Static- and dynamic-circuit models of PWM buck-derived DC-DC convertors

A systematic derivation of DC-circuit and small-signal-circuit models and characteristics for pulse-width-modulated buck-derived convertors operating in the continuous conduction mode is presented. Starting from voltage- and current-transfer functions of an idealised switching part of the convertor and using the linearisation technique, pure linear-circuit models of lossless convertors are derived. To obtain the models of lossy convertors, the principle of energy conservation is used to derive an equivalent averaged resistance of all parasitic resistances and an equivalent averaged voltage of offset voltage sources of switches. The advantage of the models is that they can be directly utilised in standard circuit simulators. The models are especially convenient in analysing complicated convertor topologies and for including parasitic components. The proposed models lead to the same characteristics as those obtained by means of the state-space-averaging method. As an example, a forward convertor is analysed, taking into account all parasitic resistances and threshold voltages of diodes. A complete set of small-signal characteristics is given for this convertor. Models and expressions for DC and small-signal characteristics that account for parasitic resistances are also given for other multiswitch and transformer buck-derived convertors such as push-pull, half-bridge, and full-bridge circuits