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.


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)}^nsum 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