Automatic Symbolic Analysis Of Circuits Using Piecewise Linear Models

There are many methods for analyzing electric circuits symbolically, but they are mostly limited to linear circuits with only one state. This limits us to non-switching circuits, or initial value problems. This paper presents a method for analyzing circuits with piecewise linear elements, as in switches, diodes etc. It is based on the idea of using a symbolic solver to solve the circuit for each possible state, and then combining the results into a tree of all possible paths. With that it is also possible to analyze circuits with periodic switches, oscillating circuits, power electronics circuits etc. Calculating everything beforehand is also faster when doing paths with a larger number of states, compared to solving the circuit each time independently.