Digital Signal Processing Reference
In-Depth Information
model can simulate a single conductor or a multiconductor bus and so can be used
to model crosstalk or differential pairs.
The Exercises for Chapter 7 show how to compute
R
and
G
for use in O and
W element circuit models.
3.4 S-Parameters
Interconnect (including traces, vias, or connector pins) can be modeled in the fre-
quency domain with
scattering parameters
(S-parameters). Although they origi-
nated in RF engineering, S-parameters are now commonly used in high-speed digital
signaling work, especially in serial signaling applications.
Because of their importance to advanced SI applications, an overview is pre-
sented here, but since S-parameters are not used in this topic, we will not go into
detail. Additional introductory information on S-parameters is presented in [11-
13]. More theoretical explanations are presented in [14-17].
3.4.1
What Are S-Parameters?
S-parameters show the degree to which sine waves are reflected (scattered) from a
signal source of known impedance (the reference impedance) by each pair of termi-
nals (ports), and the amount of the signal appearing between ports. This means that
S-parameter models show loss, impedance mismatch (reflections), and the coupling
between ports (crosstalk between traces).
A trace over a ground plane has two pairs of terminals and so is an example of
a simple two-port network, as shown in Figure 3.1.
Subscripts are used to indicate the terminal pair being measured (identified by
the subscript
m
) and the terminal pair injecting the signal (the subscript
i
). This is
shown in (3.1).
S
(3.1)
mi
For instance, measuring the signal at port 2 and injecting a signal into port 1
gives
S
21
(the
insertion loss,
since it shows how much the signal is attenuated be-
tween ports 1 and 2).
Simultaneously injecting a wave and observing the reflection at port 1 yields
S
11
(the
reflection loss
because it shows how much of the signal is reflected back
to the generator). Interconnects such as transmission lines and vias have the same
behavior in both directions, so for traces
S
21
S
22
.
In S-parameter models the
S-parameter coefficients
are tabulated for a range
of frequencies and are represented by two numbers, one for the amplitude and the
other for the phase. A sample S-Parameter listing of just the amplitude for a 4-mil
(0.11-mm)-wide half-ounce 50 stripline on FR4 is shown in Table 3.2.
=
S
12
and
S
11
=
3.4.2 What Is Insertion Loss?
For a lossless transmission line, the insertion loss (
S
21
) and its twin (
S
12
) are 0, since
that indicates that no signal energy is lost when the transmission line is inserted
