Digital Signal Processing Reference
In-Depth Information
7.6
How Does the Skin Effect Change the Inductance?
The total trace inductance of a trace or round wire is the sum of the inductance
internal to the trace (the internal inductance) and the inductance due to the trace
geometry (the external inductance) [5, 13].
The internal inductance is small and its value is reduced as the skin effect
causes the current to move away from the center of the trace and migrate outward,
toward the trace surface. This leaves fewer lines of magnetic flux present inside the
conductor, lowering the internal inductance. Because this behavior is driven by the
skin effect, the internal inductance decreases as the square root of the increase in
frequency (the same rate at which the resistance increases).
For instance, at 500 MHz the internal inductance of a 4-mil-wide 50
stripline
trace is about 5% of the total inductance. It falls to less than 1% at 20 GHz. As-
suming that the capacitance does not change, this reduction in inductance causes
the trace impedance to be about 2% lower at 20 GHz than it is at 500 MHz.
Ω
7.7
Understanding Stripline and Microstrip Impedance
A trace's dimensions (its width, thickness, and distance to the ground plane or
planes) determine its impedance. To understand how these interact, (7.3) (simplified
from [14]) calculates stripline impedance, and (7.4) calculates microstrip imped-
ance. For clarity, (7.4a) is slightly modified from [15], and uses a more comprehen-
sive equation for the effective dielectric constant (7.4b) [16].
More complex (and accurate) equations appear in Chapter 17, but these equa-
tions are simple enough to show how the trace dimensions interact and determine
the impedance. The traces are assumed to be perfectly rectangular, and the stripline
is assumed to be centered between the return planes.
94
bw
+
⎛
⎞
Z
=
ln
⎜
⎟
(7.3)
o
⎝
⎠
wt
+
ε
r
60
7.5
h
⎛
⎞
Z
=
ln
⎜
⎟
(7.4a)
o
⎝
⎠
wt
+
1.25
ε
r f
_
⎛
⎞
ε
+
1
ε
−
1
w
wh
r
r
ε
=
+
(7.4b)
⎜
⎟
r f
_
2
2
+
10
⎝
⎠
From these equations we see that:
When holding the distance to the trace (
b
or
h
) constant, the impedance
gradually goes down as the trace gets wider (
w
) or as it gets thicker (
t
).
•
