Digital Signal Processing Reference
In-Depth Information
of the capacitance can be estimated by measuring the area under the capacitive
dip. The area is calculated by integrating equation (3-108) after subtracting the
dc offset, assuming that
R
t
=
Z
0
where
τ
=
Z
0
C/
2
v
s
2
(
1
e
−
[2
(t
−
2
τ
d
)/Z
o
C
]
)
v
capacitor
=
−
∞
v
s
2
v
s
2
(
1
−
e
−
[2
(t
−
2
τ
d
)/Z
0
C
]
)dt
A
cap
=
−
2
τ
d
∞
v
s
2
v
s
CZ
0
4
e
−
2
t
/Z
0
C
dt
=
=
(3-115)
0
4
A
cap
v
s
Z
0
C
=
Example 3-8
Calculate the value of the shunt capacitance for the waveform in
Figure 3-47 assuming the circuit shown in Figure 3-46.
SOLUTION A fine grid was overlaid on the waveform in Figure 3-47 so that
the area under the curve can be estimated. The total number of squares under the
capacitive dip is about 60. The area per square is
10
−
9
)
=
10
−
13
A
square
=
(
0
.
04
)(
0
.
01
×
4
×
The total area is therefore
10
−
11
A
tot
=
60
A
square
=
2
.
4
×
1.2
1
0.8
0.6
0.4
0.2
0
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
Time, ns
Figure 3-47
TDR waveform for Example 3-8.
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