Using Mason's Gain Formula on a signal flow graph with two forward path gains P_1 = 6, P_2 = 2, and two loops L_1 = -4, L_2 = -2 (all loops touch all paths), the overall transfer function T = Y/X is:

Home › MCQs › Electrical Engineering › Question #2182

Electrical Engineering QUESTION #2182

Question 1

Using Mason's Gain Formula on a signal flow graph with two forward path gains $P_1 = 6$, $P_2 = 2$, and two loops $L_1 = -4$, $L_2 = -2$ (all loops touch all paths), the overall transfer function $T = Y/X$ is:

$\dfrac{8}{7}$✔️
$\dfrac{8}{3}$
$4$
$\dfrac{6}{7}$

Correct Answer Explanation

Graph determinant $\Delta = 1-(L_1+L_2) = 1-(-4-2) = 7$. Since loops touch all paths, cofactors $\Delta_1 = \Delta_2 = 1$. $T = \frac{P_1\Delta_1+P_2\Delta_2}{\Delta} = \frac{6+2}{7} = \frac{8}{7}$.

More Options