Scientific data loggers
 
About dynamic range

How to select the right product for your application

This document will help you to decide which features are required for your application.

  • Data loggers
What has to be known for the right decision:
    • LSB: the smallest voltage increment that can be measured by the digitizer. It is defined as the maximum voltage amplitude divided by the largest quantifiable value by the A/D converter . Example: with a +/-5V maximum excursion, the LSB for a 24bit AD converter is 10/224=596nV.
    • Dynamic range: the theoretical definition of the dynamic range of an A/D converter is given as the ratio of the power of a full scale sine wave versus the power of the shortened input noise. For a regular successive approximation converter with a LSB of amplitude q, the statistical digitization noise power is q2/12. If N is the number of bits of the converter, a full scale sine wave power is given by (2N-1 *q)2/2.
r=(q2/12)/((2N-1 *q)2/2)

After some trivial simplifications, 10*log10(r) is:

Dyn= 6.02*N + 1.76 dB

This formula can then be used to compute the dynamic range of any converter even when the notion of quantization LSB disappears i.e. when using a sigma-delta converter. If the shortened input noise power is measured and the maximum excursion is known, then the dynamic range can be computed and the number of equivalent bits can be obtained using the above formula. A perfect 24bit converter has a dynamic range of 146dB.
Using the variance of the signal recorded on the shortened input as a measure of the noise power at a given sampling rate, one can deduce the dynamic range at that frequency.
    • Selectable gain: in some particular cases, selectable gains may be usefull to take into account the variability of the maximum excursion expected for different sensors. Note that software selectable gains always add noise since more electronics is involved in the analogical circuitery.
    • Full scale span of the sensor: as mentionned earlier, the full scale span of the sensor, or the maximum excursion will determine the appropriate LSB (and maximum input span)..
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