Digital Signal Processing Reference
In-Depth Information
To obtain the inductance in nH/inch, set
K
7 to 32; set it to 12.6 for nH/cm.
The equation is written this way to show the importance of the length-to-width
ratio in determining the inductance. As with the capacitance, the
h
and
w
units can-
cel, so
L
can be found in terms of either inches or meters for
h
and
w
in any units,
provided that the units for
K
7 and length match.
For example, the inductance of a 10-cm-long, 50-mil-wide plane placed on a
1-mil-thick block of laminate is 2.5 nH (
K
7
1)
when the current is injected along the plane's wide edge. This is 0.25 nH/cm. Be-
cause the length is in centimeters, 12.6 was chosen for
K
7 rather than 32.
The inductance of those same planes when current is injected along the narrow
edge is found to increase to 63 nH (
K
7
=
12.6,
Length
=
10,
w
=
50,
h
=
=
12.6,
Length
=
50,
w
=
10,
h
=
1). This
is 1.3 nH/cm.
This example shows that simply by swapping
Length
and
w
, the inductance of
the setup has increased fivefold. This illustrates the advantage in using wide con-
ductors rather than narrow ones when it is important to reduce inductance.
17.8.2 Capacitance
The capacitance is found with:
w
CK L h
h
(17.16)
=×
8
××
ε
r
where
K
8 is 0.225 to calculate the capacitance in pF/inch length or use 0.885 for pF/
cm length. Because the units for
w
and
h
cancel, they can have inch or metric units
when using either value for
K
8.
For example, the capacitance of a 10-cm-long, 50-mil-wide plane placed on a
1-mil-thick block of laminate with a dielectric constant of 4 is 177 pF (
K
8
=
0.885,
Length
4). Because the length is in centimeters, 0.885 was
chosen for
K
8 rather than 0.225. Notice that since the capacitance is determined
by the area, it does not change if
Length
and
w
are swapped (but be sure to keep
track of the units so the correct value for
K
8 is used).
=
10,
w
=
50,
h
=
1,
ε
r
=
17.9
Calculating Trace Loss from a Circuit Model
Lossy transmission line models in SPICE use the AC resistance (
R
ac
) and conduc-
tance (
G
) to model conductor and dielectric loss (see Chapter 8) in transmission
lines. These lines may be circuit board traces or cables. Equation (17.17) shows
how to calculate the total loss (
α
t
) in decibels when these values are known:
⎛
R
⎞
(
)
(17.17)
α
=
4.3
ac
+
GZ
×
⎜
⎟
t
o
⎝
Z
⎠
o
Since
R
ac
and
G
are given for a specific frequency and length of line,
α
t
is only
valid at that one frequency and length.
