The Signal Flow Graph is a directed graph-based method for analyzing linear microwave networks that maps scattering parameters ($S_{ij}$) onto nodes representing incident and reflected wave variables at each port. Theoretically, the network behavior is defined by branches with coefficients equal to S-parameters connecting specific pairs of nodes (input-to-output), subject to formal rules governing series multiplication, parallel addition, self-loop elimination via determinant terms $(1 - \text{loop gain})$, and node splitting for complex topologies. This concept serves as a mathematical abstraction within microwave engineering that translates circuit topology into algebraic systems solvable using Mason's Gain Formula principles.
The Signal Flow Graph is a directed graph-based method for analyzing linear microwave networks that maps scattering parameters ($S_{ij}$) onto nodes representing incident and reflected wave variables…