Jitter Presentation

8/20/2019 Jitter Presentation

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Jitter Fundamentals


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Agendaı Jitter basics

Measurement types (period, half period, cycle to cycle, TIE)

Measurement tools (histogram, track, spectrum) Jitter basics lab

ı Sources of error in jitter measurements

noise, trigger jitter, sampling jitter

Jitter error lab

ı Jitter analysis Jitter track and spectrum

Types of jitter (Rj, DCD, DDj, Pj, BUj)

Jitter track and spectrum lab

DCD measurement on a clock

ı Jitter as a random variable

Jitter PDF models

Jitter, total jitter and bit error rate

Lab: using the dual Dirac jitter model

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What is Jitter?

lJitter is “the short-term variations of signal timing”

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l Jitter includes instability in signal period, frequency, phase, duty cycle or some other timing

characteristicl Jitter is of interest from pulse to pulse, over many consecutive pulses, or as a longer term

variation

l Very long term variations (


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Jitter Measurements

ı

Key measurements to characterize clock signals


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Timing Measurement in Oscilloscopes

ı Time is measured at the point where the waveform amplitude crosses

a predefined thresholdı Samples are spaced at the sample interval (50 ps at 20 Gs/s for

example)ı interpolation is used on the waveform transition to find the exact

crossing time

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threshold

Threshold crossing time

50 ps50 ps

Interpolated samples


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Jitter Analysis Tools

l Statistics

l '+Peak‘, '-Peak‘, RMS, mean value, standard deviation, number of measurements

l peak-to-peak jitter calculated by subtracting '+Peak‘, from '-Peak‘l Persistence

l Emulation of phosphorous screen of an analog oscilloscope an eye pattern in order to

determine the total jitter for a given time or sample size.

l color grading, including a measurement of the total jitter with cursors.

ı Histogram

Waveform histogram and measurement histogram

Displays the Probability density function (PDF)

ı Track

measurement results over time for acquired waveforms

Reveals trends of change in the analysis

Preserves timing relationship of the measurement results Displays frequency modulated signals


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Traditional Measurement Method: Persistence Display

l Simple setup

l Pixel or screen resolution limits accuracy

l Single waveform period introduces trigger jitter

l No control over jitter transfer function – high pass characteristic

T jitter


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Lab 1: Basic Jitter Measurementsı Period Jitter

Press PRESET

Connect the active probe to the 10MHz_CLK and to channel 1 of the scope Press AUTOSET

Set the trigger to positive edge on the clock

Set the trigger offset to -100 ns (1 clock period)

Set the horizontal scale to 100 ps/div

Draw a horizontal histogram box vertically centered on the trigger point andmake the vertical dimension of the box minimum

Measure the max – min and standard deviation of the histogram

ı N-cycle jitter

Adjust the trigger offset to -N*100 ns (for example -500 ns for N = 5)

ı Analog trigger

Connect a passive probe to the 10 MHz CLK and to the AUX TRIG IN

Set the trigger source to Ext

Adjust the trigger offset to center the rising edge on the screen ( about -1.2 ns)

Measure the max – min and standard deviation of the histogram (already on)

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Instrument Limitations for Jitter Analysis

time

V A

VN

Δts Δtl


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Lab 2: Noise and its Effect on Jitter Measurements

ı

Connect the active probe to the 10 MHz CLK and to channel 1ı PRESET the scope followed by AUTOSET

ı Disconnect the signal from the signal board and measure the AC RMS noise

ı Note the measured noise level

ı Reconnect the probe to the 10 MHz CLK and set the time base to 200 ps/div

ı Use cursors to measure the slew rate of the signal near the trigger level (

enable “track waveform” in the Cursor Results box)

ı Compute the expected jitter value Vn/Ts

ı Enable a horizontal histogram centered at the trigger level and with minimum

height

ı Measure the standard deviation of the histogram and compare this value with

the computed jitter noise floor

ı Repeat this measurement using the 825 MHz sine wave

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Jitter Track

ı Display of measurement results: time-correlated to waveform

ı Very useful to analyze any changes in the signal


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Jitter Track Analysis Functions

ı 3 ways of viewing jitter results: track; histogram; spectrum

Time Domain

Waveform

Cyc to Cyc

measurement

Track curve

Histogram

Spectrum


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Jitter Structure

Data-Dependant Jitter (DDJ)Duty-Cycle Distortion (DCD) Periodic Jitter (PJ)

Deterministic Jitter (DJ)(bounded)

Random Jitter (RJ)(unbounded)

Total Jitter (TJ)


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Types of JitterBasic Types


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Periodic jitter

ı Periodic variations in the edge timing of the signalı Caused by non-data related sources

Power supply Crosstalk

EMIı Measured in the frequency domain using the jitter spectrum

Data dependent spectral content must be removed Noise threshold delineates Pj from noise floor

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Data Dependent Jitter (ISI and DCD)

0 5 10 15 20 25 302

1

0

1

2

effect of band limiting on serial data

bit sample points (UI)

a m p l i t u d e .

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wmwpDCD = |wp – wm|

ISI results from

channel

imperfections

and bandwidth


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Bounded, uncorrelated jitter

ı

Jitter that is uncorrelated with the data pattern Includes Pj

Other sources that are not periodic over the observation time

ı OBUj = Other Bounded Uncorrelated Jitter

Non-periodic but bounded jitter sources

Appears as elevated noise floor in jitter spectrum

Must be measured from the jitter histogram (Q-scale or BERT)

ı Sources of OBUj

Crosstalk from long repeating data pattern

High rate FM on Pj component

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Lab 3: Jitter Track and Spectrum

ı PRESET the scope

ı

Connect the 825 MHz sine wave signal to channel 1 using the SMA to BNCcable

ı Set the coupling of channel 1 to 50 ohms

ı Disable Auto Adjustment in the HORIZONTAL -> Resolution menu

ı Press AUTOSET

ı Set the time base to 2 us/div

ı Measure the period and enable the track on the measurement

ı Perform FFT of track and set the start and stop frequencies to 0 and 500 MHz

respectively

ı Set the FFT resolution bandwidth to 500 KHz

ı Enable averaging on the FFT

ı Scale the FFT display to 50 fs/div and set the offset to 0

ı Measure the frequency and amplitude of any lines in the spectrum

What is the spacing between the lines

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Lab 4: Measure DCD of clock

ı

PRESET the scopeı Connect the 825 MHz sine wave signal to channel 1 using the SMA to BNC

cable

ı Set the coupling on channel 1 to 50 ohms

ı Press AUTOSET

ı Set trigger to edge mode and slope to both

ı Set the trigger level to 0 V

ı Offset time base to – 606 ps

ı Set time base to 50 ps/div

ı Draw horizontal histogram centered at 0V (the trigger level) and with minimum

height

ı Measure the distance between the peaks of the histogram using the verticalcursors – this is the DCD

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Jitter as a Random Variable

ı Jitter is a random process that is a combination of randomand deterministic sources

ı The jitter histogram is used as an estimate of theprobability 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

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Probability Density Functions

ı The PDF is a function that gives the probability that arandom variable takes on a specific value

ı In the case of jitter, this is the probability that a transitionhappens at a specific time from its expected location

ı The histogram of a random measurement is an estimate ofthe PDF for that measurement from which the analyticfunction can be derived – this is the essence of jitter

measurement

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Random Jitter (Gaussian Model)

In theory, the peak to peak value of random signal jitter will grow towithout bound. To define the random jitter you must specify a

measurement time.

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

1,000,0005,000,000

100,000,000

1,000,000,000,000


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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 Rjı Dj(δ−δ) and σ are chosen to best

fit the measured histogram in the

tails

ı Model Predicts jitter for low bit

error ratesı Note that the model does not fit

the central part of the measured

distribution

σ = Rj

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L R Dj µ µ δ δ −=− )(

)(*)( δ δ −+= Dj Rj BERQTj G


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Bit Error Rate

ı Bit error caused by signal transition

during sampling time

ı Minimum BER is the point where

left and right jitter distribution tails

intersect

ı Actually applies in 2 dimensions

(noise and jitter)

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Jitt d Bit E R t


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Jitter and Bit Error Rate

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Jitter PDF

B E R

UI0 1

Assumption: Bit

errors are caused

by signal transitions

at the wrong time


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Total Jitter Curve

ı The specified BER isanother way of

expressing aconfidence intervalor observation time

ı Total jitter isdetermined byintegrating theprobability density

function (PDF)separately from theleft and right sides todetermine thecumulativeprobability density(CDF)

ı

The width of thiscurve at thespecified BER (orconfidence interval)gives the total jitter

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CDF(total jit ter)

PDF

Total j itter and PDF for a Gaussian

distribution with standard deviation = 1


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Lab 5: Using the Dual Dirac Jitter Model

ı Start with the DCD measurement from LAB 4

ı Adjust the reference point to 0% and measure the standard deviation of the

histogram (this isolates the right jitter peak)

ı Adjust the reference point to 100% and measure the standard deviation of the

histogram (this isolates the left jitter peak)

ı Compute the jitter using the dual Dirac model:

Tj = 14*(σL + σR)/2 + DCD

ı Compare this measurement with 14 times the standard deviation with the

reference point set to 50%

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