hello. you can call me fraser, if you like!

I have no qualms about using technology! I have matlab, but I'll be damned if I can figure out how to do anything useful on it. I will check out Scilab, thanks for the recommendation.

 

hello. you can call me fraser, if you like!

I have no qualms about using technology! I have matlab, but I'll be damned if I can figure out how to do anything useful on it. I will check out Scilab, thanks for the recommendation.

I'm quite sure all 4 of us have an appreciation for both the old ways and the new ways.

I think The-Electrician would recommend Mathematica for a computer based algebra system. I agree that's good, but I prefer to use Maxima because it's free.

One open question that remained in my mind was whether the cancellation of the w^6 terms was due to a careful balancing of the component values, or was an automatic result of the topology. This is a critical question because the component values have a tolerance, and will never be precise, whereas the alternative is not based on the exact values. To answer this question, I used Maxima to crank out the full algebraic answer, and it's clear that the w^6 terms cancel based on topology, which is good and makes the problem a reasonable one.

The Maxima commands and output are as follows.

collectterms(factor(determinant(matrix( 
[1-w^2*(L1+L3)*C1,w^2*L1*C1,w^2*L3*C1], 
[w^2*L1*C3,1-w^2*(L2+L1)*C3,w^2*L2*C3], 
[w^2*L3*C2,w^2*L2*C2,1-w^2*(L3+L2)*C2] 
))),w);

\(w^4(C_2C_3L_2L_3+C_1C_3L_2L_3+C_1C_2L_2L_3+C_2C_3L_1L_3+C_1C_3L_1L_3+C_1C_2L_1L_3+C_2C_3L_1L_2+C_1C_3L_1L_2+C_1C_2L_1L_2)
-w^2(C_2L_3+C_1L_3+C_3L_2+C_2L_2+C_3L_1+C_1L_1)\; +\; 1\)

EDIT: by the way, in case you couldn't tell, I use the symbol \(C_1\) for the 1F cap, \(C_2\) for the 2F cap, and \(C_3\) for the 3F cap. A similar convention is used for the coils. \(L_1\) is the 1H coil, \(L_2\) is the 2H coil, and \(L_3\) is the 3H coil,.

 

That's very interesting. May consider putting it in my assignment answer, though could risk getting a reputation as a teachers pet for trying too hard!