(b) Draw the signal flow graph of a system represented by the following block diagram and find C/R using Mason's gain formula. C R a b. e

Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
icon
Related questions
Question

Asap please

The task is to draw a signal flow graph for a control system based on a given block diagram and calculate the transfer function \( C/R \) using Mason's Gain Formula.

### Block Diagram Description:

- **Inputs and Outputs:**
  - The system begins with an input \( R \) which leads to the output \( C \).

- **Blocks:**
  - The blocks represent system components with specific transfer functions labeled as \( a, b, c, d, e, f, g, h, i, \) and \( j \).

- **Connections:**
  - The input \( R \) passes through block \( a \) and then encounters a summing junction which receives additional feedbacks.
  - The signal then proceeds through blocks \( c, b, i, j \), and \( f \) sequentially with intermediate feedback and feedforward paths intersecting.
  - From block \( i \), a feedback path feeds back into the summing junction before block \( c \).
  - After block \( j \), the output branches into two paths: one proceeds to block \( f \) and then to \( g \), and the other feeds into block \( h \).
  - Outputs of blocks \( g \) and \( d \) go into a summing junction leading to the final system output \( C \).
  - Feedback is provided from the output \( C \) back to the input summing point via block \( e \).

### Instructions for Constructing the Signal Flow Graph:

1. **Nodes:**
   - Create nodes for each junction/interconnection in the diagram.

2. **Branches:**
   - Draw directed branches for each signal path between nodes.
   - Label each branch with the corresponding transfer function block (i.e., \( a, b, c, \) etc.).

3. **Loops and Paths:**
   - Identify and label forward paths from \( R \) to \( C \).
   - Identify any loops and their respective gains for applying Mason's Gain Formula.

### Mason’s Gain Formula:

To determine the transfer function \( \frac{C}{R} \), use Mason's Gain Formula:

\[
T = \frac{1}{\Delta} \sum_{k=1}^{N} P_k \Delta_k
\]

Where:
- \( T \) is the overall system gain.
- \( P_k \) is the gain of the kth forward path.
- \( \
Transcribed Image Text:The task is to draw a signal flow graph for a control system based on a given block diagram and calculate the transfer function \( C/R \) using Mason's Gain Formula. ### Block Diagram Description: - **Inputs and Outputs:** - The system begins with an input \( R \) which leads to the output \( C \). - **Blocks:** - The blocks represent system components with specific transfer functions labeled as \( a, b, c, d, e, f, g, h, i, \) and \( j \). - **Connections:** - The input \( R \) passes through block \( a \) and then encounters a summing junction which receives additional feedbacks. - The signal then proceeds through blocks \( c, b, i, j \), and \( f \) sequentially with intermediate feedback and feedforward paths intersecting. - From block \( i \), a feedback path feeds back into the summing junction before block \( c \). - After block \( j \), the output branches into two paths: one proceeds to block \( f \) and then to \( g \), and the other feeds into block \( h \). - Outputs of blocks \( g \) and \( d \) go into a summing junction leading to the final system output \( C \). - Feedback is provided from the output \( C \) back to the input summing point via block \( e \). ### Instructions for Constructing the Signal Flow Graph: 1. **Nodes:** - Create nodes for each junction/interconnection in the diagram. 2. **Branches:** - Draw directed branches for each signal path between nodes. - Label each branch with the corresponding transfer function block (i.e., \( a, b, c, \) etc.). 3. **Loops and Paths:** - Identify and label forward paths from \( R \) to \( C \). - Identify any loops and their respective gains for applying Mason's Gain Formula. ### Mason’s Gain Formula: To determine the transfer function \( \frac{C}{R} \), use Mason's Gain Formula: \[ T = \frac{1}{\Delta} \sum_{k=1}^{N} P_k \Delta_k \] Where: - \( T \) is the overall system gain. - \( P_k \) is the gain of the kth forward path. - \( \
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
8051 Microcontroller
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,