MASON'S GAIN FORMULA
The relation between an input variable and an output variable of a signal flow graph is given by Mason's Gain Formula.
For determination of the overall system, the gain is given by:
Pk = forward path gain of the Kth forward path.
∆ = 1 - [Sum of the loop gain of all individual loops] + [Sum of gain products of all possible of two non-touching loops] + [Sum of gain products of all possible three non-touching loops] + .......
∆k = The value of ∆ for the path of the graph is the part of the graph that is not touching the Kth forward path.
From the above SFG, there are two forward paths with their path gain as -
There are 5 individual loops in the above SFG with their loop gain as -
There are two possible combinations of the non-touching loop with loop gain product as -
In above SFG, there are no combinations of three non-touching loops, 4 non-touching loops and so on.
Draw the Signal Flow Diagram and determine C/R for the block diagram shown in the figure.
The signal flow graph of the above diagram is drawn below
The gain of the forward paths
P1 = G1G2G3 ∆1 = 1
P2 = -G1G4 ∆2 = 1
L1 = - G1G2H1
L2 = -G2G3H2
L3 = -G1G2G3
L4 = G1G4
L5 = G4H2
Non touching Loops = 0