Exact Dynamic Modeling of PWM DC-to-DC Power Converters—Part I: Continuous Conduction Mode

This paper follows on from the first paper, Part I, where a general\r\nformulation of a describing function approach to frequency response\r\ndetermination of switched linear networks, such as PWM converters, was\r\nsimplified and updated. The models assume a piecewise linear state space\r\nequation description of the system and results in a closed form solution for\r\nthe sought after frequency response. In Part I, model derivation was\r\ndemonstrated for the case of PWM converters operating in the continuous\r\nconduction mode (CCM). This operating mode does not feature any state dependent\r\nswitching times. In this paper, Part II, frequency response models for any\r\ntransfer function for PWM converters operating in discontinuous conduction mode\r\n(DCM) are derived based on the theory presented in Part I. This operating model\r\nfeatures state dependent switching times. The describing function models\r\ndeveloped are exact and therefore, in terms of accuracy, are to be preferred\r\nover averaged models which are widely used. The example of a boost dc-to-dc\r\nconverter operating in DCM is simulated to obtain the control to output and\r\ninput to output frequency responses and are compared with the models derived\r\nhere. Excellent agreement between the simulated and model responses was found.\r\nMatlab code implementing the analytical models is also presented which the user\r\ncan adapt for any other PWM converter topology. The models derived here may be\r\nused as a basis from which simplified models may be derived while still\r\npreserving required accuracy.