Consider the signal flow graph shown in the figure.
The gain $x_{5} / x_{1}$ is

\frac{1 - (b e + c f + d g)}{a b c}

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\frac{b e d g}{1 - (b e + c f + d g)}

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\frac{a b c d}{1 - (b e + c f + d g) + b e d g}

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\frac{1 - (b e + c f + d g) + b e d g}{a b c d}

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Solution

The correct option is C $\frac{a b c d}{1 - (b e + c f + d g) + b e d g}$
$P_{1} = a b c d, Δ_{1} = 1$
$L_{1} = b e, L_{2} = c f, L_{3} = d g$
Non- touching loops are $L_{1}$ & $L_{3} = b e d g$
$∴ \frac{X_{5}}{X_{1}} = \frac{a b c d}{1 - (b e + c f + d g) + b e d g}$

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