# Using Modeling to Analyze Backplane Deterministic Jitter

Low bit-error rates (BER), low cost, and high speed are the key objectives that designers must achieve when crafting of any communication backplane design. In order to reach these goals, designers must effectively manage jitter in their design.

Total jitter, the peak-peak jitter measured at a specified BER, is composed of random (RJ) and deterministic (DJ) components. Many techniques have been developed for decomposing jitter into RJ and DJ and in evaluating active interconnect systems. However, few techniques have been developed for measuring the performance of a passive interconnect platform.

In this article, we'll show a method of relating specific physical structures to eye degradation, amplitude noise, and peak-to-peak DJ for measuring passive interconnect performance. These simple structures can be integrated into a complete model for a backplane where each jitter and amplitude modulation (AM) noise contributor can be identified topologically. Note: The driver-receiver physical layer (PHY) is precluded as part of this method since the focus of this article if is only on the passive interconnect performance.

**Passive Interconnect Jitter Problem **

As described above, total jitter (TJ) is composed of random and deterministic jitter described by probability density functions (PDF). Deconvolution, the mathematical process of separating these PDFs, enables different pathologies of the active PHY to be analyzed. Unlike the PHY, the backplane does not generate RJ. However, further separation of the DJ into finer classification is advantageous for the passive interconnect platform.

**Figure 1** shows how TJ can be further broken down and be analyzed using a topological measure-based model.

**Jitter Extraction Using Selective De-Embedding**

To illustrate the impact of the model shown in Figure 1, let's look at a simple system (except for the exclusion of a board-board connector this example represents backplane daughter card) that includes SMA launch, differential traces, board-board connector, differential traces, SMA launch.

A typical method of analyzing the channel of the example simple system would be to inject a PRBS, K28.5, CJPAT-type pattern with a BER tester (BERT) pattern generator and observe the corresponding eye closure related to reflections due to impedance discontinuities, loss, and stubs or reflections using a DSO or sampling oscilloscope. Although this is a valuable measurement, it does not represent the method shown in Figure 1, since violations or eye degradation does not relate to the physical topology.

**Figure 2** shows time domain reflection (TDR) data and the accompanying reference waveform. From this data, we calculate a true impedance profile, which represents our first step in analyzing the system for reflections and crosstalk.

The impedance profile is used to assess impedance variations due to launches, problems with traces, and all jitter inducing effects except for lossy structures such as longer transmission lines. We will use the impedance profile to generate the model of SMA launch, and will model this as a lossless structure, where the balance of the transmission line will be modeled as a lossy line.

A signal integrity analysis tool is used to both calculate the true impedance profile and to extract the W-element parameters for the lossy transmission system. In **Figure 3** we see the launch model simulation results and comparison against the reference and reflected TDR data.

At this point in the measurement process, we generate a model consisting of a stimulus using the de-embedded reference TDR, SMA launch, and a lossy transmission line. We then model, simulate, compare, and verify against the original TDR data in order to provide the baseline for all future deterministic jitter analysis.

Importantly, a BERT or signal pattern generator with a digital storage oscilloscope (DSO) cannot perform the jitter analysis described above since the analysis is not a direct SMA-circuit-SMA measurement (no transmission capability). The proposed analysis method relies on generating a verifiable model using only reflected TDR data, creating a simulated eye diagram, and then measuring the resulting DJ.

**Exploring DJ Contributors**

We now have a model that can be used to explore DJ contributors throughout the system by selective de-embedding. This is done by first obtaining the DJ of the entire system via simulation, then simply de-embedding each DJ contributing element selectively to get obtain a complete jitter picture of each pathology.

One example of selective de-embedding can seen through the poor impedance control of the SMA launch in the proposed test system

**Figure 4** shows the correspondence between the de-embedded discontinuity and the simulation including it. **Figure 5**, on the other hand, shows the corresponding S11 for each launch , as calculated by a signal integrity tool.

Interestingly, since we cannot terminate the trace into a 50-ohm load both S11 values were calculated via simulation only, where the model incorporated 50-ohm load. First a model was developed, and then confirmed to match the collected data. Then the model had a characteristic (C discontinuity in this case) selectively de-embedded such that we can predict the behavior if we eliminated this specific signal integrity issue.

Despite the above measurements, the question still remains: How much DJ does the launch itself contribute? Some of the possible DJ contributors include:

- The launch has poor impedance control in a significant region higher than 50-ohms in impedance profile.
- There is a large capacitive-like discontinuity of launch.
- The launch has a high-frequency resonance issue.
- The transmission line has significant loss evident from rise-time degradation of reflected TDR.

To remove DJ at launch, a jitter analysis process is employed with no dielectric and skin effect losses for the transmission line (making it loss-less) in the composite model. The launch signal integrity is then de-embedded with a uniform simple transmission line of 50 ohms—a perfect fictitious launch. **Figure 6** shows the resulting perfect eye with no attendant DJ, as would be expected from a model that has all DJ contributors de-embedded.

**Selective De-Embedding Using Test Structures**

Connectors can be a major source of DJ in backplanes. Significant impedance control, resonance, and crosstalk degrade connector performance.

Often backplane losses and connector performance dominate passive interconnect platform jitter performance. Picking out the key DJ contributors requires selective de-embedding.

Evaluation boards can incorporate de-embedding structures allowing specific structures to be characterized, such as connectors. This technique however, requires de-embedding traces exactly matched to the launch traces into the connector. By de-embedding the launch and trace into the connector, we can essentially measure the contributing DJ of the connector itself.

**Figure 7** illustrates the difference between rise time of cable going into fixture and cable plus the calibrated trace, where the risetime is 47 and 239 ps (10 to 90 percent), respectively. In Figure 7, the calibrated trace exactly matches the trace going into the connector to that losses can be replicated. This allows the final DJ contribution measured of the connector to be separated from the DJ de-embedded from the launches into the connector.

**Eye diagram Analysis**

The question that designers need to now as is how much does this impact the resulting DJ measurement on a 10-Gbit/s signal? To answer this question, designers need to look at the eye diagram of the 10-Gbit signal.
Measuring and modeling are two approaches to eye diagram analysis. Measuring is a direct approach incorporating a fast source using a BERT pattern generator, or alternatively using a TDR sampling head. It does not require a model, such as the last example.

Signal integrity analysis software can generate a measured eye diagram using three TDR signals including reference, reflected and transmitted data. For a coupled loss type system five measurements are required, which includes TDR and time domain transmission (TDT) for both odd and even modes of signal transmission.

Comparing **Figures 8** and **9**, we can see there is a jitter difference of 7.7 ps peak-to-peak between the analysis that includes losses only and the analysis that include both losses and reflections, all due to properly de-embedding a very good launch and an approximate 3-in. coupled differential stripline trace. De-embedding using measured eye diagrams proves very useful since evaluating the DJ with a simple BERT transmission would have seriously been overstated, even with the excellent launch and relatively short trace.

**Verifying De-Embedding Structures**

The DJ measurement method discussed above assumes that the de-embedding structure matches the launch impedance profile for the backplane under test. This assumption must be tested in every case.

In the connector case, half of the structure did indeed match, but the structure being differential had some glaring differences that resulted in underestimating the DJ for the de-embedded measurement case. The following will show that for differential systems, de-embedding a single line system launch is not the correct method for differential systems.

It is important to note that the DJ difference between connector measurements of both trace launch de-embedded and simple cable de-embedding should have been the DJ peak-to-peak measured for the simple launch and trace. This discrepancy accounts for 3.7 ps peak-to-peak of DJ. In fact, the via to the connector, while being differential driven, has a dramatically different impedance profile than the single-ended calibration SMA trace via system that was single ended **(Figure 10)**.

Since the de-embedding structure is a non-coupled, single-ended structure, the odd mode impedance is significantly different than the self-impedance of the actual structure— 37 vs. 58 ohms according to calculated impedance profiles. Thus, as shown in Figure 10, one structure is highly capacitive while the other is more inductive.

The de-embedding structure needs to be redesigned such that the odd impedance of the coupled structure matches the impedance of the launch and trace into the connector. Quite simply, the de-embedding requirement for differential systems mandates differential de-embedding structures to account for the impedance change due to coupling.

As an ancillary tip, it is always a good idea to compare reference and reflected TDR voltage risetimes to see what the risetime degradation occurs through the launch. Considering that the risetime degradation is time of flight to the end of the structure and back, the launch risetime into the DUT is definitely faster as would be measured with TDT instead of TDR.

**Wrap Up**

Essential elements to extracting DJ from a structure is to selectively de-embed, model, compare and verify model correspondence, and then simulate DJ for a specific topological physical element.

There are two methods of using measure-based methods for determining DJ for a particular structure. The first is to capture TDR reference selectively, matched TDR signal and TDT signal, and then compute eye diagram using a signal integrity tool The second is to capture TDR reference selectively, matched or open TDR, and although not required TDT, or transmission. Both are effective techniques for reducing DJ and, in turn, for improving performance in passive interconnect backplanes.

**About the Author**

**Alfred Neves** is ana senior member of the technical staff at Teraspeed Consulting Group. He can be reached at al@teraspeed.com.

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