Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

Switching Function Analysis

The process of defining the instantaneous voltage and current relationships based on the switching state (ON or OFF). This function dictates the system's behavior and is crucial for deriving the averaged model equations.
📜

The statement of the theorem

Let s(t)∈{0,1}s(t) \in \{0, 1\} be the switching state. The instantaneous voltage vsw(t)v_{sw}(t) across the inductor is defined piecewise: vsw(t)=s(t)Vin−(1−s(t))Voutv_{sw}(t) = s(t) V_{in} - (1-s(t)) V_{out} The system dynamics are governed by the state equation dx⃗dt=f(x⃗,u⃗,s(t))\frac{d\vec{x}}{dt} = f(\vec{x}, \vec{u}, s(t)), where ff incorporates the switching function s(t)s(t) and its associated voltage/current relationships.