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Signals and Systems by Smarajit Ghosh

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5.6 MASON’S GAIN FORMULA

To find the transfer function of a complicated system of block diagram reduction technique is a cumbersome process because step by step reduction of block diagram is required. On the other hand, it is possible to get the transfer function very easily by using Mason’s gain equation given below:

 

image

 

where

N = Total number of forward paths

Pi = Gain of ith forward path

∆ = 1 – (Σ all individual feedback loop gain including self loops)

       + (Σ gain product of all possible combinations of two non-touching loops)

       – (Σ gain product of all possible combination of three non-touching loops)

       +— — — — — — — 

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