Quadratic DC/DC converter with autotransformer at the output side

A quadratic step-down converter with one low side switch and an autotransformer at the output is presented and treated in detail. The voltage transformation ratio, the voltage stress and the relationship of the inductor currents in dependence of the load current are calculated. An idealized mathematical description of the converter is derived and the large signal and the small signal model are determined. Furthermore, the transfer functions between the output voltage and the duty cycle and the input voltage are calculated. Dimensioning hints and equations are given. The most important voltage and current shapes and the step responses are shown by simulations.