Digital Signal Processing Reference
In-Depth Information
Again, to calculate the impedance, we must first recalculate the capacitance for
ε
r
=
1.
10
−
12
)
2
πε
ln
(b/a)
=
2
π(
1
)(
8
.
85
×
10
−
12
F
/
m
C
=
=
×
80
.
2
ln
(
2
)
1
c
2
C
ε
r
=
1
1
10
−
9
H
/
m
L
=
=
10
−
12
)
=
138
.
5
×
10
8
)
2
(
80
.
2
(
3
×
×
138
.
5
×
10
−
9
Z
0
=
=
27
.
3
184
.
5
×
10
−
12
Comparing this result to
Z
0
,
fieldmap
shows reasonable accuracy but demonstrates
the inherent errors that are inevitable when using hand sketches.
Example 3-3
Use field mapping techniques to calculate the impedance and
the effective dielectric permittivity of the microstrip transmission line shown in
Figure 3-26, where
w/h
=
1 and the permittivity of the dielectric material is
ε
r
=
4
.
0.
SOLUTION It is inherently more difficult to apply mapping techniques to a
microstrip because the fields are difficult to draw accurately and the dielec-
tric is not homogeneous. Figure 3-26 shows a drawing of the field lines. Note
1
1
1
1
1
1
w
e
r
=
1
1
1
0.5
0.5
0.5
1
1
1
0.5
1
1
1
11
1
e
r
=
4
1
1
1
1
1
h
1
1
1
1
1
1
1
1
1
1
1
1
Figure 3-26
Field map used to calculate the effective dielectric permittivity and the
impedance of a microstrip.
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