Linear Circuit Models of PWM Flyback and Buck/Boost Converters

A new method of modeling PWM converters operating in continuous conduction mode (CCM) is introduced. The procedure of deriving the models consists of three steps. First, static voltage and current transfer functions of the idealized switching part of the converters are found. Second, the linearization of these transfer functions at the operating point is carried out and the idealized switching part is replaced by dependent current and voltage sources. Third, the equivalent average resistance (EAR) of parasitic resistances and equivalent average voltage (EAV) of offset voltage sources of switches are determined using the principle of energy conservation. The method leads to linear dc and small-signal circuit models of a PWM converter. The obtained models give the same dc and small-signal characteristics as the state-space averaging method. To illustrate the method, the analysis of the PWM flyback converter is given, taking into account parasitic resistances of the transformer, the filter capacitor, the switch, and the diode as well as the diode threshold voltage. Design equations for dc voltage transfer function, efficiency, and small-signal characteristics are derived.