D-Q models for resonant converters

A systematic modeling method for resonant converters is proposed. This method develops low frequency D-Q models for resonant converters. For a given resonant tank, its orthogonal counterpart is constructed. By combining these two orthogonal tanks, a complex circuit is obtained. The complex circuit is then expressed into a D-Q form circuit. Every variable in the D-Q circuit can be treated as a rotating vector with its envelope modulated by a low frequency function. By removing high frequency terms, the low frequency D-Q model of the resonant converter is derived. This D-Q model has a DC operating point and can predict large signal transitions of the resonant converter with little computation. By perturbing the D-Q model around its DC operating point, equivalent circuits for the small signal models are derived. As an example, the series-parallel resonant DC/DC converter is analyzed by the proposed method. Startup process by the D-Q model agrees with the PSPICE simulation results very well. From the equivalent circuits of the small signal model, transfer functions of input-to-output, control-to-output are obtained as well as the output impedance. They are all verified by SIMPLIS simulation. This modeling technique is applicable to any resonant converter and need little computation.