LeCroy DDA 7 Zi series, Operator'S Manual

Page: 438 / 544

WavePro 7Zi
437
WP700Zi-OM-E-RevA
Automatic Renormalization of the Q-scale
This is the heart of the (patent pending) method for analysis of EDF, yielding best estimates of the underlying
PDFs defining the measured system’s behavior.
The procedure is straightforward: create the symmetric EDF for each side of the distribution.
The method can be described in steps as:
1. Forming a set of elements to be fitted, which are 3 values each, a vertical (Q-scale) value, a horizontal
coordinate (for the case of time variable jitter, but the method is extensible to vertical noise analysis or, in
fact, any variable), and an associated error. Statistically, the error of the input variable
n
is furnished as
the square root of the total population of observations (the same sum) contributing to the estimate (of EDF
in this case). Upper and lower values of BER are obtained for these variations, and an error inversely
proportional to the error is assigned to the data point.
2. Varying the Q-Scale normalization factor over a range of plausible values, the “best” fit to linear behavior is
determined.
3. Using this value to correctly scale the probability, an intercept (with Q
norm
(BER)=0 ) is obtained for both the
right-hand side and the left-hand side of the CDF(Q
norm
(BER) . This value may be interpreted as the mean-
value associated with the noise/jitter contributor with sigma equal to the reciprocal of the slope obtained
from the best linear fit, and amplitude (area) equal to the best normalization factor itself.
4. Under the assumption of symmetric noise/jitter contributions a single ideal normalization may be obtained
and used, however, ideally both extremes of the EDF must be treated independently, yielding strengths
(
norm
) and sigmas (reciprocal slope) to characterize the extremal behavior of each side of the EDF
distribution. In this case we show only an example of one side of the EDF.