# 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: Where,

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. ### Forward Path

From the above SFG, there are two forward paths with their path gain as - ### Loop

There are 5 individual loops in the above SFG with their loop gain as - ### Non-Touching Loops

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.

Where,  ## Example

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

Individual loops

L1 = - G1G2H1

L2 = -G2G3H2

L3 = -G1G2G3

L4 = G1G4

L5 = G4H2

Non touching Loops = 0  ### Feedback   