For the signal flow Graph shown in the figure, the value of \frac{C (s) }{R (s) } is

Correct Answer is : G1G2G3G41+G1G2H1+G3G4H2+G2G3H3+G1G2G3G4H1H2

{G_{1}G_{2}G_{3}G_{4}}/{1−G_{1}G_{2}H_{1}−G_{3}G_{4}H_{2}−G_{2}G_{3}H_{3} + G_{1}G_{2}G_{3}G_{4}H_{1}H_{2}}

{G_{1}G_{2}G_{3}G_{4}}/{1 + G_{1}G_{2}H_{1} + G_{3}G_{4}H_{2} + G_{2}G_{3}H_{3} + G_{1}G_{2}G_{3}G_{4}H_{1}H_{2}}

{1}/{1 + G_{1}G_{2}H_{1} + G_{3}G_{4}H_{2} + G_{2}G_{3}H_{3} + G_{1}G_{2}G_{3}G_{4}H_{1}H_{2}}

{1}/{1−G_{1}G_{2}H_{1}−G_{3}G_{4}H_{2}−G_{2}G_{3}H_{3} + G_{1}G_{2}G_{3}G_{4}H_{1}H_{2}}

GATE Electronics and Communications (EC) 2015 Shift 2 Solved Paper

Question : 30 of 65

Marks: +1, -0

For the signal flow Graph shown in the figure, the value of

\;{C\;(s)\;}/{R\;(s)\;}

$\;{G_{1}G_{2}G_{3}G_{4}}/{1−G_{1}G_{2}H_{1}−G_{3}G_{4}H_{2}−G_{2}G_{3}H_{3} + G_{1}G_{2}G_{3}G_{4}H_{1}H_{2}}$
$\;{G_{1}G_{2}G_{3}G_{4}}/{1\;+\;G_{1}G_{2}H_{1} + G_{3}G_{4}H_{2} + G_{2}G_{3}H_{3} + G_{1}G_{2}G_{3}G_{4}H_{1}H_{2}}$
$\;{1}/{1\;+\;G_{1}G_{2}H_{1} + G_{3}G_{4}H_{2} + G_{2}G_{3}H_{3} + G_{1}G_{2}G_{3}G_{4}H_{1}H_{2}}$
$\;{1}/{1−G_{1}G_{2}H_{1}−G_{3}G_{4}H_{2}−G_{2}G_{3}H_{3} + G_{1}G_{2}G_{3}G_{4}H_{1}H_{2}}$

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