Question

In the signal flow graph of figure the gain C/R will be

• A. $11/9$
• B. $22/15$
• C. $24/23$
• D. $44/23$

Answer 1

The correct option is D $44/23$

By using Mason's gain formula,
$\frac{C}{R}=\frac{\sum P_k{\Delta }_k}{\Delta }$
$\frac{C}{R}=\frac{(1\times 2\times 3\times 4\times 1)+(1\times 5\times 1)\times (1+3)}{1-(-2-3-4-5)+(-2)\times (-4)}$
$\frac{C}{R}=\frac{24+20}{1+14+8}=\frac{44}{23}$