Troubleshooting an Op Amp Circuit: Iterative Problem-Solving Methods

[Vishera]

Homework Statement

Homework Equations

The Attempt at a Solution

Here is my attempt: http://i.imgur.com/oKjwI8O.png

The problem is at the end, I get 0=0. What did I do wrong?

 

[berkeman]

Homework Statement

Homework Equations

The Attempt at a Solution

Here is my attempt: http://i.imgur.com/oKjwI8O.png

The problem is at the end, I get 0=0. What did I do wrong?

Can you post a drawing of your opamp circuit, with the resistor names labeled? Thanks.

 

[Vishera]

Can you post a drawing of your opamp circuit, with the resistor names labeled? Thanks.

Sure, here is the drawing of the general circuit that I am aiming to design:

For that general circuit, the following equation applies:

Here is an example in the textbook:

 

[rude man]

You sure it isn't Vo = 3V2 - 2V1?

 

[donpacino]

You sure it isn't Vo = 3V2 - 2V1?

I agree with rude man.

In all cases an input to the negative side of an single op-amp circuit will be inverted, while an input to the positive side will not be inverted.

 

[Vishera]

You sure it isn't Vo = 3V2 - 2V1?

Is there any specific reason why you can't the following equation to:

to:

v_o=3v₁-2v₂?

I understand that I get 0=0 but why do I get 0=0? Algebraically speaking, why would it matter if it were v_o = 3v₂ - 2v₁ or v_o=3v₁-2v₂?

 

[gneill]

It might be helpful to write:

$3 v_1 - 2 v_2 = v_1 + 2(v_1 - v_2)$

Then a really simple circuit solution might come to mind.

 

[donpacino]

Is there any specific reason why you can't the following equation to:

to:

v_o=3v₁-2v₂?

I understand that I get 0=0 but why do I get 0=0? Algebraically speaking, why would it matter if it were v_o = 3v₂ - 2v₁ or v_o=3v₁-2v₂?

combing your two equations the way you initially had them -R2/R1 would have to equal three.

that would imply that you have a negative resistance, which is impossible

 

[donpacino]

I would solve this problem through an iterative method.

1. determine the relationship between R2 and R1 based on the V1 coefficient (hint R2/R1 = ?)
2. choose resistor values such that the relationship is true
4. determine R3 and R4 values based on the V2 coefficient and R1 and R2.
5. If needed go back to step 1

 

[Vishera]

combing your two equations the way you initially had them -R2/R1 would have to equal three.

that would imply that you have a negative resistance, which is impossible

I understand that negative resistance is impossible in the real world, but shouldn't I at least get an answer with negative resistances in the math? I didn't even get an answer in the algebra which is confusing me.

 

[donpacino]

you got unlucky with the numbers. for that particular (wrong) arrangement of equations there is no solution. why don't you try it again with the correct number orientation. If you don't believe you got unlucky, change coefficients in the equation to some random combination and see what happens.

I do want to point out that the best way to solve these problems is an iterative process.
I recommend following the process I gave you above.