Llc Converter, simulataneous equations

[treez]

Hello,

I am trying to solve simulataneous equations to find Lm and Llkp in equation 8, page 4 of the following

http://www.fairchildsemi.com/an/AN/AN-4151.pdf

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?

[Sch3mat1c]

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.

Easy one,
Lm = Lp - Likp (8a)

Some work,
Lr = Likp + (Lm || Likp) (8b )
= Likp + Lm * Likp / (Lm + Likp)
= Likp * ( 1 + 1 / (1 + Likp / Lm) )

Substitute,
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.

Finally,

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.

Tim