S-parameters are a sine of the future

If you work with high-speed serial links such as PCIe, USB, SATA, Infiniband or gigabit ethernet, you have encountered S-parameters. This method of describing the electrical properties of interconnects, standard in the microwave world for more than 60 years, is becoming the de facto standard in the high-speed digital world as well.

S-parameters are a formalism that describes the electrical properties of an interconnect by quantifying how sine waves interact with the interconnect.

Signals and their return paths enter interconnects at ends called ports. An S-parameter element is nothing more than the ratio of the sine wave coming out of a port, compared with the sine wave going into a port.

As the ratio of two sine waves, each S-parameter element has a magnitude and phase. And, of course, there will be a value of each S-parameter at every selected frequency.

In this way, S-parameters describe the ‘behaviour’ of the interconnect - how a sine wave at a specific frequency is changed or ‘scattered’ by the interconnect. If we know how every frequency sine wave will be changed, we really know how any arbitrary waveform in the time domain will be affected. For this reason, the S-parameters of an interconnect are often referred to as a ‘behavioural model’ of an interconnect.

The behavioural model is also called a ‘black box’ model in the sense that you don’t really need to know what is going on inside the model to use it.

Many circuit simulators and emulators can use an S-parameter black box model representation of an interconnect to predict the response of any arbitrary wave through it.

For example, Figure 1 shows a pseudo random bit sequence (PRBS) input signal as the incident wave to a backplane interconnect. The S-parameters of one differential channel have been measured with the LeCroy Model 4004E ‘SPARQ’ signal integrity network analyser from 10 MHz to 20 GHz.

Figure 1: S-parameters can be used as a behavioural model of an interconnect to simulate the eye diagram response at any bit rate.

This is the behavioural model of the complete channel. We can use this information to simulate what the output waveform would look like after the PRBS signal goes through the interconnect.

We can take the received PRBS signal, slice it up referenced to its clock and superimpose all the bits and create an eye diagram. This is what we would expect the eye to look like coming through the interconnect, all based on the behavioural model of the interconnect. S-parameters are a very powerful formalism.

As an electrical description of an interconnect, an S-parameter model can be created directly from a measurement, simulated in a circuit or simulated by an electromagnetic field solver.

This is illustrated in Figure 2 which also includes an image of the analyser used to make the measurements in Figure 1. The SPARQ analysers are designed specifically for signal integrity applications, featuring an automatic calibration capability.

Figure 2: S-parameters can be created by measurement, circuit simulation or electromagnetic simulation.

In addition to the 4-port model shown in Figure 2, 8- and 12-port units will soon be available, along with 2-port models as well.

Regardless of where it comes from, the information in an S-parameter model is stored in an ASCII file in a Touchstone format. It is nothing more than the list of each S-parameter term - the value of the magnitude and phase of each element at every frequency.

The file name extension identifies how many ports the model corresponds to. For example, a file with the extension .s2p would contain an S-parameter model for an interconnect with two ports. There would be four different S-parameter elements, each combination of a coming-out port with a going-in port.

A glimpse at the numbers inside the touchstone file is shown in Figure 3.

Figure 3: Example of the actual touchtone file for a 2-port interconnect. Each row is at a different frequency showing the magnitude and phase of the ratio of the wave coming out to the wave going in at each combination of the two ports of the interconnect.

It is tempting to look at an S-parameter black box model of an interconnect and see numbers with five digits and frequencies above 10 GHz and think an S-parameter model must be a very accurate way of describing an interconnect.

In fact, the quality of the model, whether it comes from measurement or simulation, is only as accurate as the starting information, the quality of the calibration or the accuracy of the approximations made in setting up the simulation.

In other words, there is nothing about an S-parameter model that will make it any more accurate than any other model description of an interconnect.

The value of the S-parameter formalism is that it is a universal description for all linear passive elements. It can be used in many simulators as the generic electrical description of the interconnect and, when created with care, can be an accurate representation of any interconnect.

This is primarily why it is becoming so popular in applications where the high-frequency properties of interconnects play a role.

Unfortunately, there is a tendency by many engineers to treat an S-parameter model as a black box and never lift the lid to sneak a peek inside. The S-parameter model from one source is moved over to another simulator and the results are accepted without question.

There is tremendous value in opening the lid and data mining the wealth of information stored within the S-parameters. We just have to keep in mind what S-parameters really measure.

S-parameters describe how sine wave signals enter an interconnect at one port and are ‘scattered’ into each port. Different properties of the interconnect affect how much signal is scattered into each of the ports. Each S-parameter element tells a different story about the interconnect.

To keep track of the coming-out and going-in ports, we use an index number to label each port. While there is no official convention, it is strongly recommended to use the labelling scheme of port one connects to port two and port three connects to port four. This is illustrated in Figure 4 in the case of a pair of coupled, uniform microstrip transmission lines.

Figure 4: Port labelling scheme for an interconnect with four ports.

Each S-parameter has two ports associated with it. These are added as subscripts to the ‘S’, in the reverse order to the signal path.

For example, S21 refers to a signal coming out at port two and going in at port one. And, in the same way, S31 refers to a signal coming out at port three and going in at port one.

Different features of the interconnect determine how a wave, entering at one port interacts with and is scattered into another port. This is why each S-parameter element tells a different story about the interconnect and why it is important to look at all the S-parameters to get a complete picture of the interconnect.

S11 is referred to as the return loss. It is the sine wave that reflects back from the port. The only feature of the interconnect that causes a signal to reflect is an impedance change.

The return loss has information about the impedance profile throughout the interconnect. A transparent interconnect would have a very small return loss at all frequencies.

S21 is often called the insertion loss. It is the sine wave that transmits through to the other port. For long interconnects, it is primarily about losses or attenuation in the interconnect. In addition, insertion loss can be affected by reflections and by signal coupling out of the interconnect.

In the case of two adjacent transmission lines, S31 is also called the near end cross talk. A sine wave goes in at port one and comes out at port three. The only way it gets to port three is by coupling into the adjacent line and propagating back to port three.

The signal coming out of the other end of the second line, S41, is the far end cross talk. In microstrip, far end cross talk can be very high. In stripline, S41 will be very small.

Figure 5 shows the measured values of these four S-parameter elements in this case of two coupled microstrip lines, measured by a signal integrity network analyser. For comparison, the same measured data, displayed in the time domain is also shown.

Figure 5: Example of the measured S-parameters for a pair of coupled microstrip transmission lines, displayed in both the frequency domain and the time domain. Exactly the same measured data is just displayed in two different domains.

While the information content is the same whether measured in the frequency domain or the time domain, the interpretation of the results from the front screen is very different whether displayed in the time or frequency domain.

This is why it is so important for all digital designers to become ‘bilingual’ and learn to view the world in both the time domain and the frequency domain.

In this perspective, the S-parameters of an interconnect are the complete electrical description of any interconnect. To know its S-parameters is to know everything about the interconnect.

Eric Bogatin is a signal integrity evangelist for Bogatin Enterprises, a LeCroy company. He teaches classes on signal integrity topics, including S-parameters.

Alan Blankman is signal integrity product marketing manager at LeCroy, focusing on signal integrity products and applications, including the SPARQ series network analysers and serial data analysis software.