Jitter Separation in High Speed Digital Design Gustaaf Sutorius Jitter & Typical Digital Development Process System Design Interconnect Design Active Signal Analysis • Accurate Design Analysis • Test & Analysis Capability • Measurement Automation Compliance Test AGENDA 1. Jitter: I. Definition and Description of Jitter II. Understanding Jitter, its Components, and Separation III. Jitter Measurement Methods and Tools 2. Actual jitter measurements Page 3 AGENDA 1. Jitter: I. Definition and Description of Jitter II. Understanding Jitter, its Components, and Separation III. Jitter Measurement Methods and Tools 2. Actual jitter measurements Page 4 Jitter Primer: Topics to be Covered 1. Definition and Description of Jitter 2. Understanding Jitter, its Components, and Separation 3. Jitter Measurement Methods and Tools Page 5 What is Jitter? • ‘Jitter ‘ is another word for shaky, quiver, tremulous… speaks of degree of instability of location. • In the Digital Design world, jitter has been defined as: The short term phase variation of the significant instants of a digital signal from their ideal positions in time. Page 6 What is Jitter: Analyzing an Edge (Transition) Ideal Location in Time (Reference) Transition Instant Early Threshold Late ∆tEarly 0 ∆tLate 1 JPP=∆ ∆tEarly Pk + ∆tlate Pk Page 7 Units for expressing Jitter 1) Seconds: if ∆tEarly =60 ps and ∆tLate=40ps JPP= 100 pseconds 2) UI: Referenced to the Data Rate, called Unit Interval (UI): For 2.5 Gb/s Data Rate, the UI (Period) = 400 pseconds JPP= 100 pseconds/400 pseconds per UI = 0.25 UI 3) Radians: where there are 2π π radians per UI: JPP= .25 UI x 2π π= π/2 radians Page 8 Jitter: Creating the Eye… E1 Eye Crossing Points Single transition Left Edge Nominal Sampling Point Right Edge E0 x=0 The EYE Diagram Unit Interval x = 1/2 T x=T Oscilloscope Eye Overlaid transitions Total Jitter, JPP Ideal Sampling Point Probability Density Function Page 9 Why Care about Jitter? • Bit Errors! Transmitted Waveform 1 0 0 1 0 1 1 0 Received Waveform 1 0 0 1 0 1 1 0 Interpretted Waveform 1 1 0 1 0 1 1 0 Page 10 Jitter as Horizontal “Timing Noise” • A low “Signal to Noise Ratio” causes errors • Voltage Noise → vertical fluctuations across the sampling point • Undesirable Amplitude Modulation • Jitter describes the same effect but horizontally – timing noise • Jitter → horizontal fluctuations across the sampling point • Undesirable Phase Modulation Page 11 Jitter – What Causes It? • • • • • • • • • • • • • • • Oscillator Topology PLL Design Noise Crystal Performance Mechanisms Thermal Noise Shot Noise Dispersion Reference Spurious System Radiated or Conducted Signals Crosstalk Mechanisms Duty Cycle Distortion mechanisms Impedance mismatch Inter Symbol Interference mechanisms Data Dependent Receiver Detector characteristics Mechanisms Clock/Data Recovery Design PRBS Mechanisms Page 12 Jitter Primer: Topics to be Covered 1. Definition and Description of Jitter 2. Understanding Jitter, its Components, and Separation 3. Jitter Measurement Methods and Tools Page 13 Representing Jitter S(t): a general digital jitter signal and P(t): a pulse train S(t)=P(Asin(2πfDt+ϕ(t))) Where ϕ(t) is overall system jitter function with many sources. ϕ(t)= ϕ B(t) +ϕ UB(t) ϕΒ(t) is composed of functions that have Deterministic (Bounded) phase deviations because their max amplitudes don’t change ϕUΒ(t) is composed of functions that have Random (UnBounded) phase deviations because their max amplitudes do change. The functions are characterized by their statistics Page 14 Lets Look at the Jitter Sources Again… Oscillator Topology PLL Design Crystal Performance Noise RANDOM Thermal Noise Shot Noise Dispersion Reference Spurious Radiated or Conducted Signals System Crosstalk Duty Cycle Distortion mechanisms Impedance mismatch Inter Symbol Interference mechanisms Receiver Detector characteristics Data Clock/Data Recovery Design PRBS Mechanisms / UNBOUNDED DETERMINISTIC BOUNDED Page 15 Example Random and Deterministic Jitter σ Random Jitter (RJ): Defined by RMS value, σ, of the Gaussian distribution JPPDJ Deterministic Jitter (DJ): The spacing between the mean values of the “earliest” and “latest” traces, JPPDJ Page 16 Expressing Total Jitter • • Usually represented as root-mean-square, Jrms, and peak-to-peak, JPP Most useful to characterize jitter as a combination of JrmsRJ and JPPDJ at a given Bit Error Ratio (BER) Random Jitter (RJ) – results from the accumulation of random processes. • Assumed to Follow a Gaussian Distribution RJ contribution to Jrms is JrmsRJ = σ • Since a Gaussian function is unbounded, RJ contribution to JPP can be large JPPRJ → ∞ Deterministic Jitter (DJ) – results from systematic effects • • E.g., duty-cycle-distortion (DCD), intersymbol interference (ISI), periodic jitter (PJ), PRBS effects, and crosstalk DJ is bounded, JPPDJ is finite. Page 17 Random jitter: JPPRJ is related to Bit Error Ratio Unit Interval Sampling Point Measure BER(x) = β(x) Gaussian Jitter Only! (No DJ) x σL σR Overlap indicates BER µ Sampling Point µ JPPRJ = n× ×σ Page 18 Random Jitter JPPRJ : What factor to use ? JPPRJ = n× ×σ JPPRJ Random jitter is UNBOUNDED, if we wait long enough we would have “hits” anywhere in the Eyediagram. We could use any Berr but 10-12 is quite common to use and 10-12 equals to 14.1 sigma. So if we measure sigma is 10 picoseconds, then we would say the random jitter is 141 Psec. Page 19 Expressing Total Jitter: RJ & DJ combined • • Since JPPRJ is unbounded, it can be defined by the BER that would result if there were only RJ. This is where the tails of the right and left distributions overlap (at the Sampling point): For a BER = 10-12 → JPPRJ = 14× ×σ Then JPPRJ ≡ n× ×σ so that JPPRJ =nxJrmsRJ The Total Jitter (TJ), JTJ, for a given BER is then: RJ DJ J TJ = n × J rms + J PP DJ = 14 × σ + J PP This assumes that the Gaussian RJ PDF ‘appends’ to the DJ PDF This is called the Dual Dirac Assumption Page 20 The Dual Dirac Assumption Total Jitter The ‘RJ’ The ‘DJ’ JPPDJ 7σ No Jitter values between deltas µL [δ ( x − µ L ) ∗ µR + δ ( x − µ R )] ∗ σ x2 exp − 2 2σ = µL = µR (x − µ L )2 (x − µ R )2 exp − + exp − 2 2 σ 2σ 2 Page 21 Jitter Probability: BER J pk − pk = J deterministic n ×σ random = Page 22 Random and Deterministic Jitter • • • Waveform Observation Pattern Note Characteristics σ = JrmsRJ JPPDJ 2 Distinct Falling Edges 2 Distinct Rising Edges Threshold JPP Jrms Lots of Zeros Page 23 Random and Deterministic Jitter • Lets Look at Deterministic Component… σ = JrmsRJ DJ J DJ J PP PP JLPPDJ JRPPDJ JLPPDJ + JRPPDJ = JPPDJ JPP The Peak-to-Peak Deterministic value is the DeltaJrms between Worst case mean trajectories around a crossing point. Page 24 Random and Deterministic Jitter • Now lets Look at the Random Component… σ = JrmsRJ JPPDJ σRJ σRJ σRJ is a measure of the process that makes these traces wide JPP Jrms Page 25 Random and Deterministic Jitter • Now lets Summarize Jitter for the Circuit Measured… DJ J DJ J PP = JrmsRJRJ σσ=J rms PP JPPT JPPT = n x σRJ + JPPDJ JPP Jrms Page 26 Total jitter: Histogram View Total Jitter is composed of random and determistic components Random Jitter (RJ) unbounded • Due to thermal noise, shot noise, etc. • Follows Gaussian distribution • Requires statistical analysis to be quantified • RJpp = 14.1 x Jrms for 10-12 BER Deterministic Jitter (DJ) bounded and composed of: DJ • Duty-Cycle-Distortion (DCD) • Inter Symbol Interference (ISI) • Periodic Jitter (PJ) RJ Page 27 Correlated Decomposing Jitter: The “jitter tree” TJ DJ DDJ ISI Uncorr RJ PJ DCD Signal jitter can be composed of several types from several mechanisms Data-Correlated Data-Uncorrelated Total ϕB(t) Jitter (TJ) Deterministic Jitter (DJ) Random Jitter (RJ) Data Dependent Jitter (DDJ) Inter-symbol Interference (ISI) Duty Cycle Distortion (DCD) Periodic Jitter PJ Page 28 Correlated TJ Example: Duty Cycle Distortion (DCD) DJ RJ DDJ Transmitter Threshold Offset Problem ISI Uncorr PJ DCD 1 1 Actual Threshold Ideal Threshold 0 0 Clock + error - error + error - error TIE Trend Waveform Note: One technique to test for DCD is to stimulate your system/components with a repeating 1-0-1-0… data pattern. Page 29 This technique will eliminat inter-symbol interference (ISI) jitter and make viewing the DCD within the spectrum display much easier . Correlated TJ Example: Duty Cycle Distortion (DCD) DJ RJ DDJ Transmitter Edge Transition Speed Asymmetry ISI Uncorr PJ DCD 1 1 Threshold 0 Clock - error + error - error + error TIE Trend Waveform Page 30 Correlated TJ Example: Inter-Symbol Interference (ISI) DJ Transmission Line Bandwidth Limitation Problem C A B 1 1 1 1 1 1 DDJ 1 1 1 ISI Uncorr RJ PJ DCD 1 1 Threshold 0 0 0 0 0 0 0 0 0 0 0 “A” = 0 preceded by string of 1’s = + error TIE Trend Waveform “C” = 1 preceded by string of 0’s = + error “B” = 1 preceded by 0 = - error Page 31 Correlated Example: Inter-Symbol Interference (ISI) TJ DJ Transmission Line Reflection / Improper Termination RJ DDJ ISI Uncorr PJ DCD Data Signal TIE Trend Waveform Each arrow shows which bit of data caused a reflection distortion on a later data bit. Page 32 Correlated TJ Example: Periodic Jitter (PJ) Uncorr DJ System Cross-talk Problem (capacitive coupling) RJ DDJ ISI PJ DCD Corrupter Threshold TIE Trend Page 33 Where Does Jitter Come From? Correlated TJ DJ DDJ ISI Transmitter Media Uncorr RJ PJ DCD Receiver •Lossy interconnect (ISI) •Impedance mismatches (ISI) •Crosstalk (PJ) •Thermal Noise (RJ) •DutyCycle Distortion (DCD) •Power Supply Noise (RJ, PJ) •On chip coupling (PJ) •Termination Errors (ISI) •Thermal Noise (RJ) •DutyCycle Distortion (DCD) •Power Supply Noise (RJ, PJ) •On chip coupling (PJ) Page 34 Jitter examples for different Jitter Distributions Different types of jitter ϕ(t) in S(t)=P(Asin(2πfDt+ϕ(t))) ϕ(t ) = mess ϕ(t ) = square wave ϕ(t ) = A Appl sin (2 π fJ t) . ϕ(t ) = DDJ Only ϕ(t ) = pulse Page 35 Jitter Examples Continued A DCD C RJ (gaussian)l B ISI D Sinusoidal E ISI and DCD Page 36 Jitter Primer: Topics to be Covered 1. Definition and Description of Jitter 2. Understanding Jitter, its Components, and Separation 3. Jitter Measurement Methods and Tools Page 37 Which Eye Has Worse Jitter? A B You can’t know unless you measure the Total Jitter or measure the jitter components! Page 38 Jitter Measurement Solutions from Agilent • Infiniium Scopes (up to 32 GHz): • EZJit Software • EZJit Plus Software • DCA-J (86100 Series Infiniium 20-80 GHz Scopes) • Jitter SW package • Infiniimax Probes to 13 GHz • N1930 Physical Layer Test System • Vector Network Analyzer or Time Domain Reflectometer • N4900 Series BERTs • Bathtub curve Extrapolation and RJ/DJ Estimation • E443x Signal Sources • E4438C-SP1 Jitter Injection Software Page 39 Tools to Measure/Analyze Jitter Transmitter Media Receiver Pattern Generator Bit Error Ratio Tester X X X X X Vector Network analyzer X Time domain Reflectometer X Real time oscilloscope X X Equivalent time oscilloscope X X Phase Noise Analyzer X Time Interval Analyzer X X Page 40 Jitter Tolerance Testing (w/Pattern Generators) Pros Low Noise (RJ) available Standard Patterns and User Definable Patterns Flexible for wide variety of technologies. RJ, PJ, and DCD can be created. Cons Cost Range: Modestly to Highly Expensive Intersymbol Interference is not available. Complex sequencing not available. Page 41 Tolerance Testing (using a Pattern Generator) Square Sinusoidal Sinusoidal, RJ and ISI* * Created with cable length Page 42 Jitter Analysis (BERTs) Pros Measures Total Jitter Directly Can Provide good estimate of total Jitter quickly with BERTScan method System Tool: Usable for Media analysis, receiver stress analysis J-Bert N4903B available for jitter stress test Cons Expensive Time of Measurement of Total Jitter is Long Need an external clock provided Page 43 Jitter Analysis: BERT BathTub Curve Scan the sampling point across the eye Scan the sampling point, x, across the eye Measure BER(x) = β(x) x 0.5 BER β(x) 10 Measure the Bit Error ratio as a function of sampling point delay, -3 Gaussian Tails 10-6 10-9 β(x) ⇒ TJβ Eye Opening at BER=10-12 10-12 0 0.5TB TB Page 44 Jitter Analysis: N1951A PLTS with Vector Network Analyzers (VNAs) or Time Domain Reflectometers (TDRs) VNAs Expensive 50 GHz BW available yields high resolution Highest Accuracy Full Differential Analysis analysis to show EMI, mode conversion locations Software Modeling and Analysis Available S-Parameters for modeling or to estimate ISI contribution of path TDRs InExpensive Limited by rise time of Pulse source (35ps) Accuracy may be sufficient in many environments. Using Normalization to increases accuracy Only magnitude TDT and TDR Software Modeling and Analysis Available Page 45 N1951A VNA Measurement of XAUI Backplane Differential Eye Diagram (from Agilent N1951A: VNA System) Xaui Backplane differences because of transmission line length 15 inches 30 inches Note increased striation because of BW limit of path Note degree of eye closure Page 46 Jitter Analysis (Real Time Oscilloscopes) Pros •Captures contiguous time record •No external clock required •Software clock recovery methods yield precise clock reconstruction •System Tool: Usable for Debug •Flexibility for many technologies and usually a growth path provided •Many views provided for insight: histograms, eyes, fft, trend, data, etc •Oscilloscope Bandwidths are going higher Cons •Expensive •Limited to current BW of scope Page 47 Agilent Infiniium Series Oscilloscopes High Bandwidth Models up to 32 GHz & 80 GSa/s per channel Deepest memory in the market up to 2 Gpoint per channel MegaZoom usable deep memory Mixed Signal Oscilloscope (MSO) models available Windows-Based Easy to Use GUI Drag-and-Drop easurements Zoom box Wide variety of analysis options Page 48 How Do Real Time Scopes Measure Jitter on Data: Ezjit Display NRZ Serial Data Recovered Clock Jitter Trend Jitter Spectrum Units in Time Units in Freq. Jitter Histogram Page 49 Agilent E2681A EZJIT Jitter Measurement Application for Infiniium Oscilloscopes Signal Histogram Trend Spectrum Page 50 Sampling Techniques • Real Time (Single-Shot) • Sequential Sampling (Repetitive) Page 51 Sampling Real Time (Single Shot) Technique • Used with either Repetitive or Single-Shot Signals • All Samples Are Taken From a Single Trigger • Samples from Previous Triggers are Erased • Sample Rate May Limit Scope’s Overall Bandwidth • Best Resolution Depends Directly on Sample Rate Each Trigger Identical Page 52 Sampling Sequential Sampling Technique • Used ONLY with Repetitive Signals • One Sample is taken for each Trigger • Multiple Trigger Events Build Up Waveform • Used in High Speed Applications with BW >10GHz • No Pre-Trigger Information 1st Trigger 2nd Trigger 3rd Trigger Page 53 Jitter Analysis (Equivalent Time Sampling Oscilloscopes) Pros InExpensive Bandwidth is Highest Available Noise floor is good TDR options for media analysis Flexibility for increasing rates Industry leading jitter separation algorithm (DCA-J) Cons External Clock or Clock related trigger is required or Hardware Clock Recovery Module Page 54 Jitter Analysis (Equivalent Time Oscilloscopes) A B Page 55 RJ DJ J TJ = n × J rms + J PP Which Eye Has Worse Jitter? A DJ = 14 × σ + J PP B Page 56 Jitter Measurements on an equivalent Time Sampling Oscilloscope, 86100C DCA-J Completely new technique for jitter analysis Pattern Lock + Eyeline internally generated pattern tr