This 120V ac power source is built with a simple 120V : 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 occuts, Q1 loses its base drive. As it turns off, the transformer voltage reverse, turning Q2 on and repeating the cycle.

source:http://apowersupply.com/12-vdc-battery-operated-120-vac-power-source-40.html