Find the Gain of a System: Solving for Output Voltage

[rzn972]

Homework Statement

Find the input impedance.

Homework Equations

The Attempt at a Solution

Input impedance= R1. I don't get why we can ignore the other resistors.

Problem 2 :

Homework Statement

Find the gain of the system.
https://www.physicsforums.com/attachment.php?attachmentid=68909&stc=1&d=1398116979

Homework Equations

The Attempt at a Solution

Gain = 2

My professor wrote
vout= (R3/R2) Vin + vin = 2Vin, so gain =2.
I understand that (R3/R2) Vin is from the output of the op amp but I do not know where the other Vin came from.
Can someone explain this please?

Thank you so much!

 

[AlephZero]

Something went wrong with your attachment. We can't see the circuit diagram.

 

[rzn972]

Fixed. Thank you

 

[gneill]

The Attempt at a Solution

Input impedance= R1. I don't get why we can ignore the other resistors.

Use the known behavior of an ideal op-amp (regarding input impedance at its inputs and the voltage between its input terminals when there's feedback) to say something about the currents though R3 and R4. What will be the voltage at input terminals of the op-amp?

Note that I'm presuming that the pin layout for the op-amp is the same as the standard 741 op-amp. It would be preferable to label the inputs as + and - on your diagrams instead of just putting pin numbers.

Problem 2 :

Homework Statement

Find the gain of the system.

Homework Equations

The Attempt at a Solution

Gain = 2

My professor wrote
vout= (R3/R2) Vin + vin = 2Vin, so gain =2.
I understand that (R3/R2) Vin is from the output of the op amp but I do not know where the other Vin came from.
Can someone explain this please?

Hmm. That doesn't look like the gain of the given circuit to me. Surely R4 and R1 should be involved in setting the gain?

 

[rzn972]

The current into 2 and 3 is zero using the golden rule. The voltage at 2 and 3 does not necessarily have to be Vin right, since current can flow to R4. So would you have to call it something else?

 

[gneill]

The current into 2 and 3 is zero using the golden rule. The voltage at 2 and 3 does not necessarily have to be Vin right, since current can flow to R4. So would you have to call it something else?

Correct, it doesn't have to be Vin. So it might be something else and you could call it something else if you wish. But don't rush ahead with that...

How about the voltage difference between the two inputs? What do the rules say for an op-amp with negative feedback?

 

[rzn972]

The voltage difference is 0. Say I call the voltage at the inputs v2. So the input current is (V2- Vin)/R1?
Zin= Vin / ((V2- Vin)/R1) But this doesn't seem right...

 

[gneill]

The voltage difference is 0. Say I call the voltage at the inputs v2. So the input current is (V2- Vin)/R1?
Zin= Vin / ((V2- Vin)/R1) But this doesn't seem right...

So, if the voltage between the inputs is zero (or near enough for practical purposes), what's the current through R2?

 

[rzn972]

The current through R2 would be zero. Therefore V2=0 since there is no current into input 3. Iin would be Vin/ R1 so the input impedance is Vin / (Vin/ R1) = R1?

 

[gneill]

The current through R2 would be zero. Therefore V2=0 since there is no current into input 3. Iin would be Vin/ R1 so the input impedance is Vin / (Vin/ R1) = R1?

Yup. Vin 'sees' what appears to be R1 connected to ground.

Now you'll have to evaluate the gain keeping in mind that R2 and R3 are essentially irrelevant.

 

[rzn972]

Thank you so much, gain = -R4/ R1! And if possible could you help me out with my second question? We are asked the voltage gain of the system, vout/vin.

 

[gneill]

Thank you so much, gain = -R4/ R1! And if possible could you help me out with my second question? We are asked the voltage gain of the system, vout/vin.

Um, the gain *is* the voltage gain...

 

[rzn972]

Oh, I meant for the second op amp, my second problem.