A New Wave Has Hit Signal Integrity
By Dr. Eric Bogatin, Bogatin Enterprises LLC

Editor’s note: This paper is adapted from a speech given by the author and is available for download on www.BeTheSignal.com

The fastest way to an answer is not always the direct path. When it comes to characterizing the electrical performance of an interconnect—like a connector, package, interposer or backplane channel—looking at its impact on digital signals isn’t the most efficient way of describing its high-speed digital performance. You may see how it behaves for one specific application, but it is difficult to extend this to other high-speed digital signals.

The solution is to borrow the approach from the RF world and use the interactions of precision sine wave signals with the connector to characterize its performance. While this seems a step backward for digital applications, it provides a simple, reproducible, and general process that has swept the signal integrity world by storm in the last five years, and has become the de-facto standard in gigabit per second applications.

In the frequency domain, all signals are sine waves with an amplitude and phase. Describing the electrical properties of a connector in terms of how sine waves interact with it means using the changes in the magnitude and phase of the sine wave as it interacts, or “scatters” off it.

Historically, when sine waves scatter off an interconnect, their response is called the Scattering Parameters, or shortened to S-Parameters. Everything you ever wanted to know about the behavior of an interconnect is contained in its S-Parameters. The S-Parameters of a connector can be used to predict the complete behavior of a connector in a system. For this reason, S-Parameters are also called a behavioral model.

A port is the connection to the device. It has a signal and return path, which in its most common form is a coax connection. When a sine wave is launched into the port to simulate or measure the S-Parameters, by definition, it must be in a 50 ohm environment. The S-Parameters are a measure of the sine waves that scatter off the device, either reflecting back from the incident port, or that get scattered into any other ports that might be connected.

If a sine wave enters a port, there are only three qualities of it that can change when it comes out again; its frequency, amplitude, or phase could be affected. For all linear, passive interconnects, which includes all interconnects except those with ferrites, the frequency of the sine wave coming out will always be exactly the same as the frequency of the sine wave going into it. That leaves the changes in the amplitude and the phase. This is what is recorded as the S-Parameters.

A typical device used in high-speed applications will be part of a differential channel with four connections on the ends. To distinguish which port we are talking about, each is labeled with an index number. Port one is an input which feeds to port two; with port three, adjacent to port one, feeding into port four.

When a sine wave goes into port one, it can do one of four things. It can scatter, or reflect back through port one, or it can be scattered out one of the other ports—two, three, or four. The ratio of the sine wave coming out to the sine wave going in, at each frequency, is the S-Parameters.

With four ports, there are 16 possible combinations of “going ins” and “coming outs.” This makes it essential to use the port index numbers to keep track of each S-Parameter. By convention, the index labels are in reverse order of their going-in and coming-out order. S21 refers to the sine wave going in at port one and coming out at port two. This would be the transmitted signal in one line of the differential pair, also called the insertion loss.

All the 16 combinations of S-Parameters can be tracked in a simple four-by-four matrix. Each S-Parameter will have a magnitude and phase at each frequency measured. This is a huge amount of information. Using the formalism to describe the S-Parameters is essential to manage the information contained in the S-Parameters.

Each S-Parameter matrix element, between its magnitude and phase, tells a piece of the behavior of the interconnect. Even though these S-Parameters might have been measured or simulated as the single-ended behavior of the channel, with a little manipulation of the terms, they can be converted into the differential S-Parameters, describing the behavior of differential and common signals on the interconnect.

If we have the behavior in the frequency domain, with a little algebra, we can always convert this into the time domain. This would look like the more traditional TDR and TDT response of the interconnect.

Even though the performance of the connector might be measured as the single-ended response in the frequency domain, it can be converted into the differential response in the time domain. The information is embedded in the original S-Parameters. It is just with a little algebra that it can be re-displayed.

One format that it can be converted into is the impulse response. If we know the impulse response of an interconnect, sometimes also called the Green’s Function, we can use this as a behavioral model to predict how any arbitrary time domain signal might interact with the interconnect. This behavioral model is a surrogate for the actual connector.

In a four port device, measured form 10 MHz to 20 GHz, including magnitude

Including the magnitude and phase, the single-ended and differential, the frequency domain, and the step and impulse time domain responses, there are more than 100,000 individual data elements. The S-Parameter formalism, borrowed from the RF world, has become a simple, compact way of manipulating and interpreting this wealth of information.
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Everything you ever wanted to know about the electrical performance of an interconnect is contained in these S-Parameters. Master S-Parameters and you master high-speed electrical performance.

Mastering S-Parameters is one of the classes taught by Dr. Eric Bogatin. The Essential Principles of Signal Integrity and High-Speed Design Principles are classes offered from September 29 to October 2 in San Jose, Calif.

Dr. Bogatin received his B.S. in physics from MIT and M.S. and Ph.D. in physics from the University of Arizona in Tucson. He has written four books on signal integrity and interconnect design, and more than 200 papers. His latest book, Signal Integrity—Simplified, was published in 2004 by Prentice Hall. He has taught more than 4,000 engineers in the last 20 years. Class descriptions and many of his papers and columns are posted on www.BeTheSignal.com. Bogatin can be reached at eric@bethsignal.com,