Receiver Tolerance Testing With Crosstalk Aggressors TT-MA2 ArvindA. Kumar, Intel Corporation Martin Miller Ph.D., LeCroy Corporation 1 Agenda Receiver compliance testing fundamentals Generating stress with crosstalk Jitter measurement methods for crosstalk aggressors Measurement Example: QPI QPI background Measurements on 45 nm and 32 nm parts Bounded nature of crosstalk jitter 2
Receiver Tolerance Basics Receiver Eye Transmitter Eye DUT Transmit known pattern Measure BER Add known amount of stress (jitter and noise) 3 Stress sources added to test signal Jitter Sinusoidal Random ISI Crosstalk (includes both amplitude and timing stress) Noise (generally random) 4
Procedure for Measuring Receiver Tolerance Calibrate total injected stress for each frequency of added sinusoidal jitter Apply serial data signal with calibrated stress at each sinusoidal jitter frequency setting Measure the bit error (or frame error) rate at each Sj frequency Compare BER with required level at each Sj frequency 5 Accuracy Considerations Tolerance is measured by observing BER but the measured value is total jitter Accuracy is directly determined by the precision of the stress injection This accuracy is, in turn, determined by the accuracy of the jitter measurement system
Jitter as a random variable Jitter is a combination of random and deterministic sources and can be treated as a random variable The jitter histogram is used as an estimate of the probability density function (PDF) of the timing values usually TIE A model is fit to the estimated CDF and is used to predict the range of timing values for any sample size Referred to as the total jitter The sample size is defined in terms of an equivalent bit error ratio The Gaussian Jitter PDF Model # Measurements 100 1,000 5,000 10,000 100,000 1,000,000 5,000,000 100,000,000 1,000,000,000,000 Peak-to peak (σ)( ±2.1 ±2.9 ±3.4 ±3.5 ±4.1 ±4.6 ±5.1 ±6.0 ±7.0 In general the peak to peak value of random signal jitter will grow g without bound *. To define the total jitter you must specify a measurement sample size.
Probability Density Functions Expected value The PDF is a function that gives the probability per interval time that the TIE value takes on a time in that interval In the case of jitter, this is the probability that a transition happens in a small interval at a specific time away from its expected location The Dual Dirac Jitter Model Fit Gaussian curve to the left and right sides of estimated jitter PDF (i.e. the measured normalized histogram) For this model, the separation of the mean values is Dj(δ δ) Sigma gives Rj The values obtained in this way can be used to Predictthe Tjfor low bit error rates Note that not all measured jitter distributions conform well to this model Rj =σ Dj ( δ δ ) = µ µ Tj= Q ( BER)* Rj+ Dj( δ δ ) G R L
Alternate Jitter Models Dual Dirac Two Gaussians Equal sigma Equal weight (0.5) Dual Gaussian Two Gaussians Different sigmas Equal weight (0.5) Weighted dual Gaussian Two Gaussians Different sigmas Different weights 3, 4, or 6 degrees of freedom σ L Dj(δ δ) µ L µ R σ R Degrees of freedom (things to find) Dual Dirac(3 degrees of freedom) One sigma 2 means Dual Gaussian (4 degrees freedom) 2 sigmas 2 means Weighted dual Gaussian (6 degrees of freedom) 2 sigmas 2 means 2 weights
Jitter and Bit Error Ratio Modeled PDF (e.g. Gaussian) BER( x) x = ) 0. 5 UI pdf ( u du 1/2 For the interval 0 to 1 UI BER 0 UI 1 x Total Jitter Curve The specified BER is another way of expressing a confidence level or observation time Total jitter is determined by integrating the probability density function (PDF) separately from the left and right sides to determine the symmetric cumulative probability density function (CDF) The width of this curve at the specified BER (or confidence interval) gives the total jitter This is also the expected peak to peak value for 1/BER measurements CDF (total jitter) PDF Total jitter and PDF for a Gaussian distribution with standard deviation = 1
Methods for estimating random jitter Spectrum-based methods (most oscilloscopes) Measure spectrum of jitter Deterministic jitter is contained in the spectral peaks Rj(σ) is measured by integrating noise floor Distribution extrapolation (BERTs) Measure the distribution of jitter EDF or integrated histogram Fit Gaussian models to the low probability section of the EDF to obtain Rjand Dj Distribution extrapolation (some oscilloscopes) Measure histogram of jitter and deduce EDF Fit Gaussian models to the low probability section of the EDF to obtain Rjand Dj Spectral Jitter Measurement Method Threshold derived from the Median in sliding window Peaks above threshold show the magnitude of Pj @ freq. Sliding window Rj (sp) = integral of noise below threshold
Spectral Pros and Cons Pros Easy to describe Converges rapidly to same answer Has parallels to traditional phase-noise analysis Cons Depends heavily on peak identification being robust Non-Gaussian aggressors (like crosstalk) do not conform to the assumptions In situ comparison to follow Jitter Estimation Using Q-Scale Analyze Statistics of the Empirical Distribution Function (EDF) using Q-Scale Renormalization Based on this observation: in the presence of deterministic contributions, the tails of the overall distribution are governed by distributions which are not whole or unity normalized Gaussian distributions.
Empirical Distribution Function k= i 1 H k k= i 1 k= 0 1 EDF( x= hi ) = = H k= 1 Ptotal k= 0 H k= 0 k k Is the observed analog of the cumulative Probability Distribution Function or CDF and is nothing more than the sum or discrete integral of the histogram A more useful variant of this is to consider a left-hand EDF and a righthand EDF each to be analyzed independently. Each formed by summing from the appropriate side of the observed histogram. A variable substitution A variable: Q is used to represent the EDF in place of BER Q BER CDF BER 1 ( ) = Gaussian ( / 2) Where the inverse Gaussian CDFis employed to obtain a value of Qfor any value of BER (closely related to ERF) Gives a simple easy to grasp view of Gaussian EDF
Q-scale Summary 2 x 2 u erf ( x) = e du 0 π CDF Gaussian x 1 + erf ( ) ( x) = 2 2 Since the CDF of a Gaussian is a linear function with erf(x), when plotted on a vertical axis in Q, it is a straight line A marvelous representation for visualizing a single Gaussian CDF Note: reciprocal slope gives sigma, intercept at Q of some BER gives Tj. Difference between intercepts gives Dj nice!
But, when Dj Rj Note: intercepts not where they re expected and σ is overestimated. A modified variable substitution Which introduces a normalization constant serves to re-linearize the view of a Gaussian EDF when the normalization is chosen to represent the correct weight for the dominating distribution component. Q BER CDF BER 1 norm( ) = ( ) 2ρnorm For the degenerate case where there is only 1 Gaussian this variable is identical to the simple Q- scale variable. So the Gaussian still manifests as an intersection of two straight line segments. (the Boy Scout tent )
Thus the dual-dirac using the new renormalized Q Note: for ρ = 0.5 intercepts are where they re expected and σ is correct. Modeled distribution for sinusoidal aggressor (Pj) Yields correct σ and µfor each side in addition to ρ More and more accurate information Some examples
Q-scale of a 1 psgaussian Time for 1 bit error @ 10 Gb/s 1 day 1 year 1000 years 1M years Big bang 1 ps Gaussian jitter Q-scale of 1 psand 3 psgaussians
Normalized Q-scale of 1 psand 3 ps Gaussians Crosstalk Aggressor Victim with Crosstalk Crosstalk is caused by a signal called the aggressor inducing a voltage or current in an adjacent conductor, the victim Occurs during aggressor transitions where dv/dtis high Fast rise time and/or high voltage swing increase crosstalk Differential signaling reduces but does not eliminate crosstalk Primarily affects the amplitude of the victim
Jitter caused by in-phase aggressor Aggressor signal Crosstalk induced into victim distorted edge Undistorted edge Victim signal with crosstalk T caused by amplitude shift Jitter caused by phase-shifted aggressor Aggressor signal Crosstalk induced into victim distorted edge Undistorted edge Victim signal with crosstalk T caused by amplitude shift
Random and deterministic jitter caused by crosstalk 120 6 110 100 5.5 p-p Dj (ps) 90 80 70 60 5 4.5 4 RMS Rj (ps) Dj(nq) Dj(sp) 14Rj+Dj Rj(nq) Rj(sp) 50 40 3.5 30 3-180 -150-120 -90-60 -30 0 30 60 90 120 150 180 victim to aggressor phase (degrees) Q-scale accurately accounts for increased Rj when the aggressor phase is offset from the victim (yellow line) Jitter measurement with crosstalk Jitter spectrum with threshold Jitter histogram with Q-fit lines Jitter caused by in-phase aggressor (near-end)
Total Jitter Measurement With Crosstalk 230 210 Total Jitter (ps) 190 170 150 130 110 90 70 Error in Tj Between Q-scale and spectral methods Tj(sp) Tj(nq) 14Rj+Dj 50 10 20 30 40 50 60 70 p-p aggressor signal induced in victim (mv) Measured Results for Tj All do well at baseline low jitter case All do well for sinusoidal aggressor Bounded uncorrelated (wideband) jitter mistaken for Rjby spectral method All do well with simple large Rj Total Jitter (ps) @ BER=1e-12 70 60 50 40 30 20 10 0 Tj Comparison baseline 8 ps Sj @ 5 MHz 8 ps BUj 100 Mb/s PRBS10 2.86 ps Rj Spectral method NQ-Scale BERT scan expected value
Impact of BUJ on High Speed Serial IO Measurements Arvind Kumar Intel Corporation Acknowledgements Tao Liang& ChristiaanBil For lots of discussions and slides used herein Mohiuddin Mazumder Remya Subramanian Timothy Wig Vishnuraj Gunasekaran Marianne Nourzad John Critchlow Bala Cadambi And Countless other folks for their help If I have seen further than others, it is by standingupon the shoulders of giants. Sir Isaac Newton
What is QPI QPI Quick Path Interconnect Replacement for the old Front Side Bus 20 Lane DC coupled Link 1 Double pumped forwarded clock link E.g. 3.2Ghz clock for 6.4Gb/s operation Differential point to point Common reference clock for 2 ends of the link The agents at the 2 ends are peers Most implementations have DLL based Rx clocking and not a clean up PLL based arch. data clk UI and Jitter definition UI definition UI Jitter definition UI-UI Jitter definition N UI Jitter definition Accumulated jitter over NUI Very important factor in true forwarded clock links Gives QPI links the ability to track/reject power supply resonance induced jitter
Benefit of Forwarded Clock System Fwd clk td H(s) Jitter characteristics H(s)(1-e -std ) data H(s) 2.5 (1-e -std ) Plotted as Function of Delay td 2 1.5 td=1.4ns Minimizing td crucial 1 PCIe gen3 CDR min 3dB BW 10MHz 0.5 jitter attenuated td=780ps 0 td=156ps 1.00E+07 1.00E+08 1.00E+09 1.00E+10 f=1/td Observations: Illustration of jitter reduction from forwarded clock signaling First zero at f=1/td for 156ps delay, 6.4GHz Jitter reduction effect reduces as delay increases
Typical method used for measurement in our Labs Clock like waveform from a single lane captured with a real time scope Wave for fed to a tool internally written in matlab Uses tail fit method to extract Rjand uses that to get DJ(δδ) Limitations The numbers of UIs that the tool can handle is limited That limitation leads to decimation headaches QPI GUI
Specs to be met at Package Pin WF de-embedded back to that point