On Mon, 28 Jul 2008 12:13:02 -0500, "Tim Williams"
wrote:

"The Phantom" wrote in message
.. .
And I suppose d(Im)/dw = 0 (imaginary extrema) gives yet another point
that
isn't quite resonance. Hmm, that damn quotient rule again.

See the attachment for the expression for the imaginary part minimum. It
is much more complicated than the other two, but it also has the property
that as R -- infinity its limit is sqrt[(Lm + Lw) / c*Lm*Lw].

Hmm, fortune produced a quadratic (in omega^2) in the expression, but seeing
no obvious way to simplify it, I left it at the incredibly awful
substitution in the quadratic formula. I'm somewhat relieved, though still
mortified, to see a similarly awful expression produced by Mathematica(?).
:^)

I wanted to have the derivation for resonance, but sadly it looks like
maxima of the modulus is the only way to go, outside of real = 0, which
turns out to be only an approximation, and it's just too complicated (and
involves a cubic) to write down.

I'm not sure what you mean by this. You said in another post, and I got
the same result, that:

"For Re = 0, I get omega = sqrt[(Lm + Lw) / c*Lm*Lw], no R term."

Are you talking about Re[Z} rather than Re[Vo/Vin]?

I guess I'll have to be satisfied to say
"steps --". :-/

Tim