A Unified Behavioral Average Model of Sepic Converters with Coupled Inductors

An average model of SEPIC converters with coupled or uncoupled inductors was developed and verified against cycle-by-cycle s i m u l a t i o n s . The model can be used as-is by any modern circuit simulator to run steady state (DC), large signal (transient) and small signal (AC) analyses. The leakage inductances were taken into account and treated separately from the mutual inductance. The primary and secondary coupling coefficients were incorporated as parameters in the model. The coupling coefficients can be set to a value from zero to almost one, representing the complete range o f poss ib le SEPIC topo log ies . a transformer, in the sense that current flows on both sides at the same time, while both sides are loaded by capacitors (Cfi, Cs and Cp, Fig. 1). The same modeling problem appears in other topologies with coupled inductors (e.g. C'uk converter). A general modeling solution, suitable for coupled inductors converters, is proposed in this paper. The average modeling methodology [3, 4] used here hinges on the observation that by continuously applying the running average voltage (for a window of one switching period) across an inductor, the inductor will produce a running averaged current. The same reasoning applies to switched capacitors. Namely, by injecting the running average current into a capacitor, the capacitor will be charged to the running averaged voltage. This observation is based on the assumption that the switching frequency is much higher than the power stage bandwidth. Therefore, the average voltages across the capacitors and average currents through the inductors do not change appreciably during one switching period. Namely, the voltages and currents that will be produced by the average model of the proposed methodology are the ripple-less values, as if we have operated the switch at infinite frequency but with the same duty cycle values.