# A new analytic approach for advanced jitter separation

The analysis of jitter components is an increasingly important task for debugging modern communication systems. Growing data rates on one hand and the cost pressure on board material, connectors or components on the other hand are driving factors for this need for analysis. This article describes a newly developed method for separating jitter components, providing electronic circuit designers with a powerful tool for debugging and characterization of high-speed signal transmissions. The separation algorithm is based on a parametric signal model and provides the user with additional details of jitter characteristics of the device under test (DUT).

**Validating the jitter budget**

The growing data rates and shrinking voltage levels of digital interfaces, combined with complexity and density of modern designs increases the significance of managing the jitter budget.

One way to validate the total jitter of an interface is to measure the bit error rate (BER). The typical target BER for high-speed interfaces such as USB or PCI Express is 10^{-12}. This means, the specification allows for a sequence of 10^{12} bits only one incorrectly transmitted bit. However, validating the total jitter with a BER tester is very time consuming and does not provide details about the individual jitter components.

An alternative is to use an oscilloscope. Because of the limited acquisition memory (maximal single-digit Gigasamples), a straightforward measurement of the total jitter for a certain BER is impossible. The following example illustrates this: the waveform acquisition time for a test pattern with 10^{12} bits at a data rate of 5 Gbps is 200 seconds. With a sample rate of 20 Gsample/s an acquisition memory of 4 Terasamples would be required. No oscilloscope has such a deep acquisition memory.

The smart solution to this dilemma was the invention of jitter separation (also called jitter decomposition) and the subsequent estimation of the total jitter in the early 2000s. The basic idea behind this approach is that the total jitter consists of deterministic and random components. The deterministic jitter is bounded, while random jitter is unbounded and therefore its peak-to-peak value scales with the BER of interest. Figure 1 shows a mapping of such jitter components in the BER bathtub curve. The “open eye” for the receiver to sample the data is the difference of the unit interval (UI) and the total jitter.

**Jitter components and their root causes**

As discussed above, the total jitter consists of random and deterministic jitter components. Figure 2 shows a further breakdown of the deterministic jitter into data-dependent, periodic and other-bounded-uncorrelated jitter components. Understanding the dominating jitter components in the signal helps the engineer decide on the measures for optimizing the design.

The different components have different root causes:

- Random jitter, for example, depends on the quality of the reference clock’s oscillator or the thermal noise of the semiconductor.
- Periodic jitter is typically caused by interferers from switched mode power supplies (SMPS) or oscillators, or gives hints for PLLs’ stability issues.
- Inter symbol interferences are mainly related to transmission loss and limited bandwidth of the circuitries and the signal transmission paths, including reflections caused by impedance mismatches.
- Duty cycle distortion, as the other part of the data dependent jitter, hints at rise/fall time mismatches of the signal edges or offset errors in the transmitter or receiver.
- The typical root cause for other bounded uncorrelated jitter finally is signal coupling (crosstalk) from adjacent signal traces.

The given examples show that jitter decomposition is an important first step to narrow down design issues and decide on suitable cost-efficient solutions.

**A new jitter sepa****ration approach**

In the last 20 years, the approaches and algorithms for jitter decomposition have evolved. The initial method such as tail-fitting for determining random jitter and the dual-Dirac model for estimating deterministic jitter are still in use and part of certain interface specifications. The conventional method to further break down the deterministic jitter reduces the input signal information from the sampling points of an analog waveform to a set of time interval error (TIE) measurements, figure 3.

The new jitter decomposition algorithm from Rohde & Schwarz introduces an analytic approach based on a parametric signal model that fully characterizes the behavior of the transmission link under test (figure 3). The core benefit of the new approach is that this new signal model utilizes the complete waveform characteristic, including horizontal and vertical components. This usage of the complete waveform information for the decomposition-processing results in more accurate and consistent measurement results even for relatively short signal sequences.

The core element of the new signal model is the step response that describes the data-dependent characteristics of the signal. Additionally, the periodical and random error terms are included in this signal model (figure 4).

For the decomposition, processing a least-square (LS) estimator compares the input signal to the signal model and calculates the signal model’s parameters in an iterative process. As a next step, the Rohde & Schwarz algorithm reconstructs, based on the input signal’s bit sequence, synthetic waveforms for the individual deterministic jitter components (figure 5). After that, the random jitter is calculated from the difference of the input signal and the data- dependent and periodic synthetic waveforms. Finally, the user can analyze the different jitter components as numerical values, or view them in histograms, track waveforms or spectrum views. Additionally, BER-bathtub plots or data eye diagrams can be calculated for in depth analysis.

**More insight into the system’s jitter characteristic**

The new jitter decomposition algorithm provides information about all common jitter components. Additionally, new information such as step response or a distinction between vertical and horizontal periodic jitter are now available. Finally, the synthetic deterministic jitter waveforms allow a high flexibility for the result analysis. Synthetic data eyes with selectable deterministic jitter components or the BER-bathtub-curve with or without period jitter components are just some examples.

The characteristic step response as a result out of the jitter decomposition calculation is new and very useful for debugging and design optimization. So far, the step response can only be measured with dedicated instruments like a time-domain-transmissometer (TDT) or a vector network analyzer. The step response tells a lot about the characteristics of the transmission link: the rise time is related to the bandwidth, overshoots or damped response give indications about frequency response characteristics, or potential dips hinting at reflections due to impedance mismatches, among others (figure 6).

The new signal model includes terms for both, horizontal and vertical periodic components. This provides very useful feedback for the user whether periodic jitter components originate from amplitude- or time-based modulations. The software reports per detected periodic jitter component the horizontal or vertical direction, as displayed in figure 7. Additionally, the spectrum of horizontal periodic jitter components is available for analysis.

**Quick setup in three steps**

The new Rohde & Schwarz jitter decomposition algorithm is integrated in the advanced jitter analysis option K133 for the R&S RTO and R&S RTP oscilloscopes.

The easiest way to get to the first jitter results is the “quick start analysis”. It executes all setups automatically, calculates a default set of jitter components and displays the respective results with pre-selected views. A user-specific adjustment of the setup and the result display is of course possible later.

Alternatively, only three steps are required for an individual setup. The first step involves selecting the signal source and signal type, and defining the clock data recovery (CDR). The selection of the respective technology (e.g. USB 3.1 Gen 1) of the DUT simplifies the CDR setup (figure 8).

In the second step, the parameters for the decomposition are configured (figure 9). To do so, the jitter components of interest must be selected, and the step response length for the processing defined. The selection of a longer length might uncover more details such as far away reflections but also requires more computation time.

The final step is the configuration of the result displays (figure 10). In this step, the user must choose between histogram, track or spectrum view for the individual jitter components. Additionally, the step response, the bathtub curve and the synthetic eye diagram are available for in-depth analysis. After this, the setup is complete and by switching on the “enable” button the decomposition processing will start.

Figure 11 shows an example for the different result views. The smartgrid function allows for arranging of the diagrams and tables according to personal preference using drag and drop.

**Conclusion**

The Rohde & Schwarz jitter decomposition algorithm uses an advanced signal model that fully characterizes the input signal. The user benefits from accurate measurement results even for relative short signal sequences. Additional result details about the signal under test provides designers with further insight on the validation and debugging of their devices with high-speed interfaces or fast clock signals.

**Guido Schulz** is product manager for oscilloscopes at Rohde & Schwarz in Munich, where he has been for over 10 years. He holds a degree in electrical engineering from the Technical University Chemnitz.

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Original article: A new analytic approach for advanced jitter separation

Author: Guido Schulze