Measuring output of op-amp current shunt circuit using ADC

Question

This is my first post here, so I hope I have done it correctly.

I am rather new to analog circuits, so undoubtedly I've overlooked something.

Here is what I want to do: Using a 24-bit LTC2400 ADC, with a precision voltage reference I want to read the output of an op-amp current shunt, the value of which is anywhere from 0mV to about 800-900mV. Since I want to be able to measure low voltage AC currents (isolated), and DC currents, both of which have the potential to output negative values. ADCs don't like negative values. How do I convert the negative part of the sine-wave to a positive part with good accuracy? I'm looking for +-.01mV resolution, and +-.1mV accuracy or better.

Now that I've described the problem, I'll explain my circuit. the circuit is based on the EEVBlog µCurrent. However, I have changed a few things. The analog side will be powered by a rechargeable 3.7V LiPo, and values read by aforementioned ADC. The measurement side is completely isolated from the microcontroller side. The microcontroller is an 8-bit Atmel. Values are read over USB using a serial connection. All resistors will be the "precision" type. I'm using a voltage follower for the V-GND.

So here are my main questions summed up:

1. Does my schematic design look correct? Anything I can add to improve noise?
2. Is there a better option for an ADC? (I'm using the LTC2400 24-bit)
3. On the ADC, how should I connect the FO pin?
4. Best way to convert the negative part of a waveform to a positive one.

On that last note, here are some examples of this that I found online:

AC voltage measurement using Arduino: AC voltage detector

Biasing an AC voltage for input to ADC

I'm still confused though, hence why I'm asking here.

Here is my schematic; sorry if it's not clear. +3.7V = +Vbat, -3.7V = -Vbat, V Gnd = Virtual Ground:

Here is an assortment of datasheets:

uCurrent Page

ltc2400 datasheet

MAX14850 datasheet

ADR4520 datasheet

MAX4239AUT op-amp datasheet

Answer 1

The biasing approach is what you need to do - offset the signal such that a zero input is somewhere near to the mid-range of the A-D scale. You then subtract the reading you get with a zero input from the A-D during measurement, and have a signed value resulting.

You can use one of your op-amps to introduce the offset.

You have a shorting relay across the input you can use for the zero measurement, but I'd suggest you use the other contacts on that relay to clamp the signal down away from the shunt, or you'll be measuring the contact resistance if there's any current present.