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Learn how oscilloscope histograms help characterize component specifications by comparing propagation delay, mean, standard deviation, and measurement spread under different conditions.
Using Oscilloscope Histograms, Part 2: Characterize Product Specifications
Learn how oscilloscope histograms help characterize component specifications by comparing propagation delay, mean, standard deviation, and measurement spread under different conditions.
In Part 1 of this series, we looked at some of the basics of histograms and how they can provide a statistical view into random variation of signal parameters. Next, let's look at how histograms can help us use statistical analysis to determine product specifications.
Figure 1: A flip-flop's propagation delay is a typical spec that can be derived using statistical analysis
Many of Teledyne LeCroy's oscilloscopes are able to create statistical-analysis histograms on a very large number of measurements. The resulting data can be displayed as histograms (a graphical view of the data distribution), as trend plots (measurements plotted in the order taken, not time correlated to the current oscilloscope acquisition), or as track plots (measurements vs. time, time correlated to the current oscilloscope acquisition). As a result, the analysis capabilities of these instruments is extended to cover accurate readouts of up to 20 key statistical measurements such as mean, standard deviation, range, and many more.
One way to use these capabilities of an oscilloscope is to characterize the specifications of a component. Suppose you needed to verify the propagation delay of a D-type flip flop at both room temperature and at 0°C. Figure 1 shows the setup while Figure 2 depicts a propagation-delay measurement performed at room temperature.
Figure 2: At right is a histogram showing the distribution of over 46,000 measurements of the propagation delay of a 74HC74 D-type flip flop at 25°C
In Figure 2, the upper left-hand trace (Ch1) is the clock. Below that is the Q output (Ch2), while the right-hand trace (M1) is the histogram of the delay between positive-going edges of the clock and the Q output. The histogram shows the distribution of over 46,000 individual measurements. Meanwhile, the statistical parameters, histogram mean, and histogram standard deviation, displayed below the waveform display, provide a quantitative measure of the histogram itself. This data can be stored for later comparison when the exercise is repeated at 0°C.
Figure 3: A comparison of the propagation delay at 0° (at left in the lower trace) and at 25°C (to the right in the lower trace)
The next set of measurements, taken at 0°C, appears in Figure 3. Trace M1 contains the data taken at 25°C earlier. Trace F1, which appears above trace M1, shows that the propagation delay taken at 0°C has shifted to a lower value. The average value, or mean, has shifted from 130 ns to 127.7 ns as shown in the statistical parameter readings. In addition, the shape of the distribution has narrowed as indicated by the decrease in standard deviation from 355 to 318 ps. This shows a reduction in the spread of the measurement values. These represent only two of the possible choices for the analysis of parameter values (see below for a complete list).
This type of component characterization is quite useful in cases where the component manufacturer has not characterized the device under specific conditions required by a given application. Moreover, you have the ability to display and compare data taken at different times and under different conditions.
Available Statistical and Histogram Measurement Parameters
Besides the numerical measurement statistics provided for a typical measurement data set (mean, minimum, maximum, standard deviation and number of measurements), the histogram distribution itself may also be quantified with the following list of histogram parameters available on most Teledyne LeCroy oscilloscopes:
FWMH: Full width (of largest peak) at half of maximum bin
FWxx: Full width (of largest peak) at xx% of maximum bin
Hist ampl: Histogram amplitude between two largest peaks
Hist base: Histogram base or leftmost of two largest peaks
Hist max pop: Population of most populated bin in histogram
Hist maximum: Highest data value in histogram
Hist mean: Average of data values in histogram
Hist median: Median data value of histogram
Hist mid: Mid of peak-to-peak range
Hist minimum: Lowest data value in histogram
Hist mode: Data value of most populated bin in histogram
Hist pop@x: Population at a bin for specified horizontal location
Hist range: Difference between highest and lowest data values
Hist rms: RMS value of data in histogram
Hist sdev: Standard deviation of data values in histogram
Hist top: Histogram top or rightmost of two largest peaks
Hist X@peak: X-axis position of specified largest peak
Peaks: Number of peaks in histogram
Percentile: Horizontal data value that divides a histogram so that the population to the left is xx% of the total
Total pop: Total population in histogram
These measurements on the histogram itself can provide additional quantifiable context of measured behaviors that is not possible with more simplistic statistical data measurements.
Steve Murphy presented a webinar How to Use Statistical Data and Histograms in Your Oscilloscope. This webinar was Part 6 of the 2022 Oscilloscope Coffee Break Webinar Series. Click the button below to watch this webinar or any other webinar in that series, or download the transcript to preview the webinar content.
Steve is an Applications Engineer who most recently developed a remotely-accessible Test Engineering Lab. Steve’s 30-year Teledyne LeCroy career includes technical, marketing and sales roles. Steve enjoys bicycling, alpine skiing and camping.
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