There are loads of examples online..
eg.
Be realistic with power ratings - whatever current you want out at 120V, it will take more than 10x that at 12V.
Car starter batteries can handle high currents but cannot stand being run down, they are wrecked very quickly - and deep cycle batteries cannot handle such high currents..
500W out will need ~50A in. Typically higher powered inverters (or UPSs) use series batteries and higher voltages, to keep the current down to practical levels. Mine use 24V or 48V, for 1500W - 2000W out, short term.
eg.
Sine Wave Inverter Circuit using PIC16F72
The post details comprehensively regarding how to build a pure sinewave inverter circuit using microcontroller circuit with PIC16F72 The following
DIY Cheap 1000W Pure Sine Wave Inverter (12V to 110V/220V)
DIY Cheap 1000W Pure Sine Wave Inverter (12V to 110V/220V): Car batteries for powering you home? Build a low cost 12V to 220V (DC-AC) Pure Sine Wave Inverter from scratch! The project is based on the low cost EGS002 SPWM driver board module. The DIY inverter board can handle up to 1kW (depending...
Be realistic with power ratings - whatever current you want out at 120V, it will take more than 10x that at 12V.
Car starter batteries can handle high currents but cannot stand being run down, they are wrecked very quickly - and deep cycle batteries cannot handle such high currents..
500W out will need ~50A in. Typically higher powered inverters (or UPSs) use series batteries and higher voltages, to keep the current down to practical levels. Mine use 24V or 48V, for 1500W - 2000W out, short term.