Advertisement

Article

Verifying Jitter Measurement Accuracy

Jitter measurements are becoming increasingly important in the characterization and qualification of high-speed computing and communication systems. This is especially true with the recent proliferation of embedded-clock serial busses. As with all measurements, the question of accuracy must be answered.

This article proposes two methods that quantify the accuracy of oscilloscope-based jitter measurements. It describes a method to determine the measurement floor when measuring a jitter-free signal, and it describes a method to verify the absolute accuracy when measuring a signal with a known amount of jitter.

Match the Target Measurement

The accuracy of jitter measurements depends not only on the characteristics of the measurement system, but also on the characteristics of the measured signal and the type of jitter being measured. This means that the same measurement system, measuring the same signal will have a different accuracy when measuring period jitter than it does when measuring cycle-to-cycle jitter. It also means that a given measurement system will have a different accuracy measuring the same type of jitter on two different signals.

For example, voltage noise is typically the dominant source of error in jitter measurements. Since the voltage noise is converted to time jitter by the slope of the signal's transitions, a jitter measurement's accuracy depends on the slew rate of the signal being measured.

So, the trick to characterizing the accuracy of jitter measurements is to match the target measurement system and target signal characteristics, while measuring a known ideal source. Sinewave sources work well for this application because they are easily adjustable in amplitude and frequency and sources with arbitrarily low jitter are readily available.

The procedures described below measure the accuracy of a specific target jitter measurement on a specific target signal using a specific target measurement system. Therefore, it is often useful to perform the target measurement prior to measuring the measurement's accuracy. Performing the target measurement first helps identify the specific characteristics of the target measurement that are needed to perform the accuracy measurements.

Measuring Jitter Measurement Floor

Although some jitter measurements underestimate the true jitter value, most measurements overestimate it. This is because the dominant jitter measurement errors tend to be uncorrelated additive random processes, like jitter is itself. Specifying jitter measurement floor is one easy way to quantify the amount that a jitter measurement overestimates the true jitter value.

Jitter measurement floor (JMF) refers to the lowest value a jitter measurement would produce if it were applied to a perfect source that had zero jitter.

Be careful however, when applying a jitter measurement floor value that is published in an oscilloscope vendor's datasheet. The published value may or may not apply to your specific jitter measurement application. For example, if the error in your jitter measurement is limited by the voltage noise of the oscilloscope, and your signal's risetime is much faster than the risetime referenced in the datasheet, then your JMF will be considerably less than the value specified in the datasheet. Comparing the published JMF values from different vendors can also be problematic because they are typically not defined in the same way.

There are many types of jitter measurements and the procedure for measuring the JMF of each type can differ slightly. Follow these steps to measure the measurement floor of a period jitter measurement.

  1. Configure the measurement system to match that of the target measurement system.
  2. Determine the slew rate of the target signal. Note that an oscilloscope's built-in differentiate function can be useful for measuring slew rate.
  3. Determine the nominal period of the target signal.
  4. Connect a low-jitter sinewave source to your oscilloscope. Duplicate the target jitter measurement setup as much as possible. If the target jitter measurement will be made through a probe, then connect the sinewave source through the same probe.
  5. Set the initial input sinewave amplitude such that it fills approximately three vertical divisions on the oscilloscope display.
  6. Set the sinewave's frequency such that the sum of an integer number of its periods matches the period of the target signal, and the sinewave's slew rate approximately equals the slew rate of the target signal. This may take some trial and error. For real-time oscilloscopes, do not use sinewave frequencies that are larger than half of the oscilloscope's sampling frequency.
  7. Adjust the sinewave's amplitude until its slew rate equals the slew rate of the target signal.
  8. Measure the jitter of the sinewave at those threshold crossings that match the period of the target signal. Note that you may need to use a more general delta-time measurement feature in order to measure an integer number of sinewave cycles.

Figure 1 shows an example of a period jitter measurement floor measurement for a PCI Express application. The target signal to be measured is a 1.0 Vpp, 2.5 GHz clock signal with a nominal slew rate of 10 V/ns. In this example, two cycles of a 0.6 Vpp, 5.0 GHz sinewave are used to mimic the period and slew rate of the target PCI Express signal. The oscilloscope is configured to measure the time interval between two clock transitions that are two cycles apart. Measurement statistics are then used to calculate the standard deviation of a large number of these two-cycle time interval measurements.


Figure 1:  Example of measuring the jitter measurement floor of a period jitter measurement. The measured JMF = 900 fs rms.

The procedure for measuring the jitter measurement floor of a cycle-to-cycle jitter or n-cycle jitter measurement is very similar to that for period jitter. The value of n in the n-cycle jitter measurement must be multiplied by the number of sinewave periods used to represent one target signal period. Since two sinewave cycles are used to represent one target signal period, an n value of two would be used on the signal from the previous example.

The JMF results shown in Table 1 were all measured using the same input signal and measurement system as was used in the example of Figure 1 . Notice that the jitter measurement floor is different for all three examples above. They are different, even though they are measuring the same signal over the same time interval. These measurement floors differ because they are all calculated from different functions of waveform transitions. Time interval error for example, is calculated from the time variation of individual waveform transitions. Period jitter, on the other hand, is calculated from the difference between the time variations of pairs of transitions. Depending on the correlation between the transition pairs, the variation of their time difference may be larger or smaller than the variation of either of the individual transitions.

Jitter Type
JMF
Period Jitter 0.90 ps rms
Cycle-to-Cycle Jitter 1.52 ps rms
Time Interval Error 0.66 ps rms

Table 1:  Comparison of jitter measurement floor measurements of three different jitter types

Though this technique is simple and very effective in most applications, it does have limitations. It does not, for example, include the effects of aliasing. Nor does it include the frequency response flatness effects that appear when measuring non-periodic signals like data signals. In addition, some time interval error applications will calculate the time interval error of the test sinewave from more transitions than would be used in the calculation of the target signal over the same total time range. This difference can in some cases, overestimate the jitter measurement floor. Fortunately, this difference is rarely significant and can be avoided by calculating the time interval error value using external post-processing.

Subtracting-Out Jitter Measurement Floor

Subtracting the jitter measurement floor from raw jitter measurements is always tempting, and often effective, but be careful. Subtracting the variance of the measurement floor from the variance of the measured value, as shown in Equation 1 , only applies if the measurement errors are completely uncorrelated to the true jitter.

Also, as the magnitude of the measured value becomes closer to the measurement floor, the relative uncertainty of the reported value grows. This technique may allow you to report a smaller jitter value, but the relative uncertainty of this value may be greatly increased.

Measuring a Known Amount of Jitter

One approach to quantifying jitter measurement accuracy is to measure the jitter of a jitter-free signal, as previously discussed. Another approach is to measure the jitter of a signal that possesses a known amount of jitter. This second approach is important because not all sources of jitter measurement error increase the measured value. Some sources of error can also decrease the measured value.

This article suggests a method to verify a known amount of jitter that is similar to the method used to measure the jitter measurement floor. As shown in Figure 2 , a second sinewave source (error sinewave) is combined with the original sinewave source (carrier sinewave) using a passive power divider. The amplitudes and frequencies of the carrier sinewave and error sinewave should match those of the target signal and jitter you plan to measure. This measurement should be repeated using multiple error sinewave frequencies in order to represent the broadband nature of the target signal's jitter spectra.

Choosing the error sinewave frequencies that best match the target jitter measurement can be tricky. Many sources of jitter originate as additive voltage errors that get converted to time or phase errors by logic circuitry. This phase modulation process causes the original voltage error spectrum to be converted to sidebands around the carrier's fundamental frequency. A 1 MHz crosstalk signal, for example, would appear as a 1 MHz spur added to the clock signal if measured at the point of coupling. However, if the same corrupted clock were measured at a downstream point, where it had already been converted to phase error, it would appear as sidebands 1 MHz from the clock and its harmonics.


Figure 2:  Graphical representation of the connection used to check your jitter measurement against a known quantity of jitter.

The following procedure describes how to verify a time interval error measurement of a signal with a known amount of jitter.

  1. Configure the measurement system to match that of the target measurement system.
  2. Determine the slew rate of the target signal. Note that an oscilloscope's built-in differentiate function can be useful for measuring slew rate.
  3. Determine the nominal period of the target signal.
  4. Connect a carrier sinewave source to your oscilloscope through a power divider. Duplicate the target jitter measurement setup as much as possible. If the target jitter measurement will be made through a probe, then connect the carrier sinewave source through a power divider, and then to the same probe. Ensure that unused input of the power divider is terminated.
  5. Set the initial carrier sinewave amplitude such that it fills approximately three vertical divisions on the oscilloscope display.
  6. Set the carrier sinewave's frequency such that the sum of an integer number of its periods matches the period of the target signal, and the carrier sinewave's slew rate approximately equals the slew rate of the target signal. This may take some trial and error. For real-time oscilloscopes, do not use carrier sinewave frequencies that are larger than half of the oscilloscope's sampling frequency.
  7. Adjust the carrier sinewave's amplitude until its slew rate equals the slew rate of the target signal.
  8. Connect an error sinewave source to the unused connector of the power divider.
  9. Set the error sinewave's frequency such that it falls within the frequency spectrum of the jitter you expect to measure on the target signal.
  10. Adjust the error sinewave's amplitude such that it produces a magnitude of jitter that falls within the range of the jitter magnitudes that you expect to measure on the target signal.
  11. Measure the actual amplitudes of both sinewaves by disabling one source while measuring the other. The sinewave amplitudes must be measured at the input reference plane of the measurement system. Otherwise cable loss or other frequency response non-flatness may corrupt the measurement. For best results, a calibrated power meter should be used.
  12. Calculate the expected jitter by dividing the error sinewave's amplitude by the carrier sinewave's slew rate. Then convert this value to rms by multiplying by 0.707.
  13. Measure the jitter of the combined sinewaves at those threshold crossings that correspond to the threshold crossings of the target signal. For example, if two cycles of the carrier sinewave were used to represent one period of the target signal, then calculate the time interval error using every other carrier sinewave threshold. In most cases, the difference between the time interval error calculated from every threshold and that calculated from every other threshold will be insignificant.
  14. Compare the measured result to the calculated result.
  15. Repeat steps 9 through 14 for multiple error sinewave frequencies.

The magnitude of jitter that a particular amplitude of error sinewave will produce, depends on the type of jitter you are measuring. When verifying the result of a period jitter measurement for example, substitute Equation 2 for the expected jitter calculation in step 12 above,

where

Ae = amplitude of error sinewave

Mc = slew rate of carrier sinewave

Tt = period of target signal

Te = period of error sinewave.

Figure 3 graphs the results of verifying a time interval error measurement of a 3 GHz clock signal with an Infiniium 54855A oscilloscope. The input reference plane used for the verification was located at the end of a 2 m coax cable, to match the conditions used in the target jitter measurement. The amplitude and frequency of the carrier and error sinewaves used in the verification were chosen to match the target jitter measurement as much as possible. The jitter measurement floor (JMF) was not subtracted from the measurement results, but was also graphed for comparison.


Figure 3:  Comparison of measured jitter to expected jitter of period jitter measurement versus jitter frequency.

As you can see in the graph, the measured jitter is as much as 50% higher than the expected jitter at low frequencies and varies strongly with frequency. Hypothesizing that this discrepancy might be caused by the frequency non-flatness of the cable used to connect the device under test to the oscilloscope, the verification experiment was repeated without the 2 m cable. Frequency non-flatness can corrupt jitter measurements by attenuating the measured signal's fundamental frequency component differently than its jitter producing frequency components. Without the cable, the measured jitter matched the expected jitter much better, indicating that the target jitter measurement setup will need to be modified by moving the oscilloscope physically closer to the device under test.

This method of verifying jitter measurement accuracy also has its limitations. It too is more difficult to use for some time interval error applications. It also does not combine the intersymbol interference affects with non-periodic data signals. Nor does it include aliasing effects. It does however, provide a simple method to measure the accuracy of many common jitter measurements.

Technique to Measure Aliasing Affects

It is important to note that this two-tone technique will show the effects of aliasing on jitter measurement accuracy, when using error sinewaves that are higher frequencies than half the oscilloscope's sampling frequency. In fact, this two-sinewave technique provides an alternative method of measuring jitter measurement floor, which includes the dominant effects of aliasing. Simply set the carrier sinewave frequency equal to the same frequency as the target signal, and set the error sinewave frequency equal to three times that of the carrier frequency. Then, phase-lock the two sinewaves together, and adjust the phase of the error sinewave to match the phase of the carrier sinewave. Adjust the amplitude of the error sinewave to match the slew rate of the target signal.


Figure 4:  Example of measuring the jitter measurement floor of a period jitter measurement using the two-tone technique. The measured JMF = 774 fs rms.

Conclusion

Engineers provide value to their companies by making good decisions. The quality of their decisions is directly related to the uncertainty of the information on which they base their decisions. Yet engineers often make decisions based on measurements of which they do not know the uncertainty. It is critical that characterize the uncertainty of their jitter measurements.

The procedures proposed in this paper provide a simple means to characterize the accuracy of specific jitter measurements, using specific measurement systems, on specific signals. Therefore, engineers should no longer have to worry about the unknown accuracy of their jitter measurements or rely on published specifications from instrument manufacturers that don't apply to their applications. They should measure the jitter measure accuracies that apply directly to their specific applications.

About the Author
Steve Draving received his MSEE in 1987 and BSEE in 1985 from Kansas State University. He has designed oscilloscopes and logic analyzers for Agilent Technologies (Hewlett-Packard) since joining the company in 1987. He holds eight patents for timebase, trigger, and probe design.

0 comments on “Verifying Jitter Measurement Accuracy

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.