Analog Digital Converter accuracy, resolution and sampling rate

Accuracy related errors

The ADC have the following errors which decrease overall DC measurement accuracy:
gain and offset errors, integral non-linearity (INL), differential non-linearity (DNL) and noise.

The first two can be minimized by the software calibration, but the last three are hardware related and have to be consider when an ADC is selected.

Often in ADC data sheets is given Total Unadjusted Error (TUE) which represent the ADC’s worst error without applying any offset or gain error correction:
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TUE = √OffsetError² + GainError² + DNL² + INL²

The noise level usually is reduced with oversampling, digital filtering or averaging.

ADC resolution

ADC resolution is given by number of bits. The minimum absolute resolution is calculated for each voltage range by the following formula:

Min resolution = Voltage range / 2^Bits

Example:

Min Resolution = 10V / 2²⁴  = 10 / 16777216 = 0.000000596 V ( ~ 0.6 uV )

Sampling rate

ADC needs time to convert the analog value into digital one which is give in the datasheets as sampling rate. It can be fixed or selectable depends on particular ADC implementation.
The value of the sampling rate can be several samples per seconds up to several thousand per seconds. The more is the sampling rate, the ADC resolution is decreasing.

Selection of ADC

For voltage measurements usually are used sigma delta ADC integrated circuits or discrete integrated ADC for high end voltmeter where high linearity is desired.

For the first prototype, I selected LTC2400 ADC which is 24 bits with 7.5 samples per seconds. 2.5 voltage reference will be used. The ADC's parameters are shown in the table below. The high accuracy version will use discrete integrated ADC which should will give better linearity.

Parameter Name	Relative value	Absolute value peak to peak
TUE	5 ppm (typ) from the Vref	12.5 uV
INL for Vref = 2.5V	2 ppm (typ) from the Vref	5 uV
DNL calculated via TUE	2.2 ppm (typ) from the Vref	5.45 uV
Offset error	0.5 ppm (typ) from the Vref	1.25 uV
Offset error drift	0.01 ppm/°C (typ) from the Vref	0.025 uV
Gain error	4 ppm (typ) from the Vref	10 uV
Gain error drift	0.02 ppm/°C (typ) from the Vref	0.05 uV
Noise		4.24 uV
Estimated ADC error budget worst case  after offset and gain calibration : INL+DNL+5°C Offset/Gain Drift+Noise		~15 uV