Digital Signal Processing Reference
In-Depth Information
290
285
280
275
150
100
270
265
50
1
2 3
Frequency, GHz
4
5
1
2 3
Frequency, GHz
4
5
(a)
(b)
0.08
170
165
160
155
0.06
0.04
150
145
0.02
0.00
1
2 3
Frequency, GHz
4
5
1
2 3
Frequency, GHz
4
5
(c)
(d)
Figure 6-25
Frequency-dependent transmission-line parameters for Example 6-4.
Step 2:
Calculate the frequency-dependent parameters of the dielectric. First,
the real and imaginary parts of the dielectric constant must be found:
ε
=
ε
r
=
3
.
32
ε
ε
=
tan
δ
=
0
.
0205
ε
=
0
.
068
ε
=
ε
−
jε
=
3
.
32
−
j
0
.
068
Equations (6-30a) and (6-30b) are solved simultaneously to get
ε
and
ε
∞
:
ε
m
2
ln
(ω
2
/ω)
ln
(
10
)
=
ε
∞
+
3
.
32
−
m
1
ε
m
2
−
m
1
−
π/
2
0
.
068
=
ln
(
10
)
where
m
1
11 are chosen to correspond to a frequency range of
10 rad/s to 100 Grad/s,
ω
is 2
π
(1 GHz), and
ω
2
=
1 and
m
2
=
10
11
.
=
ε
=
0
.
997
ε
∞
=
3
.
2
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