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

 FWMH full width (of largest peak) @ half of maximum bin FWxx full width (of largest peak) @ xx% of maximum bin Hist amp 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 the 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