Small-Signal Modeling of SIMO DC-DC Converters and Comparative Continuous/Discrete-Time Results

Fundamental small-ripple approximation in a well- known averaging technique tends to limit the accuracy of continuous-time (CT) small-signal models of pulse-width- modulated (PWM) DC-DC converters up to 1/10^th of the switching frequency. This paper shows that their accuracy significantly degrades even at much lower frequencies for single-inductor- multiple-output (SIMO) DC-DC converters due to higher current ripple with multiple switch configurations. CT small-signal models are derived for a SIDO buck converter, and the transfer functions using circuit averaging and state-space averaging (SSA) techniques are found to be identical. Thereafter, exact discretetime (DT) large-signal models and accurate small-signal models are derived. Both CT and DT small-signal models are compared, and the accuracy of the latter is justified with the actual switch simulation using MATLAB. Frequency responses demonstrate significant inaccuracies using CT small-signal models for varying system parameters. The results will be useful for accurate modeling and stability analysis using DT modeling for SIMO DC- DC converters and also to understand the underlying dynamics.