Fundamentals of Applied Electromagnetics (7th Edition)
7th Edition
ISBN: 9780133356816
Author: Fawwaz T. Ulaby, Umberto Ravaioli
Publisher: PEARSON
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Chapter 2, Problem 40P
FM broadcast station uses a 300 Ω transmission line between the transmitter and a tower-mounted half-wave dipole antenna. The antenna impedance is 73 Ω. You are asked to design a quarter-wave transformer to match the antenna to the line.
- (a) Determine the electrical length and characteristic impedance of the quarter-wave section.
- (b) If the quarter-wave section is a two-wire line with D = 2.5 cm, and the wires are embedded in polystyrene with ϵr = 2.6, determine the physical length of the quarter-wave section and the radius of the two wire conductors.
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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. 2CQCh. 2.2 - What constitutes a TEM transmission line?Ch. 2.2 - Prob. 4CQCh. 2.2 - Prob. 1ECh. 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. 7CQCh. 2.6 - What is a standing-wave pattern? Why is its period...Ch. 2.6 - Prob. 9CQCh. 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. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 10ECh. 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. 12CQCh. 2.8 - Prob. 13CQCh. 2.8 - if the input impedance of a lossless line is...Ch. 2.8 - Prob. 12ECh. 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. 16CQCh. 2.9 - What fraction of the incident power is delivered...Ch. 2.9 - Prob. 18CQCh. 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. 23CQCh. 2.10 - Use the Smith chart to find the values of ...Ch. 2.11 - Prob. 24CQCh. 2.11 - Prob. 25CQCh. 2.12 - What is transient analysis used for?Ch. 2.12 - Prob. 28CQCh. 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. 15PCh. 2 - A transmission line operating at 125 MHz has Z0 =...Ch. 2 - Prob. 17PCh. 2 - Polyethylene with r=2.25 is used as the insulating...Ch. 2 - Prob. 20PCh. 2 - Prob. 21PCh. 2 - Prob. 22PCh. 2 - Prob. 23PCh. 2 - A 50 lossless line terminated in a purely...Ch. 2 - Prob. 26PCh. 2 - Prob. 27PCh. 2 - Prob. 29PCh. 2 - Prob. 30PCh. 2 - Two half-wave dipole antennas, each with an...Ch. 2 - Prob. 34PCh. 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. 47PCh. 2 - Use the Smith chart to determine the input...Ch. 2 - Prob. 52PCh. 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. 59PCh. 2 - Prob. 62PCh. 2 - Determine Zin of the feed line shown in Fig....Ch. 2 - Prob. 73PCh. 2 - A 25 antenna is connected to a 75 lossless...Ch. 2 - Prob. 75PCh. 2 - Prob. 76PCh. 2 - Prob. 77PCh. 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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