A computer method for modelling periodically switched networks

Based on systematic decomposition of circuit graphs, a computer method for modelling a class of periodically switched networks is developed. The method is applicable to any switched network whose switching frequency is much greater than the natural frequencies of the constituent topologies. The method involves identifying the “fast” part of the circuit and separately modelling it as a time-invariant N-port. In modelling the “fast” part, the remaining “slow” part is treated as being composed of constant sources. The dynamics of the “slow” part is then restored in the final stage of the overall modelling. In this paper, the authors specifically discuss the modelling of the “fast” part of a periodically switched circuit such as the DC/DC converter, and demonstrate how it can be used to obtain a complete averaged model. The method is suited for any pulsewidth modulated (PWM) converter that operates in either operating modes. To illustrate the proposed method, the Cuk converter is considered and its averaged models derived for the three possible operating modes, namely continuous inductor current mode, discontinuous inductor current mode, and discontinuous capacitor voltage mode