This is a part of a review I'm studying, NOT a graded assignment, please do not reject. Thank you!Am I doing this problem right? I would like someone to verify I'm doing this correctly, thank you!I understand that there are multiple questions here, but I've already answered some of them and most are very simple problems, I appreciate your understanding! **Title: Application of Mason's Rule to Determine the Transfer Function**This educational content explores how to find the transfer function \( T(s) = \frac{Y(s)}{R(s)} \) using Mason's rule. Below is the detailed transcription and explanation of the given calculations.---**1. Problem Statement:**Find the transfer function, \( T(s) = \frac{Y(s)}{R(s)} \), using Mason's rule.**2. Variables Defined:** - **a)** Number of forward paths, \( K \) - **b)** Single loop gains - **c)** \(\Delta\) - **d)** \(\Delta_k\) - **e)** \( T(s) \)---**3. Signal Flow Graph:**The signal flow graph is shown above, illustrating paths and loops with their respective gains.**4. Detailed Steps:****a) Number of forward paths, \( K = 3 \)****b) Single Loop Gains:** \[ L_1 = -\frac{3}{s+1} \quad (forward) \] \[ L_2 = -\frac{5}{s+1} \quad (forward) \]**c) Calculation of \(\Delta\):** \[ \Delta = 1 - (L_1 + L_2) = 1 - \left(\frac{-9s}{s+3s+2}\right) = \frac{15s + 4}{s^2 + 3s + 2} \]**d) Calculation of \(\Delta_k\):** - \(\Delta_1 = \Delta_2 = \Delta_3 = 1\)**e) Transfer Function \( T(s) \) Calculation:** \[ T = \frac{Y_R}{\Delta} = \frac{P_1 \Delta_1 + P_2 \Delta_2 + P_3 \Delta_3}{\Delta} \] where: \[ P_1 = \frac{3s}{s^2 + 3s + 2} \] \[ P_2 = \frac{-4}{s + 1} \] \[ P_3 = 6

Answered: Y(s) R(S) a) The number of forward…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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This is a part of a review I'm studying, NOT a graded assignment, please do not reject. Thank you!

Am I doing this problem right? I would like someone to verify I'm doing this correctly, thank you!

I understand that there are multiple questions here, but I've already answered some of them and most are very simple problems, I appreciate your understanding!

**Title: Application of Mason's Rule to Determine the Transfer Function**

This educational content explores how to find the transfer function \( T(s) = \frac{Y(s)}{R(s)} \) using Mason's rule. Below is the detailed transcription and explanation of the given calculations.

---

**1. Problem Statement:**

Find the transfer function, \( T(s) = \frac{Y(s)}{R(s)} \), using Mason's rule.

**2. Variables Defined:**
- **a)** Number of forward paths, \( K \)
- **b)** Single loop gains
- **c)** \(\Delta\)
- **d)** \(\Delta_k\)
- **e)** \( T(s) \)

---

**3. Signal Flow Graph:**

The signal flow graph is shown above, illustrating paths and loops with their respective gains.

**4. Detailed Steps:**

**a) Number of forward paths, \( K = 3 \)**

**b) Single Loop Gains:**
\[
L_1 = -\frac{3}{s+1} \quad (forward)
\]
\[
L_2 = -\frac{5}{s+1} \quad (forward)
\]

**c) Calculation of \(\Delta\):**
\[
\Delta = 1 - (L_1 + L_2) = 1 - \left(\frac{-9s}{s+3s+2}\right) = \frac{15s + 4}{s^2 + 3s + 2}
\]

**d) Calculation of \(\Delta_k\):**
- \(\Delta_1 = \Delta_2 = \Delta_3 = 1\)

**e) Transfer Function \( T(s) \) Calculation:**
\[
T = \frac{Y_R}{\Delta} = \frac{P_1 \Delta_1 + P_2 \Delta_2 + P_3 \Delta_3}{\Delta}
\]
where:
\[
P_1 = \frac{3s}{s^2 + 3s + 2}
\]
\[
P_2 = \frac{-4}{s + 1}
\]
\[
P_3 = 6

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Step 1: Parameter needs to be calculated

From the given signal flow graph, the transfer function of the system needs to be calculated along with individual parameters calculation

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