Combining principles; Theorem 2

A combining network driven by multiple voltage sources as shown in the figure of Theorem 1 is equivalent to the same network driven by a single voltage source as shown below.

Single source equivalent network

Combining principles; Theorem 1

Let there be \( M \) branches in the arbitrary combining network shown below. The output voltage \( v_{load} \) of the network is proportional to the source voltages \( v_{src}^{\langle k \rangle} \) scaled by the arbitrary networks interconnecting the branches to the combining node and the combining node to the load.

Abstract, arbitrary combining network

Two port parameter definitions

Since there are numerous valid definitions of two parameters depending on the reference point used, the reference currents and voltages used as the basis of further work will be described here. The diagram below shows the orientation of reference currents and voltages.

Two port reference diagram

Relating admittance and scattering parameters

By returning to the original S-parameter definitions by Kurokawa [1] and taking some care to preserve the noncommutative properties of the matrix expressions then relatively simple expressions valid for an arbitrary number of ports may be derived.

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