Mason’s Gain Formula

Mason’s Gain Formula

Transfer function of a system in a Signal Flow Graph is the overall gain between the output node and the input node.
Using Mason’s Gain Formula one can reduce a given system into its transfer function in just one step.

Where,
C(s) = output
R(s) = input
T = Transfer Function of the system
$\small P_i$ = the $\small i^{th}$ forward path gain
∆ = 1 + $\small {(-1)}^n$sum of product gain of all the combinations of n non touching loops.
where, n is set of natural numbers
$\small \triangle i_{}$ = 1- gain of the part of graph which does not touch the $\small i^{th}$ forward