Here is my dilemma, put simply:

I'm looking for any ideas or designs to have an input signal (+/- 5V AC/DC) amplified/attenuated/inverted based on the values of 2 pots. The best way to explain this is that one pot sets the upper rail value and the other pot sets the lower rail value. So, if each pot is set to a value between -5V and +5V, the signal will be offset, scaled, and/or inverted according to how the pots are set to each other.

For clarity, here are a few examples:

Upper rail pot is set to +5V and the lower rail pot is set to -5V, the gain will be 1.
Upper rail pot is set to +5V and the lower rail pot is set to 0V, the gain will be 0.5 and the offset will be +2.5V.
Upper rail pot is set to -5V and the lower rail pot is set to 0V, the gain will be -0.5 and thr offset will be -2.5V.

I realize that this can be done trivially by using separate pots for gain and offset, and my concept combines the offset and gain as the function of the pots value and their relation to each other's value, but I feel like there has to be a method of getting this done by setting the rails.

Also, I understand that this would be very easy to do digitally, but I want to keep it completely analog. My first idea was to have the pots as voltage dividers and each running to the supplies of an opamp which would change the rail voltage, but I have no idea what would happen when the rail voltages are inverted, and I'm thinking that as the rail votages get within a volt or 2 of each other that most op amps are gonna drop out. I also looked at using VCAs and opamp so together, but I could not get it done simply- it requires using the VCAs as variable restistors to control the opamp's gain or using several more pots, which isn't what I'm going for.

If I'm missing something simple or anyone has any novel ideas I'd really love to hear it. I have been working on this for several weeks now without really anything to show for it. I've also checked data sheets and online design resources without any luck, mainly because I'm not really sure how to properly (and concisely) create a search term for this. Let me know if there's anything I can clarify. Thank you!

-Ben

 

Sounds like a good application for an analog multiplier and some opamps.

http://www.analog.com/en/education/education-library/multiplier-application-guide.html

 

Interesting!
I would start with:

Two such amplifiers, one that "comes" in non-inverting input and another on inverting input of another operational amplifier.

I think there must be two signals, of different amplitudes, one of them inverted that will gather.

Control voltage of -5V ... 5V I would convert it by adding it with a fixed voltage in 0V ... 10V.

You can post LT Spice simulations.

 

I agree with Dick.
An analog multiplier along with some op amp circuits is likely the best way to do this in analog.
If you feed a signal into one input of the multiplier and a DC voltage into the other input, then the output gain will be controlled by the DC voltage and the DC polarity will determine the output signal polarity.
So you would need some op circuits to convert your 5V signals into the appropriate signals to the multiplier to get the desired results.

If you create a table to map representative 5V signals into the needed multiplier signals to give the desired output, that will give you a good start as to what's needed.

For example, below is the LTspice simulation of a multiplier with an op amp circuit that shows a variation in output offset and gain for an op amp signal on the Y input, with a DC variation on the X input.
The DC variation is summed at the op amp input to get an offset change along with the gain change.
It doesn't do what you want but it should help you understand what you would need to do to get there.

 

Upper rail pot is set to +5V and the lower rail pot is set to -5V, the gain will be 1.
Upper rail pot is set to +5V and the lower rail pot is set to 0V, the gain will be 0.5 and the offset will be +2.5V.
Upper rail pot is set to -5V and the lower rail pot is set to 0V, the gain will be -0.5 and thr offset will be -2.5V.

And if
Upper rail pot is set to +4V and the lower rail pot is set to -4V, offset will be 0V and the amplitude of the signal 4V ? gain 4/5
Upper rail pot is set to +5V and the lower rail pot is set to +5V, offset will be 5V and the amplitude of the signal 0V ? gain 0


The offset is easily obtained by adding these two voltages.
Then you need a signal with a required amplitude.