience.
Yes
Generally, sign wave transformer will handle the same power in square wave too
While designing a transformer, sign or squire is an insignificant design parameter.
According to area product method, sign wave transformer sizes are 10% less than square wave transformer.
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