Variable structure modeling and design of switched-capacitor converters

Switched-capacitor (SC) converters are a type of variable structure systems. The conventional approach of maintaining regulation in these converters is a feedback control developed from linear systems theory, and it is based on the approximate small-signal linearized models of these circuits. However, the simplicity of such an approach sacrifices performance (poor transient response and sometimes steady-state instability are the result of a design based on the use of an approximate linearization) for convenience and cost. This paper discusses the (SC) converters from the viewpoint of nonlinear systems, and based on this, takes a variable structure feedback approach. The (SC) circuits theory is revisited, and a new approach of modeling, which gives an accurate nonlinear description of their operation is discussed. Based on the principle of energy balance applied to the output filter capacitor, an exact relationship between the instantaneous output and input currents in the charging and discharging phases is derived, leading to the derivation of a unique large-signal dynamic model for both alternative operating phases. Together with a defined switching function, it forms the proposed variable structure model. The resulting solution shows that a nonlinear approach can deliver an improved performance in the dynamic and steady-state behavior. Experimental results performed on a two-phase (SC) converter verify the theory.