A Comparative Study of Multi-Frequency and Sampled-data Models for PWM DC-DC Converters

PWM DC-DC converters have recently been modeled by the high order multi-frequency approach for operating point calculations, steady-state ripple and small-signal stability analysis. In most applications of this method, it is assumed that inductor currents are in continuous mode and the discontinuous mode is largely neglected. In this paper, the derivation of low-order sampled-data models are summarized by an example. It is shown that the sampled-data models can also handle discontinuous inductor current and transitions between the continuous and discontinuous modes. Next, the use of the low order sampled-data models in reproducing the results obtained using the far more computationally intensive multi-frequency models in the literature is studied by examples. Specifically, using the sampled-data models, it is shown that the steady-state ripple for such converters in continuous inductor current mode and discontinuous inductor current mode can be easily computed. For converters with state feedback, the small-signal stability of the operating point, following the multi-frequency literature, is assessed using a Jacobian needed in the steady-state computations