Solving for Vo: Nodal Analysis Approach

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Discussion Overview

The discussion revolves around determining the output voltage Vo(t) in terms of the input voltage Vs using nodal analysis. Participants are exploring the application of nodal equations in the context of an ideal operational amplifier circuit.

Discussion Character

  • Homework-related, Technical explanation, Exploratory

Main Points Raised

  • One participant proposes a set of nodal equations for the analysis, questioning their correctness.
  • Another participant agrees that the proposed equations are a good starting point.
  • There is a question about whether V1 equals V2, which is affirmed based on the characteristics of an ideal op amp with feedback.
  • A participant presents a derived expression for Vo, seeking validation on its correctness.
  • Another participant expresses that the derived result looks acceptable but notes the difficulty in assessing it without the full derivation.
  • There is a discussion about the comparison of results, with one participant indicating that the differences are within a plausible rounding error range.
  • It is noted that the expression for Vo was not in a typical final form, prompting further clarification on isolating Vo in terms of Vs.

Areas of Agreement / Disagreement

Participants generally agree on the validity of the initial nodal equations and the relationship between V1 and V2. However, there is no consensus on the final form of the expression for Vo, and the discussion remains open regarding the comparison of results.

Contextual Notes

The discussion includes assumptions about the ideal behavior of the op amp and the need for complete derivations to fully validate the results. There are also indications of unresolved mathematical steps regarding the isolation of Vo.

eehelp150
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Homework Statement


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Determine the output voltage Vo(t) in terms of Vs

Homework Equations

The Attempt at a Solution


If I were to use Nodal Analysis to solve this, would these be the proper nodal equations?\frac{V1}{-j1.6} + \frac{V1-Vs}{175} = 0
\frac{V_{I2}-Vo}{10k} + \frac{V_{I2}}{1k} = 0
 
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Sure, those would be a good start.
 
gneill said:
Sure, those would be a good start.
Is V1 = V2?
 
eehelp150 said:
Is V1 = V2?
Well, it's an ideal op amp with feedback to the negative input. So that would be a yes.
 
gneill said:
Well, it's an ideal op amp with feedback to the negative input. So that would be a yes.
I end up with:
j25.45Vo + 0.233Vo = 2.56Vs
Does this look good so far?
 
I think that looks okay. Hard to tell without seeing the full derivation, but it certainly yields a result for Vo that's almost spot on compared to what I calculate.
 
gneill said:
I think that looks okay. Hard to tell without seeing the full derivation, but it certainly yields a result for Vo that's almost spot on compared to what I calculate.
How far off am I compared with your results?
 
eehelp150 said:
How far off am I compared with your results?

Within plausible rounding error range. The expression you provided was not in a typical final form, since Vo was not isolated. So I "solved" it for Vo in terms of Vs and compared the proportionality constant with what I derived. Here:

upload_2016-10-13_16-56-1.png
 
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