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do inverters work how i think they work?

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ok, this is how i think a 12v to 240v (or 120v for the US) ac inverter works

12 volts goes into amplification circuit (solid state, and a DC-AC rectification circuit (multivibrator?)
amplified and rectified current is "forced" into 12 - 0 - 12 to 120 or 240 v step up conventional or toroidal transformer.

correct me if im wrong

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Nope. Not in simple square-wave inverters.
There is no rectifier. A rectifier converts AC to DC. The big battery is already DC.

There is no amplifier. The transformer steps-up the voltage.

An oscillator (also called a multivibrator) with very high input and output currents has two opposite outputs that drive the center-tapped low voltage winding (12 - 0 - 12) of a stepup transformer. 

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