Digital Signal Processing Reference
In-Depth Information
6-4
Show that the Debye dielectric model [equation (6-28)] satisfies the
Cauchy-Riemann equations for
i
=
1:
n
ε
i
ε
=
ε
∞
+
(6-28)
1
+
j(ω/ω
2
i
)
i
=
1
6-5
Given the cross section in Figure 6-29, estimate the bulk value of the
dielectric permittivity. Assume that
ε
r,
glass
=
=
6
.
1 and
ε
r,
epoxy
3
.
2.
Glass bundle
Epoxy
6.2 mils
2.1 mils
3.8 mils
13 mils
Figure 6-29
Cross section for Problem 6-5.
6-6
Assume that a series of 1-in.-long parallel transmission lines routed adja-
cent to each other are measured. The TDR waveforms are shown in
Figure 6-30. Estimate the variation in the dielectric permittivity due to
the fiber-weave effect.
t
r
=
25 ps
0
-
1
V
step
1.10
1.05
τ
d
,
Z
0
50
ohms
50
ohms
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
Time, ns
Figure 6-30
TDR for Problem 6-6.
6-7
Assuming a conductor width of 5 mils and a loss-free dielectric thick-
ness of 4 mils, create an equivalent-circuit model of the corner cases in
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