Op Amp Circuit: Find Vo | Homework Statement & Equation

[Studious_stud]

Homework Statement

Find the output voltage Vo in the following circuit

Homework Equations

V = IR

The Attempt at a Solution

Hey everyone, this question has me stumped. The answer to the question is -IR_2 but I'm interested as to how this answer comes about. I'm not particularly amazing at circuit theory

Thanks in advance everyone

 

[Zryn]

Firstly, what sort of rules do you know about Ideal Op-Amp Analysis?

There are two golden rules which everyone should know, the first concerning the voltages at the + and - terminals and the second concerning the current at the + and - terminals.

Secondly, are you aware of Thevinin and Norton transform theories?

And lastly, you're right that you require Ohms Law, but the other two are more important.

 

[Studious_stud]

Firstly, what sort of rules do you know about Ideal Op-Amp Analysis?

There are two golden rules which everyone should know, the first concerning the voltages at the + and - terminals and the second concerning the current at the + and - terminals.

Secondly, are you aware of Thevinin and Norton transform theories?

And lastly, you're right that you require Ohms Law, but the other two are more important.

Ideal is infinite gain right?

v+ = v- = 0

i+ = i- = 0 as well

Yes I'm aware of Thevenin and Norton but not incredible at working them out...

 

[Zryn]

Ideal is infinite gain right?

Yep!

v+ = v- = 0

i+ = i- = 0 as well

Correct!

Can you do the Thevinin transformation, finding the voltage and resistance for the picture below?

 

[Studious_stud]

Yep!



Correct!

Can you do the Thevinin transformation, finding the voltage and resistance for the picture below?

I'm not too sure honestly. For R_th you start with opening the current source, right? So that leaves the resistor by itself.

I'm not too sure where to go from there, I've never seen an example really like this before.

 

[Zryn]

I'm not too sure honestly. For R_th you start with opening the current source, right? So that leaves the resistor by itself.

Yep. Open the current sources (and short the voltage sources) and you're left with just the resistance, so R_th = R1.

V_th is merely the voltage you would see at the terminals of that circuit. So using the terms (I and R1), how can you describe the voltage seen at those terminals?

 

[Studious_stud]

Yep. Open the current sources (and short the voltage sources) and you're left with just the resistance, so R_th = R1.

V_th is merely the voltage you would see at the terminals of that circuit. So using the terms (I and R1), how can you describe the voltage seen at those terminals?

By using Ohms law? V = IR1

 

[Zryn]

By using Ohms law? V = IR1

Yep! Too easy.

So now you can replace the parallel current source and resistance with a series voltage source and resistance.

Now we have a standard negative feedback Ideal Op-Amp to analyze. Have you done these before? Looking at the picture attached, its a fairly standard set of steps:

1) Introduce the input and output side currents i1 and i2 and draw directional arrows (done). Keep in mind that we already know that the current at the inverting terminal i- = 0.

2) Do KCL at the node where i1, i2 and i- meet.

3) Write i1 and i2 in terms of voltages and resistances (using Ohms Law) instead of currents.

4) Solve the resulting equation and hopefully you get a good answer.

If you do these 4 steps (with varying levels of complication depending on how complicated the circuit is) you can pretty much solve any circuit problems of this nature. Feel free to post your workings and your results if you get stuck!

 

[Studious_stud]

Yep! Too easy.

So now you can replace the parallel current source and resistance with a series voltage source and resistance.

Now we have a standard negative feedback Ideal Op-Amp to analyze. Have you done these before? Looking at the picture attached, its a fairly standard set of steps:

1) Introduce the input and output side currents i1 and i2 and draw directional arrows (done). Keep in mind that we already know that the current at the inverting terminal i- = 0.

2) Do KCL at the node where i1, i2 and i- meet.

3) Write i1 and i2 in terms of voltages and resistances (using Ohms Law) instead of currents.

4) Solve the resulting equation and hopefully you get a good answer.

If you do these 4 steps (with varying levels of complication depending on how complicated the circuit is) you can pretty much solve any circuit problems of this nature. Feel free to post your workings and your results if you get stuck!

Well thanks a lot Zryn, you've really been helpful. I wish my tutors were nearly this good

 

[Dmytry]

Well, or you can simply see that the voltage across the r1 will be zero (any nonzero voltage would give -infinity at the infinite gain amplifier's output ;) ), meaning that zero current will flow through r1, and the current I will flow through r2 , so the voltage will be -I*r2

 

[Zryn]

Well, or you can simply see that the voltage across the r1 will be zero (any nonzero voltage would give -infinity at the infinite gain amplifier's output ;) ), meaning that zero current will flow through r1, and the current I will flow through r2 , so the voltage will be -I*r2

Seeing the answer doesn't usually come until you have a fair level of experience with how something works (which I don't believe is the stage the OP is at), so its probably not so simple at all.

Also, how would you justify your statement mathematically to prove that you are not seeing the wrong thing (i.e. an exam answer)?