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Terminated transmission line. A 502, 10.5-m long air transmission line terminated with a load impedance of Z = 70 +j102 is excited by a sinusoidal voltage source, as shown in Figure 3.71. (a) Calculate the load reflection coefficient IL and the standing wave ratio S on the line. (b) Find all the Vmax and Vmin positions (in actual lengths) on the line. (c) Find all the Imax and Imin positions on the line. (d) Find the input impedance Zin seen at each Vmax and Vmin position. (e) Find the line impedance Z (z) seen at the source end of the line and draw the equivalent lumped circuit with respect to the source end. (f) Find the phasor voltages V,, V+, V¯, and VL. (g) Find the Vmax and Vmin values. (h) Find the Imax and Imin values. (i) Find the time-average powers P+, P¯, Pr,, PL, and Psource- What percentage of the power carried by the incident wave reflects back towards the source? G) Repeat parts (a) through (i) for a load impedance of Z = 15 – j352. 1= 10.5 m 500 Air line Vo = 10e/0 v (f= 300 MHz) Zo= 502 VL ZĻ = 70 + j102 Figure 3.71 Terminated transmission line. Problem 3.25.

Terminated transmission line. A 502, 10.5-m long air transmission line terminated with a load impedance of Z = 70 +j102 is excited by a sinusoidal voltage source, as shown in Figure 3.71. (a) Calculate the load reflection coefficient IL and the standing wave ratio S on the line. (b) Find all the Vmax and Vmin positions (in actual lengths) on the line. (c) Find all the Imax and Imin positions on the line. (d) Find the input impedance Zin seen at each Vmax and Vmin position. (e) Find the line impedance Z (z) seen at the source end of the line and draw the equivalent lumped circuit with respect to the source end. (f) Find the phasor voltages V,, V+, V¯, and VL. (g) Find the Vmax and Vmin values. (h) Find the Imax and Imin values. (i) Find the time-average powers P+, P¯, Pr,, PL, and Psource- What percentage of the power carried by the incident wave reflects back towards the source? G) Repeat parts (a) through (i) for a load impedance of Z = 15 – j352. 1= 10.5 m 500 Air line Vo = 10e/0 v (f= 300 MHz) Zo= 502 VL ZĻ = 70 + j102 Figure 3.71 Terminated transmission line. Problem 3.25.

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
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**Terminated Transmission Line** A 50Ω, 10.5-meter long air transmission line terminated with a load impedance of \( Z_L = 70 + j100Ω \) is excited by a sinusoidal voltage source, as illustrated in Figure 3.71. The source voltage \( V_0 \) with a value of \( 10e^{j0}V \) operates at a frequency of 300 MHz. This problem involves several calculations and analyses as outlined below: **Tasks:** (a) **Calculate the Load Reflection Coefficient (Γ_L) and the Standing Wave Ratio (S) on the Line:** - Determine the reflection coefficient Γ_L at the load. - Calculate the standing wave ratio S on the transmission line. (b) **Find the \( V_{max} \) and \( V_{min} \) Positions (in actual lengths) on the Line:** - Determine the positions along the transmission line where the voltage reaches its maximum (\( V_{max} \)) and minimum (\( V_{min} \)) values. (c) **Find All the \( I_{max} \) and \( I_{min} \) Positions on the Line:** - Locate the positions of maximum (\( I_{max} \)) and minimum (\( I_{min} \)) current along the line. (d) **Find the Input Impedance \( Z_{in} \) Seen at Each \( V_{max} \) and \( V_{min} \) Position:** - Calculate the input impedance at each \( V_{max} \) and \( V_{min} \) position along the line. (e) **Find the Line Impedance \( Z_{(z)} \) Seen at the Source End of the Line and Draw the Equivalent Lumped Circuit with Respect to the Source End:** - Determine the impedance looking into the line from the source end and represent the equivalent lumped circuit. (f) **Find the Phasor Voltages \( V_s \), \( V^+ \), \( V^- \), and \( V_L \):** - Compute the source voltage \( V_s \), and the forward (\( V^+ \)) and reflected (\( V^- \)) traveling voltages, as well as the load voltage \( V_L \). (g) **Find the \( V_{max} \) and \( V_{min} \) Values
Transcribed Image Text:**Terminated Transmission Line** A 50Ω, 10.5-meter long air transmission line terminated with a load impedance of \( Z_L = 70 + j100Ω \) is excited by a sinusoidal voltage source, as illustrated in Figure 3.71. The source voltage \( V_0 \) with a value of \( 10e^{j0}V \) operates at a frequency of 300 MHz. This problem involves several calculations and analyses as outlined below: **Tasks:** (a) **Calculate the Load Reflection Coefficient (Γ_L) and the Standing Wave Ratio (S) on the Line:** - Determine the reflection coefficient Γ_L at the load. - Calculate the standing wave ratio S on the transmission line. (b) **Find the \( V_{max} \) and \( V_{min} \) Positions (in actual lengths) on the Line:** - Determine the positions along the transmission line where the voltage reaches its maximum (\( V_{max} \)) and minimum (\( V_{min} \)) values. (c) **Find All the \( I_{max} \) and \( I_{min} \) Positions on the Line:** - Locate the positions of maximum (\( I_{max} \)) and minimum (\( I_{min} \)) current along the line. (d) **Find the Input Impedance \( Z_{in} \) Seen at Each \( V_{max} \) and \( V_{min} \) Position:** - Calculate the input impedance at each \( V_{max} \) and \( V_{min} \) position along the line. (e) **Find the Line Impedance \( Z_{(z)} \) Seen at the Source End of the Line and Draw the Equivalent Lumped Circuit with Respect to the Source End:** - Determine the impedance looking into the line from the source end and represent the equivalent lumped circuit. (f) **Find the Phasor Voltages \( V_s \), \( V^+ \), \( V^- \), and \( V_L \):** - Compute the source voltage \( V_s \), and the forward (\( V^+ \)) and reflected (\( V^- \)) traveling voltages, as well as the load voltage \( V_L \). (g) **Find the \( V_{max} \) and \( V_{min} \) Values
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