LeCroy DDA 7 Zi series, Руководство оператора

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WavePro 7Zi
435
WP700Zi-OM-E-RevA
Where in both cases we explicitly incorporate the transition density[This is the ratio of transitions between bit
values to the total number of bits (so upper bounded by 1) but normally about 0.5 for standard test patterns and,
in particular, for PRBS patterns. See white paper from LeCroy on this subject.] , since the purpose of the alpha
factor is to calculate
Tj , and transition density is required for this purpose (since jitter is only pertinent for bit errors
that have transitions).
Application of Error Function to Measured Jitter CDF
(on Q-scale)
There is a notion in science of “preferred coordinates.” The notion goes a bit like this: “a physical-mathematical
relationship can be most simply expressed when the coordinates of the problem are well chosen.” An example is
Kepler's Laws. When expressed in the usual Cartesian coordinate system, those laws are rather obscure; but,
expressed in polar coordinates, they are quite simple.
The problem of analyzing the EDF in order to predict a CDF is best served by a coordinate transformation for the
variable BER.
The subject of Q-Scale has been proposed and described by several sources[Fibre Channel – Methods for Jitter
and Signal Quality Specification – MJSQ, T11.2 project 1316-DT Rev. 14, June 9, 2004
Jitter Analysis: The Dual-Dirac Model, RJ/DJ, and Q-scale, Ransom Stephens, Agilent Technologies white paper,
December 31, 2004] .
The desired transformation is to a new variable Q obtained from BER as follows:
The Cumulative Distribution Function, for a normal Gaussian is related to the error function in the following way
(see
graphic ).
The CDF being the function that provides the probability for an event (for a system obeying a Gaussian probability
density function) occurring to the left of the value x . Note also, by inspection:
The reason this is such an interesting (and thus preferred) representation for the CDF and EDF is that on this
scale the CDF of a Gaussian PDF is a straight line. When the CDF or EDF is of the modified symmetric form,
then their graphs appear as the upper lines of a triangle. Below is a plot of an EDF (simulation) for a Gaussian
PDF with a sigma of 1 picosecond.