1
GATE EE 2015 Set 1
+1
-0.3
For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function $${\left. {{{Y\left( s \right)} \over {{X_2}\left( s \right)}}} \right|_{{x_1}\left( s \right) = 0}}?$$
A
$${{{G_1}} \over {1 + {G_2}\left( {1 + {G_1}} \right)}}$$
B
$${{{G_2}} \over {1 + {G_1}\left( {1 + {G_2}} \right)}}$$
C
$${{{G_1}} \over {1 + {G_1}{G_2}}}$$
D
$${{{G_2}} \over {1 + {G_1}{G_2}}}$$
2
GATE EE 2014 Set 3
+1
-0.3
The signal flow graph of a system is shown below. $$U(S)$$ is the input and $$C(S)$$ is the output.

Assuming $${h_1} = {b_1}$$ and $${h_0} = {b_0} - {b_1}{a_1},$$ the input-output transfer function, $$G\left( S \right) = {{C\left( S \right)} \over {U\left( S \right)}}$$ of the system is given by

A
$$G\left( S \right) = {{{b_0}s + {b_1}} \over {{s^2} + {a_0}s + {a_1}}}$$
B
$$G\left( S \right) = {{{a_1}s + {a_0}} \over {{s^2} + {b_1} + {b_0}}}$$
C
$$G\left( S \right) = {{{b_1}s + {b_0}} \over {{s^2} + {a_1}s + {a_0}}}$$
D
$$G\left( S \right) = {{{a_0}s + {a_1}} \over {{s^2} + {b_0}s + {b_1}}}$$
3
GATE EE 1993
+1
-0.3
Signal flow graph is used to obtain the
A
stability of a system
B
transfer function of a system
C
controllability of a system
D
observability of a system
4
GATE EE 1992
+1
-0.3
The overall transfer function of the system in Figure, is
A
$${G \over {1 - GH}}$$
B
$${{2G} \over {1 - GH}}$$
C
$${{GH} \over {1 - GH}}$$
D
$${{GH} \over {1 - H}}$$
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