Digital Signal Processing Reference
In-Depth Information
where
K
4 is 0.45 for results in pF/inch or 0.18 for results in pF/cm.
Because in both of these equations the units cancel,
K
3 and
K
4 can have differ-
ent units than
h
and
w
.
For example, the capacitance of a 5-mil-wide stripline centered between two
planes spaced 66 mils apart when
ε
r
= 4.0 is 0.77 pF/cm (
K
4 = 0.18,
w
= 5,
h
= 66).
This is 15% higher than the actual value of 0.67 pF/cm.
17.7 Finding Microstrip Inductance and Capacitance When Trace
Geometry Is Known
Often the width, thickness, and impedance of a microstrip are known, but the time
of flight is not. In that case the (17.12), (17.13) and (17.14) can be used to estimate
the inductance and capacitance.
17.7.1 Microstrip Inductance
Inductance of a microstrip trace not covered in solder mask can be estimated (with-
out accounting for trace thickness) with (17.12). This has been simplified and
curve-fitted [3] from [5].
5ln6.3
h
⎛
⎞
LK
=×
×
(17.12)
⎜
⎟
⎝
⎠
w
Set
K
5 to 5.1 to obtain the inductance in nH/inch or to 2 for nH/cm. Because
the units cancel,
K
5 can have different units than
h
and
w
.
For example, the inductance of a 5-mil-wide microstrip spaced 11.5 mils above
the ground plane is 5.35 nH/cm (
K
5 = 2,
w
= 5,
h
= 11.5). This is 7% lower than
the actual value of 5.46 nH/cm.
17.7.2 Microstrip Capacitance
Because the dielectrics are not homogeneous, it is not proper to use the reciprocity
principle to find the capacitance when the inductance is known, as was done with
stripline.
Equation (17.13) is simplified from [6] and used to find the capacitance once
the effective dielectric constant has been found with (17.14) [7] (repeated here from
Chapter 7).
K
6
8
×
ε
r f
_
C
=
hw
wh
⎛
⎞
ln
+
(17.13)
⎜
⎟
⎝
⎠
4
⎛
⎞
⎜
⎟
ε
+
1
ε
−
1
1
ε
=
r
+
⎜
r
×
⎟
r f
_
(17.14)
2
2
10
h
w
⎜
⎟
1
+
⎜
⎟
⎝
⎠
