Noise Reduction in Jitter and Phase Noise … › us › en › assets › 7018-07012 › ...Noise reduction on differential signals requires two copies of the difference signal. The

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Noise Reduction in Jitter and

Phase Noise Measurements

Using Keysight Infiniium Real-Time Oscilloscopes

Introduction

Keysight Technologies recently implemented a new noise reduction technique in our

Infiniium real-time oscilloscope’s TIE (time-interval error) and single-sideband phase

noise measurements that dramatically improves sensitivity. This document describes how

this feature works to directly measure clock jitter that was previously obscured by the

oscilloscope’s noise floor. It also describes how to make the best use of this new feature,

assuming the reader is already familiar with conventional TIE and phase noise

measurements.

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What it Does

Real-time oscilloscopes are commonly used to measure jitter on clock signals. Sometimes however, the

clock’s jitter is too low for the oscilloscope to measure it because the measurement result is dominated by

the oscilloscope’s voltage noise. Keysight’s noise reduction method measures a clock signal using two

different oscilloscope channels simultaneously, and then computes the TIE or phase noise using a cross-

correlation technique. The computation removes the oscilloscope’s noise and jitter that is uncorrelated

between or unique to each oscilloscope channel.

Figure 1. Example of phase noise measurement using noise reduction technique. (m1) - true phase

noise of signal measured using an E5052B signal source analyzer, (m2) – DSOZ334A oscilloscope with

noise reduction, (m4) – DSOZ334A oscilloscope without noise reduction.

Figure 1 demonstrates the improved sensitivity of a phase noise measurement using the new noise

reduction technique. The measurement compares the phase noise a 100 MHz output from an 81134A pulse

generator. Memory 1, (m1) shows pulse generator’s true phase noise. This trace was measured using an

E5052B signal source analyzer and then saved to the oscilloscope’s Memory 1. Memory 4, (m4) was

measured using a DSOZ334A real-time oscilloscope without noise reduction. Memory 2, (m2) was

measured using a DSOZ334A real-time oscilloscope with noise reduction. Without noise reduction, the

integrated jitter from 150 kHz to 40 MHz of the oscilloscope measurement was 1.58 ps rms. With noise

reduction, the integrated jitter of the scope measurement dropped to 760 fs rms. The signal source analyzer

reported an integrated jitter of 750 fs rms.

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The new noise reduction technique also works on TIE measurements. Figure 2 shows the noise reduction

technique’s improvement on a TIE trend measurement. The bottom trace, (m2) shows a conventional TIE

measurement trend waveform of a 10 GHz clock signal. The top trace, (mt) shows a TIE measurement

trend of the same clock signal using the new noise reduction technique.

Figure 2. TIE trend waveform measurement with (mt) and without (m2) noise reduction.

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How to Use It

Connections

Noise reduction needs to digitize the SUT (signal under test) using two different input channels

simultaneously.

Single-ended signals

The best way to split single-ended signals into two copies is by using passive power splitters or dividers

because they don’t add noise or jitter to the measurement. Resistive dividers are a little simpler to use than

reactive dividers because they don’t have a low frequency cutoff, and a generally flatter frequency

response. Resistive dividers do attenuate the signal more than reactive dividers (-6 dB instead of -3 dB),

but that rarely matters for clock signal measurements because clock signals are usually so large that

needed at least 3 to 6 dB of oscilloscope attenuation anyway. Much less common is to split a single-ended

signal into a differential signal using a passive balun transformer.

You can also use buffers or amplifiers to fan-out your SUT, provided you ensure the buffer or amplifier

doesn’t add appreciable jitter of its own to the measurement. Even the two differential outputs of a

differential buffer can be used if the buffer doesn’t have significant common-mode noise. Any common-

mode noise from a fanout buffer will be correlated across the two copies of the SUT and therefore will be

added to the measurement result.

Differential signals

Noise reduction on differential signals requires two copies of the difference signal. The best way to do this

is to split the two polarities of the signal into two copies is by using passive power splitters or dividers as

shown below. This method requires four oscilloscope channels, but most oscilloscopes do have 4 channels.

You then configure the four individual channels as two differential channels from within the Channel Setup

dialogue menu.

Figure 3. Connection diagram for differential SUT using two power splitters/dividers.

This connection method doesn’t add noise or jitter to the measurement because it uses passive devices.

In addition, the subtraction of two digitized signals further reduces the contribution of the oscilloscope

channel’s voltage noise an additional 3 dB.

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Another effective method of duplicating a differential signal is to first convert the two polarities of the

differential signal into a single difference signal using a balun transformer, and then split the difference

signal into two copies using a power splitter/divider (see Figure 4). Again, using passive devices doesn’t

add noise or jitter to the measurement, but physical balun transformers do introduce errors that the

subtraction of oscilloscope channels does not. It’s important to use a balun that has adequate insertion loss

and common-mode rejection over the full bandwidth of the measurement.

Figure 4. Connection diagram for differential SUT using a balun transformer and a power splitter/divider.

PCI Express clock jitter measurements for example, may only measure a 100 MHz clock, but they require

a full measurement bandwidth of 5 GHz.

You can also use buffers or amplifiers to fan-out your differential SUT, if the buffer or amplifier doesn’t add

appreciable jitter of its own to the measurement. Differential buffers used with differential measurements

offer a little more benefit than they do for single-ended measurements because they also perform the

difference operation.

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Probes

It’s not very common for people to measure jitter using oscilloscope probes, and it’s even less common for

them to measure phase noise using probes. That’s because the probe’s large attenuation of the SUT

significantly reduces the measurement’s SNR (signal-to-noise ratio). Infiniium’s new noise reduction

technique however, removes the both the channel’s noise as well as the probe’s noise. So, high-quality

jitter and phase noise measurements can now be made using probes.

Figure 5. Connection diagram for differential SUT using two differential probes.

To use the noise reduction technique with oscilloscope probes simply double-probe the SUT. In other

words, probe the SUT using two different probes as shown in Figure 5. This does double the capacitive

loading on the probed voltage node, but that’s not usually a problem for clock signals.

Edge Polarity

Both jitter and phase noise measurements compute their results using threshold crossing times of voltage

transitions, and you must select which transitions to use; rising, falling or both. In general, you should only

use both edges for double data rate clocks. Otherwise, select the single edge polarity used in your

application.

If you’re using one of the connection methods where the two copies of the signal have opposite polarities,

you’ll need to invert one of them using the Invert check box within the Channel Setup menu. This way, the

same edges on both polarity signals will be correlated with each other.

Also, note that Infiniium oscilloscopes perform their clock recovery on both edges of the source signals by

default. This is appropriate for TIE measurements using both edges, but not for measurements using only

one edge. It usually doesn’t matter, but the best practice is to recover the clock using the same edges as

the TIE measurement. The edges used for clock recovery are controlled through the [Measure/Mark][Clock

Recovery…][Advanced…] menu.

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De-Skew

Single-ended signals

It’s important that the jitter you want to measure remains correlated across the two different oscilloscope

channels used to digitize the SUT. That means they need to be acquired simultaneously. If the two copies

of the SUT arrive at the oscilloscope at different times, then they need to be de-skewed so that the

oscilloscope treats them like they did arrive at the same time. The two copies of the SUT don’t have to be

aligned particularly closely. They only need to be aligned within about 5% to 10% of their period.

Differential signals

The alignment required between the two copies of a difference signal used to apply the noise reduction

technique is the same as that for single-ended signals. The alignment between the two polarities of a

differential signal however, may need to be much tighter. How closely aligned the two polarities need to be

depends on the slew rate of the differential signal. You need to align the two polarities close enough to

achieve an acceptable amount of common mode rejection by the subtraction of the two digitized signals.

Vertical Scale

The vertical scale used for jitter measurements should maximize the signal’s displayed vertical size to

minimize the measurement error contributed by the oscilloscope’s voltage noise. It shouldn’t be so large

however, that adds jitter from aliased harmonic distortion. Harmonics that fall above the Nyquist frequency

can fold back down to lower frequencies with random phase variations, causing jitter. Some harmonic

distortion can be tolerated, but not large amounts from digitizer hardware clipping for example.

Note that not all displayed

waveforms that clip the display also

clip the digitizer. In the example of

Figure 6, the square wave signal is

correctly maximized without clipping

the digitizer. The same signal

however, clips the display after a

bandpass filter has been applied to

it. For this reason, it is best to adjust

the signal’s vertical scale with all

post-acquisition filtering disabled.

It is not necessary for vertical scales

or offsets to be the same for all

channels used in noise-reduced

measurements. It is best to optimize

each signal’s vertical scale settings

individually.

Figure 6. Example showing that optimum vertical scaling can

sometimes cause the displayed signal to clip the display. m1:

digitized clock signal, m2: same clock signal after applying post-

acquisition bandpass filter

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Phase Noise Setup

Phase noise measurements are enabled and

configured using the Phase Noise Setup

dialogue menu, which is accessed from the

[Analyze][Measurement Analysis (EZJIT)…] pull-

down menu. The Phase Noise Setup dialogue

menu, shown in Figure 7 has two Source

controls. Selecting signals for both source inputs

will automatically cause the phase noise

measurement to use noise reduction. Otherwise

(Source 2 = none), a conventional phase noise

measurement will be performed on Source 1.

Noise-reduced phase noise measurements can

be performed on a pair of signals acquired during

a single acquisition, or they can be performed on

a collection of multiple pairs of signals acquired

over many acquisitions. When using multiple

acquisitions, the Number of Correlations control

allows you to aggregate the phase noise results

using averaging, cross-correlation or a

combination of both. Setting the number of cross-

correlations to 1 will cross-correlate the two

sources once per acquisition and then average

that result with all the previous results. Setting Correlations to a larger value will cross-correlate results from

new acquisitions together until the specified value is reached. Then that cross-correlated result will be

averaged with all previous cross-correlated results. You can also specify a very large value which will never

be reached so that all acquisitions are cross-correlated together. The reason you may choose to limit the

number of cross-correlations is that until all the uncorrelated phase noise from the two sources has been

removed, cross-correlating will lower (in dBc/Hz) the phase noise trace, but it will not make it smoother.

Averaging will make the phase noise trace smoother but will not remove the uncorrelated noise.

Here's a helpful hint when averaging or cross-correlating with a large number of acquisitions. Stop any

continuously running acquisitions prior to making any oscilloscope configuration changes. The Infiniium

oscilloscope software architecture was written to respond quickly to user interface actions, but many

interface interrupt requests cause the analysis to abort immediately and clear all accumulated results. You

can still add a marker or measurement during the middle of a long multiple-acquisitions measurement. To

do so, press Stop, wait for the currently computation to finish, make your change, then press Run to

continue. Note that the Single button only performs single acquisitions and cannot be used to append a

new acquisition to previous ones.

Figure 7. Phase Noise Setup dialogue menu.

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TIE Setup

Enable a cross-correlated TIE measurement by opening the [Measure/Mark][Add Measurement…] setup

window and applying a XCorr TIE measurement to a pair of measured waveforms. Enabling a TIE

measurement measures the waveform’s TIE and reports the measurement statistics in a window at the

bottom of the screen. To display the results as a measurement trend waveform, open the

[Analyze][Measurement Analysis (EZJIT)…] setup window and check the Trend box.

The Cross-Correlated TIE Setup dialogue menu is shown in Figure 8. As with phase noise measurements,

selecting signals for both source inputs will automatically cause the XCorr TIE measurement to use noise

reduction. Otherwise (Source 2 = none), a conventional TIE measurement will be performed on Source 1.

Recall that the length of the digitized waveform’s time range affects the frequency content of TIE

measurements. Longer acquisition time ranges include lower frequency content than do shorter time

ranges. Section Correlations Versus Time Range below, explains that increasing the acquisition time range

improves the amount noise reduction achieved per acquisition, but that it also changes the frequency

content of the measurement. The Time Range control in the XCorr TIE Setup menu allows you to control

the time range of the acquisition and the time range of the measured TIE trend independently. That allows

you to remove more uncorrelated noise without adding lower frequency content. When the Time Range

control is set to a value less than the acquisition time range, then the total acquisition time range is divided

into multiple measurement time range segments, computed separately and then cross-correlated together.

The XCorr TIE Time Range’s automatic setting, simply tracks the acquisition time range.

Figure 8. Cross-Correlated TIE Setup dialogue menu.

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Figure 9 demonstrates what the XCorr Time Range control does. In this example, the XCorr Time Range

control was initially equal to the acquisition time range of 2 us, and the TIE trend from a single acquisition

was saved in memory 2, (m2). Next, the acquisition time range was increased to 100 us and the XCorr

Time Range was allowed to increase with it to 100 us. The TIE trend from this acquisition was saved in

memory 1, (m1). Finally, the XCorr Time Range was reduced to a manual value 2 us, while the acquisition

time range remained at 100 us, (mt).

You can see in this example, how the XCorr Time Range control allows you to achieve more noise reduction

for a desired measurement time range.

One feature of the XCorr TIE measurement you may find confusing at first, is that the XCorr TIE’s Std Dev

value reported in the measurement results window can sometimes be considerably smaller than the

standard deviation of the XCorr TIE trend waveform. Refer to the example of Figure 9 again. The standard

deviation of the TIE trend waveform, ACVrms(mt) is reporting 690 fs rms, while the Std Dev value for XCorr

TIE(1,3) is only reporting 210 fs rms. As explained in section Correlations Versus Time Range below, the

rms value reported in the Std Dev column for XCorr TIE(1,3) benefits from more uncorrelated noise

reduction than the TIE trend waveform does.

Figure 9. Demonstration of the XCorr TIE Time Range control.

m2: XCorr TIE trend of 2 us acquisition with XCorr TIE Time Range set to automatic

m1: XCorr TIE trend of 100 us acquisition with XCorr TIE Time Range set to automatic

mt: XCorr TIE trend of 100 us acquisition with XCorr TIE Time Range set to 2 us.

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How it works

The Math

Here’s a simple explanation of how cross-correlation removes measurement error. This explanation is

simplified in that it describes the computation of the standard deviation of a random variable, C, in the

presence of measurement errors, A and B. Infiniium’s calculations of TIE and phase noise are slightly more

complicated, but the noise reduction mechanism is the same. Consider a random variable, C of which we

want to determine its standard deviation. Since standard deviation is directly related to variance by a square

root function, the following description will refer only to the variance calculation and leave the conversion

to standard deviation to the reader. It will also assume all random variables have a zero mean to simplify

the formulas. Ideally, we’d measure a set of individual values of C, and then compute its variance using the

following formula:

𝑣𝐶 = 𝐸[𝐶2] =∑ 𝐶𝑖

2𝑁𝑖=1

𝑁 − 1

In real life however, we can’t measure C directly because our measurement device adds its own error, A.

So, all we get to calculate is the variance of C+A. Given the measured values, 𝑀 = 𝐶 + 𝐴, the formula

below shows how the presence of A corrupts our desired measurement of C.

𝑣𝑀 = 𝑣𝐶+𝐴 = 𝐸[(𝐶 + 𝐴)2] = 𝐸[𝐶2 + 𝐴2 + 2𝐶𝐴] = 𝐸[𝐶2] + 𝐸[𝐴2] + 𝐸[2𝐶𝐴]

9Consider the three terms in the right-hand portion of the above equation when C and A are uncorrelated

to each other. The first two terms, 𝐸[𝐶2] =∑ 𝐶𝑖

2𝑁𝑖=1

𝑁−1 and 𝐸[𝐴2] =

∑ 𝐴𝑖2𝑁

𝑖=1

𝑁−1 both sum to positive, non-zero values

because A2 and C2 are always positive. The last term, 𝐸[2𝐶𝐴] =∑ 2𝐶𝑖𝐴𝑖𝑁𝑖=1

𝑁−1 however, sums to zero because

A and C don’t always have the same sign and the sum of their product eventually approaches zero as the

sample size increases. So, when C and A are uncorrelated, the variance of their sum becomes.

𝑣𝑀 = 𝑣𝐶+𝐴 = 𝐸[𝐶2] + 𝐸[𝐴2]

Now, consider measuring C using two independent measurement devices. One device adds an

uncorrelated random error, A and the other device adds an uncorrelated random error, B. This time, we’ll

use the following equation to calculate the variance of C.

𝑣𝑀 = 𝐸[(𝐶 + 𝐴)(𝐶 + 𝐵)] = 𝐸[𝐶2 + 𝐶𝐵 + 𝐴𝐶 + 𝐴𝐵] = 𝐸[𝐶2] + 𝐸[𝐶𝐵] + 𝐸[𝐴𝐶] + 𝐸[𝐴𝐵]

In this case, all three error terms in the right-hand portion of the equation above average to zeros because

A, B and C are all uncorrelated. This leaves only the desired error-free variance of C in our measurement

result. Like magic!

𝑣𝑀 = 𝐸[𝐶2] = 𝑣𝐶

Note that this noise reduction technique does not remove all of the oscilloscope’s measurement error. It

only removes the error that is uncorrelated between the two measurements, such as pre-amplifier voltage

noise. It does not remove low-frequency phase noise that is present on the oscilloscope’s timebase clock.

Because that single timebase clock is split and distributed to both channel’s digitizers, it’s jitter is common

to or correlated between both measurement channels.

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Noise Reduction Versus Sample Size

This noise reduction technique doesn’t remove all the error instantly, but rather reduces the error with

increasing sample size, similar to averaging. This means that there can be a measurement accuracy versus

measurement time trade-off. If necessary, you can increase the number of waveform acquisitions or

increase the waveform record size to improve the amount of noise reduction. Every 10-times increase in

the amount of measurement data analyzed will reduce the residual uncorrelated errors by another -5 dB.

Correlations Versus Offset Frequency

Consider phase noise measurements. Single-

sideband phase noise measurements are

normally plotted using a logarithmic horizontal

scale. This makes their frequency resolution, and

hence their effective noise bandwidth increases

logarithmically with increasing frequency along the

X axis. As the effective noise bandwidth increases

each phase noise data point becomes comprised

of increasingly more statistically-independent

information. Infiniium’s noise reduction technique

uses this increasing information to apply more

cross-correlations to the higher offset frequencies

than the lower ones at a processing advantage of

an additional -5 dB noise reduction per decade of

offset frequency.

Figure 10 shows how more uncorrelated noise is

removed from higher offset frequencies than from

lower offset frequencies. In this simulation

example, a jitter-less clock is measured with a

single acquisition, using two digitizers that each have 1 ps rms jitter. The red trace did not use the noise

reduction technique. You can see that its phase noise, comprised entirely of measurement error, is a

constant -144 dBc/Hz. The blue trace was computed from the same simulated data but used the noise

reduction technique to compute the result. You can see that the measurement error at low offset

frequencies starts at -145 dBc/Hz but then decreases at -5 dB/decade for higher offset frequencies.

Correlations Versus Time Range

For each waveform acquisition of a cross-correlated TIE measurement, Infiniium cross-correlates the

individual TIE trend of each digitized channel together and then cross-correlates each cross-correlated TIE

trend waveform with the previous ones. So, as you would expect, the uncorrelated noise in the TIE trend

waveforms is reduced at a rate of -5 dB per 10X increase in accumulated acquisitions. See Figure 11. It

shows a simulation applying the noise reduction technique to a jitter-free signal using two independent

oscilloscope channels that each have 1 ps rms of jitter error. The simulation compares 1, 10 and 100

acquisitions. You can see that the standard deviation of the TIE trend waveforms, std(TIE trend) decreases

at a rate of about -5 dB per 10X increase in the number of acquisitions.

Figure 10. Simulation results showing increased

noise reduction at higher offset frequencies. Red:

measurement error is constant versus offset

frequency without noise reduction; blue:

measurement error decreases at higher offset

frequencies with noise-reduction.

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Learn more at: www.keysight.com

For more information on Keysight Technologies’ products, applications or services,

please contact your local Keysight office. The complete list is available at:

www.keysight.com/find/contactus

This information is subject to change without notice. © Keysight Technologies, 2018, Published in USA, December 10, 2018, 5992-3576EN

Calculating the standard deviation of the

TIE trend waveforms is a valid method of

determining the TIE’s rms jitter, but it’s not

the best method. Infiniium takes

advantage of the independence of each

data point in the TIE trend waveform and

computes the rms value of the TIE trend

using additional cross-correlation across

all points in the record.

Notice that Infiniium’s reported rms value

for each case, TIErms is about 10 times

lower than the standard deviation of TIE

trend waveforms. That’s because

Infiniium also cross-correlates all 10,000

individual points in the TIE record

together, for an additional -20 dB of noise

reduction.

Conclusion

Oscilloscope users have tried a variety of techniques to measure jitter on clock signals which is lower than

can be measured directly by the oscilloscope. The most common technique being to measure the

oscilloscope’s baseline voltage noise and then subtract the amount of error it probably added to the

measured jitter. This subtraction is only effective however, if the oscilloscope’s measurement error doesn’t

exceed the clock’s actual jitter. Also, the noise measured at the oscilloscope’s baseline isn’t always the same

amount of noise as the oscilloscope actually adds to the measured clock signal. That’s because the signal’s

voltage traverses a large portion of the oscilloscope’s input voltage range. Keysight’s new noise reduction

technique is significantly better than previous techniques because it doesn’t make assumptions. It directly

computes the results in a way selectively eliminates measurement error contributions that are unique to each

oscilloscope input channel.

Figure 11. Simulation comparing the noise reduction achieved

by cross-correlated TIE measurements using increasing

numbers of acquisitions. std(TIE trend) is the standard

deviation of the TIE trend waveforms. TIErms is the reported

rms value computed by cross-correlating all points within each

trend together. Red: 1 acquisition, Blue: 10 acquisitions,

Green: 100 acquisitions.

Documents

Noise Reduction in Jitter and Phase Noise … › us › en › assets › 7018-07012 › ...Noise reduction on differential signals requires two copies of the difference signal. The