|Figure 1: Histograms of the period, width,|
and TIE of a clock waveform show
different distributions of time jitter
Statistical analysis gives us a window to the view we want of this random variation in our DUT's behavior. A particularly handy tool in this vein is histograms, which many oscilloscopes (including most Teledyne LeCroy models) can generate as a means of visualizing and quantifying random processes (Figure 1). The histogram display shows the shape of the distribution of parameter values. Associated statistical parameters provide accurate, yet concise, measurements of that distribution. From this data, we can learn quite a bit about our signal.
|Figure 2: This histogram shows a|
random, or Gaussian, distribution
of amplitude values
The distribution of measurement values shown in a histogram is related to the underlying process that generates the distribution. In Figure 2, we see an example of a random process that produces a Gaussian (or normal) distribution of amplitude values. The Gaussian distribution is a good indication that a random process is shaping variations in the measurement.
|Figure 3: The effect of passing|
Gaussian noise through
an envelope detector
|Figure 4: The uniform distribution|
of delay due to a timing synchronizer
In this example, note that the main distribution of the measured delay varies uniformly over a range of 2.5 ns as expected. However, a longer delay occasionally occurs, which shows up in the persistence display on Ch2 and as the secondary distribution in the histogram. By comparing the total populations of each section of the histogram, we find that the delayed event occurs 0.6% of the time. This highlights an advantage of the statistical study of measured data in that it quantifies rarely occurring events that might otherwise be overlooked.