Digital Signal Processing Reference
In-Depth Information
17.12 Finding Stripline Impedance
The impedance of a stripline trace can be found very accurately even for narrow
traces with (17.24) [11, 12]. It accounts for effects of trace thickness and fringing
and is accurate to better than 2% for wide traces under about 65
Ω
, provided that
b
w
bt
≥
is 2.6 mils (66
μ
m) or more. The trace must be wide enough so that
0.35,
and
−
accuracy improves for larger ratios. This is usually the case for 65
or lower traces
on FR4. Other equations are presented in [3, 11-13] for higher impedance traces.
Equation (17.24) has been recast in a simpler form similar to that presented in
[13]:
Ω
94.15
Z
=
o
C
(17.24)
⎛
⎞
w
K
b
f
ε
9
+
⎜
⎟
r
⎝
8.854
ε
⎠
r
The constant
K
9 is found with (17.19), and the fringing capacitance
C
f
is found
with (17.25):
(
)
(
)
(
)
⎡
⎤
2
(17.25)
C
=
5.656
×
ε
×
K
9
×
ln
K
9
+
1
−
K
9
−
1 ln
K
9
−
1
⎣
⎦
f
r
Although the fringing capacitance is in pF/m, the impedance equation (17.24)
has been scaled so that
w
,
b
, and
t
can be in either mils or centimeters.
For example, for a 5-mil-wide, 0.65-mil-thick stripline on FR4 (
4.0) locat-
ed midway between ground planes spaced 66 mils apart,
K
9 is found from (17.19)
to be 1.01. From (17.25) the fringing capacitance,
C
f
is found to be 17.34 pF/meter
(
w
ε
r
=
=
66).
By using that value for
C
f
in (17.24),
Z
o
is found to be 88
5,
t
=
0.65,
b
=
Ω
. This is 12% lower
than the actual value of 100
Ω
. This inaccuracy is expected because this trace fails
w
bt
≥
the
test.
0.35
−
Lowering the impedance by reducing the plane spacing to 12 mils passes the
test and makes
K
9
=
1.057 and
C
f
=
18.85. Using this in (17.24) produces an im-
pedance of 48.8
Ω
, about 1.5% lower than the actual value.
17.13
Finding Exposed Microstrip Impedance
The impedance of a microstrip not covered in solder mask can be found with
(17.26) [11, 12]. It works best for traces under 60
on FR4 that are at least twice
as wide as the distance from the return plane (
h
in Figure 17.1). The accuracy is
better than 5% [3] in those cases and improves for wide, lower impedance traces.
Ω
