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State equations based resonant converters modeling technique

State equations for resonant converters are developed by using orthogonal circuit synthesis. Low frequency state variables are selected for the resonant circuit, such as envelopes of resonant inductor current and resonant capacitor voltage, phase angle between inverter output voltage and output current. For a given resonant tank, its orthogonal counterpart is constructed. These two orthogonal tanks are combined into a complex resonant tank. By applying Kirchhoff 's Voltage Law (KVL) and Kirchhoff 's Current Law (KCL) to the complex circuit, complex differential equations are derived. By separating real and imaginary parts of the complex differential equations, state equations for the resonant tank are obtained. For resonant DC/DC converters, other state equations are derived from rectifier stages. These derived state equations for resonant converters contain only low frequency state variables and can predict large signal transitions. By perturbing these equations around the DC operating point, transfer functions such as input-to-output, control-to-output are derived. The proposed method is verified by SIMPLIS simulation results. This method can aid closed-loop control design for resonant converters.