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Zs Zin x = -1 Transmission Line Zo 1 Co x = 0 A 1.05-GHz generator circuit with series impedance Z§ =10 № and voltage source Vs is connected to a load Z₁-(100+j50) 2 through a 50-, 67-cm-long lossless transmission line as shown above. The phase velocity of the line is 0.7c, where c is the velocity of light in a vacuum. a) Find the wavelength. (b) Find the reflection coefficient at the load (x=0). c) Find Zin. ZL

Zs Zin x = -1 Transmission Line Zo 1 Co x = 0 A 1.05-GHz generator circuit with series impedance Z§ =10 № and voltage source Vs is connected to a load Z₁-(100+j50) 2 through a 50-, 67-cm-long lossless transmission line as shown above. The phase velocity of the line is 0.7c, where c is the velocity of light in a vacuum. a) Find the wavelength. (b) Find the reflection coefficient at the load (x=0). c) Find Zin. ZL

Introductory Circuit Analysis (13th Edition)
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...
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### Transmission Line Problem #### Circuit Description: - **Generator**: 1.05-GHz generator circuit. - **Series Impedance (\(Z_s\))**: 10 Ω. - **Voltage Source (\(V_s\))**: Connected to the load through the transmission line. - **Load Impedance (\(Z_L\))**: \( (100 + j50) \) Ω. - **Transmission Line**: 50-Ω, 67-cm-long, lossless. - **Phase Velocity**: 0.7c, where c is the speed of light in a vacuum. #### Diagram Explanation: - The diagram shows the voltage source \( V_s \) connected to a transmission line. - The series impedance \( Z_s \) is in line with the transmission path. - Input impedance \( Z_{\text{in}} \) is indicated at the point \( x = -l \). - The characteristic impedance of the transmission line is \( Z_0 \). - Load impedance \( Z_L \) is located at \( x = 0 \). #### Tasks: (a) **Find the Wavelength.** (b) **Find the Reflection Coefficient at the Load (\(x = 0\)).** (c) **Find \(Z_{\text{in}}\).** (d) **Find the Reflection Coefficient at \(x = -l\).** These tasks involve analyzing the transmission line and its components to solve problems related to wave propagation, reflection, and impedance matching.
Transcribed Image Text:### Transmission Line Problem #### Circuit Description: - **Generator**: 1.05-GHz generator circuit. - **Series Impedance (\(Z_s\))**: 10 Ω. - **Voltage Source (\(V_s\))**: Connected to the load through the transmission line. - **Load Impedance (\(Z_L\))**: \( (100 + j50) \) Ω. - **Transmission Line**: 50-Ω, 67-cm-long, lossless. - **Phase Velocity**: 0.7c, where c is the speed of light in a vacuum. #### Diagram Explanation: - The diagram shows the voltage source \( V_s \) connected to a transmission line. - The series impedance \( Z_s \) is in line with the transmission path. - Input impedance \( Z_{\text{in}} \) is indicated at the point \( x = -l \). - The characteristic impedance of the transmission line is \( Z_0 \). - Load impedance \( Z_L \) is located at \( x = 0 \). #### Tasks: (a) **Find the Wavelength.** (b) **Find the Reflection Coefficient at the Load (\(x = 0\)).** (c) **Find \(Z_{\text{in}}\).** (d) **Find the Reflection Coefficient at \(x = -l\).** These tasks involve analyzing the transmission line and its components to solve problems related to wave propagation, reflection, and impedance matching.
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