S-parameters
have become the de facto standard for describing
the electrical properties of interconnects. S-Parameters
are one of the few concepts which a microwave
designer working with frequency domains, and the
digital designer who works with time domain can
both use in their analysis and measurement of
interconnect data.

The
S-Parameters provide information about the electrical
properties of an interconnect¡Xa connector, a
scope probe, a circuit-board trace, a circuit-board
via, or a cable¡Xis contained in the interconnect¡¦s
S-parameters. But you need to use a consistent
method for assigning the port index labels to
inputs and outputs or you risk obtaining misleading
S-parameter values, which will lead to incorrect
interpretations.

Designers
know that whether S-parameters comes from measurements,
circuit simulations, or electromagnetic simulations,
the same formalism applies and the S-parameters
behave the same. S-parameters describe how sine
waves interact with and ¡§scatter¡¨ from an interconnect.
Each interconnect has ¡§ports,¡¨ defined as the
ends of the interconnect into which signals enter
and from which they leave. Each port has connections
to the signal conductor and its return path. Index
numbers label the ports into which a signal enters
and from which it scatters.

Consistency
is paramount when you are labeling these ports.
Software used to calculate S-parameters uses a
defined scheme to assign port designations, and
you need to be consistent with that scheme. If
you create S-parameter data-files based on one
port-labeling scheme and use a data file that
assumes a different labeling, the interpretation
of the S-parameters and the results obtained using
them will be wrong. This very basic issue of port
assignment causes the most common problem when
using S-parameter models: incorrect interpretation
of the data.

By
following one simple guideline, you can eliminate
this problem. You will also be able to look at
an S-parameter model and immediately determine
if it assumed the incorrect port assignment.

**Return
loss and insertion loss**

Each
S-parameter is the ratio of the wave coming out
of a port to the wave going into a port (Figure
1). The formalism of S-parameters describes the
combination of sine waves scattered from the ports
of an interconnect. Every combination of this
input-output port ratio makes up an S-parameter¡¦s
matrix elements. Each matrix element is defined
by the input port number (the stimulus) and the
output port number (the response). This formalism
applies regardless of whether the interconnect
has just one port or 100 ports.

S-parameters, Figure 1

FIGURE
1. Each S-parameter is the ratio of a scattered
sine wave from a port to an incident sine wave
into a port.

In
a two-port interconnect such as a PCB (printed-circuit
board) trace or a cable, there¡¦s only one way
to assign the index port labels: port 1 on one
side and port 2 on the other side. The S-parameter
matrix element corresponding to a wave that goes
into port 1 and reflects back out of port 1 is
labeled as S11. For historical reasons, S11 is
also referred to as return loss. Because impedance
changes along the interconnect cause reflected
waves, return loss is very sensitive to the interconnect¡¦s
impedance profile. The S-parameter corresponding
to the wave going into port 1 and coming out port
2 is labeled S21 and is referred to, for historical
reasons, as the insertion loss. It has information
about reflections and is also sensitive to the
losses in the interconnect.

One
confusing aspect of S-parameters is the order
of the index numbers used to label each S-parameter
matrix element. If a signal were to go into port
1 and come out port 2, you might assume its label
would be ¡§S12.¡¨ The label would be easy to remember
at a glance: The signal goes into port 1 and comes
out port 2.

Unfortunately,
as a consequence of the matrix math formalism,
the labeling scheme follows the opposite structure.
The S-parameter matrix element containing information
about the wave going into port 1 and coming out
port 2 is actually S21.

At
the lowest frequency, where the physical length
of the interconnect is really short compared to
? of a wavelength, the reflection off the front
of the interconnect and the reflection from the
back end of the interconnect mostly cancel out
one another, so the return loss, S11, is nearly
zero. In decibels (dB), the return loss for a
through interconnect at low frequency is almost
always a large negative decibel value.

The
transmitted signal, described by S21, is due to
the initial transmitted signal, and a small contribution
from the signal reflects off port 2 to port 1,
then reflects back to port 2 and, finally, out
port 2. At the lowest frequency, all of the signal
gets through and comes out port 2.

The
insertion loss of a through-interconnect at low
frequency will be close to 0 dB.

As
frequency increases, the losses in all interconnects
cause the insertion loss to fall, which means
a larger and more negative insertion loss in decibels.
An example of the measured return and insertion
loss of a typical 50-£[ trace on a circuit board
is shown in Figure 2.

S-parameters, Figure 2

FIGURE
2. The return loss (red, S11) and insertion loss
(yellow, S21) of a circuit board¡¦s transmission-line
measurements show the characteristic behavior
of return loss starting with a large, negative
decibel value and an insertion loss starting with
0 dB at low frequency.

This
is an important observation: For virtually all
interconnects, at the lowest frequency, you can
expect the insertion loss to be nearly 0 dB. This
is an easy and direct way to determine which matrix
element is really the insertion loss, independent
of the port labeling.

**More
than two-port S-parameters**