Preliminary accuracy estimation for the voltmeter

It is time to make preliminary accuracy calculation before making the first PCB prototype.

Initially I had target of 100ppm year accuracy for the low accuracy version with off-the-shelf ADC and 20ppm for multi-slope ADC version. Lets see if selected components will fit into the sub 100ppm target.

The relative accuracy of the voltmeter is given as +/- percent of reading plus percent of the range. The reading corresponds to the gain error of the voltmeter and the range is related to the offset error. Because the voltmeter contain several components, the worst case error is the sum of all errors from each component, but if errors are uncorrelated, root sum square method can give more accurate estimation.

I will try to estimate the accuracy for one year period and for 10 °C temperature range between 18 and 28 °C.

The picture below shows all components contributing to the accuracy errors of the voltmeter:

The accuracy estimation is shown in the table below. I used the worst maximum values extracted from the datasheets of the components.
The accuracy of the LTC2057 op-amp is calculated twice : as input buffer and as buffer in front of the SPDT switch. The accuracy of the voltage divider resistors LT5400 is only calculated for the 20V range, because it is used only for this range. The gain error of the op-amps are calculated based on the open loop gain value. The gain error of the ADC is calculated when the offset is subtracted from the Full Scale Error (FSE).

		2V Range		20V Range
		Gain error, ppm	Offset error, ppm	Gain error, ppm	Offset error, ppm
LTC2057
	Offset		2.50		0.25
	Offset drift temp.		0.13		0.01
	Gain	0.18		0.18
LTC2057
	Offset		2.50		0.25
	Offset drift temp.		0.13		0.01
	Gain	0.18		0.18
LT5400
	Temp drift	0.00		10.00
	Long term year	0.00		2.00
LT1001A
	Offset		7.50		0.75
	Offset drift year		6.00		0.60
	Offset drift temp.		3.00		0.30
	Gain	3.33		3.33
LTC2440
	INL		5.00		5.00
	Offset		2.50		0.25
	Offset drift temp.		0.10		0.01
	Gain (FSE-Offset)	8.00		8.00
	Gain drift temp.	1.92		1.92
LTC6655
	Temp drift	20.00		20.00
	Long term year	20.00		20.00
		2V Range		20V Range
Accuracy		Reading, ppm	Range, ppm	Reading, ppm	Range, ppm
Using worst case method		53.61	29.35	65.61	7.44
Using root sum square method		29.65	12.04	31.35	5.12

Using the worst case method, I got ~83ppm for full-scale measurement for the 2V range and ~73ppm for the 20V range.

Using the root sum square method, I got ~42ppm for full-scale measurement for the 2V range and ~36ppm for the 20V range.

The actual accuracy can be reduced even more with the software calibration for the gain and the offset and only temperature drift and long term gain and offset errors will remain. 

Looking into the table data, the voltage reference will contribute the most for the gain error and the ADC buffer for the offset error, except for the 20V range, where the ADC INL is dominant.

Of course, the final accuracy shall be measured after one year usage of the voltmeter using a laboratory grade voltmeter or with voltage standard.