Digital Signal Processing Reference
In-Depth Information
C
13
1
2
3
C
12
C
23
C
10
C
20
C
30
Ground
plane
L
11
Trace 1
C
10
L
12
L
13
C
12
L
22
Trace 2
C
20
C
13
L
23
L
33
C
23
Trace 3
C
30
Figure 9.1
(a) Trace cross-section and (b) circuit model of a small segment of line showing the
capacitances and inductances for three traces.
CCC
CC C C
CCC
11
12
13
(9.1b)
=
21
22
23
31
32
33
The self-inductance (
L
s
) of trace 1 is
L
11
and is measured with no current flow-
ing in the other traces. The mutual inductance (
L
m
) linking trace 1 to 2 is
L
12
.
The self-capacitance (
C
s
) and mutual capacitance (
C
m
) are similar, but as shown
in (9.2),
C
11
and the other diagonal terms such as
C
22
in the matrix is the capaci-
tance to ground (
C
10
in Figure 9.1) plus the sum of all the mutual capacitances
when they are grounded.
(9.2)
CCCC
=++
11
10
12
13
By rearranging (9.2), we find that the capacitance to ground of just trace 1
(
C
10
) is the self-capacitance (
C
11
) minus all of the mutual capacitance.
To illustrate, the inductance and capacitance matrices per meter for a pair of
traces are found by a 2D field solver to be:
2.876E-07
3.564E-08
9.859E-09
L
=
3.564E-08
2.863E-07
3.564E-08
(9.3a)
9.859E-09
3.564E-08
2.876E-07
