Statistical and System Transfer Function Based Method For Jitter and Noise Estimation In Communication Design and Test

Transcription

1 Statistical and System Transfer Function Based Method For Jitter and Noise Estimation In Communication Design and Test Mike Li and Jan Wilstrup Wavecrest

2 Purposes Illustrate the shortfalls of simple parametric based jitter/noise determination methods (Peak-to-Peak or RMS only) Introduce the PDF and CDF based statistical jitter/noise determination methods Introduce the jitter/noise transfer function and its role in serial data link Apply both statistical analysis and transfer function for jitter, noise, and BER in designing and testing > 1 Gb/s systems

3 Outline Overview of jitter and noise basic Shortfalls for parametric peak-to-peak PDF and CDF for jitter, noise, and BER Overview of serial communication systems Jitter/noise transfer functions Methods for estimating and testing jitter, noise, and BER Conclusion

4 Jitter And Noise Basics Timing Jitter : Any deviation from ideal timing Amplitude Noise: Any deviation from ideal amplitude Timing jitter occurs when there is an edge transition Amplitude noise is a constant activity Reference Amplitude v 0 Reference Timing t 0 v: amplitude noise t: time jitter

5 Jitter And Noise Viewed From Signal Theory Jitter/noise is a statistical process Jitter/noise has a distribution Jitter/noise has many different components Jitter/noise can only be completely quantified by its PDF!!!

6 Jitter/Noise Classification Scheme (Statistical Based) Jitter/Noise Deterministic Random Static BU Periodic BU: Bounded uncorrelated Multi-Gaussian Gaussian

7 Relationship Between Total PDF And Component PDFs: Convolution An example for timing jitter PDF p TJ ( t) = p RJ ( t)* p DJ ( t) = p DJ ( τ ) p RJ ( t τ ) d τ

8 Why Deterministic Parametric (i.e, Peak- To-Peak or RMS) No Longer Sufficient? Peak-to-peak or RMS alone cannot determine a general PDF Peak-to-peak will be an unstable and size sample size dependent estimation in the presence of random component RMS will be an inaccurate estimation for a Gaussian random in the presence of deterministic component

9 Peak-To-Peak Shortfalls a.) Sample Size Dependency Peak-To-Peak in UI Total Number of Hits x 10 4

10 Peak-To-Peak Shortfalls b.) Probability distribution is un-symmetrical Hits Peak-to-Peak

11 Peak-To-Peak Shortfalls c.) Peak-to-peak cannot define a unique PDF Probability Which one? PDFs Peak-to-Peak t

12 A RMS Shortfall Case Study RMS RJ sigma RMS > N 1 = N 1 σ n= 1 ( t t i ) 2 E ven ts N_min N_lmax, N_rmax σl σr µl µr Jitter

13 A Deterministic And Random PDF Estimation Method: TailFit Total jitter PDF = DJ PDF * RJ PDF RJ PDF is a Gaussian ( t µ )2 p( t) = 1 e 2σ 2 2 π Tail parts of distribution preserve information on RJ process. DJ pdf RJ pdf Total pdf *

14 What Does The TailFit Offer? Gaussian Tailfits prob density Jitter pdf t RJ PDFS DJ PDF (via deconvolution) Subspace statistical parameters

15 DJ PDF Via Deconvolution TJ PDF and DJ PDF TJ PDF Remainder t (UI) DJ PDF Error t (UI) -2

16 A Jitter/Noise Spectrum Estimation Method: Autocorrelation (Patented) Ideal Clock 0 1 N UI Data t0 t1 tn PSD ( f ) = FFT ( c 2 * Rxx ( t( n)))

17 What Does The Autocorrelation Offer? PJ R J psd(f) RJ PSD PJ PSD DDJ (DJ without PJ and BUJ) PSD f

18 itter And Noise In One View: Eye-Diagram Timing jitter pdf Amplitude noise pdf

19 Jitter, Noise, And BER ts eye-diagram zero level UI pdf opening t BER (cdf) 0 1 ts

20 BER: metric for overall system performance BER: CDF from jitter and noise PDFS Jitter, Noise, And BER Cont ( ) ( ) ( ) ( [ 2 1 ) ( ) ( t d t s t tr P t d t s t tl P t CDF t ER s s + = =

21 A Serial Data Communication System Data Medium D C Q Data Clock/ PLL PLL CR/ PLL Transmitter Receiver

22 Magnitude (db) A PLL Frequency Response Function HL(f) fc Frequency (f)

23 Receiver Jitter Transfer Function Jitter in θi CR/ PLL + - Jitter out θe Receiver sees a difference function for jitter A difference function

24 What Does A Difference Function Mean? Jitter is referenced to a recovered bit clock Receiver has a jitter transfer function Intrinsic jitter referenced to an ideal bit clock is not the jitter seen by the receiver BER of the system should be estimated based on jitter seen by the receiver

25 Jitter Transfer/Tolerance Functions For Data Recovery HT (f) Jitter Tolerance Magnitude (db) HH(f): Jitter Transfer fc Frequency (f)

26 What Constitutes A Valid Jitter Estimating/Testing Method? Data in + - CR/ PLL Measurement System Estimate the jitter as the receiver sees!!! CR/PLL and difference functions or their equivalents are required

27 Compliance Estimating/Testing:Total Jitter And BER Function Total jitter = UI eye 10-12

28 A Valid Jitter Estimating/Testing Method For Serial Links Estimating/testing total jitter PDF via an appropriate bit clock reference Estimating/Testing BER/CDF function to < Estimating/Testing total BER = or smaller Pass/Fail

29 Jitter Transfer Function For PCI Express System block diagram for common clock mode Ref Clock (100 MHz) Tx PLL 25X PLL 25X D Rx C PI D C Q

30 Jitter Transfer Function For PCI Express Cont.. System Transfer Function Block Diagram Tx PLL H 1 (s) + - PI H 3 (s) Y(s): Jitter At The Rx X(s): Ref Clock Jitter Rx PLL H 2 (s)

31 Jitter Transfer Function For PCI Express Cont.. Math Relationships H t ( s) = ( H ( s) H ( s)) H ( s) Y ( s) = H ( s) X ( s) t

32 Summary And Conclusion Deterministic parametric methods for jitter and noise no longer sufficient (e.g., Peak-to-Peak) Statistical functional (PDF/CDF) methods are required for jitter, noise, and BER estimation/test Tailfit offers deterministic and random PDF/CDF estimation/test Autocorrelation offers PSD for periodic and random components Transfer function is required in estimating relevant jitter, noise, and BER for the system Statistical PDF/CDF + transfer function gives a complete and accurate system performance estimation/testing