(b) Draw the signal flow graph of a system represented by the following block diagram and find C/R using Mason's gain formula. R a b. d e g
(b) Draw the signal flow graph of a system represented by the following block diagram and find C/R using Mason's gain formula. R a b. d e g
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![Certainly! Here’s a transcription and explanation suitable for an educational website:
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**Task: Signal Flow Graph from Block Diagram**
**Objective:** Draw the signal flow graph of a system represented by the following block diagram and find \( C/R \) using Mason’s Gain Formula.
**Diagram Description:**
This diagram consists of a series of interconnected blocks, each representing a system component with specific transfer functions. The blocks are labeled as \( a, b, c, d, e, f, g, h, i, j \).
- **Input and Output:**
- The input is represented by \( R \) and the output by \( C \).
- **Flow Connections:**
- The flow begins from the input \( R \) moving to block \( a \).
- From \( a \), the signal splits; one path leads directly to a summing junction, while another path loops through block \( e \) back to the initial summing junction.
- After the initial summing, the path leads vertically through a series of blocks \( c, b, i, j, f \).
- Each block has feedback and feedforward paths connecting them in various configurations.
- A side path connects these sequential blocks to parallel blocks \( g \) and \( h \) before reaching another summing point.
- The path then proceeds through block \( d \) before arriving at the final output summing junction, resulting in the output \( C \).
**Signal Flow Analysis:**
Understand the complex interactions between the elements by converting this block diagram to a signal flow graph, which is essential for applying Mason's Gain Formula effectively. The goal is to derive the transfer function \( C/R \) that correlates the input \( R \) with the output \( C \).
The blocks are likely to represent various processes or gains in a control system, and their interconnections through summation points and branching paths represent feedback and feedforward paths, which are crucial for system behavior analysis.
By applying Mason’s Gain Formula on the deduced signal flow graph, one can calculate the transfer function:
\[ T = \frac{C}{R} \]
Where \( T \) is the overall gain of the system.
**Conclusion:**
The diagram signifies a classic representation in control system theory, illustrating how various components in a system interact. By understanding and using Mason's Gain Formula, one can simplify the analysis of complex systems efficiently.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F938060d6-da51-4e19-a893-25a1024e8a07%2F13c595a9-26e0-48a5-9fed-c25d32649c9d%2Ffy7sw6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here’s a transcription and explanation suitable for an educational website:
---
**Task: Signal Flow Graph from Block Diagram**
**Objective:** Draw the signal flow graph of a system represented by the following block diagram and find \( C/R \) using Mason’s Gain Formula.
**Diagram Description:**
This diagram consists of a series of interconnected blocks, each representing a system component with specific transfer functions. The blocks are labeled as \( a, b, c, d, e, f, g, h, i, j \).
- **Input and Output:**
- The input is represented by \( R \) and the output by \( C \).
- **Flow Connections:**
- The flow begins from the input \( R \) moving to block \( a \).
- From \( a \), the signal splits; one path leads directly to a summing junction, while another path loops through block \( e \) back to the initial summing junction.
- After the initial summing, the path leads vertically through a series of blocks \( c, b, i, j, f \).
- Each block has feedback and feedforward paths connecting them in various configurations.
- A side path connects these sequential blocks to parallel blocks \( g \) and \( h \) before reaching another summing point.
- The path then proceeds through block \( d \) before arriving at the final output summing junction, resulting in the output \( C \).
**Signal Flow Analysis:**
Understand the complex interactions between the elements by converting this block diagram to a signal flow graph, which is essential for applying Mason's Gain Formula effectively. The goal is to derive the transfer function \( C/R \) that correlates the input \( R \) with the output \( C \).
The blocks are likely to represent various processes or gains in a control system, and their interconnections through summation points and branching paths represent feedback and feedforward paths, which are crucial for system behavior analysis.
By applying Mason’s Gain Formula on the deduced signal flow graph, one can calculate the transfer function:
\[ T = \frac{C}{R} \]
Where \( T \) is the overall gain of the system.
**Conclusion:**
The diagram signifies a classic representation in control system theory, illustrating how various components in a system interact. By understanding and using Mason's Gain Formula, one can simplify the analysis of complex systems efficiently.
---
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