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 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 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 - Non-Touching LoopsThere 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, 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 |