Explanation Given data: Refer to Problem 2.72 in the textbook. The characteristic impedance of the loss less line is 50 Ω . The load impedance of the feed line 1 is ( 50 + j 50 ) Ω . The load impedance of the feed line 2 is ( 50 − j 50 ) Ω . The length of each transmission lines are same as λ 4 . Calculation: The reflection coefficient of the feed line 1 is given as, Γ 1 = Z 1 − Z 0 Z 1 + Z 0 Here, Z 1 is the load impedance, Z 0 is the characteristic impedance, and Γ 1 is the reflection coefficient of line 1. Substitute ( 50 + j 50 ) for Z L and 50 for Z 0 in the above formula. Γ = ( 50 + j 50 ) − 50 ( 50 + j 50 ) + 50 = ( j 50 ) ( 100 + j 50 ) The input impedance of the feed line 1 is given as, Z in1 = Z 0 ( 1 + Γ 1 e − j 2 β l 1 − Γ 1 e − j 2 β l ) Here, Z in1 is the input impedance of the feed line 1 and l is the length of the feed line. Substitute λ 4 for l , 2 π λ for β , 50 for Z 0 and ( j 50 ) ( 100 + j 50 ) for Γ 1 in the above formula. Z in1 = 50 ( 1 + ( j 50 ) ( 100 + j 50 ) e − j 2 × 2 π λ × λ 4 1 − ( j 50 ) ( 100 + j 50 ) e − j 2 × 2 π λ × λ 4 ) = 50 ( 1 + ( j 50 ) ( 100 + j 50 ) e − j π 1 − ( j 50 ) ( 100 + j 50 ) e − j π ) = 50 ( 1 + ( j 50 ) ( 100 + j 50 ) ( cos ( π ) − j sin ( π ) ) 1 − ( j 50 ) ( 100 + j 50 ) ( cos ( π ) − j sin ( π ) ) ) = 50 ( 1 + ( j 50 ) ( 100 + j 50 ) ( − 1 − j 0 ) 1 − ( j 50 ) ( 100 + j 50 ) ( − 1 − j 0 ) ) Further solve the above expression. Z in1 = 50 ( 1 − ( j 50 ) ( 100 + j 50 ) 1 + ( j 50 ) ( 100 + j 50 ) ) = 50 ( 100 100 + j 100 ) = ( 50 1 + j ) Ω The admittance of the upper branch of the network is given as, Y in1 = 1 Z in1 Here, Y in1 is the admittance of the upper branch of the network. Substitute ( 50 1 + j ) for Z in1 in the above formula. Y in1 = 1 ( 50 1 + j ) = ( 1 + j 50 ) S The reflection coefficient of the feed line 2 is given as, Γ 2 = Z 2 − Z 0 Z 2 + Z 0 Here, Z 2 is the load impedance of the feed line 2 and Γ 2 is the reflection coefficient of line 2. Substitute ( 50 − j 50 ) for Z L and 50 for Z 0 in the above formula. Γ = ( 50 − j 50 ) − 50 ( 50 − j 50 ) + 50 = ( − j 50 ) ( 100 − j 50 ) The input impedance of the feed line 2 is given as, Z in2 = Z 0 ( 1 + Γ 2 e − j 2 β l 1 − Γ 2 e − j 2 β l ) Here, Z in1 is the input impedance of the feed line 1 and l is the length of the feed line

Fundamentals of Applied Electromagnetics (7th Edition)

7th Edition

ISBN: 9780133356984

Author: ULABY

Publisher: PEARSON

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Chapter 2, Problem 73P

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The Zin of the feed line.

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Chapter 2, Problem 72P

Chapter 2, Problem 74P

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Chapter 2 Solutions

Fundamentals of Applied Electromagnetics (7th Edition)

Ch. 2.2 - What is a transmission line? When should...Ch. 2.2 - Prob. 2CQ Ch. 2.2 - What constitutes a TEM transmission line?Ch. 2.2 - Prob. 4CQ Ch. 2.2 - Prob. 1E Ch. 2.2 - Calculate the transmission line parameters at 1...Ch. 2.4 - Verify that Eq. (2.26a) indeed provides a solution...Ch. 2.4 - A two-wire air line has the following line...Ch. 2.6 - The attenuation constant represents ohmic losses....Ch. 2.6 - How is the wavelength of the wave traveling on...

Ch. 2.6 - Prob. 7CQ Ch. 2.6 - What is a standing-wave pattern? Why is its period...Ch. 2.6 - Prob. 9CQ Ch. 2.6 - For a lossless transmission line, = 20.7 cm at 1...Ch. 2.6 - A lossless transmission line uses a dielectric...Ch. 2.6 - Prob. 7E Ch. 2.6 - Prob. 8E Ch. 2.6 - Prob. 10E Ch. 2.6 - A 140 lossless line is terminated in a load...Ch. 2.8 - What is the difference between the characteristic...Ch. 2.8 - What is a quarter-wave transformer? How can it be...Ch. 2.8 - Prob. 12CQ Ch. 2.8 - Prob. 13CQ Ch. 2.8 - if the input impedance of a lossless line is...Ch. 2.8 - Prob. 12E Ch. 2.8 - A 300 feedline is to be connected to a 3 m long,...Ch. 2.9 - According to Eq. (2.102b), the instantaneous value...Ch. 2.9 - Prob. 16CQ Ch. 2.9 - What fraction of the incident power is delivered...Ch. 2.9 - Prob. 18CQ Ch. 2.9 - For a 50 lossless transmission line terminated in...Ch. 2.9 - For the line of Exercise 2-14, what is the...Ch. 2.10 - The outer perimeter of the Smith chart represents...Ch. 2.10 - What is an SWR circle? What quantities are...Ch. 2.10 - What line length corresponds to one complete...Ch. 2.10 - Which points on the SWR circle correspond to...Ch. 2.10 - Prob. 23CQ Ch. 2.10 - Use the Smith chart to find the values of ...Ch. 2.11 - Prob. 24CQ Ch. 2.11 - Prob. 25CQ Ch. 2.12 - What is transient analysis used for?Ch. 2.12 - Prob. 28CQ Ch. 2.12 - What is the difference between the bounce diagram...Ch. 2 - A transmission line of length l connects a load to...Ch. 2 - Show that the transmission-line model shown in...Ch. 2 - A 1 GHz parallel-plate transmission line consists...Ch. 2 - For the parallel-plate transmission line of...Ch. 2 - In addition to not dissipating power, a lossless...Ch. 2 - For a distortionless line [see Problem 2.13] with...Ch. 2 - Prob. 15P Ch. 2 - A transmission line operating at 125 MHz has Z0 =...Ch. 2 - Prob. 17P Ch. 2 - Polyethylene with r=2.25 is used as the insulating...Ch. 2 - Prob. 20P Ch. 2 - Prob. 21P Ch. 2 - Prob. 22P Ch. 2 - Prob. 23P Ch. 2 - A 50 lossless line terminated in a purely...Ch. 2 - Prob. 26P Ch. 2 - Prob. 27P Ch. 2 - Prob. 29P Ch. 2 - Prob. 30P Ch. 2 - Two half-wave dipole antennas, each with an...Ch. 2 - Prob. 34P Ch. 2 - For the lossless transmission line circuit shown...Ch. 2 - A lossless transmission line is terminated in a...Ch. 2 - The input impedance of a 31 cm long lossless...Ch. 2 - FM broadcast station uses a 300 transmission line...Ch. 2 - A generator with Vg=300 V and Zg = 50 is...Ch. 2 - If the two-antenna configuration shown in Fig....Ch. 2 - For the circuit shown in Fig. P2.44, calculate the...Ch. 2 - The circuit shown in Fig. P2.45 consists of a 100 ...Ch. 2 - An antenna with a load impedance ZL=(75+j25) is...Ch. 2 - Prob. 47P Ch. 2 - Use the Smith chart to determine the input...Ch. 2 - Prob. 52P Ch. 2 - A lossless 50 transmission line is terminated in...Ch. 2 - A lossless 50 transmission line is terminated in...Ch. 2 - Use the Smith chart to find yL if zL = 1.5 j0.7.Ch. 2 - Prob. 59P Ch. 2 - Prob. 62P Ch. 2 - Determine Zin of the feed line shown in Fig....Ch. 2 - Prob. 73P Ch. 2 - A 25 antenna is connected to a 75 lossless...Ch. 2 - Prob. 75P Ch. 2 - Prob. 76P Ch. 2 - Prob. 77P Ch. 2 - In response to a step voltage, the voltage...Ch. 2 - Suppose the voltage waveform shown in Fig. P2.77...Ch. 2 - For the circuit of Problem 2.80, generate a bounce...Ch. 2 - In response to a step voltage, the voltage...

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The Z in of the feed line.

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The Zin of the feed line.

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Chapter 2 Solutions