Solving for Vo: Nodal Analysis Approach

In summary, the conversation involved solving for the output voltage Vo(t) in terms of the input voltage Vs using Nodal Analysis. The equations used were the nodal equations for the circuit, and it was confirmed that V1 is equal to V2 due to the ideal op amp with feedback to the negative input. The final equation for Vo was j25.45Vo + 0.233Vo = 2.56Vs, which yielded a result that was almost spot on compared to the speaker's calculated result. However, it was noted that the provided expression was not in the standard final form, so the speaker "solved" it for Vo in terms of Vs and compared the proportionality constant with their own derivation. The result was
  • #1
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?[tex]\frac{V1}{-j1.6} + \frac{V1-Vs}{175} = 0[/tex]
[tex]\frac{V_{I2}-Vo}{10k} + \frac{V_{I2}}{1k} = 0[/tex]
 
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  • #2
Sure, those would be a good start.
 
  • #3
gneill said:
Sure, those would be a good start.
Is V1 = V2?
 
  • #4
eehelp150 said:
Is V1 = V2?
Well, it's an ideal op amp with feedback to the negative input. So that would be a yes.
 
  • #5
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?
 
  • #6
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.
 
  • #7
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?
 
  • #8
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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1. What is nodal analysis and how is it used to solve for Vo?

Nodal analysis is a method used in circuit analysis to determine the voltage at a specific node in a circuit. It involves setting up equations based on Kirchhoff's Current Law and solving for the unknown voltage using algebraic techniques. Vo is typically the output voltage of the circuit and can be solved for by using nodal analysis to determine the voltage at the output node.

2. What are the steps involved in solving for Vo using the nodal analysis approach?

The steps involved in solving for Vo using nodal analysis are as follows:
1. Identify all the nodes in the circuit.
2. Choose a reference node and label it as 0V.
3. Write Kirchhoff's Current Law equations for each node (except the reference node) in terms of the unknown voltages.
4. Simplify the equations using algebraic techniques.
5. Solve the resulting equations for the unknown voltage (Vo).
6. Verify the solution by checking if all the currents in the circuit add up to 0.
7. If the solution is correct, Vo is equal to the voltage at the output node.

3. Can nodal analysis be used for circuits with multiple voltage sources?

Yes, nodal analysis can be used for circuits with multiple voltage sources. However, the number of equations required to solve for the unknown voltages will be equal to the number of nodes plus the number of voltage sources minus one. This is because one of the equations will be redundant due to the presence of multiple voltage sources.

4. What are the advantages of using the nodal analysis approach to solve for Vo?

Some advantages of using the nodal analysis approach are:
- It is a systematic and structured method for solving circuit problems.
- It can be used for circuits with multiple voltage sources.
- It can handle complex circuits with multiple nodes and branches.
- It allows for the use of algebraic techniques to simplify the equations and solve for the unknown voltage.

5. Are there any limitations to using nodal analysis to solve for Vo?

One limitation of using nodal analysis is that it can become tedious and time-consuming for larger, more complex circuits. It also requires a good understanding of Kirchhoff's Current Law and algebraic techniques. Additionally, nodal analysis may not be the best method to use for circuits with non-linear components or dependent sources.

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