MASON'S GAIN FORMULAThe 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,
P_{k} = forward path gain of the K^{th} forward path. ∆ = 1  [Sum of the loop gain of all individual loops] + [Sum of gain products of all possible of two nontouching loops] + [Sum of gain products of all possible three nontouching loops] + ....... ∆_{k} = The value of ∆ for the path of the graph is the part of the graph that is not touching the K^{th} forward path. Forward PathFrom the above SFG, there are two forward paths with their path gain as  LoopThere are 5 individual loops in the above SFG with their loop gain as  NonTouching LoopsThere are two possible combinations of the nontouching loop with loop gain product as  In above SFG, there are no combinations of three nontouching loops, 4 nontouching loops and so on. Where, ExampleDraw 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 P_{1 = G1G2G3 ∆1 = 1} P_{2} = G_{1}G_{4} ∆_{2} = 1 Individual loops L_{1} =  G_{1}G_{2}H_{1} L_{2} = G_{2}G_{3}H_{2} L_{3} = G_{1}G_{2}G_{3} L_{4} = G_{1}G_{4} L_{5} = G_{4}H_{2} Non touching Loops = 0
Next TopicExamples with Explanation
