High-Throughput, High- Sensitivity Measurement of Power Supply-Induced Bounded, Uncorrelated Jitter in Time, Frequency, and Statistical Domains

Transcription

1 DesignCon 2013 High-Throughput, High- Sensitivity Measurement of Power Supply-Induced Bounded, Uncorrelated Jitter in Time, Frequency, and Statistical Domains Daniel Chow, Ph.D., Altera Corporation Yujeong Shim, Ph.D., Altera Corporation Shishuang Sun, Ph.D., Altera Corporation

2 Abstract Power supply induced jitter (PSIJ) is typically categorized as bounded, uncorrelated jitter (BUJ). Unlike other jitter components, BUJ lacks concise definitions in time, frequency, or statistical domains. Thus, BUJ characterization is challenging, with BUJ often misidentified as other jitter components. Current BUJ methodologies involve analysis of low-probability events or phase noise spectra, which typically yield only a peak-to-peak or rms value with limited information on its statistical distribution. We present a methodology for characterizing BUJ in clock signals using de-modulated real-time sampling. This technique allows for fast, high-throughput measurement and analysis of BUJ in time, frequency, and statistical domains. We demonstrate this methodology by analyzing power supply induced BUJ in a PLL, showing results as jitter time series, jitter spectrum, and jitter histogram. Authors Biography Dr. Daniel Chow is a Principal Signal Integrity Engineer at Altera Corporation. His responsibilities include defining design, testing, and validation methodologies for signal integrity, power integrity, and jitter analysis in high-speed components. Specifically, he is responsible for developing Altera s knowledge base on jitter-related issues. Before joining the industry, he was a research physicist with the U.S. Department of Energy. Dr. Chow received his Ph.D. from the University of California, Davis. Yujeong Shim is a senior signal integrity engineer at Altera Corporation. Her responsibility includes the power supply noise effect on analog circuits with consideration of power distribution networks on chip-package-pcb. She received the B.S, the M.S and the Ph.D degree in electrical engineering from Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea in 2005, 2007, and 2011 respectively. She worked as a visiting researcher at Silicon Image, Inc., Sunnyvale, California, US in In 2009, she was involved as an internship in RF and mm-wave modeling and characterization team at IMEC, Leuven, Belgium. She received the Best Paper Award at the 2007 Electromagnetic Compatibility (EMC) Compo, Torino, Italy. Shishuang Sun is a manager of signal integrity and transceiver characterization group at Altera Corporation. His research interests include signal integrity in high-speed transceiver, on-chip and system-level power delivery network design and modeling, and jitter and timing impact from on-chip PDN noise. He received a PhD degree in electrical engineering from Missouri University of Science and Technology (formerly known as the University of Missouri-Rolla), Rolla. He received paper awards from DesignCon He has authored more than twenty journal and conference papers.

3 Introduction As data rates increase, timing and jitter budgets become stricter. In high-speed serial data communications, jitter intrinsic to the data path is generally well-understood with mature analysis techniques for modeling, simulation, and measurement. These jitter components include random jitter (RJ), deterministic jitter (DJ), inter-symbol interference (ISI), periodic jitter (PJ), etc. However, jitter caused by aggressors extrinsic to the data path, such as crosstalk from neighboring channels and power supply induced jitter (PSIJ), are not very well defined. This type of jitter is generally referred to as non-periodic bounded, uncorrelated jitter (BUJ or NPBUJ), which only offers a limited description of its properties. Furthermore, recent studies have shown that, depending on the aggressor s properties and coupling mechanism, crosstalk and PSIJ may appear to have similar behavior as some common jitter components such as RJ, PJ, or ISI [1]. Limitations of Current BUJ Analysis Methods Current studies in test and measurement of BUJ are typically based on oscilloscopes, bit error rate testers (BERT), and phase noise spectrum analyzers. For BUJ on data signals, typical methods involve using an oscilloscope or BERT to analyze low probability jitter beyond the extent of the BUJ s peak-to-peak value [2, 3]. However, since the probabilistic reach of BUJ is often unknown, this method is generally very timeconsuming. Additionally, this method assumes that the probability density function (PDF) and cumulative density function (CDF) of the BUJ is distinctively different from low probability jitter such that decomposition is possible within practical constraints. Furthermore, this method does not provide any time- or frequency-domain information, which is often necessary in characterization and/or simulation correlation. Lastly, for BUJ occurring at low jitter frequencies, real-time scope waveform captures must be sufficiently long enough to resolve the BUJ, which further increases test time. For BUJ on clock signals, typical methods involve using a phase noise spectrum analyzer [4]. Because of its hardware architecture, phase noise analyzers have typical noise floors much lower than state-of-the-art oscilloscopes. For small-amplitude phase modulations, phase noise has a well-known linear relationship with jitter which allows for estimating jitter from phase noise measurements. By comparing phase noise spectra with and without external aggressors, it is possible to measure the impact of BUJ. However, this method only provides an rms value for BUJ which cannot be related to a peak-to-peak value needed for total jitter (TJ) estimation. This method does not provide time- or statistical-domain information. Demodulated Real-Time Sampling Recently, some power spectrum analyzers have added real-time sampling capabilities, typically referred to as analysis bandwidth options [5, 6, 7]. This feature is usually intended for testing rf standards such as LTE, HSPA, and WiMAX. We exploit this capability for the purpose of BUJ measurement.

4 Architectural Overview The typical architecture of a power spectrum analyzer is given in Figure 1. The power spectrum analyzer takes an input signal and down-converts various frequencies to the baseband. The resolution bandwidth of the measurement is given by a narrow band pass filter. The signal s power within the resolution bandwidth is measured by an envelope detector. The down-conversion frequency is swept over the range of interest to construct the power spectrum in the frequency domain. Figure 1: Typical architecture of a power spectrum analyzer. Some high-end spectrum analyzers further analyze the input signal with a real-time sampler such that the frequency content down-converted to the base band can be digitized as a time-domain waveform. Typical bandwidths are ~100 MHz and typical sampling rate is ~300 MSamples/s. Phase Noise Waveform Measurements For a clock signal, phase noise appears as side bands around the carrier frequency. A swept-frequency power spectrum analyzer typically measures phase noise spectra by down-converting and measuring the power in the side bands. The power is re-scaled as dbc/hz and the span is given as offset frequency from the carrier. The addition of the real-time sampling capability allows phase noise to be measured as a time-domain waveform. The waveform can be further binned into histograms for statistical analysis analogous to jitter probability density functions (PDFs). This technique is effectively hardware demodulation of the phase noise from the carrier and directly measuring the phase noise in the time domain. This technique has a higher throughput than oscilloscopes, which must capture the clock signal waveform prior to extracting the phase noise by software. This technique also has a superior noise floor compared to oscilloscopes. As a time-domain measurement which can be post-processed for statistical information, this technique is superior to conventional power spectrum analyzers, which can only provide rms values for BUJ. This is also comparable to techniques based on a hardware clock/data recovery (CDR) module [8], but with the similar advantages of lower noise floor, wider bandwidth, higher sampling rate, and higher throughput.

5 Application to PSIJ, BUJ Measurements In the case of BUJ on a clock signal [4], the impact of PSIJ is easily identified in the phase noise spectrum. The demodulated real-time sampling technique allows us to define the sampling rate and length to effectively isolate a particular bandwidth of interest, allowing us to observe the phase noise waveform only in the bandwidth of the PSIJ, thus minimizing broadband noise from other frequencies. With the ability to switch the PSIJ aggressors on and off, we can deconvolve the quiet case PDF from the noisy case and extract the PSIJ PDF. Experimental Setup We used a test chip with known limitations in the power distribution network (PDN) such that the PSIJ impact is well-understood [4]. The victim channel is a clock-data recovery (CDR) phase-locked loop (PLL) in the devices Rx. The incoming data is PRBS at 12.5 Gb/s. We routed the recovered clock at 6.25 GHz to the Tx, where it is measured. We stimulated PSIJ on the victim PLL by toggling five nearby Tx and Rx aggressor channels with PRBS data patterns synchronously at 12.5 Gb/s. The transfer impedance profile between the victim and aggressors is given in Figure 2. The dominant resonant peak is located near 50 MHz. Figure 2: Test chip PDN impedance profile between victim and aggressors. We characterized the victim channel using a conventional sweep power spectrum analyzer (Agilent PXA) and a real-time sampling spectrum analyzer (Tektronix RSA) in the quiet condition (aggressors off) and in the noisy condition (aggressors on). Phase Noise Spectra Correlation We measured phase noise spectra from the Agilent PXA with the Tektronix RSA with and aggressor channels disabled (Figure 3). Across the entire measurement bandwidth, we see that the phase noise spectra correlate very well. There are prominent spurs at MHz and 625 MHz, which is the CDR training reference clock frequency and 2 nd harmonic. There are also a prominent spurs at ~39 MHz and ~10 MHz, which are a subharmonics of the reference clock created by dividers in internal circuitry.

6 Figure 3: Comparison of phase noise spectra in the quiet condition. Integrating the phase noise from 1 MHz to 300 MHz to obtain rms jitter, the PXA gives 686 fs rms and the RSA gives 718 fs rms. We enabled the aggressor channels and measured the phase noise spectra (Figure 4). Again, we see that the two instruments correlate very well. We see PSIJ increase the phase noise over the range from 10 MHz to nearly 1 GHz. The PSIJ peaks near 50 MHz, as expected from the impedance profile. Integrating the phase noise from 1 MHz to 300 MHz to obtain rms jitter, the PXA gives 1.25 ps rms and the RSA gives 1.23 ps rms. Figure 4: Comparison of phase noise spectra in the noisy condition. Assuming that PSIJ is independent of the victim channel s phase noise, we can estimate the contribution of the PSIJ by subtracting in quadrature, giving ~1.02 ps rms. Traditionally, spectrum analyzer-based BUJ analysis can go no further, since no peak-topeak value, PDF, or CDF information is available. Phase Noise Waveforms Analysis bandwidth capability allowed us to real-time sample phase noise as a waveform. And example of a phase noise waveform is shown in Figure 5. The x-axis is time and the y-axis is phase noise in degrees. In clock signals, phase is time-varying such that only relative phase is meaningful and absolute phase is meaningless. Therefore, acquisitions of phase noise waveforms are presented as being relative to the initial value, which is defined to be 0. As the data is

7 sampled, the phase noise changes relative to the initial value. In the next acquisition, the initial phase is reset to 0 again, and relative phase noise is measured. Figure 5: Example of a real-time sampled phase noise waveform. The resetting of the initial phase value with every acquisition is analogous to a PLL with a loop divider tracking a reference clock. The output of a PLL makes phase corrections at the loop frequency to realign the phase, but the output of the PLL may drift between successive phase corrections. Effectively, the phase noise waveform is equivalent to the phase noise observed by an Rx PLL with a loop frequency equal to the inverse of the waveform acquisition length. Phase Noise PDF We configured the RSA for free-running (no trigger) acquisitions at a sampling rate of 150 MSamples/s (110 MHz effective bandwidth) and acquisition time of 1 μs. We accumulated quiet condition phase noise over 24 million waveforms at a rate of nearly 80,000 waveforms per second in a persistent mode similar to oscilloscopes, resulting in a density plot shown in Figure 6. The density plot shows repeating structures evenly spaced by ~12.5 ns caused by cyclostationary noise due to phase resets in every acquisition. Figure 6: Phase noise density plot for quiet condition. Yellow and blue lines denote maximum and minimum envelope. We enabled the aggressor channels and measured the phase noise waveform density plot (Figure 7). We see that the amplitude of the phase noise increased. We also see cyclostationary noise at the same frequency.

8 Figure 7: Phase noise density plot for noisy condition. Yellow and blue lines denote maximum and minimum envelope. Correlation Between PDF and Spectral Integration Combining the density plots over time, we obtained the normalized total phase noise PDF for quiet and noisy conditions (Figure 8). The width of the quiet PDF is 740 fs rms and the width of the noisy PDF is ps rms, which are consistent with the rms values obtained by integrating phase noise spectra. The waveform acquisition is an effective windowing function such that the bandwidth is equivalent to a brick wall filter from approximately 1 MHz to 300 MHz. Figure 8: Phase noise PDF in linear and log scales. The PDFs appear resemble a Gaussian. However, examining the cumulative density function (CDF) and the Q-scale [9] reveals that the PDFs are not Gaussian for both quiet and noisy cases (Figure 9). In the Q-scale, Gaussian distributions are straight lines with a slope of 1/RJ(rms). Nonlinear behavior in the Q-scale have been correlated to bounded- Gaussian BUJ [10] in addition to DJ. The Q-scale plots in Figure 9 are inconsistent with bounded-gaussians or typical DJ PDFs. Furthermore, we found that convolution of a Gaussian with any bounded PDF (with peak-to-peak value within observable limits) cannot fit the Q-scale behavior observed. This non-gaussian behavior is challenging to reproduce in oscilloscopes due to the bandlimiting nature of the spectrum analyzer. However, earlier work has demonstrated that

9 crest factor, defined as the ratio of peak-to-peak value to the rms value, is dependent on band limitations [11] which suggests non-gaussian behavior. Figure 9: Phase noise CDF and Q-scale. Multi-Gaussian Model for PDF Fitting We found that the quiet phase noise can only be fitted with a PDF constructed by a sum of multiple Gaussians, given by PDF t N n n 2 t n e 2, Eq. 1 where t is the phase noise jitter, σ n is the Gaussian width parameter for each n, and N is the total number of terms. We refer to this technique as a multi-gaussian model. The quiet PDF in linear and log scales fitted with a multi-gaussian model is shown in Figure 10 as well as the corresponding CDFs and Q-scale plots. We see that the multi-gaussian model fits the data very well within the range of ±5 ps, beyond which discrepancies exist in low probability regions. Random jitter has long been speculated to contain Gaussian and multi-gaussian components [12]. In this case, the appearance of multi-gaussian behavior may be due to the cyclostationary noise, which is pseudo random in nature. In the quiet case, the clock was recovered from PRBS data, which stimulates self-aggression in the PDN, causing some amount of PSIJ. While the multi-gaussian model empirically fits the data, its theoretical origins are a topic for further study. Deconvolution of PSIJ PDF We deconvolved the quiet PDF from the noisy PDF to find the contribution of BUJ, shown in Figure 11 as a PDF in linear scale, PDF in log scale, CDF, and Q-scale. Again, we used a multi-gaussian model to achieve best results. The width of the PSIJ PDF is 841 fs rms, which is ~17% lower than 1.02 ps rms obtained by quadrature subtraction of integrated phase noise spectra.

10 Figure 10: Phase noise quiet condition fitted to a multi-gaussian. Applying the analytical multi-gaussian PSIJ model to the quiet PDF gives the modeled noisy PDF, CDF, and Q-scale shown in Figure 12, compared to noisy condition measurements. The multi-gaussian model matches the data very well in PDF, CDF and Q-scale up to the range of ±5 ps, with only small discrepancies beyond that. Thus, we have demonstrated the validity of the multi-gaussian model for describing PSIJ behavior in this case. The multi-gaussian PSIJ model is analytical, allowing for accurate calculation of its impact on total jitter and BER. For BUJ stimulated by PRBS with 50% transition density, we expect the peak-to-peak to be bounded at ± 6.6 ps, which corresponds to a CDF value of Unfortunately, there is insufficient data beyond probability to confirm this. Summary, Conclusions We have demonstrated a technique using spectrum analyzers with real-time sampling capability to capture BUJ caused by PSIJ. Phase noise spectra were correlated with a conventional power spectrum analyzer. Compared to oscilloscope or BERT solutions for BUJ, this technique has a significantly lower noise floor and higher throughput. Compared to sweep spectrum analyzer solutions for BUJ, this technique offers measurements in time and frequency domains, allowing for accumulation of statistics which allow for peak-to-peak modeling as a function of probability or BER.

11 Figure 11: PSIJ model from de-convolution. Figure 12: Noisy condition compared with PSIJ model convolved with quiet condition.

12 By deconvolving the quiet condition measurements from noisy conditions, we found that, in this case, PSIJ appears to have non-gaussian behavior which is empirically modeled with a multi-gaussian distribution. Future work in this area includes correlation with oscilloscope BUJ methodologies, investigation of cyclostationary effects, studies into non-gaussian broadband jitter models, and possible extension of methodology into data signals. Acknowledgements The authors wish to acknowledge Tektronix for use of their equipment, fast-turnaround for modifications to the software/firmware to enable these measurements, and technical support on understanding hardware architecture and data analysis techniques. References [1] D.Chow, Analysis of Crosstalk Effects on Jitter in Tranceivers, DesignCon, [2] P.Zivny, M.Agoston, Accurate Analytical Model of Bounded Uncorrelated Jitter and Noise Improves the Accuracy of Crosstalk Impaired Link Evaluation: Theory, Validation, Practical Results, DesignCon, [3] M.Miller, M.Schnecker, Quantifying Crosstalk Induced Jitter in Multi-lane Serial Data Systems, DesignCon, [4]S.Sun, K.Ren, D.Chow, W.Ding, T.Hoang, K.Daxer, M.Li, S.Shumarayev, PDN Noise to Jitter Transfer in High Speed Transceiver, DesignCon, [5] Data sheet for Agilent N9030A PXA: [6] Data sheet for Rohde & Schwarz Spectrum Analyzers: [7] Data sheet for Tektronix RSA6000: Time_Spectrum_Analyzers_Datasheet_37W _0.pdf [8] D.Derickson, M.Müller, Degital Communications Test and Measurement, Prentice Hall, [9] Fibre Channel - Methodologies for Jitter Specification, National Committee for Information Technology Standardization (NCITS) Technical Report T11.2/Project 1230/Rev 10.0, Jun [10] M.Shimanouchi, M.Li, D.Chow, New Modeling Methods for Bounded Gaussian Jitter (BGJ)/Noise (BGN) and Their Applications in Jitter/Noise Estimation/Testing, ITC, [11] R.Stephens, M.Müller, Analysis of Random Noise and the Effect of Band-Limited Noise on Stressed-Eye Receiver Tolerance Tests, DesignCon, [12] M.Li, Jitter, Noise, and Signal Integrity at High-Speed, Prentice Hall, 2007.