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(ELEC344)344_midtsol_2005.pdf
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ELEC344 Microwave Engineering, Spring, 2005, HKUST Midterm Exam Time: 17:00 --- 19:00, Apr. 4, 2005
MIDTERM EXAM SOLUTIONS
Open book (Pozar, 3rd Ed.), notes, homework, homework solutions, calculator Exam duration is 2 hours
17:00 PM C 19:00 PM Attempt all problems Total Grade 100 points

Instructions:
1.
Please take your time to think about solutions before starting to write them down. Make sure you attempt each problem.

2.
To obtain information on physical constants and material properties, please check the appendix in the text book.

3.
Start a new page in the answer book for a new question.


1. (10 points) TEM Transmission Lines and S-parameters.
(a) [5 pts] Give five distinct characteristics of a TEM line (1 pt. each). DO NOT simply list equations for TEM waves.
Solution: The characteristics associated with a TEM line are given below:
1.
Requires two (or more) conductors

2.
Requires a homogeneous dielectric

3.
No longitudinal field components (Ez = Hz = 0)

4.
Transverse fields can be found by solving Laplaces equation (electrostatic problem)

5.
Zero cutoff frequency (kc = 0) --- TEM wave can theoretically propagate for all frequencies

6.
Phase velocity (and wave impedance) do not vary with frequency (non-dispersive)


(b) [5 pts] A transistors S-parameters are measured to be S11 = 0.65 /-140o, S21 = 2.4 /50o, S12 = 0, S22 = 0.70 /-65o, in a 50 . system. Write down the S-parameters measured in a 100 . system.
Solution: The S-parameters are the same as those measured in a a 50 . system.
2. (25 points) Microstrip transmission lines A microstrip transmission line of Zo = 50. is to be made using Gallium Arsenide as the dielectric and Gold as the conductors.

a) [9 pts] If the dielectric thickness is d = 50 m, neglecting finite ground plane width
and conductor thickness and assuming r = 1, what is the width w required for Zo =
50.? (hint: for material parameters, check the appendix in the text book.)
b) [2 pts] What is eff at low frequencies?
c) [5 pts] At f = 10 GHz, what is the skin depth s?
d) [9 pts] At f = 10 GHz, what is the attenuation c due to conductor loss? What is the attenuation d due to dielectric loss? Be sure to identify units of your answers.
Solution:
a) From Appendix G, Gallium Arsenide: r = 13, (1 pt for finding this in Appendix G)
Using the formula (3.197) from Pozar, 60
r + 1 r - 1 0.11
A = + (0.23 + ) = 2.41
Zo 2r + 1 r
8eA
w/d = e2A-2 = 0.73, so w = 0.73(50) = 36.5 m
b) From (3.195)
r + 1 r - 1 1eff = + = 8.4
22
1 + 12d/wc) Gold: = 4.1x107 (1 pts, found from Appendix F) 2
Skin depth s =
= 7.86x10-7 m = 0.8 m
Rsd) From (3.199), c = Zow

At f = 1010, Rs =

= 3.10x10-2
2and c = 17 Np/m = 147.5 dB/m
tan = 0.006 (1 pt) kor(eff -1)tan
From (3.198) d =
= 1.7 Np/m = 15.1 dB/m
2
eff (r -1)
3. 20 points: The