Electronic – Inherent DC Bias in ADC sampling

Elementary, Watson. You sortof had the idea with #2, except that you don't want a negative gain but rather a gain between 0 and 1. In other words, you want to attenuate the 0-15 V input signal to match the input range of your A/D.

This is easily accomplished with two resistors in a "resistor divider" configuration. If your A/D has a native range of 0-5V, then you want to divide the input voltage by 3. This can be accomplished, for example, with 2K Ohms in series followed by 1K Ohms to ground.

Anything you do to a signal will always change it slightly. In this case, some of the high frequencies will be lost. However, at impedances of 10s of K Ohms, this won't be a problem with a sample rate of 1KHz or less. That implies a upper frequency limit of 500Hz maximum, rather less in practise. Even 100s of K Ohms used in the resistor divider should be able to pass such low frequencies without losing the part you care about.

It would be good if you characterised the signal from the pH probe. I've never used one so am not familiar with the type of signals they put out. I think they are a few mV and quite high impedance, but am not sure. I could look it up, but this is your project and therefore your job.

Let's assume you have a very high impedance signal to amplify, and the voltage range is +-100mV.

First, the 741 opamps you show are totally inappropriate. They have way too low input impedance. Please return them to whatever museum you found them in. There are plenty of good high impedance amps out there to chose from, but watch the input offset voltage.

As for the differential part, you have one side of the probe connected to ground, so you only have a single ended signal to start with. Ultimately you need a single ended signal if you're going to feed it into a microcontroller A/D. Some stand alone A/Ds can take differential signals in, but once you add your own amplification you will generally have a single ended signal anyway.

Your circuit only has a overall gain of 3 as shown. That would only result in 300mV peak if the input is really limited to 100mV. I expect the micro's A/D to want more than that for full resolution.

One characteristic of pH signals is that they are slow. This means you can apply significant low pass filtering, and can use a high resolution but slow A/D like a delta sigma type. These have enough resolution over the 100mV range that you don't need any amplification.

However, since pH probes aren't cheap and this is unlikely a high volume product, I'd make it easy on yourself. Get a decent instrumentation amplifier. These can be had with high input impedance, fixed and accurate gain, low input offset, and can generally level shift the result. A gain of 20 would give you a 4V output range, which should be about right for a 5V A/D. Level shift the output so that the 0 signal is at half the A/D range, and the rest is firmware.