ece382-fall2011-block-diagram-signal-flow-graph-slides-4-pages3

S george lee purdue univ block diagrams signal flow

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Unformatted text preview: amp; Signal-Flow Graphs ECE382 15 / 31 Converting Block Diagram to Signal Flow Graphs C. S. George Lee (Purdue Univ.) Block Diagrams & Signal-Flow Graphs ECE382 16 / 31 Converting Block Diagram to Signal Flow Graphs Mason's Gain Formula The Mason's gain formula is given as: Ci (s) Tij (s) = = Rj (s) where k Pk k Pk : is the path gain of k th forward path. k : is the cofactor of the k th forward path determinant of the graph with the loops touching the k th forward path removed. : is the determinant of the graph. C. S. George Lee (Purdue Univ.) Block Diagrams & Signal-Flow Graphs ECE382 17 / 31 C. S. George Lee (Purdue Univ.) Block Diagrams & Signal-Flow Graphs ECE382 18 / 31 The Determinant The determinant can be interpreted as = 1 - (sum of all individual loop gains) + (sum of gain products of all possible combination of 2 non-touching loops) - (sum of gain products Summary on Mason Gain Formula 1 2 3 + (-1)k (sum of gain products of all possible combination of 3 non-touching loops) + + 4 5 of all possible combination of k non-touching loops). That is, =1- i 6 Li + 2 j Lj - 3 j Lj + + (-1)k k j Lj 7 19 / 31 C. S. George Lee (Purdue Univ.) Block Diagrams & Signal-Flow Graphs ECE382 C. S. George Lee (Purdue Univ.) Determine the number of closed loops and let it...
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