Oscilloscope persistence displays

Persistence displays retain waveform traces on the screen, allowing them to decay over a user set time duration, they allow users to see a history of signal variations on the screen. This feature is very useful if you are adjusting a signal, as it allows you to see the changes as they are made. Some oscilloscope applications require displaying a history of events in order to see how the signal varies over time. Persistence displays are key tools for viewing such signal changes as a function of time over multiple acquisitions. The most common applications that use persistence displays include jitter analysis of a serial data transmission and eye diagrams used for digital communications systems (Figure 1).

Figure 1 The persistence display of timing jitter on an edge. Multiple acquisitions are retained on the display of the edge to show the variation in its timing. Source Arthur Pini

 This is an analog persistence view of jitter on a clock edge, it is a monochrome display where the brighter areas are the more often occurring signal paths and the duller areas occur less often. The center area of the transition is brighter, meaning more edges pass at that time than during the times corresponding to the outer edges.

The same data can be viewed in color-graded persistence, a tool used to map the frequency of occurrence spectrally. Most frequent events appear in red while the least frequent events are shown in violet (Figure 2).

Figure 2 A color graded persistence display of the same edge jitter. The red areas occur more often than violet areas. Source Arthur Pini

The intermediate frequency of occurrence is mapped spectrally, from most to least often occurring as red-orange-yellow-green-blue-indigo-violet.

Multiple acquisitions are acquired and stored in a persistence map which shows signal variations over time. The persistence decay time is user-selectable with a time constant from half a second to infinite. A saturation control allows users to control the mapping of frequency of occurrence to intensity or color. 

Eye and state transition diagrams

Persistence displays also help analyze data communications signals, where they are used to display eye diagrams and state transition diagrams (Figure 3).

Figure 3 The eye diagrams of the I and Q components and state transition diagrams of a 16-QAM signal rendered in monochrome analog persistence. Source: Arthur Pini

The eye diagrams of a 16-QAM signal show the results of 12,890 acquisitions of the I and Q signal components, which are also cross plotted as an X-Y plot, forming the state transition diagram shown in the upper right corner. Again, the intensity variations are proportional to the amount of time a waveform falls on a particular point on the display. The highly repetitive elements of a signal are brighter than the rarely occurring signal events. The data states, which appear as horizontal lines in the I and Q traces, are written more often and show up brighter than the transitions, which take different paths and occur with less frequency at any given point. The same is true of the state transition diagram where the data states appear as bright dots and the transition paths have a lower intensity.

Persistence histograms

All the data behind the persistence display is available and can be used to quantify the acquired data statistically. One example is to generate a histogram from the persistence display. The oscilloscope used in this article has a function called persistence histogram, it lets the user define either a horizontal or vertical slice through the

persistence display and then forms a histogram as shown in Figure 4.

Figure 4 A persistence histogram with a horizontal slice of the jitter persistence display centered at a level of 0 mV with a width of 10 mV. Source: Arthur Pini

The persistence histogram appears in the trace below the persistence display. Cursors are used to mark the location where the histogram slice originates. In a vertical slice, each bin of the histogram contains a class of related amplitude levels. A horizontal slice, used in the example, produces a histogram where each bin contains a class of related time values.

In the example, the vertical axis of the histogram reads the number of times a specific horizontal pixel is hit. The peak of the histogram corresponds to the central area with a light blue color, while the falling sides correspond to the persistence display changing from indigo to violet. The histogram can be measured using the oscilloscope’s measurement parameters, the measurement parameters P1 through P3 beneath the display grids read the mean, the standard deviation, and the range of the histogram. Parameter help markers annotate the locations of these measurements on the histogram itself.

Persistence histograms can also be applied to eye diagrams showing the horizontal timing uncertainty as well as the vertical deviation (Figure 5).

Figure 5 Application of persistence histogram to an eye diagram permits analysis of noise and jitter on the eye. Source: Arthur Pini

The histogram in the center trace was taken from a horizontal slice through the eye crossing and shows the range of variation in the time of the crossings. The lower histogram was taken using a vertical slice centered between the crossings, it shows the uncertainty in the amplitude of the eye in the center. Some oscilloscopes may not offer measurements that quantify eye characteristics such as eye height and width, .these can actually be obtained using persistence histograms and their associated statistical measurements.

 Persistence trace functions

Persistence trace functions take the histogram of the persistence values over a number of vertical slices set by the user and extract the mean, standard deviation, and range of the persistence data at each slice. It then plots the extracted statistical parameter over time (Figure 6).

Figure 6 Examples of the persistence trace mean (second from the top), persistence trace sigma (third from the top), and persistence trace range (bottom) traces. Source: Arthur Pin)

The persistence trace mean function plots the mean value of the histograms at each of the user’s selected intervals. The resultant plot is the average value of the source persistence trace. In this example, the trace is taken from one thousand points along the persistence trace. This function shows the underlying waveform without vertical noise. Persistence trace sigma plots the minimum and maximum values of the standard deviation about the mean using an extrema plot. The plot shows mean + and – one standard deviation. This function provides a view of the rms noise on the source waveform. The persistence trace range plots the minimum and maximum values of the persistence histogram about the mean and shows the range of the histogram. It is the worst-case range of possible values, especially noise, at each point.

Persistence trace mean is the most useful of the functions allowing a quick determination of the average value of a persistence trace. It is also useful to smooth out traces acquired with low sample point counts (Figure 7).

Figure 7 The persistence trace mean shows all the possible states in waveform with a low sample count by retaining multiple acquisitions. Source: Arthur Pini

Waveforms with low sample counts, displayed with linear interpolation, may appear angular and discontinuous however they are not, and over multiple acquisitions, they trace a smooth waveform. Using persistence trace mean to view the waveform allows the persistence history to fill in the intermediate states and smooth the waveform, showing its actual structure.

3-D persistence display

Adding vertical height to a persistence display proportional to the rate of occurrence gives you a three-dimensional (3-D) effect. This 3-D persistence display creates a topographical view of your waveform.

As shown in Figure 8, this is most useful when studying X-Y plots of signals such as QPSK.

Figure 8 The in-phase and quadrature components of a QSPK signal and a three-dimensional persistence plot of a QPSK state transition diagram. Source: Arthur Pini

The three-dimensional plot retains the color or intensity coding of the persistence displays but adds height proportional to the frequency of occurrence of the display pixels. The shape of these peaks provides an alternative view of the frequency of occurrences in your signals. In this example, the data states of the signal which occur most frequently appear as the highest elements in the X-Y display and are coded in red. Transition paths have more variation and occur less repetitively. They are lower on the display and coded in yellow/green. Off path regions are at the bottom of the display, coded in violet. Controls allow for rotating the 3-D plot to view it from different angles.

The 3-D display can be rendered in three different qualities. The first is as a solid, as is shown, and is the default quality. It can also be rendered in the wireframe quality; this is constructed using lines of equal intensity to create the persistence map. The third quality is shaded, which is only available in monochrome persistence. Shaded quality shows the 3-D object as if it were illuminated by projected light, the shading emphasizes the shape of the object.

The value of persistence displays

Whether used to measure jitter, eye diagrams, or state transition diagrams, persistence is a valuable display technique. When combined with math persistence analysis tools and related measurements, it becomes a powerful tool for quantifying signal variations.

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

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