Comprehensive Canonical Small-Signal Model for Digital Control-Based DC–DC Converters Incorporating Current Control Loop

The canonical small-signal model, a standard representation of each small-signal model for three basic DC–DC converters (buck, boost, and buck-boost), is instrumental in capturing the dynamic behavior of DC–DC converters operating in continuous conduction mode. Analytical transfer functions derived from this canonical model are readily applicable to DC–DC converters employing voltage control loop. However, for converters incorporating a current control loop, certain resultant transfer functions related to the inductor current necessitate additional mathematical operations for accurate application because the actual inductor is replaced by an equivalent inductor in the canonical model and the current flowing through this equivalent inductor differs from the actual inductor current, particularly in boost and buck-boost converters. Hence, this paper proposes a comprehensive canonical small-signal model suitable for three basic DC–DC converters accommodating both current and voltage control loops. This model is formulated by initially fixing the position of the inductor and then repositioning all components around it, ensuring that current sources do not traverse the actual inductor during the development process of the comprehensive canonical small-signal model. Consequently, the resultant transfer functions from this canonical model can be directly applied to all three basic DC–DC converters without requiring further manipulations. Subsequently, open-loop transfer functions and closed-loop input/output impedances incorporating the current control loop are derived based on this proposed canonical model. These derivations are validated through simulations using MATLAB and switching model based PLECS software, as well as through representative experimental results for the digital control-based boost converter.