Digital Signal Processing Reference
In-Depth Information
SOLUTION
The ac resistance will exist when the frequency gets high enough so that
the skin depth is smaller than the conductor thickness. Above this frequency, dc
resistance ceases to exist; only ac (skin effect) resistance is present. The frequency
can be calculated by setting a skin depth equal to the conductor thickness using
(5-10) and solving for the frequency:
2
ωµσ
δ
=
2
.
1 mils
=
10
−
7
H
/
m and 2
.
1 mils
10
−
6
m:
Since
ω
=
2
πf, µ
=
µ
0
=
12
.
56
×
=
55
.
3
×
2
2
2
πσµ
0
(
53
.
3
10
6
Hz
=
=
×
f
1
.
53
10
−
6
)
×
Therefore, at 1.53MHz, dc resistance does not exist and ac resistance begins to
increase with
√
f
.
Stripline Losses (Smooth Conductors)
In a stripline transmission line, the cur-
rents of a high-frequency signal are concentrated in the upper and lower edges
of the conductor. The current density will be dependent on the proximity of
the local reference planes. If the stripline is referenced equidistant from both
planes, the current will be divided equally in the upper and lower portions of
the conductor as depicted in Figure 5-8. In an offset transmission line, the cur-
rent densities on the upper and lower edges of the transmission line will be
dependent on the relative distances between the ground planes and the con-
ductor (
h
1
and
h
2
in Figure 5-8). The current density distributions in each
stripline reference plane will be governed by an equation similar to equation
Reference plane
h
1
w
1
J
(
d
)
∝
2
d
h
x
t
1
+
d
(Skin depth)
h
2
Reference plane
d
Figure 5-8
Current distribution in the signal; conductor and reference planes of a
stripline.
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