Digital Signal Processing Reference
In-Depth Information
Increased charge
density
e
r
=
1
e
r
>
1
Figure 3-14
At high frequencies, the proximity of the fields concentrates the charge in
the bottom of the strip nearest the reference plane.
The frequency-dependent nature of the effective permittivity in a microstrip
will cause the spectral components of the digital waveform (as calculated with a
Fourier transform) to travel at different speeds, which will distort the waveform.
This is known as
dispersion
. A relatively simple formula for calculating how
the effective dielectric permittivity for a microstrip changes with frequency due
to the nonhomogeneous nature of the dielectric was developed empirically by
[Collins 1992], and is given by
ε
r
−
ε
eff
(f
=
0
)
ε
eff
(f )
=
ε
r
−
(3-37)
1
+
(f/f
a
)
m
where
f
b
f
a
=
0
.
332
ε
−
1
.
73
0
.
75
+
(
0
.
75
−
)(w/ h)
r
tan
−
1
ε
r
ε
eff
(f
47
.
746
h
√
ε
r
−
ε
eff
(f
=
0
)
−
1
f
b
=
=
ε
r
−
ε
eff
(f
=
0
)
0
)
m
=
m
0
m
c
≤
2
.
32
w
h
0
.
32
1
−
3
1
m
0
=
1
+
+
√
w/h
+
+
1
+
w/h
0
.
15
0
.
235
e
−
0
.
45
(f/f
a
)
1
.
4
w
h
≤
1
+
−
0
.
7
1
m
c
=
w
h
1
>
0
.
7
where
ε
eff
(
f
0) is calculated with (3-35),
f
is in gigahertz, and the units of
w
and
h
are millimeters.
∗
=
∗
Fortunately, a frequency-dependent effective dielectric permittivity does not pose significant obsta-
cles to modeling transmission lines. In Chapter 10, techniques that employ frequency-dependent
equivalent circuits using tabular SPICE models are described that allow a unique value of the
transmission-line parameters to be described at every frequency point.
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