The following image is the schematic diagram of 1000W power inverter circuit:
The circuit is based RFP50N06 MOSFET, converting 12VDC battery to become 110V or 220V AC voltage depended to the transformer used in the circuit. This inverter circuit produces stable square wave at 60Hz. Recommended IC1 is LT1013 which offers better drive, but you may use LM358. The heatsink should be use for the MOSFET.
Using a rebuilt Microwave transformer as shown below, it should handle about 500W Maximum