The averaged models of switch-mode DC-DC power converters are discussed. Two methods of averaged model derivation are considered - the first, based on statespace averaging and the second, on the switch averaging approach. The simplest converters: BUCK, BOOST and BUCK-BOOST working in CCM (continuous conduction mode) or DCM are taken as examples in detailed considerations. Apart from the ideal converters, the more realistic case of converters with parasitic resistances is analyzed. The switch averaging approach is used more frequently than the other and is believed to be more convenient in practical applications. It is shown however, that in the deriving the averaged models based on the switch-averaging approach, some informalities have been made, which may be the source of errors in the case of converters with parasitic resistances, or working in DCM mode.
The separation of variables approach to formulate the averaged models of DC-DC switch-mode power converters is presented in the paper. The proposed method is applied to basic converters such as BUCK, BOOST and BUCK-BOOST. The ideal converters or converters with parasitic resistances, working in CCM and in DCM mode are considered. The models are presented in the form of equation systems for large signal, steady-state and small-signal case. It is shown, that the models obtained by separation of variables approach differ in some situations from standard models based on switch averaging method.
Small-signal transmittances: input-to-output and control-to-output of BUCK converter power stage working in CCM or DCM mode are discussed. Ideal converter case and converter with parasitic resistances are considered separately. Derivations of small-signal transmittances, based on different approaches to finding the converter averaged models, are presented and the results are compared. Apart from theoretical considerations, some results of numerical calculations are presented.
In the description of small-signal transmittances of switch-mode power converters several characteristic frequencies are usually used, corresponding to poles and zeros of transmittances. The knowledge of these frequencies is important in the design of control circuits for converters and usually are assumed to be constant for a given power stage of a converter. The aim of the paper is to evaluate the influence of converter primary parameters and load conductance on characteristic frequencies. Analytical derivations and numerical calculations are performed for an ideal and non-ideal BUCK converter working in continuous or discontinuous conduction mode.
Averaged models: an AC large signal, DC and AC small signals of a current-controlled buck converter are described. Only peak current mode control of a converter working in the continuous conduction mode (CCM) is considered. The model derivation differs from the typical approaches presented in the literature and doesn’t refer to the multi-loop concept of a current controlled converter. The separation of the variables method is used in the model derivation. The resulting models are presented in the form of an equation set and equivalent circuits. The calculations based on the presented models are verified by measurements and full-wave PSpice simulations.