then △=1-B1=1GH and △1=1-0=1 final C PA G R△1±GH 2022-2-3 31
2022-2-3 31 1 P11 1 GH 1 1 0 1 GH P G R C T 1 1 1 then and final
Example The signal flow graph of the resistance network 1/2 R determine the voltage gain T' There is one forward path R VR2 v v 2022-2-3 32
2022-2-3 32 Example: The signal flow graph of the resistance network, determine the voltage gain There is one forward path 1 3 v v T
Hence the forward path gain is RR 3 RR 2 There are three feedback loops 1/R, R 1/R2 R 1/R2 R 4 L。op1 Loop 2 Loop 3 Hence the lo oop gains are r R4 RR 21 R R2 2022-2-3 33
2022-2-3 33 Hence the forward path gain is 1 2 3 4 1 R R R R P There are three feedback loops: Hence the loop gains are , 1 3 11 R R P , 2 3 21 R R P 2 4 31 R R P
There are two non-touching loops loops one and three Hence Pl2= gain-Product of the only two non-touching RR OopS R,R There are no three loops that do not touch Therefore △=1-(P1+ 21 P2,)+ 31 12 RRRRR 1+3++2+ RRR R. 2 rR2+rR3+rR4+r2R3+r3R 4 Rr 2022-2-3 34
2022-2-3 34 P12 1 2 3 4 11 31 R R R R P P 11 21 31 12 1 (P P P ) P 1 2 3 4 2 4 2 3 1 3 1 R R R R R R R R R R 1 2 1 2 1 3 1 4 2 3 3 4 R R R R R R R R R R R R There are no three loops that do not touch. Therefore There are two non-touching loops, loops one and three. Hence Gain-Product of the only two non-touching loops =
Since all loops touch the forward path, A,=1 Fi ina T: B△ RR v A RR+rR+rr+rR+RR 2022-2-3 35
2022-2-3 35 Since all loops touch the forward path, 1 Finally, 1 1 2 1 3 1 4 2 3 3 4 1 1 3 4 1 3 RR RR RR R R R R P R R v v T