AIN SHAMS UNIVERSITY Problem Set 2
Microwaves
AIN SHAMS UNIVERSITY
Faculty of Engineering
Laboratory ECE Department
CHEP
COMM 362 –
Spring 2014
Prof. Amr Safwat
Problem Set 2
Parallel Plate Waveguide
Problem
1
1
Calculate the attenuation due to conductor loss for the mode of a parallel plate waveguide.
*Problem
2
2
Consider the partially filled parallel plate waveguide shown in Fig. 1. Derive the solution (fields and cut-off frequency) for the lowest order TE mode of this structure. Assume the metal plates are infinitely wide. Can a TEM wave propagate on this structure?
*Problem
3
3
Figure 1
Consider the partially filled parallel plate waveguide shown in Fig. 2. Derive the solution (fields and cut-off frequency) for the TE modes. Can a TEM wave exist in this structure? Ignore fringing fields at the sides, and assume no dependence.
Figure 2
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Problem
5
4
A parallel-plate waveguide is known to have a cutoff wavelength for the TE and TM modes of mm. The guide is operated at wavelength mm. How many modes will propagate?
Problem
6
5
A parallel-plate guide is to be constructed for operation in the TEM mode only over the frequency range GHz. The dielectric between plates is to be Teflon (
Determine the maximum allowable plate separation, .
).
Problem
7
6
A lossless parallel-plate waveguide is known to propagate the TE and TM modes at frequencies as low as 10 GHz. If the plate separation is 1 cm, determine the dielectric constant of the medium between plates.
Problem
8,9
7
A cm parallel-plate guide is made with glass (refractive index ) between plates. If the operating frequency is 32 GHz:
(a) Which modes will propagate?
(b) Determine the difference between the group delays of the highest-order mode (TE or
TM) and the TEM mode. Assume a propagation distance of 10 cm.
Problem
10
8
The cutoff frequency of the TE and TM modes in an air-filled parallel-plate guide is known to be GHz. The guide is used at wavelength velocity of the TE and TM modes.
cm. Find the group
Problem
11
9
A parallel-plate guide is partially filled with two lossless dielectrics as shown in Fig. 3 where and cm. At a certain frequency, it is found that the mode propagates through the guide without suffering any reflective loss at the dielectric interface.
(a) Find this frequency.
(b) Is the guide operating at a single TM mode at the frequency found in part (a)?
[
Hint: Remember Brewster’s angle?
]
Figure 3. Problems 9 and 10.
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Problem
12
10
In the guide of Fig. 3, it is found that modes propagating from left to right totally reflect at the interface, so that no power is transmitted into the region of the dielectric constant .
(a) Determine the range of frequencies over which this will occur.
(b) Does your part (a) answer in any way relate to the cutoff frequency for modes in either region? [ Hint: Remember the critical angle?
]
Problem
4
11
Calculate the group velocity for a waveguide mode propagating in an air-filled guide. Compare this velocity to the phase velocity and speed of light.
Problem
13
12
Show that the group dispersion parameter,
⁄
, for a given mode in a parallel-plate waveguide is given by:
( ) [ ( ) ] where is the radian cutoff frequency for the mode in question.
⁄
References:
“Microwave Engineering,” David. M. Pozar. 3 rd
edition, Wiley, 2005.
1) Chapter 3, problem 2.
2) Chapter 3, problem 9.
3) Chapter 3, problem 10.
4) Chapter 3, solved example 3.9.
“Engineering Electromagnetics,” W. H. Hayt and J. A. Buck. 7 th
edition, McGraw Hill, 2006.
5) Chapter 14, problem 9.
6) Chapter 14, problem 10.
7) Chapter 14, problem 11.
8) Chapter 14, problem 12.
9) Chapter 14, problem 13.
10) Chapter 14, problem 14.
11) Chapter 14, problem 15.
12) Chapter 14, problem 16.
13) Chapter 14, problem 22.
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