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Mesh-Current Analysis, VCCS with phasors

  • Thread starter Tet
  • Start date
  • #1
Tet
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http://img247.imageshack.us/img247/7035/problemso9.jpg [Broken]

Ok so I have to do mesh-current analysis and I think I'm doing it correctly but my answer doesn't match the one given. This has to be done using phasors.

I labeled my meshes from left to right 1, 2, and so on.

Mesh 1:
33.8 = 1I1 + j2I1 + 3(I1 - I2) + (-j5)(I1-I2)
33.8 = 1I1 + j2I1 + 3I1 - 3I2 - j5I1 + j5I2
33.8 = (4 - j3) I1 + (-3 + j5) I2

Mesh 2:
0 = j5(I1 - I2) - 3(I1 - I2) + 2(I2 - I3)
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - 2I3

(mesh current with the VCCS)
I3 = -0.75 Vx
where
Vx = (-j5)(I1 - I2)
I3 = -0.75 * (-j5)(I1-I2)
I3 = j3.75(I1 - I2)

substituting into Mesh 2 equation:
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - 2( j3.75 (I1 - I2) )
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - j7.5(I1 - I2)
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - j7.5I1 + j7.5I2
0 = -3I1 + (5+j2.5)I2

I know:
I = I1

I put both mesh equations in a matrix and the answer isn't what it's displayed in that picture (I get I = I1 = 8.98021 angle -1.828).


Am i missing something here? I'm thinking I'm approaching this totally wrong. I always have a hard time with Mesh analysis and always prefer Nodal over it... but I'm almost certain that it has something to do with the VCCS (voltage controlled current source) and my equations for it.
 
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Answers and Replies

  • #2
Tet
3
0
Solved this by simply adding a third equation with
I3 = -0.75 Vx
where
Vx = (-j5)(I1 - I2)
I3 = -0.75 * (-j5)(I1-I2)
I3 = j3.75(I1 - I2)

I3 - (j3.75)I1 + (j3.75)I2 = 0 (third equation)

I put the previous 2 Mesh equations and this one in a matrix and got the values of all 3 currents.

(4 - j3) I1 + (-3 + j5) I2 = 33.8 (mesh 1)
(-3 + j5) I1 + (5 - j5) I2 - (2)I3 = 0 (mesh 2)
(- j3.75)I1 + (j3.75)I2 + I3 = 0 (third equation derived from Vx)

I1 = i = 29 + j2 or 29.07 angle 3.95



In this case this should be corrected:
Mesh 2:
0 = j5(I1 - I2) - 3(I1 - I2) + 2(I2 - I3)
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - 2I3

(mesh current with the VCCS)
I3 = -0.75 Vx
where
Vx = (-j5)(I1 - I2)
I3 = -0.75 * (-j5)(I1-I2)
I3 = j3.75(I1 - I2)

substituting into Mesh 2 equation:
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - 2( j3.75 (I1 - I2) )
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - j7.5(I1 - I2)
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - j7.5I1 + j7.5I2
0 = -3I1 + (5+j2.5)I2

^ red text not used
 
Last edited:

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