Here is a simple 12 volts DC to AC inverter circuit. This 120V AC power source is built with a simple 120V:24V or 110V:24V center-tapped control transformer and four additional component. This circuit outputs a clean 200-V pk-pk square wave at 60 Hz and can supply up to 20W. The circuit is self-starting and free-running.
If Q1 is faster and has a higher gain than Q2 is will turn on first when you apply the input power and will hold Q2 off. Load current and transformer magnetizing current then flows in the upper half of the primary winding, and auto transformer action supplies the base drive until the transformer saturates.
When that action occurs, Q1 loses its base drive. As it turns off, the transformer voltage reverse, turning Q2 on and repeating the cycle.
The output frequency depends on the transformer iron and input voltage but not on the load. The frequency range between 50 to 60 Hz with a 60-Hz transformer and car battery or equivalent source. The output voltage depends on turns ratio and the difference between input voltage and transistor saturation voltage. For higher power, use larger transformers and transistors.
This type of 12V inverter normally is used in radios, phonographs, hand tools, shavers and small fluorescent lamps. It will not work with reactive loads (motors) or loads with inrush currents, such as coffee pots, frying pans and heaters.