How Do You Solve an Op Amp Circuit Using Superposition?

[Asphyxiated]

Homework Statement

A picture of the original problem can be seen http://images3a.snapfish.com/232323232%7Ffp733%3C2%3Enu%3D52%3A%3A%3E379%3E256%3EWSNRCG%3D335%3B%3B84268347nu0mrj" along with some extra labels.

Homework Equations

superposition

The Attempt at a Solution

So I tried to solve A) with superposition, but first we know that:

$$V_{0}=V_{0_{1}}+V_{0_{2}}$$

$$V_{1}=V_{2}$$

and

$$i_{V_{1}}=i_{V_{2}}=0$$

just meaning there is no current going into the op amp.

Superposition: 4v source off with a short circuit in its place. We now have a current-to-voltage converter which follows this formula:

$$\frac {V_{0_{1}}}{i_{s}}=-R$$

$$\frac {V_{0_{1}}}{.001a}=-2000\Omega$$

$$V_{0_{1}}=-2V$$

Now turn the current supply off and you have a non-inverting amplifier circuit with negative feedback. I am not really sure how to calculate this. To me it looks like:

$$V_{0_{2}}=V_{in}=4v$$

and putting it together:

$$V_{0}=-2v+4v=2v$$

which is the correct answer but I have no idea if I did it correctly or not. I do not know how to work out B but maybe if I get help here I will understand. Thanks!

 

[KataKoniK]

Hello! Great job using superposition to solve part A of the problem. Your understanding of the concept is correct and your calculations seem to be accurate as well. To solve part B, you can use the same approach of superposition but with a different set of sources.

First, turn off the 4V source and replace it with an open circuit. This will leave you with a voltage divider circuit with R1 and R2. Use Ohm's law to calculate the voltage at the output of the divider, which will be the input voltage for the op amp inverting input.

Next, turn off the 1mA current source and replace it with a short circuit. This will leave you with a simple non-inverting amplifier circuit with negative feedback. Use the formula for an inverting amplifier to calculate the output voltage.

Finally, add the two voltages calculated in the previous steps together to get the total output voltage.

I hope this helps! Let me know if you have any other questions.