Calculating V0 on a Complex Op Amp Circuit

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Discussion Overview

The discussion centers on calculating the output voltage (V0) in a complex operational amplifier (op amp) circuit. Participants explore the simplification of the circuit and the application of the superposition principle to analyze the circuit behavior. The scope includes theoretical reasoning and mathematical calculations related to circuit analysis.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions their simplification of the op amp circuit, suggesting they subtracted voltages and added resistors in series.
  • Another participant asserts that the two voltage sources do not work against each other, indicating they have the same direction.
  • A participant suggests using the superposition principle to analyze the circuit, proposing to set one voltage source to zero at a time and solve for the output voltage.
  • Some participants challenge the validity of the simplified circuit, stating it does not accurately represent the original circuit.
  • There is a discussion about the values of resistors used in calculations when applying superposition, with one participant seeking clarification on which resistors to consider when short-circuiting the voltage sources.
  • One participant presents calculations for V0 using superposition, arriving at a total output voltage of -8 V, while another acknowledges a minor typo in the calculations but confirms the result is correct.
  • Clarifications are made regarding the configuration of the voltage sources, with a participant noting that they are in parallel and share the same direction of voltage.

Areas of Agreement / Disagreement

Participants express disagreement regarding the simplification of the circuit, with some asserting it is invalid while others attempt to clarify the reasoning behind the original participant's approach. There is no consensus on the correct simplification, and the discussion remains unresolved in that aspect.

Contextual Notes

Participants express uncertainty about the application of the superposition principle and the correct identification of resistor values in the context of the circuit analysis. There are also unresolved questions regarding the interaction of the voltage sources and their configuration.

dbakg00
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Homework Statement





See attached picture. My objective is to calculate V0 on the 2k resistor. I'm used to seeing op amps that are more simple looking. I'm trying to reduce this op amp circuit to a simpler one (my attempt is the bottom picture). My question is: did I simplify the circuit correctly? I subtracted the 1v from the 2v source since they are working against each other and I added the resistors since they are in series. Thanks in advance for any help you can give.


Homework Equations





The Attempt at a Solution

 

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Those two sources do not work against each other, they both have the same direction.
 
How could they both have the same direction? The negative terminal of the 1v touches the negative terminal of the 2v. Sorry if this is a dumb question...I'm new to circuits.
 
dbakg00 said:
How could they both have the same direction? The negative terminal of the 1v touches the negative terminal of the 2v. Sorry if this is a dumb question...I'm new to circuits.

Use superposition principle.

1. let V1 = 0 and solve for Vout.
2. let V2 = 0 and solve for Vout.
3. add the two Vout s.

Your "simplified" circuit is invalid, sorry.
 
I agree, your simplified circuit is not the same. Try calculating the voltage at the inverting input of the op amp of the top circuit and show us what you get.
 
rude man said:
Use superposition principle.

1. let V1 = 0 and solve for Vout.
2. let V2 = 0 and solve for Vout.
3. add the two Vout s.

Your "simplified" circuit is invalid, sorry.

So if I let the 1V source = 0, do I still consider both the 5k and the 2.5k resistors? I know that in an inverting amplifier, vo = (-R2/R1)vi. R2 is obviously 10k. What is confusing me is what value I would use for R1. If I did the superposition as you suggested, when I killed the 1V source, would R1 = 5k? And then when I killed the 2V source, R1 = 2.5k? Am I on the right track?
 
When I do superposition, I get the following:

(short circuiting the 1V source)
V01 = Vs1(-R2/R1)
V01 = 2(-10/2)
v01 = -4 V


(short circuiting the 2V source)
V02 = Vs2(-r2/R1)
V02 = 1(-10/2.5)
V02 = -4 V

V0 = V01 + V02
V0 = (-4) + (-4)
V0 = -8

how does that look?
 
dbakg00 said:
So if I let the 1V source = 0, do I still consider both the 5k and the 2.5k resistors? I know that in an inverting amplifier, vo = (-R2/R1)vi. R2 is obviously 10k. What is confusing me is what value I would use for R1. If I did the superposition as you suggested, when I killed the 1V source, would R1 = 5k? And then when I killed the 2V source, R1 = 2.5k? Am I on the right track?

Yes.
 
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dbakg00 said:
When I do superposition, I get the following:

(short circuiting the 1V source)
V01 = Vs1(-R2/R1)
V01 = 2(-10/2)
v01 = -4 V


(short circuiting the 2V source)
V02 = Vs2(-r2/R1)
V02 = 1(-10/2.5)
V02 = -4 V

V0 = V01 + V02
V0 = (-4) + (-4)
V0 = -8

how does that look?

Very good. You made a typo on V02 (2nd line) but still came up with the right answer.
 
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  • #10
Thanks to all for the help!
 
  • #11
dbakg00 said:
How could they both have the same direction? The negative terminal of the 1v touches the negative terminal of the 2v. Sorry if this is a dumb question...I'm new to circuits.
They are "in parallel" - not exactly due to the resistors, but they share the same direction of voltage between ground and the negative input of the op amp.
 

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