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Mason's Rule




: M = rac{y_{out}}{y_{in}} = \sum_{k=1}^N rac{M_k \Delta\ _k}{ \Delta\ }

where yin = input-node variable
yout = output-node variable
M = gain between yin and yout
N = total number of forward paths between yin and yout
Mk = gain of the kth forward path between yin and yout
Δ = 1 - (the sum of the gains of every individual loop) + (the sum of the products of the gains of all possible combinations of two non-touching loops) - (the sum of the products of the gains of all possible combinations of three non-touching loops) + ... and so on and so forth.
Pmr = the gain product of the mth possible combination of r non-touching loops (1 ≤ r ≤ N ) (Two parts of a signal-flow graph are non-touching if they do not share a common node)