Electronic – How to determine whether this is a “rail to rail” opamp from its datasheet

Since there is no resistor in series with the - input, you really are using the opamp as a comparator and the feedback resistor can be removed. Your circuit is a inverting comparator, BUT, its threshold level is 0 V since that's what you are feeding into the + input.

There are several things you need to do to fix this circuit:

1. Set the threshold voltage about halfway between the high and low voltage of the digital signal. Assuming the digital signal goes between power and ground of something like a 3.3 V or 5 V supply, all you need is a resistor divider. Connect around 10 kΩ between the digital supply and the + input, and another 10 kΩ between the + input and ground. This will float the + input at half the supply voltage, which we are assuming is the middle of the digital signal voltage range.

2. Make sure the opamp is properly powered. If you want the output to swing ±15 V, then the supply needs to be at least ±15 V. Most opamps that can take such a large supply range can't swing their outputs all the way to the supply rails. This headroom can be almost 3 V in some cases. Check the datasheet. The TL081 you show is known for having a rather large headroom.

   However, don't just blindly connect ±18 V or whatever power to the opamp. Check the datasheet to make sure you don't exceed the maximum supply voltage the opamp can tolerate. If your opamp can't handle enough to guarantee ±15 V out, then you either have to live with a smaller output voltage range or get a different opamp.

3. Lose R1. It does nothing useful. It could even hurt the digital output when swinging well past the digital supply range.

It sounds like you want to drive the LED roughly in response to the amplitude of the sum of the two audio signals. Making a signal that is proportional to the amplitude of another is called AM demodulation. There are various options for doing that. Such circuits have been around for a long time since they are fundamental to a AM radio receiver. Yours will run a much lower frequencies, but the concept is the same.

In your case, you also probably want to threshold the signal a little. In other words, instead of the brightness being proportional to volume, the brightness will be 0 below some volume. LEDs are diodes, so have a threshold voltage built in to first approximation. For example, a common green LED drops about 2.1 V when fully lit. But, the current, and therefore the brightness falls off rapidly as the voltage gets lower. At 1.5 V it will be so dim you won't notice it on in normal office illumination.

So what I'd do for experimenting is to start by AM detecting the sum of the two audio signals. Using a opamp amplifier with two pots, allow for adjusting both the gain and offset of this signal. Then connect that to the LED with a resistor in series. The resistor should be sized so that the LED current never exceeds its maximum rating even with the largest possible voltage coming out of the amplifier.