# Multifunction DAQ

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## Accuracy of the difference of two measurements

Usually there are two specifications for the accuracy of a measurement, that is linearity error (in percentage of reading) and offset (absolute value or percentage of range). My questions is about how two measurements are correlated. Is the offset error for both measurements (at different input values (voltage, current or else)) the same? This would mean calculating the difference of the two measurements would eliminate the offset and the linearity error is the same as for one measurement. Or is there no correlation, than the offset error of the difference (assuming a statistical distribution for the offset error) would be sqrt(2)=1.41 times higher than the offset of one measurement (the same for the linearity error)? Calculating worst case the error would be 2 times higher)
My current setup is measuring two voltages (V1,V2) and two currents (I1,I2) and calculating the value (V1-V2)/(I1-I2). As accuracy is crucial here, the answer to that is important for me.

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## Re: Accuracy of the difference of two measurements

Hello, manfroe. What do you want to measure? There is a little error in every measurement, so no one can say that the error is the same. If you calculate the difference between two measurements returns you less error than before.

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## Re: Accuracy of the difference of two measurements

Hello Vazgen_H,

maybe in other words: When I measure two values (current or voltage) with the same device do errors compensate or not? For example the first value has an offset error, as well as the second one. Are both offsets equal and compensate? That would mean that the difference between both values has no offset error. Or both offsets are different (in the worst case off1 = -off2) then the error will not compensate and the difference of both values has an offset error of 2*off1. The same applies for the linearity error.

In a statistical view: if the offset errors do not correlate (and follow a random distribution) the standard deviation of both errors can be added geometrically and result in:  sqrt(2) * stddev(off1).

If the offsets are equal (correlation =1) the error of the result is 0 (full correlation).

Usually ADCs are used for such measurements and they compensate their offsets internally, but still some error remains, that is noise. For a single measurement this noise looks like a small offset error. When I calculate the difference between two measurements both offsets (due to noise) are not correlated and can not compensate.

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## Re: Accuracy of the difference of two measurements

No one can guarantee you, that offsets are the same.

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## Re: Accuracy of the difference of two measurements

That's depend what module do you use, read the offset in the datasheet. If it satisfies you, then ok, if not, try to use another module.

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## Re: Accuracy of the difference of two measurements

It is not a question, if the offset is satisfying me. I need to know the accuracy of the complete measurement result (V1-V2)/(I1-I2), which is only a part of a complete tolerance chain. Furthermore I do not decide, which device is used, so I have to live with the given equipment. For the current clamp (from a different supplier) I got all these answers. Nevertheless thank you for helping me.

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