LeCroy DDA 7 Zi series, Operator'S Manual

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Operator's Manual
WP700Zi-OM-E-RevA
434
And the complementary error function
But more importantly, the inverse error function erf-1(x) is the inverse function (neither reciprocal nor
complementary). This function gives the displacement x , for which a given value is the error function of that
displacement. (See http://mathworld.wolfram.com/InverseErf.html for more detail on the inverse error function.)
And
for -1< z >1
The figure below can help to put the general shapes of these functions in perspective. In particular, remember not
to confuse the complementary error function
(erfc) with the inverse error function ( erf
-1
).
The Relationship between the Inverse Error Function
and Total Jitter
It is noteworthy that the inverse error function has no closed analytical form. It is also noteworthy that the heuristic
jitter equation is linearly related to this inverse error function. Recall this equation:
Usually when this equation is presented, a qualifying remark might be "and the function (BER) is the number of
standard deviations for a Gaussian with sigma of 1, that corresponds to the specified bit error ratio (BER)." Now, it
turns out that
(BER) is to within a constant factor, exactly the inverse error function, erf
-1
(1-BER) . That is: