Small-signal modeling of current-mode controlled modular DC-DC converters using the state-space algebraic approach

Abstract

Small-signal models are useful tools to preliminary understand the dynamics of interconnected systems like modular dc-dc converters which find a wide range of industrial applications. This work proposes a state-space-based averaged small-signal model in symbolic form for a peak current-mode controlled parallel-input/parallel-output buck converter operating in the continuous-conduction mode. In modeling the converter power-stage each module is independently represented. For modeling the current-mode control the state-space algebraic approach is used to incorporate the current-mode control-law into the power-stage equations. For each module two parasitic elements in addition to the current-loop sampling action are included in the derivation. Furthermore, the control-to-output voltage transfer functions are presented in symbolic form for two cases of interest: the first when the converter has two non-identical modules to study the effect of inductor mismatch, and the second when the converter is composed of n-connected identical modules to assess the effect of varying the number of modules. All responses from PSIM cycle-by-cycle simulations are in good agreement with the mathematical model predictions up to half the switching frequency.