EXAMINATION
14 February 2013
United States Naval Academy
Electrical and Computer Engineering Department
EE 372
Exam 1
14 February 2013
1. You must present your work completely and legibly to receive partial credit. You must show
sufficient steps to justifY intermediate results as well as final answers.
2. Put all your work on the exam. If you need more space than that provided, ask your instructor
for paper. Write your answer clearly and use appropriate units. You have one hour and 50
minutes to work this examination.
Problem
1
2
3
4
5
Questions
Total
Value
25
25
25
25
25
25
150
Score
~~---c-~~o~~~/~-~G~~~)·________________________________
Name _____
I have neither given nor received assistance while completing this exam.
Signed and date
1
EXAMINATION
(1)
14 February 2013
(25 points) A 50Hz generator is connected to an air-spaced transmission line ( &,
=1 )
of length 1.5A. with characteristic impedance 100 Q. The transmission line is
terminated with load impedance ZL= 80-j40 n as shown in the figure below. Find the
following:
(a)
The reflection coefficient at the load,
(b)
The voltage
(c)
The voltage VL at the load.
(d)
The voltage
i7,
at the input to the transmission line.
V(z)
as a function of position z along the transmission line.
f - - - - - - /.
5 ;A_ ------~
( 3'0- j
t.;o) -/oo_
(Fo -J'IIl) .f-/CN~
(6)
160/V
vfz);
v l:t-)
r.
::
2
-
. '1°_
-2 0 - j
/J?O-j~o
EXAMINATION
14 February 2013
(2) (25 points) For the transmission lines shown below, the characteristic ~mpedance of line I is
50 Q, and the characteristic impedance of lines 2 and 3 is I 00 Q. The incident wave in line I has
100
V. The input impedance ofline 3 is -50j Q.
a complex amplitude of 3.5e
(a) The average power carried by the incident wave in line I.
(b) Find the power carried by the reflected wave in line I.
(c) Find the power absorbed by the I 00 Q load.
~ il1e.3
I
___....,..,____ ?.,-;, -t!
r-
2,- 2-o
..Z,+ 2r>
/r I
;:::.
;It·:
2.. - - - - - i '
(:;_" - -I.J o)- s-o
2D
-:_j'ID +- s-D
;;,62-)2-(2<. r-)
/)1J
3
-
J o--LfO
7o--'-IO
J
= - t;7
~
'vV
-j 'fl/ 0
-= c;, 6 2 e
EXAMINATION
14 February 2013
(3) (25 points) A 15 V generator with impedance 50 n, is attached to the transmission lines
as shown below. Find the average power absorbed by each load resistor.
/',4
~
.2
)/z.
j<'
.. joe~
"'%-t -
2I~};{;
~
~~~~-v
::::-
2-o
(s-o)
2
~
:::
/00
2.
- 2~)
jL
4;iTv/v /oo~ ~ -2.•7{
-6/1 -: :-21/
4
-2-.}") ~2.
':;
-=::: / C/ a J\.._)
2.;~ /16.:.~
2
s-r//b~_.A,. ~ '2o~
EXAMINATION
14 February 2013
(4) (25 points)A 50 Q transmission line is terminated with load impedance ZL = 60 + j50Q.
Using a Smith chart, find the following: (Please annotate the Smith chart for full credit)
(You must use the Smith chart for this problem.).
(a) The voltage standing wave ratio.
(b) The load admittance
(c) The input impedance 0.4/.. away from the load.
(d) The distance from the load to the nearest voltage maximum.
(e) The distance from the load to the nearest current maximum.
6.?
2.
(ev)
a)
I~
6o
f-
so
-
s-<::>
/.2
f-J/
s-
(!), :;-
- - 0· '-}
j
(C) 2. ~ 0 · l( ~ t-j (), q I
J
">'"
s--o
(t
I )
;..
~
'-/
r·~o.s-__rJ
j
(J)
5
The Complete Smith Chart
Black Magic Design
RI\DIAUYSCAU!D PARAMI!TI!IlS
•IG040
zo
10
2.5
zo
•411 30
15
10
8
1
I
o.t
0.1
0.7
0.9
0.6
0.8
0.1
o.2
o.s
0.4
0.3
1.1
2
•
0.2
1.6
1.4
U 11 I
15
lOWAltO LOAD->
5
7
II
6
9 10
11
14
zo
0.6
o.s
0.4
0.3
D.05
D.1
0.01
0.7
0.3
0.4
o.s
0.6
0.1
0.8
0.9
0.1
D.1
1.1
0.99
u
1.1
0.2
0.1
30
0
0 I
<-'IOWAitDCI!NI!IlJITOil
2
I
10
1.2
0.4
1.3
0.95
1.4
0.9
1.3 1.4
0.6 0.11
I.S
1.6
I
s
s
4
1.11 2
1.5
1.6 1.7 1.8 1.9 2
0.7
0.6
0.8
2.5
o.s
0.4
0.3
10
4
0.2
C1!NT2R
0.0
OIUCIN
1.1
IJ
1.3
1.4
1.5
1.6
1.7
1.8
zo
.
10 IS.
6
1.9
' 0.1 10•0
EXAMINATION
14 February 2013
(5) (25 points) A 50 n lossless transmission line is to be matched to an antenna with ZL =
100- j50 Q using a stub terminated in an open as shown below. Use the Smith chart to
determine the stub length and the distance between the antenna and stub for the single stub
tuner.
J.
l
j
d
~
1
--;2-jl-
~ I-= o, 'f f- j o, 2
Ytf,.
I
I/=
h.
I')
.:
I
-rJ· I
-·I
J
6
The Complete Smith Chart
__ ..-------BlackMagic Design
I
j
•10040 :10
10
•40 30
0
20
I
0.9
"-'
0.7
0.6
0.8
7
G.5
G.7
0.3
0.4
0.6
8
9
u
1.6
U
O.f
II I
0.3
12
If
C'-05
0.2
:10
15
30
cu
0.1
0
0.01
0 I
<- TOWAIU>GI!NI!RJ\1'01.
2
I
10WAIU>LOAD-•
10
7
5
II
I
10
cu
0.2
0-'
1.8
6
10
IS
2
0.8
z
1.S
1.1
0.99
u
1-1
u
u
o.2
0.4
0.6 0.8
l.l
1.3
0.90
1.4
0.9
1.:1
1.6
I
1.1 2
4
5
5
1.5
1.6 1.7 1.8 1.9 2
0.6
0.8
0.7
2-'
u
f
OA
0.3
0.2
CI!NTI!R
0.0
ORIGIN
OJ
0.2
0-3
0.4
0.5
0.6
0.7
0-8
0-9
1.1
1.2
1.3
u
u
1.6
1.7
1.8
-
10 :10
10 1,_
6
1.9
•0.1
10•
0
EXAMINATION
14 February 2013
Questions:
(1) (5 points) In your introductory circuits class, why were you able to ignore the length of
the wires connecting circuit elements?
.r/;~ /
/,~
(J ~ o.ol/\)
(3) (5 points) Draw the lumped element circuit model for a lossless transmission line.
(4) (5 points) Give an example where a quarter wave transformer would be preferred over a
single stub tuner as a matching technique.
7