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.
Inverter, is an electronic device or circuitry that changes direct current (DC) to alternating current (AC). The input voltage, output voltage and frequency, and overall power handling depend on the design of the specific device or circuitry. The inverter does not produce any power; the power is provided by the DC source.
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Using a rebuilt Microwave transformer as shown below, it should handle about 500W Maximum