Analysis of feedback networks with multiple dependent sources by superposition

We present an analytical method for the derivation of the return ratio in linear circuits with multiple dependent sources. We show how to find the matrix return ratio from the circuit, by using a superposition of test and input sources, and how to obtain the closed-loop behavior using a linear fractional transformation. The return ratios and closed-loop transfer function are presented in matrix form. The suggested procedure does not require one to solve the circuit; instead, the components of the relevant matrices are computed directly. Deriving the return ratio in matrix form allows us to apply standard tools to study the closed-loop behavior of the circuit and the influence of the components on the latter.