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

Discussion in 'General Electronics Chat' started by freshtapescent, Dec 27, 2015.

  1. freshtapescent

    Thread Starter New Member

    Dec 27, 2015
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    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.
     
  2. crutschow

    Expert

    Mar 14, 2008
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    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.
     
  3. sailorjoe

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    Jun 4, 2013
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  4. freshtapescent

    Thread Starter New Member

    Dec 27, 2015
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    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?
     
  5. kubeek

    AAC Fanatic!

    Sep 20, 2005
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    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
     
  6. KeepItSimpleStupid

    Well-Known Member

    Mar 4, 2014
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    O suppose you mean divide x / (a?
     
    Last edited: Dec 27, 2015
  7. freshtapescent

    Thread Starter New Member

    Dec 27, 2015
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    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.
     
  8. sailorjoe

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  9. ErnieM

    AAC Fanatic!

    Apr 24, 2011
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    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.
     
  10. freshtapescent

    Thread Starter New Member

    Dec 27, 2015
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    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?
     
  11. crutschow

    Expert

    Mar 14, 2008
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    As I previously stated, you can't.
     
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