Modeling of DC–DC Buck Converters for Large-Signal Frequency Response and Limit Cycles

A zeroth-order-hold equivalent discrete-time model of the buck converter for computing its large-signal frequency response is developed and experimentally verified. It is shown that, with a dc bias and a sinusoidal variation of the input duty cycle, the frequency response of the output voltage from the converter shifts from underdamped behavior to damped behavior with increasing amplitude of the input sinusoid. It is observed that, with a given dc input bias and a given input amplitude beyond the range of the state-space linearized small-signal model, the converter behavior varies from exclusively continuous inductor current mode at low frequencies to behavior with continuous and discontinuous inductor current modes at high frequencies. The use of this sinusoidal input large-signal frequency response in predicting limit cycles induced by feedback of the output voltage using proportional and integral controllers for such converters is studied. Experimental results confirming the use of this large-signal frequency response are presented