# Two point calibration for analog signal chain

1- Question: How do you account for offset error if you do not consider the bottom 50 mv of FS?

2-Question: Suppose you need a resolution that ask LSB of 31.2mv ( 16 bit ADC, Vref 2.048 v) how you deal with that if you need to keep working with 16 bit, Vref 2.048 v ?

Thank you in advance for some help

• 16 bit resolution with 2.048 V reference gives 31.25 uV, not 31.25 mV. May 20, 2017 at 4:39
• @ The Photon , yes you are right I miss three zeros.Thank you. May 20, 2017 at 14:39
• "I must confess that I have learned a lot during that search", this is what many people miss when they ask lousy questions.
– pipe
Jul 26, 2017 at 11:57

Think about what a two point calibration means, you measure some parameter and read what ADC value you get, then do the same thing at another parameter value and draw a straight line between them (Which you then extend to 0 and full scale in a fit of optimism).

This implies an expectation of linearity, which is to say it implies an expectation that the line really is straight all the way.

Now real electronics near the rails is often not in fact all that linear, things start to saturate, gains fall, feedback starts to misbehave, maybe there is a small offset, maybe even your sensor becomes slightly non linear. If you take your cal points where all that stuff is going on then your entire calibration is off, even over the 90% or so of the range where those effects are minimal, if you cal at say 10 and 90% (or whatever makes sense) then you can still read (possibly somewhat inaccurately) over the full range but are less likely to have an error over most of the range.

Concrete example:

Lets say there is a temperature sensor that drives a 10 bit ADC, we measure a temperature T1 =24C with a calibrated reference instrument and get an ADC reading V1 = 150, measure temperature T2=100C and get a value of say 827 from the ADC, this constitutes input to our two point cal. A 10 bit ADC has a single ended range of 0->1023 so 150 is just a bit bigger then 10% of the range which is a reasonable cal point, 827 just a bit smaller then 90% of full scale so also a reasonable cal point.

Now, 24C = 150, and 100C = 827, so we can trivially calculate the slope, (100C-24C)/(827 - 150) = 0.1123 Celsius per ADC step.

Calculate the temperature that should give 0 on the ADC, which I make to be about 7 Celsius, and the full scale value which I make to be about 122 degrees.

Now those bits at the end of the scales assume things are linear, but they probably really are not (Which is why we try to keep the cal points away from the total extremes), so take with a caution.

Also notice that our ADC values are quantised, so are out cal points, the line is really an area touching the corners of the quatisation step at each cal point (A good reason to keep the cal points far apart).

• I saw in some App. Notes that for two point calibration of a signal chain (op amps and ADC) they use as calibration points a good ground reference in order to get the system offset and some value near FS range to get the correction gain, here you can see that : cypress.com/sites/default/files/inline/ui/2_5/images/blogs/… . So that how I can relate what you said for low end FS range with the fact that is necessary to ground the system input to get the offset? May 21, 2017 at 20:50
• You can use ground, and get an offset directly, but it stresses that assumption of linearity, so depending on the details of the circuit and the sensor it may or may not be a reasonable plan. If I know my signal conditioning electronics are in no danger of clipping and that I can make a reasonable assumption of linearity for my sensor at that operating point, then why not? If on the other hand I have something like a single supply rail to rail opamp in the signal conditioning doings, or a sensor that is voltage output and run from a single rail then I may wish to pick some other point. May 22, 2017 at 8:56
• @ The Photon would you be so kind to tell me how can I upload a PDF? I cannot find where it is explained. Thank you very much in advance. May 22, 2017 at 14:59