AC Circuit Analysis: Solving 4x4 Matrix w/ Imaginary Numbers, Real #s & Phasor

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Discussion Overview

This discussion revolves around solving a 4x4 matrix resulting from loop/mesh analysis in an AC circuit, specifically dealing with terms involving imaginary numbers, real numbers, and phasor format. Participants express confusion regarding the matrix solution process and seek advice on efficient methods for handling these types of equations.

Discussion Character

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

Main Points Raised

  • One participant expresses confusion about solving a matrix with mixed terms (imaginary numbers, real numbers, phasors) and seeks tips for an efficient approach.
  • Another participant suggests converting all terms into complex or phasor format to simplify the calculations and mentions using calculators like the TI-89 or MATLAB for solving the matrix.
  • A question is raised about how to convert phasor format into imaginary numbers, indicating a need for clarification on this conversion process.
  • One participant provides a rough example of converting a phasor to complex form, emphasizing that operations are easier in complex format.
  • There is a suggestion to reduce the number of unknowns in the system to simplify the problem, with a participant noting that systems with fewer unknowns are easier to solve.
  • Some participants discuss the relative ease of operations in complex form versus phasor format, with differing opinions on which format is easier for addition, subtraction, multiplication, and division.
  • Repeated requests for guidance on using the TI-89 to input the matrix indicate a desire for practical assistance in solving the problem.

Areas of Agreement / Disagreement

Participants express varying opinions on the ease of operations in complex versus phasor formats, indicating a lack of consensus on this aspect. Additionally, there is no agreement on a definitive method for converting phasors to complex numbers, leaving the discussion unresolved on this point.

Contextual Notes

Participants mention the potential limitations of certain calculators in handling phasors and complex numbers, as well as the need for a textbook reference for conversion methods, suggesting that some assumptions and definitions may be context-dependent.

Who May Find This Useful

This discussion may be useful for students and practitioners dealing with AC circuit analysis, particularly those encountering challenges with matrix solutions involving complex numbers and phasors.

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Hey,

This is a problem involving loop/mesh analysis on an AC circuit. I'm less confused about the circuit theory, I'm more confused with how to solve the resulting matrix. I get 4 equations with 4 unknowns... Which is something I'm accustomed to solving, but there are three different types of terms. Imaginary numbers, real numbers, and the phasor format (magnitude<angle - 4<60)

Here's the problem. I solved it the same way this person did, I'm just stuck on the matrix.

http://synthdriven.com/images/deletable/EEN201-17.jpg

Any tips on an easy/efficient way to go about this?

Thanks!
 
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Doing that by hand along with the complex numbers and phasers are a real pain, but not impossible. Just convert them all into complex or phasor fomat.

If you have a TI-89 or Ti86, then you can just punch those numbers that you have there into a matrix and it will solve it for you. I believe the Ti-83 has some limitations on the phasors and complex numbers in matrices, but I'm not sure. Also MATLAB will work.
 
How do you convert from phasor format into imaginary numbers??
 
I was hoping you wouldn't ask that, but I guess your instructor isn't going to let you use a calculator on a test.
Your textbook should have an explanation of how to do it. Its about the same the same way as breaking a vector into components. I'm a bit rusty on circuits and my notes and textbook are 400 miles away :mad: . Hopefully someones else will comes along and help.

Simple rough example

(4<30)

4 cos 30 = 3.46
4 sin 30 = 2

z = 3.46 + 2j


It's easier to add, subtract, multiply and divide in complex format than phasor.
 
Since I_2 = 4 \angle 30, this is a system of 3 (instead of 4) unknowns. It would be nice if you can further reduce that to 2 unknowns since systems of equations with 2 unknowns are very much easier to solve than 3.

As far as the solution goes, you'd perhaps need to convert all the terms into the complex equivalent as suggested by teknodude.

teknodude said:
It's easier to add, subtract, multiply and divide in complex format than phasor.
I think it's easier to add and subtract in complex form, but multiplication and division are easier in phasor.
 
doodle said:
I think it's easier to add and subtract in complex form, but multiplication and division are easier in phasor.

Crap.. wtf was I thinking. Yea doodle is right on that.
 
teknodude
Please, can you explain how to punch the matrix into a ti 89, it will help save a lot of time and possible mistake. o:)
Thanks
 
dh19440113 said:
teknodude
Please, can you explain how to punch the matrix into a ti 89, it will help save a lot of time and possible mistake. o:)
Thanks

Read the instruction manual or go to the ti website and download it. I rarely use my 89 except for integration checking. I like my aging ti86 more.
 

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