Teledyne LeCroy AORM - Advanced Optical Recording Measurements - Manual (Page 105)

AORM Software Package
923133 Rev A ISSUED: June 2013
103
THEORY OF OPERATION
An understanding of statistical variations in parameter values is needed for many waveform
parameter measurements. Knowledge of the average, minimum, maximum, and standard
deviation of the parameter may often be enough, but in many other instances a more detailed
understanding of the distribution of a parameter’s values is desired.
Histograms provide the ability to see how a parameter’s values are distributed over many
measurements. They divide a range of parameter values into sub-ranges called bins. A count of
the number of parameter values calculated (events) that fall within its sub-range is maintained for
each bin.
While the range can be infinite, for practical purposes it need only be defined large enough to
include any realistically possible parameter value. For example, in measuring TTL high-voltage
values a range of ±50 V is unnecessarily large, whereas one of 4 V ±2.5 V is more reasonable. It
is this 5 V range that is subdivided into bins. And if the number of bins used were 50, each would
have a sub-range of 5 V per 50 bins or 0.1 V/bin. Events falling into the first bin would then be
between 1.5 V and 1.6 V. The next bin would capture all events between 1.6 V and 1.7 V. And so
on.
After several thousand events, the graph of the count for each bin (its histogram) provides a good
understanding of the distribution of values. Histograms generally use the X-axis to show a bin’s
sub-range value, and the Y-axis for the count of parameter values within each bin. The leftmost
bin with a non-zero count shows the lowest parameter value measurements. The vertically
highest bin shows the greatest number of events falling within its sub-range.
The number of events in a bin, peak, or histogram is referred to as its population. The next figure
shows a histogram’s highest population bin as the one with a sub-range of 4.3 to 4.4 V, which is
to be expected of a TTL signal. The lowest value bin with events is that with a sub-range of 3.0 to
3.1 V. Because TTL high voltages need to be greater than 2.5 V, the lowest bin is within the
allowable tolerance. However, because of its proximity to this tolerance and the degree of the
bin’s separation from all other values, additional investigation may be desirable.
Teledyne LeCroy DSO Process
Teledyne LeCroy digital oscilloscopes generate histograms of the parameter values of input
waveforms. But first, the following must be defined:
• The parameter to be histogrammed
• The trace on which the histogram will be displayed
• The maximum number of parameter measurement values to be used in creating the
histogram
• The measurement range of the histogram
• The number of bins to be used
Once these are defined, the oscilloscope is ready to make the histogram.