Introduction - LeCroy WavePro 7 Zi series Operator's Manual

Operator's Manual
Per model noise figures are supplied as a built-in database for each SDA oscilloscope, and a procedure for
updating the values for a specific oscilloscope channel and probe are provided.

Introduction

Jitter is an important aspect of signal integrity for both optical and electrical serial data streams (and clocks). The
SDA (serial data analysis) software is designed to measure the jitter and its components: random jitter (Rj),
deterministic jitter (Dj), data dependent jitter (DDj) duty cycle distortion (DCD), and periodic jitter (Pj). The SDA
uses a powerful method called "Normalized Q-scale Analysis" to estimate/measure the random and bounded,
uncorrelated jitter components. The following section presents the technical background underlying this method.
For the purposes of this discussion (in connection with jitter measurements[The "normalized Q-scale" method can
be applied to other statistical studies and measurements; in particular, for examining the nature of vertical noise
distributions.] ) the entire subject surrounds the matter of interpreting the observed distribution of timing errors.
This observed distribution is the histogram of Time Interval Error (TIE) values, obtained through analysis of either
clock or NRZ data waveforms acquired by a digital recording instrument (such as a digital oscilloscope).
A histogram is nothing more than a form of data representation that expresses the frequency of occurrence of
measurement values sorted or "binned" into adjacent, equal width contiguous intervals (or bins). When the timing
errors (TIE) are collected as a histogram, the histogram serves as an approximation to the Probability Density
Function (PDF) of this statistically based phenomenon (jitter). The PDF is (in theory) a smooth function
determined by the underlying physics of the measured phenomenon (and of course what we actually observe
includes the physics of the instrumentation as well).
The PDF is a continuous function, and reflects integrals of the probability (see
http://en.wikipedia.org/wiki/Probability_density_function) over each interval of measurement value, x.
That is to say, the density of probability as a function of the measured quantity when integrated over a given
region gives the probability that any measurement value will be within that region.
The process of forming a histogram is based upon a pre-specified set of bin boundaries (meeting the above
conditions of contiguity and equal width). A further constraint, which is usually unspoken, is that the histogram
range must cover all possible observation values if it is to be useful.
The set of observations (of measured quantity x) are "binned" or counted for each range of histogram bin. The
resulting histogram is a collection of populations (or counts) for each bin region.
Now a measurement histogram (like the one we will analyze to estimate jitter) represents a single experiment,
with some number of trials or individual TIE measured values. It is only an approximation of the PDF insofar as
the true PDF plays its probabilistic role and so is reflected in the resulting observations.
For this case (jitter) the observed distribution is the histogram of time interval error (TIE) values, obtained through
analysis of either clock or NRZ data waveforms acquired by a digital recording instrument (like a digital
oscilloscope).
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