Transformers as equivalent circuits for switches: general proofs and D-Q transformation-based analyses

The equivalent circuits for the switches in DC-DC, DC-AC, AC-DC, and AC-AC converters are proved to be time-varying transformers. This result is used in the analyses of DC-DC converters, an eight-order current source rectifier-inverter, and a buck-boost inverter. The circuit D-Q transformation is proposed for the analyses of the AC converters such as inverters, rectifiers, and cycloconverters which include the time-varying transformers. Gyrators appear in the D-Q transformed inductors and capacitors of the AC converters. Few equational manipulations are required to determine the steady-state operating points and the small signal gains of the converters. The analysis result for the rectifier-inverter shows that the circuit has self-short-circuit protection capability and strong immunity in the parasitic inductor resistance