Why you want to use BJT as switch in your inverter circuit. The switching mechanism of inverter must have low response time. That is why most inverter circuits use MOSFET for switching. The following post on EG has full design for Modified Sine Wave Inverter with MOSFETs – engineersgarage.com/contribution/completing-modified-sine-wave-inverter-design-full-bridge-circuit-and-step-transformer-part. If any way, you want to make that with BJT, search for H-Bridge BJT and have a try on couple of H-Bridge BJT driver circuits.
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