SAR converter applications.
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converter absorbs the computational
overhead of the digital filtering function, there is a slight
variation for digital output to digital output. The accuracy of
the digital output code is affected by the cumulative noise at
the time of the conversion. This noise can be generated by
the circuit and injected into the A/D converter through the
input pins, reference pin or power supply connections.
Alternatively, the noise can also be generated by the device
itself. Effective resolution is defined as the statistical stan-
dard deviation (Vrms) of multiple conversions. A sample
size of 256 was used to characterize the ADS121x family of
products. Smaller sample sizes are also appropriate.
Although noise is a random event and any amplitude is
theoretically possible, the occurrence of each output over time
can be reliably predicted with the Gaussian distribution statis-
tical model. When the rms value is multiplied by twice the
crest factor, a peak-to-peak equivalent can be computed. The
Gaussian distribution, shown in Figure 1, illustrates that the
likelihood of large values decrease with increased magnitude.
The probability of exceeding a value above the rms (one
standard deviation) can be anticipated with a crest factor
(peak/rms). Peak-to-peak values can be predicted with a 2x
crest factor. Figure 1 illustrates the probability of a specific
output deviation for the average output vs the 2x crest factor
multiple. For instance, with an effective resolution of 1碌Vrms,
the probability of a sample exceeding
鹵2.625碌V
(2x crest
factor = 5.25) from the average output is 0.01. If a 2x crest
factor of 6.6 is applied, the probability of the output exceeding
鹵3.3碌V
of the average output is 0.001.
P-P NOISE CALCULATIONS FROM RMS
1.0
0.1
1
3
4
Probability of Higher Peaks
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
0.00000001
0.000000001
2
3
4
5
6
7
8
9
10
11
12
2x Crest Factor (Vp-p/Vrms)
FIGURE 1. When converting rms noise to peak-to-peak
noise a crest factor can be used as a multiplying constant
which predicts the probability of peaks occurring beyond the
peak-to-peak noise calculation.
AB-120
漏
1997 Burr-Brown Corporation
1
Printed in U.S.A. September, 1997
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