For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function
$\frac{Y (s)}{X_{2} (s)} |_{x_{1} (s) = 0}$ ?

\frac{G_{1}}{1 + G_{2} (1 + G_{1})}

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\frac{G_{2}}{1 + G_{1} (1 + G_{2})}

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\frac{G_{1}}{1 + G_{1} G_{2}}

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\frac{G_{2}}{1 + G_{1} G_{2}}

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Solution

The correct option is B $\frac{G_{2}}{1 + G_{1} (1 + G_{2})}$

$\frac{Y (s)}{X_{2} (s)} |_{x_{1} (s) = 0} = \frac{G_{2}}{1 - (- G_{1} G_{2} - G_{1})} = \frac{G_{2}}{1 + G_{1} (G_{2} + 1)}$

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