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Question

The transfer function of the open loop system G(s) which is represented by the singal flow graph shown in the figure below is

A
G1G21+G1H1+G2H2
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B
G1G21G1H1+G2H2
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C
G1G2(1+G1H1)(1+G2H2)
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D
G1G21+(G1+H1)(G2+H2)
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Solution

The correct option is A G1G21+G1H1+G2H2
Forward path gain
P1=G1G2

Loops
L1=G1H1
L2=G2H2

No non-touching loop
Δ=1(L1+L2)
=1+G1H1+G2H2

Therefore according to Mason gain formula
T(s)=C(s)R(s)=P1Δ1Δ

=G1G21+G1H1+G2H2

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