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You are working with a ref derived from Vdd, so Vdd needs to be quiet. Your
lsb = ~ 1.2 mV. So look at Vdd and Vref bypassed for an indication of how much
noise you will be digitizing.
Some other considerations -
1) You have a R-C settling time associtaed with mux, its C, and A/D input C.
Using standard exponentials you can calc setting time to 1 lsb and see if
its satisifactory.
2) If your are having nosie related problems, consider shutting off as many digital
peripherals as you can while you are doing SAR conversions and mux switching.
Painful but sometimes prudent. Especially any operations switching pins with a lot of
load current, like an LED, or C load.
3) You can always do signal averaging, but that is most effective when noise
is white, not correlated. UP based noise generation tends to be highly correlated.
Food for thought.
Regards, Dana.
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