# How to get y=x/(a*(x-1)+1) with opamps?

#### freshtapescent

Joined Dec 27, 2015
4
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.

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#### crutschow

Joined Mar 14, 2008
25,994
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.

#### freshtapescent

Joined Dec 27, 2015
4
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?

#### kubeek

Joined Sep 20, 2005
5,736
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

#### KeepItSimpleStupid

Joined Mar 4, 2014
4,371
post #1 said:
y=x/(a*(x-1)+1)

and

4. x-(a*(x-1)+1= no idea
O suppose you mean divide x / (a?

Last edited:

#### freshtapescent

Joined Dec 27, 2015
4
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.

#### ErnieM

Joined Apr 24, 2011
8,078
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.

#### freshtapescent

Joined Dec 27, 2015
4
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?

#### crutschow

Joined Mar 14, 2008
25,994
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.