for AZ you add caps in series to your ota input pair. the nodes connected between your ota pair and the az cap I will call internal inputs, the other node of the caps will be called the external inputs. in AZ mode you need to sample the offset onto these caps, to do this you will be removing your input caps and placing the az caps into your circuit as if they are the input caps. so you open the switches from your input (removing them from the circuit), close switches from the external inputs to cm (shorting inputs to cm) and close the switches between your internal input and your feedback caps( gives you a single sided equiv of integrating your cm, this will capture the difference of inputs on your input cap) You will see that on one side of the az caps you have cm voltage tied(same voltage potential), on other side, the internal input sides, you have isolated nets thats ideally are equal (your high impedance ac ground) these are your input offset sources. at this point you now have the caps sampling your offsets with respect to cm. then when you go to normal operation, you keep the az caps in series with the ota amp inputs, but change the feedback cap from internal input to external input(this puts the inverted az cap voltage in series with your input offset voltages canceling them out. The az references I have in books are for single ended only but you should be able to see how i expanded this to the full diff version i described. This would be Allen and Holberg CMOS Analog Design, just look up Auto Zero in the index.
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I'll anwser the last question before the middle stuff , cause tis easier and less thinking this morning, although offset is a bit of an unknown number until you get silicon, you know it is consistent. It will never change polarity in the use of the circuit, and under the same gain and feedback network it will not change in magnitude. Relying on this you can cancel it out by relying on the symmetry of a fully diff amp. since pos, neg input/output are switchable(as long as you switch the input and the output, you will not notice a difference in signal(except in the non symmetric offset). Thats the premisses of ping ponging the inputs and doing a double integrate. To do this you never do a sample per say, I will simplify this for easier passage of thought. 1st integrate your + input on side P with respect to - input on side N, then change your summing junctions and outs polarities of your amp with respect to the feedback networks (results in flipping the ota within the feedback network). Now that I think of it, I believe this is the common method for chopping.
The above is just a method for flipping the ota to cancel out offset, but you can do the timing 2 different ways. one way is to keep the timing and feedback caps the same across the board and accept you will be adding offset on 1 output and removing it with the next output, so your output steps would be out + vos, out - vos, out+vos, out - vos, etc. this makes your steps have a delta of 2 vos. but average to 0(net integration of vos =0)
If you want your steps to be equal as well as the net int being 0, you need to adjust the timing and the caps. half your input caps and integrate two times faster , and sampling your integrator every two integrates.
I would atm disregard my comments about the equation , I misunderstood something.
1 question though, it sounds like you are using such a tiny ratio because your inputs are so large. have you thought about using something other the cm as a reference? for example using cm + dV for pos reference and cm-dV for neg , where abs(-dv) = dv. this would give you gain reduction without having to use such large caps. (this is typically used in flash converters, for sizing signals).