Digital Signal Processing Reference
In-Depth Information
i
1
+
v
1
C
1
g
C
13
C
12
−
i
2
+
v
2
C
2
g
C
23
−
i
3
+
v
3
C
3
g
−
Figure 4-6
Circuit with three coupled capacitors.
simply a direct consequence of the fact that we defined the diagonal elements to
be the total capacitance of the individual traces. This is necessary to simplify the
mechanics of our circuit calculations while guaranteeing correct results, as we
illustrate with an example.
Example 4-1
Equivalent Capacitance for a Coupled Pair We apply equation
(4-18) to the two-line case, so that
C
11
C
22
−
C
12
C
=
−
C
21
Driving the lines with
dv
1
/dt
=
dv/dt
and
dv
2
/dt
=
0 gives
i
1
=
C
11
(
dv/dt
)
and
i
2
=
C
1
g
+
C
12
,weconfirm that our
solution matches the result given in equations (4-12) and (4-13). Additional anal-
ysis of the odd- and even-mode cases will also confirm our earlier results, and
is left as an exercise for the reader.
=−
C
21
(dv/dt)
. Recalling that
C
11
4.1.3 Field Solvers
The capacitance and inductance matrices are typically obtained as the output
from an electromagnetic field solver. These tools model the electromagnetic fields
between transmission lines in a multiconductor system, providing the basis for
equivalent circuit models and the inputs to transmission-line simulators such as
HSPICE. Field simulators fall into two general categories, two-dimensional (2D)
quasistatic and three-dimensional (3D) full-wave solvers. Examples of commer-
cially available tools include Linpar [Djordjevic et al., 1999] for the 2D quasistatic
case, and HFSS for 3D full-wave solvers.
Quasistatic tools use techniques similar to those outlined in Chapter 3, where
Laplace's equation is solved to calculate the capacitance for a given set of
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