Mesh Analysis: Converting from Time to Frequency Domain with Correct Equations

In summary: Thanks for your help!In summary, the conversation discusses the steps for converting from time to frequency domain, using mesh analysis to solve for I1, I2, and I3, finding Ve, and converting it back to the time domain. The conversation also mentions using KVL and the equation V=IR. The conversation concludes with a discussion about using software packages and shortcuts for solving a system of three equations with complex variables.
  • #1
eehelp150
237
0

Homework Statement


pHJ8FSj.png
[/B]
1. Convert from time to freq domain
2. Use mesh analysis to find I1, I2, I3
3. Find Ve and convert it to time domain

Homework Equations


KVL
V=IR

The Attempt at a Solution


Are these mesh equations correct?
45cos(500t) -> 45V
80mH -> 40j
50mH -> 25j
25uF -> -80j
12.5uF -> -160j

Mesh1
(100+40j+25j+200)I1 - 200I2 - 400jI3 = 0
Mesh2
-45 + (200-80j)I2 - (200I1) + 80jI3 = 0
Mesh3
(-80j-160j+25j)I3 + 80jI2 -25jI1 = 0
 
Last edited:
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  • #2
I don't see the 200 Ω resistor being affected by I1 in the first mesh equation.
 
  • #3
gneill said:
I don't see the 200 Ω resistor being affected by I1 in the first mesh equation.
Can't believe I missed that. Do the other two look fine?
Are there any "shortcut strategies" for solving a system of three equations with complex variables?
 
  • #4
eehelp150 said:
Can't believe I missed that. Do the other two look fine?
Are there any "shortcut strategies" for solving a system of three equations with complex variables?
The others look okay to me.

No shortcuts other than using a software package to do the heavy lifting. I'm partial to Mathcad myself, putting the equations into matrix form and using the built in solver.
 
  • #5
gneill said:
The others look okay to me.

No shortcuts other than using a software package to do the heavy lifting. I'm partial to Mathcad myself, putting the equations into matrix form and using the built in solver.
For mesh1, it should be -25jI3 instead of 400jI3
I used an online calculator and got this:
upload_2016-10-11_10-59-40.png
 

Attachments

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  • #6
Your 1,3 entry of the matrix should be identical to the 3,1 entry.

Here's a Mathcad version:
upload_2016-10-11_14-1-3.png
 
  • #7
gneill said:
Your 1,3 entry of the matrix should be identical to the 3,1 entry.

Here's a Mathcad version:
View attachment 107300
Is the voltage across Ve simply (I3-I2) * Impedance of 25uF capacitor?
 
  • #8
eehelp150 said:
Is the voltage across Ve simply (I3-I2) * Impedance of 25uF capacitor?
Make that (I2 - I3)*Z25μF. I2 flows into the top of the capacitor, so it'll produce a voltage drop in the correct direction.
 
  • #9
gneill said:
Make that (I2 - I3)*Z25μF. I2 flows into the top of the capacitor, so it'll produce a voltage drop in the correct direction.
I ended up getting 9.988 < -43.347 volts.
Converting to time domain would give: 9.988cos(500t - 43.347) right?
 
  • #10
eehelp150 said:
I ended up getting 9.988 < -43.347 volts.
Converting to time domain would give: 9.988cos(500t - 43.347) right?
That looks a bit small. Can you show that calculation in detail?
 
  • #11
gneill said:
That looks a bit small. Can you show that calculation in detail?
(I2-I3) * (-j80)
= (0.086 + 0.091j) * (-j80)
= -6.88j - 7.248j^2
=7.248-6.88j

sqrt(7.248^2 + 6.88^2) = 9.99 < -43.5 degrees
 
  • #12
What values are you using for I2 and I3?
 
  • #13
gneill said:
What values are you using for I2 and I3?
I2 = 0.1188 + 0.1314j
I3 = 0.0329 + 0.0408j

EDIT:
Are these the correct values?
I2 = 0.52013055631408 +0.24535752634041i
I3=0.15152422756397 +0.07991035923825i
 
  • #14
eehelp150 said:
I2 = 0.1188 + 0.1314j
I3 = 0.0329 + 0.0408j
They don't match your results from post #5. Has something changed?
 
  • #15
gneill said:
They don't match your results from post #5. Has something changed?
Lack of sleep I guess :P
I plugged in the wrong value to the calculator.

New value for Ve: 32.3<65.88 degrees
 
  • #16
eehelp150 said:
Lack of sleep I guess :P
I plugged in the wrong value to the calculator.

New value for Ve: 32.3<65.88 degrees
Better. Confirm the sign of the angle.
 
  • #17
gneill said:
Better. Confirm the sign of the angle.
Why is it -65.88 instead of 65.88? I recall this being covered in class but I forgot. The calculator spits out 65.88
 
  • #18
eehelp150 said:
Why is it -65.88 instead of 65.88? I recall this being covered in class but I forgot. The calculator spits out 65.88
What are the Cartesian components of the complex value?
 
  • #19
gneill said:
What are the Cartesian components of the complex value?
Fourth quadrant.
I get it now.
 

1. What is mesh analysis?

Mesh analysis is a method used in circuit analysis to determine the voltage and current values in a circuit. It involves dividing the circuit into smaller loops or meshes and applying Kirchhoff's voltage law to each mesh to solve for the unknown variables.

2. Why is mesh analysis important?

Mesh analysis is important because it allows us to analyze complex circuits and determine the voltage and current values at any point in the circuit. This information is crucial in designing and troubleshooting electronic circuits.

3. How do you convert from time to frequency domain using mesh analysis?

To convert from time to frequency domain using mesh analysis, we use a technique called the Fourier transform. This involves representing the time-domain equations in terms of complex numbers and then solving for the frequency-domain values using the appropriate equations.

4. Are there any special equations that need to be used in mesh analysis for converting to the frequency domain?

Yes, there are specific equations that need to be used in mesh analysis for converting to the frequency domain. These include the impedance equation, the complex power equation, and the impedance matrix equation.

5. Is mesh analysis the only method for converting from time to frequency domain?

No, mesh analysis is not the only method for converting from time to frequency domain. Other methods include nodal analysis and using Laplace transforms. The choice of method depends on the complexity of the circuit and the desired accuracy of the results.

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