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You use your 12V to power an oscillator. The output of this oscillator is fed to a transformer which then steps it up to 220V AC. There are various techniques employed to make the step-up as efficient as possible. Try looking here for invertors/convertors/switchmode power supplies. Then try Wikipedia and Google.
Frank
For a low distortion output with high efficiency you can use a PWM circuit modulated by a 50Hz oscillator. The PWM circuit controls power MOSFETs which drive a transformer to get the 220V AC output.
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