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Understanding the Q-Factor Results
The variable decision threshold method used by the Output Levels
measurement makes it possible to determine the Q-factor of a signal.
N O T E
The Q-factor method and the related calculations have been published under Margin
Measurements in Optical Amplifier Systems by Neal S. Bergano, F. W. Kerfoot, and
C. R. Davidson in IEEE Photonics Technology Letters, Vol. 5, No. 3, March 1993.
Mathematical Background
Bit errors are caused by noise, and the Q-factor describes the signal-to-
noise ratio at the decision circuit.
It is possible to calculate the Q-factor from a limited number of
measured BER vs. threshold data points. It is also possible to calculate
expected bit error rates from the Q-factor. This is a method for
predicting very low bit error rates (typically below 10
-11
) that would take
a long time to measure.
The Q-factor is calculated as:
where
μ
1,0
is the mean level of the 1 and 0 rails, respectively, and
σ
1,0
is
the standard deviation of the noise distribution on the 1 and 0 rails.
The
μ
1,0
and
σ
1,0
values are calculated from a selected range of data
points. This calculation is correct if the noise distribution has Gaussian
characteristics. Then, the bit error rate can be expressed as:
where D is the decision threshold,
μ
1,0
and
σ
1,0
are the mean and
standard deviation of the 1 and 0 rails, and erfc (x) is the
complementary error function.
This formula is the sum of two terms. It considers the probabilities of
deciding that a "0" has been received when a "1" was sent, and that a "1"
has been received when a "0" was sent.
For the following calculations, the assumption is made that the BER is
dominated by only one of the terms noted above, depending on whether
the threshold is closer to the 1 or 0 rail.
For the complementary error function
5
Advanced Analysis
216
Agilent J-BERT N4903 High-Performance Serial BERT
Содержание J-BERT N4903
Страница 1: ...S Agilent J BERT N4903 High Performance Serial BERT User Guide s Agilent Technologies...
Страница 68: ...2 Setting up Patterns 68 Agilent J BERT N4903 High Performance Serial BERT...
Страница 158: ...4 Setting up the Error Detector 158 Agilent J BERT N4903 High Performance Serial BERT...
Страница 314: ...6 Evaluating Results 314 Agilent J BERT N4903 High Performance Serial BERT...
Страница 374: ...7 Jitter Tolerance Tests 374 Agilent J BERT N4903 High Performance Serial BERT...
Страница 394: ...8 Solving Problems 394 Agilent J BERT N4903 High Performance Serial BERT...
Страница 434: ...Index 434 Agilent J BERT N4903 High Performance Serial BERT...