Digital Signal Processing Reference
In-Depth Information
e
r
=
1
e
r
=
4
(a)
e
r
=
4
(b)
Figure 3-11
Electric fields of (a) a microstrip and (b) a stripline.
of a microstrip line, the electric field fringes through both the dielectric material
and the air, which lowers the effective dielectric constant; thus, the signals will
propagate more quickly than those on an internal layer. Note that this description
assumes that the relative magnetic permeability of the dielectric material under
consideration is unity (
µ
r
=
1).
In Sections 3.4.3 and 3.4.4 we describe how to derive the effective dielec-
tric permittivity of a microstrip using quasistatic approximations of Maxwell's
equations. Furthermore, there are many commercially available two-dimensional
electromagnetic field solvers available which will produce accurate results. How-
ever, in the absence of a field solver, equation (3-35) has been shown to produce
results of reasonable accuracy [Hammerstad and Jensen, 1980] for structures
where the conductor thickness
t
is much smaller than the dielectric thickness
h
.
49
ln
u
4
18
.
7
ln
1
18
.
1
+
(u/
54
)
2
u
4
1
1
u
3
a
=
1
+
+
+
+
0
.
432
0
.
564
ε
r
−
0
.
053
0
.
9
ε
r
+
b
=
(3-35)
3
1
−
ab
ε
r
+
1
ε
r
−
1
10
u
ε
eff
(u, ε
r
)
=
+
+
2
2
where
u
=
w/h
and the dimensions are defined in Figure 3-12a.
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