
Bits, Noise, and Linearity; the Imperfections of ADCs
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Full scale range
What range of signals needs to be recorded? The electrical power grid may carry 60 kV at 120 kA, while a biological cell may have ion currents ~ fA at potential to a few μV. ADC boards typically have full scale ranges no bigger than ±15 V, but may have uni or bipolar settings and ranges as low as 10 mV. The number of bits one needs interacts with the range. Suppose a measurement is needed with a resolution of 10 μV. To ensure that one can see noise on top of this range, one least significant bit might need to be 1 μV. If one were using a unipolar ADC, at 12 bits full scale would have to be 2^{12} * 1 μV = 4.096 mV, a most unlikely combination. At 16 bits, full scale would be
2^{16} * 1 μV = 65.54 mV, still smaller than is common, but conceivable. But for a 24 bit converter, full scale would be 2^{24} * 1 μV = 16.77 V, bigger than any common range. So a real 24 bit converter would be used on the ±5 V range, with a least significant bit magnitude of about 10 V/2^{24} = 0.6 μV.






