# Op amp design need advice

1. Homework Statement
Design an op-amp that uses a variable 50k ohm resistor. when this variable resistor is at one extreme, the gain is 13, and at the other extreme, the gain is 3. you may use up to 2 op-amps, and up to 7 resistors (including the variable resistor)

3. The Attempt at a Solution

here is the circuit i came up with:

I made it so all I would have to find is Rf to satisfy the design.

here is how I solved for Rf

first extreme:

$$(1 + \frac{R_f}{60k-ohms}) = 13$$

next extreme:

$$(1 + \frac{R_f}{110k-ohms}) = 3$$

combine the two equations:

$$11 + \frac{R_f}{110k-ohms} = 1 + \frac{R_f}{60k-ohms}$$

$$10 = R_f (\frac{1}{60k-ohms} - \frac{1}{110k-ohms})$$

$$R_f = 1.32M-ohms$$

this answer gives a gain of 13 on one extreme of the variable resistor and 23 on the other. whoops. any help?

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Gokul43201
Staff Emeritus
Gold Member
Two equations in one variable? Why should they have the same solution? As expected, if you solve them individually, you find they do not.

How would you fix this?

you're right, I get a different resistor values for each equation, yet it needs to be the same value.

Mathematically, I should have one equation for each variable. There's only one but I forget how to solve an equation that has an answer of 3 OR 13...

either i need more variables or i need less equations

yeah i need another pointer

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What I make the 60kohm resistor R1 (or another unknown)...

that way I could have two equations with two unknowns. Is this the correct way to approach this problem?

Gokul43201
Staff Emeritus
Gold Member
Yes, that would be one way to fix it. To solve a problem with n independent boundary values, you need n independent parameters.

Good, cause it worked. I got R1 = 10k ohm and Rf = 120k ohm which give me the correct gain(s). Thank you so much I appreciate all the help this forum gives me.

But out of curiousity, you said that's "one" way to solve it. got another trick up your sleeve?

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AlephZero
Homework Helper
But out of curiousity, you said that's "one" way to solve it. got another trick up your sleeve?
There are a huge number of ways you could design the circuit within the constraints you are given. For example this is a completely different idea which doesn't need any algebra to figure it out.

(Except its deliberately wrong because it has gains of -3 to -13, so its not a complete solution to your question!)

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berkeman
Mentor
(Except its deliberately wrong because it has gains of -3 to -13, so its not a complete solution to your question!)
Getting kind of sneaky there, are we?

Gokul43201
Staff Emeritus