Electronic – Isolate low power i2c ADC

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.

There is virtual zero benefit in using differential inputs for your application. Assuming the sensor is close to the uC, you'll be able to get almost identical results from either single ended or differential, +/- a couple LSB.

The real benefit of differential signals is in long cable runs and noisy environments, for increased common mode rejection. They're also very useful in instrumentation, when dealing with very small signals. A common way to deal with sensors that vary their resistance in small amounts, such as strain gauges and pressure cells, is to use a Wheatstone Bridge.

^{simulate this circuit – Schematic created using CircuitLab}

This configuration by itself centers the measurement in the ADC span. \$V_+-V_-=V_{differential}\$ It's important to match the default resistance as close as possible. Any deviation from the default resistance will show up as offset in the measurement.

Again, this is done because:

1. the changes in resistance are very small
2. more often than not, the sensors are far away from the data acquisition and processing equipment