Find the Gain of a System: Solving for Output Voltage

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Discussion Overview

The discussion revolves around finding the gain of an op-amp system and determining the input impedance. Participants explore the relationships between various resistors in the circuit and the implications of ideal op-amp behavior on these calculations.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant states that the input impedance is R1 but questions why other resistors can be ignored.
  • Another participant suggests using the known behavior of an ideal op-amp to analyze the currents through resistors R3 and R4.
  • There is a claim that the gain is 2 based on a professor's equation, but a participant expresses confusion about the additional Vin in the equation.
  • Some participants argue that R4 and R1 should be considered in determining the gain, indicating a potential oversight in the initial gain calculation.
  • Discussion on whether the voltage at the op-amp inputs can be assumed to be Vin, with some suggesting it may need to be labeled differently.
  • One participant proposes that the voltage difference between the op-amp inputs is zero, leading to a calculation of input current and impedance.
  • Another participant confirms that the current through R2 is zero, leading to the conclusion that V2 equals zero and reaffirms the input impedance as R1.
  • A later reply suggests evaluating the gain while considering that R2 and R3 may be irrelevant.
  • One participant concludes that the gain is -R4/R1, while another clarifies that they were referring to a second op-amp in a follow-up question.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of certain resistors in calculating gain and input impedance. There is no consensus on the correct approach to determining the gain, as some participants challenge the initial calculations and assumptions.

Contextual Notes

Participants note the importance of labeling inputs correctly and the implications of feedback in op-amp circuits. There are unresolved questions about the role of R2 and R3 in the gain calculation.

rzn972
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Homework Statement


Find the input impedance.
pic2_zpsd5423e07.png

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!
 
Last edited:
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Something went wrong with your attachment. We can't see the circuit diagram.
 
Fixed. Thank you
 
rzn972 said:

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?
 
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?
 
rzn972 said:
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?
 
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...
 
rzn972 said:
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?
 
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?
 
  • #10
rzn972 said:
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.
 
  • #11
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.
 
  • #12
rzn972 said:
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...
 
  • #13
Oh, I meant for the second op amp, my second problem.
 

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