This is the scheme diagram of 500W power inverter circuit which build using 10 pieces of well-known NPN power transistor 2N3055 to amplify the AC signal produced by multivibrator. The frequency generator / multivibrator is built based on transistors too. All of the components is easy to gathered from the electronic store.
This 500W power inverter converts a 12V input voltage from the car battery (rated at 12V/50A for maximum power output). The output will be 220V AV output, or you may use 110V transformer if you want to achieve 110V AC output. The power transistor 2N3055 should be mounted on heatsink, so the heat will be spread over the heatsink and prevent the transistor from overheeating.
Warning: This is a high voltage circuit, use safety equipment when trying to run this circuit.