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Theoretical Half-Bridge Inverter Explainantion

Hello fellow engineers !!!

We recently learned about the half-bridge inverter, but I can't really understand why we used capacitors in the bridge.

wikipedia says "Low-order current harmonics get injected back to the source voltage by the operation of the inverter. This means that two large capacitors are needed for filtering purposes in this design."

but it needs more explanation for newbies.

any help?
 
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I don't like the term half bridge because it can mean two different circuits.
I don't like the term inverter because it can mean two different things.
 
here you go, I think this is a well known circuit. but maybe there are variants.

About the terminology, I agree. I think I should use "DC\AC Converter".
 

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