11 February 20 14
1, (35 pts) A lossless 50 Q (Zo = 50 Q) transmission line has the following phasor
voltage at 100MHz, V(z) = 6e ^
z
'+3e^
(a) (5 pts) Find the reflection coefficient at the load
r-
(b) (3 pts) Find the voltage standing wave ratio, S.
(c) (3 pts) What is the phase velocity of the signal?
"A
2.7T * 2JT
^
/V '-"
/"!
(d) (6 pts) .Find V(z)\.
nz
V
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11 February 20 14
(e) (4 pts) What is the load impedance?
/
- 37*& /-
/ - *.
(f) (2 pts)What is the angular frequency , to, of the sinusoidal signal?
(/&0//0
}
(g) (12 pts) What is the expression for F(z) in the time domain, v(z,t). Use numerical
values where possible.
^/
\/
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11 February 20 14
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2. (35 pts)A lossless transmission line of length 0.625 A, with characteristic impedance
Zo=50Q is terminated with load impedance ZL= 200 Q as shown below.
z L =20o n
V. =
-o
(a) (7 pts) Find the input impedance, Z;n at the input to the transmission line.
=2.
-/'- /
^ ,
-X .,,
_
2-j,
-0-dsn
(b) (8 pts) Find the voltage, F. and the current, /. , at the input to the transmission line.
»
I
—^
-
V / • -^ \~~~^
f JttL.
V
*
Vi *»•
V/
(c) (4 pts) Find the average power absorbed by (delivered to) the load ZL-200 Q.
—i ?/
11 February 20 14
(d) (5 pts) Find the average power supplied by the source where Vg - 20ej50° V
(e) (3 pts) Find the reflection coefficient at the load.
(f) (5 pts) Find the complex amplitude V* of the incident wave along the transmission
line.
V
(g) (3 pts) Find the average power incident at the load.
/
/
•*/•'/
2 z*r>
?
&
s
S"
2 /3i
\I
^~™'
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11 February 20 14
3. (30 pts) For the circuit shown below where the characteristic impedance of line 1 is
100 Q , of line 2 is 60 Q and of line 3 is 50 Q, find:
Z g =100Q
line 2 =X/4
12 Q
(a) (20 pts) Zm at BB'.
/z
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11 February 20 14
If the incident voltage wave in line 1 has a complex amplitude, F0+ = 3ej40° V, find the
average power absorbed by (delivered to) each load.
(b)(10pts)
tf
-t
r
J£/LJL
4
vgLoadZx
Pav
avg Load Zy
Z ~
avg Load Zz
/
0O
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11 February 20 14
Short Problems and Questions
(1) (10 pts) You wish to design a 10 GHz 0.318 pF capacitor using a 50 Q lossless
transmission line terminated with an open. What length of line in a fraction of a
wavelength is needed to build your design.
(L.
j
J
*
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(2) (5pts) A Smith chart is made up of two overlapping graphs one of which represents
the normalized input impedance z = r + jx. The other graph represents
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11 February 20 14
(3) (5 pts) Which graph below represents V(z) for a lossless transmission line
terminated with a short? Circle the correct graph below.
\V(<
z=0
(4) (5pts) Why were you able to ignore the signal propagation time in EE221?
0-01
•€
(5) (5 pts) Is microstrip a TEM line? Why or why not?
J
^
-8-