W2308EP Datasheet, PDF (15/26 Pages) Keysight Technologies – Quick Start for Signal Integrity

A Diversion into S-Parameters
If you pushed into the hierarchy, you’d have noticed some
components were defined using S-parameters. So let’s
take a short break from the keyboard and first say why we
use network parameters in general and S-parameters in
particular, to characterize high frequency structures and
components.
For low speed digital logic we only consider the forward
propagation of signals, because, although reflections
exists, they generally die down quickly if the interconnec-
tion flight time (propagation time) is short compared to the
rise and fall times and the bit period. In fact, the incident
signal or wave is partly transmitted and partly reflected:
Lightwave analogy
Incident
Reflected
Transmitted
Keysight Application Note AN 1287-1, “Understanding the
Fundamental Principles of Vector Network Analysis”
http://literature.cdn.keysight.com/litweb/pdf/5965-7707E.pdf
So, instead of a single transfer function, it might seem
we now need two parameters to characterize a 2-port
component at each frequency. In fact, the situation is more
complex. The output port is also being bombarded with
waves reflected off of the component in front of it in the
cascade. These reverse waves are also partly transmitted
(backwards down the cascade) and partly reflected off
of the output port (heading back up the cascade). So we
actually need four numbers per frequency point. Each is a
complex number, representing magnitude and phase of the
respective wave, relative the incident wave.
For reasons given below, it is convenient to collect the four
numbers together in a two-by-two matrix called network
parameters. There are several formats each of which has
their pros and cons. The most convenient format for mea-
surement purposes is the S-parameter format, because you
can measure S-parameters using standard load, source,
and connector impedances such as 50 Ω. In contrast,
direct measurement of, say, Z parameters requires opens
and short loads and sources, which are difficult to make at
high frequencies and can damage some components. Once
you have the S-parameters measured, there are simple
calculations to convert to other formats if needed.
For a 2-port network, the S-parameters are:
Description
Desired transmission forwards of forward wave
incident on the input port
Unwanted reflection backwards of forward wave
incident on the input port
Unwanted transmission backwards of backward
wave incident on the output port
Unwanted reflection forwards of backward wave
incident on the output port
Symbol
S21
S11
S12
S22
The beauty of network parameters is that you don’t have to
sum an infinite series of partly reflected and partly trans-
mitted waves bouncing up and down the cascade. The trick
is that you can easily calculate the network parameters of
arbitrary cascade of two-port components using a simple
matrix calculation. All the internal reflections inside the
newly created “black box” can be ignored, and the cascade
treated as a composite two-port network, characterized by
only four parameters per frequency point.
Network parameters can be generalized to more than
two-ports and more than simple cascade connection. Here
we’ll use a 4 X 4 matrix S-parameters to represent a four-
port network: a pair of coupled transmission lines such as
those used in a differential interconnect.
One of the things ADS does really well is convert fre-
quency domain S-parameters into a time-domain model.
Other tools often leave you with an incorrect non-causal or
non-passive conversion.
For more information on S-parameters, please see Keysight
Application Note AN 95-1, S-Parameter Techniques for
Faster, More Accurate Network Design, by Richard W.
Anderson:
–– Scan of the classic 1968 article:
http://literature.cdn.keysight.com/litweb/pdf/5952-0918.pdf
Now let’s return to our PCI Express project…
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