Impedance Analysis of Digital Control Based DC–DC Converter for Both Single and Dual Control Loop

This paper analyzes the closed-loop input and output impedances of the digital control based DC–DC converter for both single and dual control loop. Unlike the previous method about impedance analysis dealing with only a single voltage control loop condition, the analytical closed-loop impedances are obtained from the mathematical diagram and expression for both the single current control loop and the dual control loop based on a canonical small-signal model where the dual control loop include an outer voltage and an inner current control loop. Since the canonical small-signal model represents common DC–DC converters (Buck, Boost and Buck-boost), the obtained closed-loop impedances can be equally applied to three DC–DC converters through only using corresponding parameters. The additional feature is that the time delay caused by digital implementation such as digital computation delay, zero-order hold, and pulse width modulator that may affect the dynamics of the control system is considered. From the theoretical analysis, it shows that the time delay influences mainly the closed-loop input impedance and as well, the difference with or without the time delay becomes obvious as the crossover frequency of an inner current control loop increases. On the other side, the closed-loop output impedance is hardly affected by the time delay across the entire frequency range. Comparative analysis between theoretical and switching model based simulations alongside experimental validations are presented to verify the theoretically derived closed-loop impedances and the effect of the time delay.