Live webinar from 2/11/14 View the On-Demand webinar, http://ubm.io/LywVYU Real Time Jitter Measurement
Real-Time Jitter Measurements
Dec 04, 2014
Jitter measurements are commonly done taking small snapshots in time, yet systems often experience jitter from sources that occur over relatively long time intervals, which may not be accounted for using short time interval measurements methods.
In this webinar we will present the application of a real time, digital clock recovery and trigger system to the measurement of jitter on clock and data signals. Details of the measurement methodology will be provided along with measurement examples on both clock and data signals.
You Will Learn:
- What is Jitter
- Different types of Jitter
- Jitter measurement techniques
- Benefits of Jitter analysis using real-time DDC techniques
In this webinar we will present the application of a real time, digital clock recovery and trigger system to the measurement of jitter on clock and data signals. Details of the measurement methodology will be provided along with measurement examples on both clock and data signals.
You Will Learn:
- What is Jitter
- Different types of Jitter
- Jitter measurement techniques
- Benefits of Jitter analysis using real-time DDC techniques
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Transcript
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
Presenter
Presentation Notes
specified as jitter in the time domain, phase noise in the frequency pulse to pulse --> period jitter over many consecutive --> cycle to cycle longer term variation (such as modulation) --> time interval error specified in time, UI, power measurement (dBm or UI2, degrees or radians
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
Presenter
Presentation Notes
Drifting of oscillators and phase jumps cause that the 90 degree phase shift at the phase detector to be unstable. A synchronization of DUT and reference source is necessary which can be done by a PLL.
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
Presenter
Presentation Notes
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
Presenter
Presentation Notes
Timing measurement in oscilloscopes are performed by finding the crossing point of the waveform at a specific level. In many cases, the rise time of the signal is very fast and with a sampling rate of say 20 GHz there are only a few samples on the edge. Simply drawing a line between the samples around the threshold is the most obvious choice for finding the crossing however this can lead to large errors when the samples are not evenly spaced on either side of the threshold. Cubic interpolation is used to fill in the samples between the acquired samples and the crossing time is found by linear interpolation between the two interpolated samples on either side of the threshold. Note that when the signal is band limited and sampled at more than 2x its bandwidth as it is in a real time oscilloscope, the interpolated line between the sampled points is exactly described by a sin(x)/x curve between samples because no higher frequency components are present. Cubic interpolation is used for computational efficiency and because it closely follows the ideal sin(x)/x curve in the crossing region.
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
Presenter
Presentation Notes
Jitter is analyzed by treating it as a random variable. While jitter consists of a complex combination of both random and non-random affects, the overall jitter is analyzed by examining its statistics and in particular the probability density function. From the PDF, the expected value and range of the jitter can be completely determined. For example, the range of a random variable can be measured for any confidence interval by integrating the PDF. The resulting cumulative distribution function or CDF gives the probability that the random variable will be within a given range. The PDF, however is never completely known since it is not directly measurable. Histograms can be used to estimate the PDF by accumulating many measurements of TIE and plotting their frequency of occurrence.
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
Presenter
Presentation Notes
Random jitter is a statistical phenomena where the likelihood of a large event increases over time. In order to specify the peak to peak value, the observation time must be specified. Here we show histograms for the same jitter measurement over increasing observation time. The range for a Gaussian distribution is determined by its standard deviation. The observation time can be quantified by the number of measurements and the range of the histogram grows with the number of measurements. The number of standard deviations covered by the range for any given number of measurements can be computed from the Gaussian PDF. The range for 1e12 measurements is +/- 7 standard deviations. This is where the 14*Rj contribution to total jitter is derived.
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
Presenter
Presentation Notes
Unlike typical measurements such as rise time and amplitude, jitter is statistical in nature and must be measured in terms of statistical averages such as mean and standard deviation. We need to know the worst case jitter for a particular observation time or measurement sample size. This sample size is generally expressed in terms of bit error rate. In order to make this sort of measurement, one needs to know the behavior of the jitter for all time. Because jitter is random in nature, it can be analyzed by its probability density function which describes the probability of the random variable taking on a particular value. The probability of the jitter taking on a value within a certain range is found by integrating the PDF to get the CDF. The jitter PDF is not directly measurable because we cannot observe the jitter for all time. The histogram is used as an estimate for the jitter PDF for the purpose of predicting the jitter over longer measurement times.
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
Presenter
Presentation Notes
As we have said, jitter is a random variable whose PDF is a complex combination of both bounded and unbounded sources. The PDF is not directly measurable however the histogram can be used as an estimate for the PDF over a certain observation time. In order to accurately account for both bounded and unbounded jitter components, a model is fit to the measured histogram. This model which is known as the “Dual-Dirac” accounts for the bounded jitter by using 2 Dirac delta functions which are convolved with a Gaussian. The position of the two delta functions as well as the standard deviation of the Gaussian are adjusted to best fit the measured histogram in the region of the tails. The spacing between the two delta functions is called the deterministic jitter or Dj(δ−δ). The d-d indicates that this is the dual dirac Dj. The value of Rj is the average of the best fit to the histogram on the left and right. The total jitter is given by the Dj plus Rj time Q(BER). Q is a function of bit error rate and gives the number of standard deviations of a Gaussian corresponding to the desired bit error rate. For the case of 1e-12 BER, Q is 14. Note that this model actually has two different standard deviations; one left and one right but in practice, the two are set equal to each other. The Dj(d-d) is not related to the actual peak to peak deterministic jitter and is often less than the actual Dj. This is because Dj(d-d) is chosen to best fit the tails of the jitter histogram. The Dual Dirac model is a valuable tool for predicting jitter performance and is the standard used for all jitter compliance tests.
Jitter and Bit Error Rate Jitter PDF
BER
UI 0 1
Presenter
Presentation Notes
Jitter and bit error rate are related. A transition that happens at a given distance from the expected time will result in an incorrectly decoded bit if the signal is sampled at that time or later. The probability of a bit error is equal to the probability that a transition happens at the sampling time or later. The cumulative density function or CDF gives the probability that the random variable (transition time) is less than some value so the bit error rate is 1 – CDF(x) where x is a particular offset from the expected value. We can plot the value of BER(x) as a function of x as x varies from the expected value to a point that is one unit interval away traces out a curve of BER vs. sampling point. This curve is commonly referred to as the bathtub curve. The distance between the sides of the bathtub curve at a given BER is the eye opening at that BER in terms of a unit interval. The total jitter at the same BER is 1-eye opening in UI.
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
Presenter
Presentation Notes
The CDF gives the probability that a random variable (the jitter in this case) is between its expected value and a specified value. The CDF is the integral of the PDF from its mean value both positively (to the right) and negatively (to the left). The vertical dimension of the CDF is probability and goes from zero at the expected value (mean of the PDF) to a maximum of 0.5 at the limit as x approaches infinity and also as x approaches negative infinity. In order to relate this to bit error rate, the scale is displayed in terms of 1-CDF so its amplitude ranges from 0.5 at the expected value to 0 at +/- infinity. The range of the CDF at a given BER gives the total jitter.
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
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