Digital Signal Processing Reference
In-Depth Information
approximately one-tenth the signal rise time if working in the time domain,
t
r
c
10
√
ε
r
z
≤
(3-22a)
or one-tenth the wavelength that corresponds to the maximum frequency of inter-
est if working in the frequency domain,
λ
f,
max
10
z
≤
(3-22b)
10
8
where
t
r
is the signal rise or fall time,
c
the speed of light in a vacuum (3
×
=
c/(f
max
√
ε
r
)
the wavelength
that corresponds to the highest frequency of interest in the simulation.
When using a distributed
LC
model for modeling transmission lines, the num-
ber of segments for time-domain simulations is determined by
m/s),
ε
r
the dielectric permittivity, and
λ
f,
max
10
l
√
ε
r
t
r
c
l
z
=
N
s
=
(3-23a)
For frequency-domain simulations,
l
z
=
10
l
λ
f,
max
N
s
=
(3-23b)
where
N
s
is the minimum number of segments required to model a transmis-
sion line of length
l
. Therefore, the capacitance and inductance per segment are
given by
lC
N
s
C
z
=
(3-24a)
lL
N
s
L
z
=
(3-24b)
where
C
and
L
are the per unit length values of the capacitance and inductance.
Example 3-1
Create a transmission-line model for the 20-cm transmission line
shown in Figure 3-10a assuming the following inductance and capacitance values
and a dielectric permittivity of
ε
r
=
4
.
5.
10
−
7
H
/
m
L
=
3
.
54
×
10
−
10
F
/
m
C
=
1
.
41
×
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