Hey guys. Got a beauty of a Matrix question in a recent assignment. http://personal.maths.surrey.ac.uk/st/J.Deane/Teach/em2/ass2.pdf this is a link to the assignment, it's question number 1 that is giving me grief.
I first apply KVL around each of the three loops to gain:
i1(1/jw + 4jw) + i2(-jw) + i3(-3jw) = 0
i1(-jw) + i2(1/3jw + 3jw) + i3(-2jw) = 0
i1(-3jw) + i2(-2jw) + i3(1/2jw + 5jw) = 0
That seems pretty easy to me. Checked it a few times, and I'm happy with it. With some simple manipulation of the terms a 1/xjw and xjw together, you can put it in matrix form like this, TAKING OUT 1/jw COMMON TO ALL:
(1 - 4w^2, w^2, 3w^2).......... (i1)
(w^2, 1-9w^2, 2w^2)..........(i2)
(3w^2, 2w^2m, 1-10w^2)....... (i3)
Now part b) asks you to solve for the non-trivial case that there are currents flowing, and the way we've been told to do this is to solve for determinant of the matrix equal to zero.
This is a lot of algebra so I won't try to write it all here, but I ended up with this answer:
-261w^6 + 152w^4 - 23w^2 + 1 = 0
Which is horrible looking lol. I understand this can give me three possible values of w^2 as it's a cubic expression but anyone able to check my working or offer any advice?
This is a beast....
I first apply KVL around each of the three loops to gain:
i1(1/jw + 4jw) + i2(-jw) + i3(-3jw) = 0
i1(-jw) + i2(1/3jw + 3jw) + i3(-2jw) = 0
i1(-3jw) + i2(-2jw) + i3(1/2jw + 5jw) = 0
That seems pretty easy to me. Checked it a few times, and I'm happy with it. With some simple manipulation of the terms a 1/xjw and xjw together, you can put it in matrix form like this, TAKING OUT 1/jw COMMON TO ALL:
(1 - 4w^2, w^2, 3w^2).......... (i1)
(w^2, 1-9w^2, 2w^2)..........(i2)
(3w^2, 2w^2m, 1-10w^2)....... (i3)
Now part b) asks you to solve for the non-trivial case that there are currents flowing, and the way we've been told to do this is to solve for determinant of the matrix equal to zero.
This is a lot of algebra so I won't try to write it all here, but I ended up with this answer:
-261w^6 + 152w^4 - 23w^2 + 1 = 0
Which is horrible looking lol. I understand this can give me three possible values of w^2 as it's a cubic expression but anyone able to check my working or offer any advice?
This is a beast....
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