Question

2?according to Mason's Rule, calculate the transfer function from diagram Fig. 2. $X(s)$ $E_1(s)$ $\frac{1}{s}$ $Y_1(s)$ $E_2(s)$ $\frac{1}{s}$ $Y(s)$ $+$ $-1$ $X(s)$ $1$ $E_1(s)$ $s^{-1}$ $Y(s)$ $E_2(s)$ $s^{-1}$ $-1$ $1$ $-2$ $(1/s)(1/s)$ $H(s) = \frac{1}{1 - [(-1/s) + (-2/s)] + [(-1/s)(-2/s)]}$ $= \frac{1}{s^2 + 3s + 2} = \frac{1}{(s+1)(s+2)}$ Fig. 2 Solution:

          2?according to Mason's Rule, calculate the transfer
function from diagram Fig. 2.
$X(s)$ \(E_1(s)\) $\frac{1}{s}$ $Y_1(s)$ $E_2(s)$ $\frac{1}{s}$ $Y(s)$
$+$
$-1$
$X(s)$ $1$ $E_1(s)$ $s^{-1}$ $Y(s)$ $E_2(s)$ $s^{-1}$
$-1$ $1$ $-2$
$(1/s)(1/s)$
$H(s) = \frac{1}{1 - [(-1/s) + (-2/s)] + [(-1/s)(-2/s)]}$
$= \frac{1}{s^2 + 3s + 2} = \frac{1}{(s+1)(s+2)}$
Fig. 2
Solution:

2?according to Mason's Rule, calculate the transfer
function from diagram Fig. 2.
X(s) E1(s) (1)/(s) Y1(s) E2(s) (1)/(s) Y(s)
+
-1
X(s) 1 E1(s) s^-1 Y(s) E2(s) s^-1
-1 1 -2
(1/s)(1/s)
H(s) = (1)/(1 - [(-1/s) + (-2/s)] + [(-1/s)(-2/s)])
= (1)/(s^2 + 3s + 2) = (1)/((s+1)(s+2))
Fig. 2
Solution:

Added by Alex S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

03/14/2023

Step 1

From the diagram, we can see that there is only one forward path, which is the path from the input (S) to the output (Y(s)). There are also two loops in the diagram. Loop 1 consists of the path from the input (S) to the summing point (+) and then back to the Show more…

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