EE 330
Lab #7
Spring 2007
Solution
The Big Game on Cable TV
1.
How far down the line can you expect to find the problem?
8
8
10
49
.
2
10
3
83
.
0
%
83
×
=
×
×
=
=
c
v
m/s
6
10
1
.
12
−
×
=
τ
s
–
This is the travel time to and back from the point on the line where the
problem is, thus the problem is expected to has occurred at about
Ft
4
.
4942
m
45
.
1506
2
=
=
v
from the distribution box. The accuracy, with which the TDR device measures distances of the
this order, is
. Hence, the problem is
m
35
.
3
Ft
11
=
m
35
.
3
45
.
1506
±
from the distribution box.
2.
How many dB of loss would you expect to see in kilometer of cable?
At 50 MHz, the loss is
dB/km
52
dB/100m
2
.
5
=
; at 100 MHz, it is
.
Assuming linear dependence and interpolating, the loss at 67.25 MHz is expected to be
dB/km
72
dB/100m
2
.
7
=
()
dB/km
9
.
58
50
25
.
67
50
100
52
72
52
=
−
⎟
⎠
⎞
⎜
⎝
⎛
−
−
+
3.
How far
back
from the slice (toward the generator) you need to place the stub?
m
7
.
3
=
=
f
v
λ
The normalized impedance at the point of measurement is
Ω
+
=
+
=
=
4
2
75
300
150
j
j
Z
Z
z
c
L
L
,
marked with a blue dot on the Smith chart.
The corresponding admittance is
1
2
.
0
1
.
0
4
2
1
−
Ω
−
=
+
=
j
j
y
L
, marked with a red dot.
The stub must be connected to the TL at a point where the admittance,
y
d
, has a real part equal to
one. There are two green points on the Smith chart, which correspond to the two options,
9
.
2
1
1
j
jb
y
d
±
=
±
=
The point representing the admittance with the positive imaginary part is closer to the measured
admittance,
y
L
, a normalized distance of
234
.
0
202
.
0
468
.
0
5
.
0
=
+
−
=
d
back from the slice.
This normalized distance is denoted by the red ark on the Smith chart. The actual distance is
cm
6
.
86
m
866
.
0
234
.
0
=
=
=
d
.
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 Spring '08
 TOFIGHIMOHAMMAD
 Impedance matching, Smith chart, stub, normalized load impedance, admittance

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