## How to Measure Jitter

Continuous advances in high-speed communication and measurement systems require higher levels of performance from system clocks and references. Performance acceptable in the past may not be sufficient to support high-speed synchronous equipment. Perhaps the most important and least understood measure of clock performance is jitter. One of the main challenges with jitter measurements is that there are currently no industry standard methods established. There are multiple variables to consider, from what test equipment is used to what the actual test conditions are. While JEDEC standards do provide definitions and suggested test conditions, there is a lack of consistency between measurements from different testers.

In this post, we will describe various practical methods of measuring jitter, including the relevance and ease of each method. These test methods are the basis for how all jitter measurements are conducted at Vectron.

There are three components that remain consistent for all forms of jitter testing: the device under test (DUT), a reference oscillator, and a power supply. Previously we have discussed how a clean power supply (in our PSR post) is to accurate testing, but the reference oscillator is a vital component for the test setup, as the equipment measuring the DUT needs to have a better noise floor than the DUT. Otherwise the performance of the DUT will be degraded by the noise of the equipment.

Standard measurement equipment (oscilloscopes, counters, signal source analyzers) contain an internal TCXO/OCXO, and for most timing devices these are sufficient. Vectron’s test equipment uses a low phase noise OCXO, locked to an external 10MHz Rubidium clock which is in turn locked to a GPS receiver.

**Time Domain Jitter Measurements**

Oscilloscopes are the main device used for time domain jitter measurements. Oscilloscopes allow for the easy viewing of waveforms and pulses, and are considered indispensable for any time and frequency lab. While there are many vendors who can offer jitter measurement test packets, they are often provided at an additional cost. An oscilloscope that is high-speed (1GHz+) and has a high sampling bandwidth (10GS/s+) should be sufficient to gather the desired data. We also need to recall that time domain jitter measurements (specifically period and cycle-to-cycle) are random and expressed in terms of mean value and standard deviation over a number of samples. JEDEC standard 65 requires a minimum of 1000 samples, but a 10,000 sample minimum is preferred by most applications.

**Period Jitter**

Although the official definition of period jitter is the difference between a measured clock period and the ideal period, in real world applications it is often difficult to quantify what the ideal period is. If we observe the output from an oscillator set to 125 MHz using an oscilloscope, the average measured clock period may be 7.996 nS instead of 8 nS. Therefore, it is more practical to treat the average observed period as the ideal period, and is a common practice by timing device manufacturers. The standard procedure for measuring period jitter involves randomly measuring the duration of one clock period 10,000 times, and using the recorded data to calculate the mean, standard deviation and peak-to-peak values. Due to the random nature of period jitter, the peak-to-peak values can vary greatly, and often times period jitter needs to be re-calculated several times to come up with an average value.

Below is an example of period jitter measured on a Wavecrest SIA-3300C signal integrity analyzer for a 200MHz XO. This analyzer platform is setup to measure 30,000 samples at a time, and is executed three times in order to obtain an average peak-to-peak value.

**Cycle-to-Cycle Jitter**

Measuring cycle-to-cycle jitter is very similar to measuring period jitter, but with one additional step. The standard procedure for measuring cycle-to-cycle jitter involves randomly measuring the duration of two clock periods 10,000 times, and taking the absolute difference between the two. The recorded data is used to calculate the mean and standard deviation values, and the peak value is simply the largest difference in periods observed. As with period jitter, the peak-to-peak values can vary greatly, and often times cycle-to-cycle jitter needs to be re-calculated several times to come up with an average value. Some digital oscilloscopes have a histogram feature, which simplifies a lot of the math.

Below is an example of cycle-to-cycle jitter measured on a Lecroy Waverunner 610ZI Digital Oscilloscope for a 50MHz XO. In this case, a jitter measurement tool, assigned to P8 and labeled ‘dper’, is used to calculate the cycle-to-cycle jitter. This analyzer platform is setup to measure 30,000 samples at a time, and is executed three times in order to obtain an average peak-to-peak value.

Measuring TIE jitter is very difficult with only an oscillator. Typically, a histogram is necessary to plot the measurement values against the frequency of occurrence of the measurements. An example of a jitter histogram for a TIE measurement is shown below. In this case, the continuous variable is mapped into 500 bins, and the total population of the data set is 3,200,000. The mean value of TIE is theoretically zero, and as can be seen in this measurement, the mean value is 0 nsec. For this plot, the distribution is approximately Gaussian with a standard deviation of 1.3 psec.

**Frequency Domain Jitter Measurements**

Whereas time domain measurements are handled primarily by an oscilloscope, frequency domain measurements are handled primarily by a signal source analyzer (SSA). Most SSA’s have a very low noise floor (-180dBc/Hz), and have integrated cross-correlation techniques that further reduces the test system noise. Cross-correlation essentially cancels noise by taking the vector sum of the measurement results of two independent measurement channels.

For measuring phase noise, Vectron prefers using the Agilent E5052B. The 5052B includes two independent PLL paths with two built-in reference sources that are uncorrelated with each other (there is also an option for an external reference source). If two signals are uncorrelated, their vector sum, meaning the total noise power from the reference sources taken through vector averaging, lowers the system noise floor by canceling the noise from its internal reference sources and other related circuits, while the noise signal from the DUT is emphasized. This allows for fast and user-friendly testing, with the main downside being that only one device can be tested at a time. The E5052B can also calculate the integrated noise over a desired range (see example below, measuring from 12kHz to 5MHz), and calculate the integrated phase jitter.

If one does not have a signal source/spectrum analyzer that can calculate the jitter by itself, any analyzer with a decent noise floor can be used to calculate the frequency domain phase jitter and integrated period jitter using the formulas below:

$latex \phi_{rms}[rad]=\sqrt{\int^{f_2}_{f_1}S_\phi(f)df}&s=1$

*RMS Noise (radians)*

$latex \phi_{rms}[deg]=\frac{360}{2\pi}\sqrt{\int^{f_2}_{f_1}S_\phi(f)df}&s=1$

*RMS Noise (degrees)*

$latex pj_{rms}[sec]=\frac{2}{2\pi\mu_0}\sqrt{\int^{f_2}_{f_1}S_\phi(f)df}&s=1$

*Integrated Period Jitter (seconds)*

As an example, these formulas were used for the same part displayed above, and only using data points 4-7, we were able to calculate RMS phase jitter of 10.0468 degrees and an integrated period jitter of 178.611fs, as compared to the E5052B’s results of 10.1156 degrees and 179.834fs. There are also several free web tools that can calculate these values based off of inputting the data. Vectron in the past has used the Jitter Labs application to confirm the measurements of our test setup.

Tags: Jitter, Oscillator, Phase Noise

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