Signal Flow Graph Analysis - Course: EE 201, Semester 1, University X

This assignment presents a detailed solution to a signal flow graph analysis problem. The solution involves analyzing the signal flow graph, identifying the relevant equations, and solving for the desired parameters. The process includes deriving equations from the graph, manipulating them to find relationships between different variables, and ultimately arriving at the final solution. This assignment is designed to help students understand and apply the principles of signal flow graph analysis in electrical engineering. This solution is available on Desklib, a platform that offers various study tools for students, including past papers and assignment solutions.

Signal Flow graph is given above.
Now, as can be seen,
X1 =R + H1 X 3----------------------------------(1)
X2 =G1 X1 −H1 X3 −H2 X4-------------------------(2)
X3 =G2 X 2------------------------------------(3)
X 4=G3 X3------------------------------------(4)
X5 =X4 +G4 R------------------------------(5)
C=X5-----------------------------------------(6)
From equations (5) and (6)
X 4=C−G4 R-------------------------------(7)
From equations (4) and (7)
X3 = X4
G3
= C−G4 R
G3
---------------------------(8)
From equations (2) and (8)
X2 = X3
G2
= C−G4 R
G2 G3
---------------------------(9)
From equations (1) and (9)
X1 =R + H1 ( C−G4 R )
G3
-----------------------(10)
Putting the values of X1 , X2 , X3∧X 4 from equations (7), (8), (9) and (10) in equation (2)

C−G4 R
G2 G3
=G1 ( R+ H 1 ( C−G4 R )
G3 )− H1 ( C−G4 R )
G3
−H2 (C−G4 R)
¿> C−G4 R
G2 G3
=G1 R+ ( C−G4 R ) ( G1 H1
G3
− H1
G3
−H2 )
¿> C−G4 R
G2 G3
= G1 G3 R + ( C−G4 R ) ( ( G1 −1 ) H1 −G3 H2 )
G3
¿>C−G4 R=G1 G2 G3 R+(C−G4 R)¿
¿> ( C−G4 R ) ( 1−G1 G2 H1 +G2 H1 +G2 G3 H2 ) =G1 G2 G3 R
¿>C= G1 G2 G3 R
1−G1 G2 H1 +G2 H1 +G2 G2 H2
+ G4 R
¿> C
R = G1 G2 G3 +G4 −G1 G2 G4 H1+G2 G4 H1+G2 G3 G4 H2
1−G1 G2 H1 +G2 H1 +G2 G3 H2
( Ans .)