Ive been doing my brain in all afternoon with this op amp circuit.

Can someone confirm which derivation is correct.
This is mine


And this is someone else's


They diverge at the 2 points I've circled in red in the first pic

 

What have you done to verify the correctness of the two options?

You have two results. Yours:

\(V_o \; = \; V_2 \; - \; \frac{R_f}{R_1}V_1\)

and theirs:

\(V_o \; = \; \frac{R_f}{R_1} \( V_2 \; - \; V_1 \)\)

So pick values that result in different answers and then see which (if either) of those answers is consistent with the original circuit.

For instance, try V1 = 1 V, V2 = 6 V, R1 = 1 kΩ and Rf = 2 kΩ.

Your solution yields V0 = 4 V while theirs equals 10 V.

So which, if either, of these results in the differential voltage at the op-amp inputs being zero?

 

Who says I haven't already?

The fact that you don't know which one is correct was a really strong hint.

Once you determine which one is wrong, look carefully at the set up equations. Remember, the set up equations is were all of the EE takes place, everything else is math. Even if all of the math is correct, a wrong set up will result in a wrong answer that is mathematically correct -- for the problem that the setup equations correspond to. It's just that the problem they correspond to is different than the one you are trying to solve.

Once you find the error, see if you can figure out what problem they correspond to (in other words, can you make a minor change to the circuit so that it matches the result obtained)?

 

Hmm 10v is always a good number for op amps. I need to check this again. I've checked it a different way. Just on the mathematical plane. I think I'm correct, but you've got me worried now. To be continued...

 

Hmm 10v is always a good number for op amps. I need to check this again. I've checked it a different way. Just on the mathematical plane. I think I'm correct, but you've got me worried now. To be continued...

Remember, if the set up is wrong the math can be right from beginning to end and you will never find an error.

This is why it is SO valuable to break things into two clearly defined steps. It's even worth drawing a horizontal line to distinguish the two steps.

First, set up the equations that describe the problem doing little or no simplification along the way. Then, before you go to the next step, verify that the equations you actually wrote are correct. Do they really model the problem you are trying to solve? You need to make the conscious effort to check the equations as you wrote them, and not as you intended to write them. Check each factor and each term. Spend the time to do this right. Don't skimp on it. This cannot be overemphasized.

Only after you are completely satisfied that the set up equations are correct do you go onto the next step, which is nothing but mathematical manipulations.

 

 

You STILL are not tracking your units!

 

ROFL soz boss

 

ROFL soz boss

I know you think it's some joke. What I don't know is why you apparently don't care about getting the right answer or catching your mistakes.

Proper tracking of units is very possibly THE most effective error detection tool available to the engineer -- and it's FREE!!

Are you going to continue feeling that way when you are up on charges for criminally negligent homicide because one of your designs failed and that failure would have been prevented if you had just tracked your units? It doesn't happen often but it HAS happened. Usually you just get fired and/or lose everything you own in the civil suits that follow.

Is your family going to feel that it's some cute joke when you don't come home some night because you got yourself killed because you couldn't be bothered to track your units? I can tell you that the neither the pregnant wife nor any of the kids of a colleague of mine felt that way when he didn't come home one night for exactly that reason.

 

Om goodness sorry Wbahn. I will, I will... it's a promise. There's no reason why I can't now, I'm much more familiar with the math and analysis so there's no reason why I shouldn't and obviously every reason why I should...

 

By the way KevinEamon , your circuit is a subtractor: http://www.mtcmos.com/subtractor/ . Just for your future, in case of other problems, you should be able to find this and other opamps configurations in the resources in the internet and books as for example:
- http://www.designers-guide.org/Books/
- https://payhip.com/b/5Srt