Jitter is a short-term variation in the timing of a digital signal from its nominal value. There are two main types of jitter, random jitter and deterministic jitter. Random jitter is unbounded, that is its value continues to increase with increasing measurement duration. Random jitter is associated with stochastic processes like noise. Deterministic jitter is bounded, and its amplitude is limited with increasing observation time. Deterministic jitter is further broken down into periodic jitter, data dependent jitter and bounded uncorrelated jitter (BUJ).

Let’s start with a measurement of clock jitter. The clock in question is a 133MHz clock with an amplitude of 150 mV and a 50% duty cycle. It is connected to the oscilloscope using 50 Ohm coupling to match its source impedance. **Figure 1** shows the clock waveform as it appears on the oscilloscope.

**Figure 1 **The 133 MHz clock with measurements of time interval error, period and rise time including measurement statistics.

The oscilloscope’s measurement parameters are used to quantify jitter. The two commonly used parameters are period and time interval error (TIE).

Period measures the time between the closest edges with the same slope. The TIE parameter measures the time difference on a data edge from its ideal position. TIE can be thought of as reporting the instantaneous phase of the data stream. TIE requires a knowledge of the data stream’s clock rate. This can be entered explicitly, or the oscilloscope can determine it during the TIE setup.

In the example measurements of the clock period, time interval error, and rise time are taken over many thousands of acquisitions. Measurement statistics displayed show the last value measured, the mean or average value, the minimum value, the maximum values, the standard deviation (sdev), and the number of measurements included in the statistics. This oscilloscope records every instance of a measurement. For the waveform shown each acquisition contains five complete cycles and seven rising edges so there are five period measurements and seven TIE and rise time measurements per acquisition.

The standard deviation is a statistical figure of merit that shows the spread of the measured values about the mean. The calculation takes the measured value (x_{i}), subtracts the mean (m), this essentially shows the instantaneous period jitter. This difference is squared. The average value of the squared differences over the total number of measurements (N) is computed and then the square root of the average is taken.

The standard deviation is a good figure of merit for the period or TIE jitter associated with this clock signal. In fact, it is the root mean square (rms) of the period or TIE jitter. The difference between the maximum and minimum values is the peak-to-peak jitter of the selected parameter.

Note the difference between the rms jitter for TIE and period. This difference is expected because TIE measures a single waveform edge while period measures the difference between two edges. In a case like this where the jitter on each edge is random and assumed independent the jitter in the period measurement is the quadratic sum of the jitter on each edge. We would expect the period jitter to be about the square root of 2 time the TIE jitter.

The rise time measurement is added in order to ensure that the oscilloscope’s sampling rate is high enough to clearly define the clock signals edge. At a minimum there should be more than two samples on the edge. In order to have two samples on the 1 ns rise time the sampling rate should be greater than 2 GS/s.

The short, 50ns, record used in this measurement can show variations in jitter at frequencies of 20MHz or higher.

In order to match the jitter with possible sources at lower frequencies it is necessary to acquire a longer data record. This should be done while maintaining the oscilloscope’s sampling rate at a fixed value. The example used a sample rate of 10 Giga Samples per second (GS/s) as the horizontal scale was increased to 50ms per division as shown in **Figure 2**.

** Figure 2 **Increasing the duration of the acquisition by increasing the acquisition memory length to 5 Mega samples the horizontal scale increases to 50ms per division. This permits jitter variations down to 2 kHz to be measured.

A horizontally expanded zoom trace, Z1, is used to see a portion of the waveform at the original 5ns per division as well as the actual acquisition. Even with this long acquisition the TIE, period, and rise time of each cycle in the acquired clock signal is measured. The standard deviation of the period remains at 5.2ps and that of TIE remains at 3.8ps.

The choice of using TIE or period measurements for the clock jitter is usually determined by the standard the user is testing to. Period based jitter measurements are generally used for qualifying clock signals. TIE can be used for either clock or data signals.

The icons beneath each measurement show the histogram of the measured values. Clicking on that icon will enable the histogram to be displayed in a math trace as shown in **Figure 3**.

** Figure 3 **The histogram shows the distribution of measured TIE values. The shape of the distribution is related to the source of the jitter.

The histogram plots the number of measurements with values within a narrow range of values called a bin. In this example the histogram is using 2000 bins spaced uniformly over 50 ps so each bin is approximately 25 fs in width. The shape of the histogram is related to the source of the period jitter. The bell-shape of the TIE values is characteristic of a Gaussian or normal distribution. This type of distribution is associated with random processes such a noise. The histogram can be quantified using histogram parameters, in this case the histogram mean, standard deviation, and range have been used. The blue lines on the histogram are parameter markers showing where the measurement for each parameter is being made. For this Gaussian distribution 68 percent of the measured values are within ± 1 standard deviation of the mean as shown in the figure. The lower the standard deviation to closer to the mean the measured values are distributed.

The final tool in the basic jitter analysis toolbox is the track function. The track function plots every measured value versus time. Track is time synchronous with the source waveform so that every point on the track occurs at the same instant as the measured edge or cycle that produced that value. Any periodic variation in the measured jitter will show up on the track function. In **Figure 4** the track function of TIE is added to the display.

** Figure 4 **The track function shows the variation of the TIE measurement over time synchronous with the acquired waveform in channel C1.

The vertical scale for the track function of TIE is in units of time and shows the instantaneous deviation from the ideal edge location for each cycle of the acquired waveform. In this example the track is flat because the jitter is random noise with no noticeable periodicity. The track is more interesting if there is periodic jitter as shown in **Figure 5**.

** Figure 5 **Measuring a clock with both random and periodic TIE jitter components. The track displays the time varying periodic component.

Adding a 47kHz sinusoidal component to the clock jitter changes the histogram to a bimodal shape. The histogram of the sine wave is saddle shaped and it is convolved with the bell shape of the Gaussian distribution to form the bimodal shape observed. The separation of the peaks is proportional to the amplitude of the periodic jitter component. The track function reveals the shape of the sinusoidal jitter component added to the random component. A boxcar smoothing function applied to the track function (blue trace in math trace F3) overlaid on the track, attenuates the noise due to the random jitter component and shows a smoothed version the sinusoidal jitter component. Measurement parameters P7 and P8 read the frequency and peak-to-peak amplitude of the extracted periodic component, 47 MHz with an amplitude of 20 ps peak-to-peak.

We’ve made some basic measurements of clock jitter using jitter measurement tools available in an oscilloscope. These measurements, with some alterations can be used to measure jitter on data signals as shown in **Figure 6**.

** Figure 6 **Jitter analysis of an NRZ data signal uses the parameter time interval error. The same tools used for analyzing clock jitter are applied to measure jitter on the data stream.

A non-return to zero (NRZ) data stream clocked at 133 MHz is the source of this analysis. The oscilloscope settings remain the same with a 500ms acquisition window sampled at 10 GS/s. The zoom trace shows part of the PRBS 7 data. Unlike the clock waveform the data waveform does not have a uniform period making the period parameter incorrect for jitter analysis. As in the case of measuring clock jitter data jitter will use the standard deviation of the TIE parameter as a measure of the rms jitter. In this measurement the standard deviation of TIE is 3.9 ps. The mean value of the TIE jitter is only 3 fs meaning that the jitter mean is close to zero.

As in the case of clock jitter the histogram and track tools provide additional insight. The histogram is centered on zero as expected from the mean of the TIE parameter. The histogram range is 36 ps and is also symmetric about zero. The track function basically shows a random variation about a mean of essentially zero. The overlaid boxcar filter output shows a small 4 ps peak-to-peak variation even with no periodic jitter. This is the results of data dependent jitter associated with the data stream. This is a form of deterministic jitter associated with the data pattern.

If periodic jitter is added to the data stream, we see a similar result to what was observed with the clock jitter as shown in **Figure 7**.

** Figure 7 **The analysis of jitter on an NRZ data stream with random and periodic jitter components. Data dependent jitter is also present.

The addition of the periodic jitter element caused the jitter histogram to become bimodal as was observed in the clock jitter case. The track function shows a distorted sinusoidal waveshape of the periodic jitter component. This is different from what occurred when the periodic component was added to the clock waveform.

The distortion is due to the addition of data dependent jitter which is related to the data pattern. All of these components are contained in the standard deviation of the TIE measurement.

Basic jitter measurements start with the timing parameters TIE and Period. Parameter statistics provide readouts of rms and peak-to-peak jitter. Histograms of the parameters provide insight into the type of jitter and its distribution. Finally, the track function helps to identify periodicities in the jitter. The jitter measurements are taken over a number of measurements reported by statistics “num” field in most cases less than 10^{8} values.

Most oscilloscopes offer more advanced jitter analysis or serial data analysis software providing extrapolation of the measured jitter values and modelling jitter out to 10^{12} measurements and beyond. They also provide eye diagram displays with associated eye analysis. These features are generally needed for serial data compliance measurements.

*Arthur Pini** is a technical support specialist and electrical engineer with over 50 years experience in electronics test and measurement.*

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