How to convert sensor volts or counts to a physical value?

Data Acquisition Systems (DAS) convert volts to counts but what does that mean physically? Say you have a DAS connected to an accelerometer-type sensor. The spec sheet for the accelerometer is 1 g = 2.6 volts. The DAS spec is 420,000 counts = 1 volt. So if the counts is 420,000 that represents 1 volt or 1/2.6 g. More generally the physical value is:

Acceleration (g's) = counts X (volt/count ) X (g/volt)

So if the reading is 200,000 counts, the value in g's is:

200,000 X (1/420,000) X (1/2.6) = 0.183 g

The conversion a sensor does from a physical quantity to volts is termed the "sensitivity" of that sensor. The same with a DAS, from volts to counts is the sensitivity of the DAS. A pressure sensor may have a sensitivity of P volts/psi (English pressure unit, pounds/sq. inch) or Pascal (Pa), metric, (Newtons/sq. Meter). If you know the sensitivities of the sensor and DAS you can easily find the actual physical value.

What's this dynamic range stuff, anyhow?

Dynamic range refers to the ratio of the largest to the smallest signal recordable, expressed in dB (decibels). Each 20 dB is a factor of 10 and each 10 dB is a factor of 3. So if an accelerometer has a range of 4 g and a dynamic range (DR) of 70 dB, the noise floor is 4g/3000 = 1.3 mg. This means that signals below 1.3 mg will be below the noise floor and not visible. The cost of an accelerometer increases with its DR, so it is not economical to specify an accelerometer with a greater dynamic range than the smallest signal of interest. Calculated the other way, if the smallest signal of interest is 4 mg and the range needed is 4 g, the DR is 20log(4.0/0.004) = 60 dB. It is prudent to add to this number about 10 dB of "headroom", so a 70 dB accelerometer would suffice.

Note: Bob Pease who died in 2011 ran a column in
Electronics Design magazine where he addressed basic issues in electronics, especially linear. The headline in his columns always was, "What's this —— stuff, anyhow". Rest In Peace, Bob!