Mason's Gain Formula
Mason's Gain Rule:
Mason's gain formula is a method for finding the transfer function of a linear signal-flow graph.
Let us consider a system,
Mason’s gain rule is given by:
1) Find the forward paths and their gains:
A forward path is a path from R(s) to C(s) that does not cross the same point more than once. There are two forward paths in this example, so we have a j = 1 and a j = 2. The two paths are:
2) Find the loops and their gains:
A loop is a closed path that can be negotiated without crossing the same point more than once. There are five loops in this example:
3) Find the Δjs:
4) Find Δ:
Since there are no non touching loop pairs in this example, D will just be one minus the sum of the loop gains:
The Solution:
