what's the working principle of this inverter circuit

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The 555 IC makes a square wave.
Q7 inverts the signal.
Q3,Q10 is on while Q6,Q9 are off, then Q3,Q100 is off while Q6,Q9 are on.
12 volts is put across 1/2 the primary then 12 volts is across the other side of the primary. (AC Square Wave)
The transformer increases the voltage.
The out put of the transformer is square wave!
 
A 555 can never give a pure square wave resulting in a DC flowing in the transformer that may lead to core saturation.

Its very necessary that the "square wave" is from a "FlipFlop" to ensure that its a pure square wave.
 
A CD4047 has an oscillator and a divide by 2 FlipFlop that produces a perfect squarewave.

Did you know that many modern electronic products will not work from a squarewave inverter? Normal electricity is a sinewave that has a peak voltage 1.414 times higher than a squarewave even when both have the same RMS average voltage. But many modern electronic products rely on charging their main filter capacitor to the peak voltage of the sinewave so when a squarewave is used then the peak voltage is too low. Notice the old fashioned incandescent light bulb as the load in the schematic? It works from the RMS average voltage, not the peak voltage of a sinewave.
 

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Normal electricity is a sinewave that has a peak voltage 1.414 times higher
I live in 120V land not 220V.
A sine wave inverter will have a 120 RMS and a peak of 160 volts.
A square wave will have +120 and -120 and no other voltage.
I have seen inverters that have a wave like this: 0, 0, 160, 0, 0, -160, 0, 0 The idea is, the peak needs to be 160 for the products that live off of peak and have a average of 120 for things like heating elements.
In this case you will have a time with no MOSFETs on, Top MOSFET on, no MOSFETs on, Bottom MOSFET on.
Last time I made one of these I used a CD4017 counter to get the timing.
 
That is called "a modified sinewave" but actually it is a modified squarewave.
 
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