LeCroy oscilloscopes, employing parameter histogram, have the capability of performing statistical analysis histograms on up to 2,000,000,000 measurements and displaying this data as histograms, trends plots (measurements in the order taken), or track plots (measurements versus time).

Statistical parameters, included with these scopes, extend the analysis capability, offering accurate readouts of up to 20 key statistical measurements such as mean, standard deviation, range, and many others.

Consider how an engineer could use these features to characterize the specifications of a component. Suppose, for example, we 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 and 2 illustrates a propagation delay measurement performed at room temperature.

Figure 1:

The propagation delay of a flip-flop is a typical specification that can be characterized by statistical analysis

The upper lefthand trace (Channel 1), in figure 2, is the clock, the trace below that (Channel 2) is the Q output, and 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. The statistical parameters, histogram mean and histogram standard deviation, displayed below the waveform display, provide a quantitative measure of the histogram. This data can now be stored for later comparison and the experiment repeated at 0°C.

Figure 2:

: A histogram showing the distribution of over 46,000 measurements of the propagation delay of a 74HC74 @ 25°C

The result of the next set of measurements is shown in figure 3.

Figure 3:

Comparing the propagation delay at 0°C (at the left in lower trace) and at 25°C (to the right in the lower trace)

Trace M1, contains the data taken at 25°C which was previously shown. Trace F1 shown above M1, shows that the propagation delay taken at a temperature of 0°C has shifted to a lower value. The average value (mean) has shifted from 130 ns to 127.7 ns as indicated in the statistical parameter readings. In addition the shape of the distribution has narrowed, as indicated by the decrease standard deviation from 355 to 318 ps, indicating a reduction in the spread of the measurements. These represent only two of the possible choices for the analysis of parameter valuest. The complete list of available statistical parameters is shown in the accompanying table.

This is a simple example of how histograms can be used to characterize component or unit specifications under selected conditions. It is extremely useful in applications where the manufacturer has not characterized the device in exactly the way required by your application. Note also the ability to display and compare data taken at different times and under different conditions. This total integration of measurement, display, and analysis is a hallmark of LeCroy oscilloscopes.

Histogram Parameters

FWMHfull width (of largest peak) @ half of maximum bin
FWxxfull width (of largest peak) @ xx% of maximum bin
Hist amphistogram amplitude between two largest peaks
Hist basehistogram base or leftmost of two largest peaks
Hist max poppopulation of most populated bin in histogram
Hist maximumhighest data value in histogram
Hist Mean average of data values in histogram
Hist medianmedian data value of histogram
Hist midMid of peak to peak range
Hist minimumlowest data value in histogram
Hist modedata value of most populated bin in histogram
Hist pop@xPopulation at a bin for specified horizontal location
Hist rangedifference between highest and lowest data values
Hist rmsrms value of data in histogram
Hist sdevstandard deviation of the data values in histogram
Hist tophistogram top or rightmost of two largest peaks
Hist X@peakx-axis position of specified largest peak
Peaksnumber of peaks in histogram
PercentileHorizontal data value that divides a histogram so that the population to the left is xx% of the total
Total poptotal population in histogram