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very accurate gain adjustment

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fala

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hi, to expand the dynamic range of voltage measurement and to get better resolution I want to use a gain stage before a 16 bit ADC. I need 2x, 10x, 100x gains. output of ADC are fed to a computer program to draw a graph. one problem I've encountered before is to adjust gain very accurately and sustainable. so when for example voltage increases in 100x range and ADC reaches its upper limit, It needs to go to 10x range and I want to read exactly 1/10 previous value so data seems coherent to user.
first from analog point of view, I need the opAmp gain be exactly 100 with less than 3x10^-6% error-so I can get less than 150uV(16 bit ADC LSB) Error in ±5V range in worst case(I know this is impossible) , realistically how much I can approach that goal and what do I need?
second as I think it is impossible to reach the above goal, software needs to correct the gain and offset error with appropriate coefficients. but how should I get thoes coefficients, should I use a multiplexer and connect a precise reference to one channel and then try to read reference with different gains at startup and calculate offset and gain coefficient for each gain? has anybody encountered a similar problem how did you solve that? thanks.
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IanP

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In application where high precision is required you will have to employ instrumentartion amplifier .. see pictures below (examples only!!!) ..

To adjust gain you will need good quality CMOS switch ( ADG78X with Ron≈2Ω; https://www.analog.com/en/prod/0,,768_833_ADG783,00.html ) as standard switches have Ron well above 10Ω ..
Other option is to use reed switches, and their contact resistance is in mΩ range, usually below 200mΩ ..

In automatic meters quite often the procedure is like this:
At first the lowest gain is selected; if signal is below certain level, say, 10%, the gain is increased by one level up .. and so on ..

At this stage I wouldn't spend time on "offset error and coefficients" ..
If necessary, you can address this issue later ..

Regards,
IanP
 

    fala

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