Engineering Electromagnetics
Engineering Electromagnetics
9th Edition
ISBN: 9780078028151
Author: Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher: Mcgraw-hill Education,
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Chapter 13, Problem 13.20P

Two rectangular waveguides are joined end-to-end. The guides have identical dimensions; where a = 2b. One guide is air-filled; the other is filled with a lossless dielectric characterized by Er'- (a) Determine the maximum allowable value of er' such that single-mode operation can be simultaneously assured in both guides, at some frequency. (b) Write an expression for the frequency range over which single-mode operation will occur in both guides; your answer should be in terms of Er'. guide dimensions as needed, and other known constants.

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Phase shift due to finite length of circuit conductors. On a particular type of circuit board, assume a signal travels at 2/3 of the speed of light. Suppose a high-speed system using this type of board can tolerate a phase shift in a sine-wave signal due to propagation delay of only 15° before failing to work. Calculate the maximum length /MAX (in m, or a suitable subdivision such as cm or mm) that a circuit-board trace carrying this signal can have at each of the following frequencies without encountering excessive phase shift due to the propagation delay along the trace: (a) f=10MHz, (b) f=30MHz, (c) f=500 MHz, and (d) f=2.5 GHz.
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3. Coaxial cable is used in applications requiring the propagation of high-frequency signal. Such cable consists of a solid conducting cylinder as the inner conductor and a solid conducting cylindrical shell as the outer conductor. A dielectric fills the region between these conductors. Consider the RG-59/U coaxial cable that is commonly used to connect a television/internet equipment. It has an inner conductor with a diameter of 0.584 mm, dielectric filler with a dielectric constant of K = 1.20, and an outer conductor with an inner diameter of 3.7084 mm. Assuming that these conductors are very long, calculate the capacitance per metre of the RG-59/U coaxial cable. Include a derivation of an equation for the capacitance per unit length of the coaxial cable and then use this equation to calculate your answer. (As discussed in class, assign a charge +Q and voltage V to the inner conductor and a charge -Q and 0 V to the outer conductor, solve for the voltage V, and then compute the…
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