Real Time Jitter Analysis

Real Time Jitter Analysis

Agenda ı Background on jitter measurements Definition Measurement types: parametric, graphical ı Jitter noise floor ı Statistical analysis of jitter Jitter structure Jitter PDF s PDF models, CDF and BER ı Jitter track analysis ı Jitter measurement methods Batch mode Real time ı Measurement example 2

Jitter Definition ı Short term variation in the timing of a signal Many parameters are included in jitter Frequency, period, phase, etc. ı Limited to timing variations at higher frequencies > 10 Hz (telecom definition) > a defined minimum frequency usually a fraction of the bit rate ( for example 1/1667 ) Hold time D Setup time clk Q 3

Jitter Measurements

Parametric Timing Measurement sampled data Interpolated samples Threshold crossing time threshold 50 ps 50 ps ı Sample points are interpolated to provide increased resolution Sinx/x interpolation is ideal ı Crossing point determined by linear interpolation between points on either side of the threshold Floating point computation Precision is limited to the floating point number 5

Graphical Timing Measurement - persistence display threshold Trigger l Simple setup l Precision limited to pixel resolution jitter l Single waveform period introduces trigger jitter l No control over jitter transfer function high pass characteristic

Instrument Limitations for Jitter Analysis V N time V A Δt s Δt l

Jitter and Bandwidth ı Sufficient bandwidth is required to measure a digital signal (clock or data) ı This is normally stated in terms of multiples of the fundamental frequency of the signal Fundamental = the clock frequency or ½ the bit rate Typical requirement = 5 x the fundamental ı Requirement based on the harmonics of a square wave Decrease with 1/f from the carrier - 13 db at 3x, -26 db at 5x for an ideal square wave Real signals typically much lower than this ı Noise and slew rate trade off Noise and slew rate are proportional to bandwidth ( ~ktb) For a given slew rate the minimum jitter noise floor is achieved at a bandwidth of B = f 8

Jitter Noise Floor (10 MHz clock) 15 mv RMS noise JNF =.015/2.16e9 = 6.8 ps 9

Jitter Noise Floor (825 MHz sine wave) 1 mv RMS noise JNF = 0.001/6e8 = 1.6 ps 10

Jitter is a Random Process ı Jitter is a random process that is a combination of random and deterministic sources ı The jitter histogram is used as an estimate of the probability density function (PDF) of the timing values (period, cycle-cycle, N-cycle, TIE) ı A model is fit to the estimated pdf 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 rate 11

Jitter Structure Total Jitter (TJ) Deterministic Jitter (DJ) (bounded) Random Jitter (RJ) (unbounded) Duty-Cycle Distortion (DCD) Data-Dependant Jitter (DDJ) Periodic Jitter (PJ)

Probability Density Functions ı The PDF is a function that gives the probability that a random variable takes on a specific value ı In the case of jitter, this is the probability that a transition happens at a specific time from its expected location ı The histogram of a random measurement is an estimate of the PDF for that measurement from which the analytic function can be derived this is the essence of jitter measurement 13

Types of Jitter

Random Jitter (Gaussian 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 (s) ±2.1 ±2.9 ±3.4 ±3.5 ±4.1 ±4.6 ±5.1 ±6.0 ±7.0 In theory, the peak to peak value of random signal jitter will grow to without bound. To define the random jitter you must specify a measurement time. 15

The Dual Dirac Jitter Model Fit Gaussian curve to the left and right sides of estimated jitter PDF (i.e. the measured normalized histogram) Separation of the mean values gives Dj(d-d) Standard deviation gives Rj Dj(d-d) and s are chosen to best fit the measured histogram in the tails Model Predicts jitter for low bit error rates Note that the model does not fit the central part of the measured distribution Tj Rj s Dj( d - d ) - Q G ( BER)* Rj Dj( d -d ) R L 16

BER Jitter and Bit Error Rate Jitter PDF Assumption: Bit errors are caused by signal transitions at the wrong time 0 UI 1

The specified BER is another way of expressing a confidence interval or observation time Total jitter is determined by integrating the probability density function (PDF) separately from the left and right sides to determine the cumulative probability density (CDF) The width of this curve at the specified BER (or confidence interval) gives the total jitter 18 Total Jitter Curve CDF (total jitter) PDF Total jitter and PDF for a Gaussian distribution with standard deviation = 1

Jitter Track ı ı Display of measurement results: time-correlated to waveform Useful to analyze any changes in the signal

Jitter Track Analysis Functions Time Domain Waveform Spectrum Track curve Histogram

Jitter measurement methods Oscilloscope is the primary instrument for jitter measurement Measurement of clock and data signals Wide range of measurement types (period, cycle to cycle, TIE, etc) Measurement methods used in oscilloscopes Real time (triggered) Batch mode

Batch Mode Jitter Measurement Analyze long signal acquisition Software clock recovery applied to timing data Many analysis features (frequency, time, statistical)

Real time Digital Clock Recovery Real time acquisition similar to triggered mode No CDR or trigger jitter Loop bandwidth not limited by acquisition window

Limitations of Batch Mode Jitter Measurement Inherent low frequency cutoff due to windowing Large time gaps in acquisition obscure transient jitter Generally impossible to measure long stress data patterns Discontinuous phase tracking can cause phase "slipping"

Acquisition Window T = N/f s (400e3 Samples)/20e9 S/s) = 20 us (100e6 Samples)/(20e9 S/s) = 5 ms

Transient jitter

1 edge Jitter Measurement With Transient Error 100 M samples @ 20x10 9 S/s Processing time 1 us

Transient jitter: 5 MHz clock with 1 runt/sec. 28

Summary ı Jitter measurements are performed on sampled signals using an oscilloscope Parametric and graphical methods Noise limits measurement sensitivity along with signal slew rate ı The most accurate method for measuring jitter uses a batch mode method Long acquisition followed by post processing in software Assumes stationary jitter statistics Limits low minimum jitter rate ı Real time jitter measurement uses graphical method combined with digital clock recovery Distributed measurement over time Measurement of transient jitter Long stress patterns 29