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 Figure 7. Phase Noise Setup dialogue menu. 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.

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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. 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.

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.

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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:

∑푁 퐶 2 푣 = 퐸[퐶2] = 푖=1 푖 퐶 푁 − 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, 푀 = 퐶 + 퐴, the formula below shows how the presence of A corrupts our desired measurement of C.

2 2 2 2 2 푣푀 = 푣퐶+퐴 = 퐸[(퐶 + 퐴) ] = 퐸[퐶 + 퐴 + 2퐶퐴] = 퐸[퐶 ] + 퐸[퐴 ] + 퐸[2퐶퐴]

9Consider the three terms in the right-hand portion of the above equation when C and A are uncorrelated ∑푁 퐶 2 ∑푁 퐴 2 to each other. The first two terms, 퐸[퐶2] = 푖=1 푖 and 퐸[퐴2] = 푖=1 푖 both sum to positive, non-zero values 푁−1 푁−1 ∑푁 2퐶 퐴 because A2 and C2 are always positive. The last term, 퐸[2퐶퐴] = 푖=1 푖 푖 however, sums to zero because 푁−1 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.

2 2 푣푀 = 푣퐶+퐴 = 퐸[퐶 ] + 퐸[퐴 ]

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.

2 2 푣푀 = 퐸[(퐶 + 퐴)(퐶 + 퐵)] = 퐸[퐶 + 퐶퐵 + 퐴퐶 + 퐴퐵] = 퐸[퐶 ] + 퐸[퐶퐵] + 퐸[퐴퐶] + 퐸[퐴퐵]

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!

2 푣푀 = 퐸[퐶 ] = 푣퐶

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 Figure 10. Simulation results showing increased offset frequency. noise reduction at higher offset frequencies. Red: measurement error is constant versus offset Figure 10 shows how more uncorrelated noise is frequency without noise reduction; blue: removed from higher offset frequencies than from measurement error decreases at higher offset lower offset frequencies. In this simulation frequencies with noise-reduction. 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.

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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 Figure 11. Simulation comparing the noise reduction achieved reduction. 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. 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.

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Find us at www.keysight.com Page 13 This information is subject to change without notice. © Keysight Technologies, 2018, Published in USA, December 10, 2018, 5992-3576EN P a g e