Digital Signal Processing Reference
In-Depth Information
(5-14) and will differ only in the magnitude, which is a function of the respec-
tive distances between the reference planes and the strip (
h
1
and
h
2
). Thus,
the resistance of a stripline can be approximated by the parallel combination of
the resistance in the top and bottom portions of the conductor. The resistance
equations for the upper and lower sections of the stripline may be obtained by
applying equation (5-17) or (5-18) for the appropriate value of
h
. These two
resistance values must then be put in parallel to obtain the total resistance for a
stripline:
(R
(h
1
)
ac, micro
)(R
(h
2
)
ac, micro
)
R
(h
1
)
ac, mico
R
ac, strip
=
(5-19)
+
R
(h
2
)
ac, micro
5.2.3 Frequency-Dependent Inductance
Section 5.1 describes how the skin effect will force high-frequency current to flow
primarily in a small layer near the periphery of the conductor, and Section 5.2
describes how this translates into frequency-dependent resistance. Another conse-
quence of the skin effect is a frequency-dependent inductance. To conceptualize
where this frequency dependence comes from, consider two filaments of current
that form a loop with the return plane immediately below the conductor over a
differential length of transmission line
z
, as depicted in Figure 5-9. Loop (a)
passes through the center of the signal conductor, and loop (b) exists only on the
conductor surfaces. As described in Section 2.5.2, the inductance is proportional
to the loop area,
ψ
1
I
1
L
11
≡
(2-97)
where
ψ
1
is the magnetic flux, which depends on the loop area. Therefore, loop
(a) will have a higher inductance than loop (b) simply because the loop is larger.
At low frequencies, the skin depth will be large compared to the conductor thick-
ness and there will be significant current flowing in the interior of the conductor,
length
=
∆
z
length
=
∆
z
Signal
Conductor
∆
I
internal
∆
I
external
Reference
Conductor
(a)
(b)
Figure 5-9
Loops for a filament of current: (a) in the center of the conductor; (b) on
the surface of the conductor.
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