On Dynamic Modeling of PCM-Controlled Converters—Buck Converter as an Example

Abstract

Peak-current-mode (PCM) control was published first time in open literature in 1976. The observed peculiar behavior caused by the application of PCM control in a power electronic converter have fascinated the researchers to attempting to capture the dynamics associated to it. It is commonly assumed that the peculiar phenomena originate from the sampling process in the PCM control. A resistor is usually connected as a load, when modeling the converter dynamics and during the frequency-response measurements. The load resistor will actually dominate the frequency responses and hide the real dynamics associated to PCM control. Other measurement problems will arise from the nonmodeled circuit elements dominating, especially, the high-frequency dynamic behavior of the converters. As a consequence of these problems, the PCM models are not usually properly validated. The investigations, in this paper, show the following: 1) the PCM models have to be accurate also at the low frequencies for ensuring, for example, stable design of output-current-feedback-controlled converters; 2) the high low-frequency accuracy can be obtained only by means of duty-ratio gain becoming infinite at the mode limit; 3) the high-frequency accuracy of the PCM models can be obtained by means of different high-frequency extensions; 4) the key for the PCM modeling lies in the proper duty-ratio constraints; and 5) the high-frequency magnitude and phase behaviors are caused by the second-harmonic-mode operation of the converter due to the frequency-response-measurement injection signal. The main objective of this paper is to show that such a modeling technique, which fully matches the aforementioned criteria, has been developed already in early 1990s and later elaborated for more a general form. Validation of the dynamic models is performed by simulation, where the converter and its operational environment are perfectly known. The load-resistor effect is removed computationally for performing the complete validation. A PCM-controlled buck converter is used as an example.