Post on 04-Dec-2014
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Live webinar from 2/11/14 View the On-Demand webinar, http://ubm.io/LywVYU
Real Time Jitter Measurement
Overview
ı Background jitter measurement methods Batch mode jitter measurement Triggered measurement Real –time digital clock recovery
ı Jitter transfer function (real time vs. batch) ı Transient and low rate jitter events ı Measurement examples Low rate jitter PRBS31
What is Jitter?
l Jitter includes instability in signal period, frequency, phase, duty cycle or some other timing characteristic
l Jitter is of interest from pulse to pulse, over many consecutive pulses, or as a longer term variation
l Very long term variations (<10Hz) are a separate class of pathologies referred to as wander (Telecommunication only)
Hold Time
Setup Time
Data
Clk
Q
Serial digital data transmitter
Time Interval Error (TIE)
TIE is the difference between the measured clock edge and the ideal clock edge locations TIE is essentially the instantaneous phase of the signal
Jitter Measurement Instruments
Real time (Oscilloscope) Single-shot or repetitive events (clock or data) Bandwidths typically 60 MHz – 30+ GHz Lowest sensitivity (highest jitter noise floor) Measures adjacent cycles
Repetitive (Sampling Oscilloscope) Repetitive events only (clock or data) Bandwidths typically 20 GHz - 100 GHz Generally can not discriminate based on jitter frequency Cannot measure adjacent cycles
Phase noise (Phase noise test set) Clock signals only Must integrate phase noise over frequency to measure jitter Highest sensitivity (lowest jitter noise floor) Cannot measure adjacent cycles Sensitivity
Flexibility
7
Spectrum Analyzer Method
8
Phase Detector Method
Reference Source
DUT PD
⊗√=90°
Low Pass Filter LNA Spectrum
Analyzer
PLL
PLL Low Pass Filter
PLL-Controlled Reference
9
Input signals of the mixer (having 90° offset, i.e. in “Quadrature“): Output signals of the mixer: After low-pass filtering and assuming ƒL= ƒR we get: For small changes in phase (simplification allowed for this kind of noise):
Phase Detector Method
Relationship between phase noise and jitter
Timing Measurement in Oscilloscopes
ı Time is measured at the point where the waveform amplitude crosses a predefined threshold
ı Samples are spaced at the sample interval (50 ps at 20 Gs/s for example) ı Sin(x)/x or cubic interpolation is used on the waveform transition followed by
linear interpolation of the points nearest the crossing to find the exact time
threshold
Threshold crossing time
50 ps 50 ps
interpolation
ı Collection of measurements
arranged in an x-y plot value vs. frequency of occurrence
ı Approximation of a PDF when normalized
ı Analyzed to "measure" total jitter and jitter components (random, deterministic, etc.)
Jitter Measurement: Histogram
ı Jitter measurement over time ı Synchronous sampling with signal transitions ı Used to measure jitter spectrum
Jitter Measurement: Jitter Track
t1 t2 t3 t4 t5
t
t
Jitter as a Random Variable
ı Jitter is a combination of random and deterministic sources and can be treated as a random variable
ı The jitter histogram is used as an estimate of the probability density function (PDF) of the timing values – usually 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
Theoretically, the peak to peak value of random jitter will grow without bound. To define the random jitter you must specify a measurement time.
The Random Component of Jitter
Peak-to peak (σ) ±2.1 ±2.9 ±3.4 ±3.5 ±4.1 ±4.6 ±5.1 ±6.0 ±7.0
# Measurements 100 1,000 5,000 10,000 100,000 1,000,000 5,000,000 100,000,000 1,000,000,000,000
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 cumulative density function is the integral of the PDF and gives the total probability of a transition happening within a certain time range of the expected transition time
ı The histogram of a random measurement is an estimate of the PDF for that measurement
The Dual Dirac Jitter Model
ı Fit Gaussian curve to the left and right sides of estimated jitter PDF (i.e. the measured normalized histogram)
ı Separation of the mean values gives Dj(δ−δ)
ı Standard deviation gives Rj ı Dj(δ−δ) and σ are chosen to best fit
the measured histogram in the tails ı Model Predicts jitter for low bit error
rates ı Note that the model does not fit the
central part of the measured distribution
Jitter and Bit Error Rate Jitter PDF
BER
UI 0 1
Total Jitter Curve ı The specified BER is
another way of expressing a confidence interval or observation time
ı 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)
ı The width of this curve at the specified BER (or confidence interval) gives the total jitter
CDF (total jitter)
Total jitter and PDF for a Gaussian distribution with standard deviation = 1
Summary of Histogram Analysis
ı Histograms are used to estimate the PDF of random variables such as jitter ı Jitter consists of both random and “deterministic” components Random jitter is assumed to have a Gaussian PDF Deterministic jitter is actually bounded and is modeled by a pair of Dirac delta
functions ı The Dual Dirac model is used to extrapolate a small set of jitter measurements
in order to predict the peak to peak range of a much larger sample ı The sample size is expressed in terms of bit error rate BER of 1e-12 equals a sample size of approximately 2e12 bits Ratio of ‘1’ to ‘0’ values is assumed to be ½
ı Rj and Dj from the Dual Dirac jitter model are specified in all serial data standards for jitter
Jitter measurement methods
ı 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)
ı Measurement methods used in oscilloscopes Real time (triggered) Batch mode
Real time jitter measurement
ı Hardware clock recovery ı Separate trigger circuit ı Timing uncertainty introduced via CDR, trigger and ADC sampling clock
Batch Mode Jitter Measurement
ı Analyze long signal acquisition ı Software clock recovery applied
to timing data ı Many analysis features
(frequency, time, statistical)
Jitter Noise Floor
Sampling clock jitter Noise
Trigger jitter
Clock recovery jitter
Sampling clock jitter Noise
Batch mode
Triggered
Typ. 330 fs
Typ. 1.5 ps
Real time Digital Clock Recovery
ı Real time acquisition similar to triggered mode ı No CDR or trigger jitter ı Loop bandwidth not limited by acquisition window
Limitations of Batch Mode Jitter Measurement
ı Inherent low frequency cutoff due to windowing ı Large time gaps in acquisition obscure transient jitter ı Generally impossible to measure long stress data patterns ı Discontinuous phase tracking can cause phase "slipping"
Jitter transfer function
N measurements
FFT Bin Response
Each bin has a sin(x)/x response Low frequency cutoff at the first FFT bin
Jitter transfer function
Jitter transfer function
1 MHz carrier with 10 KHz sinusoidal jitter measured over a 100 us time window
Jitter transfer function
1 MHz carrier with 10 KHz sinusoidal jitter measured over a 50 us time window
Transient jitter
Example of transient jitter
histograms of low rate jitter measured using batch and continuous modes. Jitter Injected at 1/3208 rate
Example of Jitter on a Long Pattern
Histograms of jitter measured on a PRBS31 data pattern. The linear trend lines on the histogram on a log scale estimate the total jitter
Summary
ı Oscilloscope jitter measurements rely mainly on batch mode processing lowest jitter noise floor time and frequency domain analysis
ı Batch mode jitter analysis has limitations transient jitter long repeating patterns
ı Applying digital methods to real time jitter analysis provides significant benefits for jitter measurements low jitter noise floor large statistical sample capture of transient jitter
Learn More
ı For more information on the instruments seen in this presentation, please visit www.rohde-schwarz-scopes.com
ı If you’re interested in a free demo of our products, please visit http://www.rohde-schwarz-usa.com/FASTDemo.html