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Posted: August 29, 2012 06:22 am
Group: Trusted Members
Member No.: 17,791
Joined: August 29, 2008
I am trying to solve simulataneous equations to find Lm and Llkp in equation 8, page 4 of the following
I have Lp = 800uH and Lr = 200uH , but i did the substitution, then the quadratic solver [x=-b+-(sqrt(b^2-4ac)/2a) and it doesnt work
do you know why?
Posted: August 29, 2012 09:01 am
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Member No.: 73
Joined: July 24, 2002
I think I've figured out that the author means "parallel" when writing "//". Not, like, double division or something.
Mathematics provides a "||" symbol to indicate parallelism, as it happens.
Lm = Lp - Likp (8a)
Lr = Likp + (Lm || Likp) (8b )
= Likp + Lm * Likp / (Lm + Likp)
= Likp * ( 1 + 1 / (1 + Likp / Lm) )
Lr = Likp * ( 1 + 1 / (1 + Likp / (Lp - Likp)) )
= Likp * ( 1 + (Lp - Likp) / ((Lp - Likp) + Likp) )
= Likp * ( (Lp + (Lp - Likp)) / Lp )
= Likp * (2 Lp - Likp) / Lp
0 = Likp^2 * (-1 / Lp) + Likp * 2 + (-Lr)
Likp = (-2 +/- sqrt( (2)^2 - 4 * (-1 / Lp) * (-Lr) ) ) / 2
Likp = -1 +/- sqrt(1 - Lr/Lp)
Evidently 0 <= Lr/Lp < 1 for a reasonable solution.
Lm = Lp - Likp = Lp + 1 -/+ sqrt(1 - Lr/Lp)
I don't think this is right because I seem to have placed an extra inductance somewhere. Algebra in text is boring, do it on paper to be sure. Or just as Wolfram Alpha, it'll solve a system this small.
Answering questions is a tricky subject to practice. Not due to the difficulty of formulating or locating answers, but due to the human inability of asking the right questions; a skill that, were one to possess, would put them in the "answering" category.
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