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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:


MASON GAIN FORMULA

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.


MASON GAIN FORMULA

Forward Path

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


MASON GAIN FORMULA

Loop

There are 5 individual loops in the above SFG with their loop gain as -


MASON GAIN FORMULA

Non-Touching Loops

There are two possible combinations of the non-touching loop with loop gain product as -


MASON GAIN FORMULA

In above SFG, there are no combinations of three non-touching loops, 4 non-touching loops and so on.

Where,


MASON GAIN FORMULA
MASON GAIN FORMULA

Example

Draw the Signal Flow Diagram and determine C/R for the block diagram shown in the figure.


MASON GAIN FORMULA

The signal flow graph of the above diagram is drawn below


MASON GAIN FORMULA

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


MASON GAIN FORMULA

MASON GAIN FORMULA




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