

Homework 6  Waveguides
Problem 1.
Determine the following waveguide characteristics for standard waveguide WR62 for
which the output dimensions are 0.702 X 0.391 inches, with a wall thickness of 0.040
inches when the exciting frequency is 10GHz. Find the free space wavelength lambda
(λ), the guide wavelength (λg), cutoff wavelength (λc), the
phase velocity (Vp), and the group velocity (Vg).
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Problem 2.
Calculate the Transverse Electric (TE) wave impedance for the WR62 waveguide specified in Problem 1.
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Problem 3.
Explain how standing waves can be produced in a waveguide. That being, what is the
spacing, in terms of wavelength, between successive minima along the standing wave pattern?
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Problem 4.
Using what you learned in transmission line theory, determine the reflection coefficient
for the electric field of a transverse electric, TE_{10} wave having a wave
impedance of 680ohms terminated as shown in the following figure, with a sheet
resistivity of the load being 500ohms per square.
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Problem 5.
From transmission line theory, determine the electric field standing wave
ratio for the waveguide conditions specified in Problem 4.
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Problem 6.
What is meant by sheet resistivity, and how does this differ from the resistivity
of a material? What are the units for sheet resistivity?
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Problem 7.
Plot on a Smith Chart the transformations that occurs in the onehalf guide
wavelength (1/2λg) short circuited section in the following figure.
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{ Smith Chart Plot }
Problem 8.
Explain the difference between radiating and nonradiating slots in a transverse
electric, TE_{10} mode waveguide.
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Problem 20.
Determine for a WR62 rectangular waveguide the cutoff wavelengths for all modes up to n = m = 2.
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Problem 21.
A standard WR187 waveguide dimensions are the outside walls 2.00 X 1.00 inches,
with a wall thickness of 0.064 inches. Find the highest frequency that can be
transmitted if only the TE_{10} mode is permitted. What modes can exist
in the waveguide if a wave having a frequency of 6GHz is present?
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Engineering key words: Waveguide homework problems, standards, rectangular, circular, taper,
wavelength, smith chart, freespace, modes, TE, TM, TEM, transverse electric, cutoff frequency,
phase velocity, group velocity, standing wave, termination, load, dimensions, slotted, guide impedance.
