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Unformatted text preview: be n. Determine each loop gain, Li . Determine the loop gains of 2 non-touching loops, 3 non-touching loops, etc. (Note that all the possible combinations of j non-touching loops n out of n loops are .) j Determine the determinant of the graph, . Determine the number of feedforward paths and let it be k . Determine all the k th forward path gain, Pk . Determine the cofactor of the k th forward path determinant of the graph with the loops touching the k th forward path removed. (i.e., Determine P k for all the feedforward paths.) P Ci (s) Tij (s) = Rj (s) = k k k
Block Diagrams & Signal-Flow Graphs ECE382 20 / 31 Mason's Gain Formula - Example 1 Mason's Gain Formula - Example 1
Number of (single) closed loops = 3 L1 = G1 G4 H1 ; L2 = -G1 G4 G2 H2 ; L3 = -G1 G4 G3 H2 Number of two non-touching loops = none
1 C(s) G3 R(s) 1 E1 1 E2 G 1G 4 H1 -H 2 G2 Number of three non-touching loops = none Determine the determinant of the graph, = 1 - L1 - L2 - L3
R(s) 1 G3 1 E2 G 1G 4 H1 -H 2 G2 1 C(s) E1 Number of feedforward path = 2 P1 = G1 G4 G2 ; P2 = G1 G4 G3 Determine the cofactor of the k th forward path, k 1 = 1; 2 = 1 The overall transfer function,
C(s) = R(s)
C. S. George Lee (Purdue Univ.) Block Diagrams & Signal-Flow Graphs ECE382 21 / 31 P k Pk k = P1 1 + P2 2 G1 G4 G...
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This note was uploaded on 02/05/2012 for the course ECE 382 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.
- Fall '08