Ultimately trying to design an AC amplifier stage that has y=x/(a*(x-1)+1) for values between 0<x<1. A is a constant where 0<a<1 Order of operations should be as follows:
1. x-1 = add -1V DC offset to x with noninverting amplifier
2. a*(x-1) = use a voltage divider and buffer
3. a*(x-1)+1 = add +1V DC offset to x with noninverting amplifier
4. x-(a*(x-1)+1= no idea

This website's section on analog computing is great (http://www.allaboutcircuits.com/textbook/semiconductors/chpt-9/computational-circuits/) and I should be able to figure out steps 1-3, but as both x and (a*(x-1)+1) are different voltages and neither constant, I'm lost. Anyone point me in the right direction?

Attached images are from the online Desmos graphing calculator and show what happens when variable a is adjusted. Higher values of A create more nonlinearity from y=x.

 

You can't multiply or divide two variable voltages together with just op amps.
Op amps only add, subtract, or multiply/divide by a constant.
You need a non-linear device such as an analog multiplier to multiply/divide two variable voltages.

 

For stage 4, you may need to use something like this.
http://www.seekic.com/circuit_diagr...t_using_an_AD532_multiplier_divider_chip.html

 

You need a non-linear device such as an analog multiplier to multiply/divide two variable voltages.

Eeek...multiplier/divider ICs are like $$-$$$. Has anyone successfully used diodes or BJTs as diodes in the feedback loop of dime-a-dozen opamps to create the nonlinearity?

 

I think you can do it with an logarithmic amplifier, that uses just bjts and opamps. Or you could build a Gilbert Cell which allows multiplication - see

 

y=x/(a*(x-1)+1)

and

4. x-(a*(x-1)+1= no idea

O suppose you mean divide x / (a?

 

O suppose you mean divide x / (a?

Yes, noticed that immediately but as I'm new on the forum won't be able to edit just yet. I mean step 4 to be the division of two variables X/a.

 

Here's a lower cost chip. http://pdf.datasheetarchive.com/datasheetsmain/Datasheets-10/DSA-196400.pdf.
Cost. Find the XR-2228 in the catalog.
Look at this thread. http://forum.allaboutcircuits.com/threads/how-to-get-1-x-function-with-op-amp.103068/ It's not complete, but it's close. Needs refinement.

 

The order of operations should be to first reduce the expression you are trying to synthesize.

Then you can do this with just a few op amps.

 

The order of operations should be to first reduce the expression you are trying to synthesize.

Then you can do this with just a few op amps.

Steps 1-3 in the original post outline how I plan on dealing with the order of operations. I can get that to work. Its the fourth step which is the division of two variables. How can I do that with just a few opamps?

 

Steps 1-3 in the original post outline how I plan on dealing with the order of operations. I can get that to work. Its the fourth step which is the division of two variables. How can I do that with just a few opamps?

As I previously stated, you can't.