On Sat, 26 Jul 2008 15:25:52 -0700, The Phantom
wrote:

On Sat, 26 Jul 2008 09:35:54 -0500, "Tim Williams"
wrote:

"The Phantom" wrote in message
. ..
In fact, doing all the algebra to "simplify" increases the possibility of
making a mistake. If you just plot the simplest expression, such as the
first one in my attachment, the one with "j's on all levels", the plot
should be the same, and with no extra algebraic simplification necessary.

Ya, in fact at one point I tested the formula by comparison with that.
Since Octave handles complex numbers natively, that's no problem. But I
want to come up with an expression for the resonant frequency (that's got to
be a bitch, I haven't even worked it yet but I forsee a quartic...eugh!), so
I can plug it back in to get Z at resonance in terms of R, M, W and C only.

The imaginary part of the impedance of this circuit:

Z o---Lm---+---C---+---GND
| |
+---R---+
| |
+---Lw--+

for the example values you gave, C = 20uF, M = 30uH, W = 1uH, R = 2 ohms,
is never zero. So even if you solve the quartic, you will find the
solution gives a value for w (omega) which is complex. You will have to
use a different definition of resonance frequency. The phase angle of the
impedance never becomes zero, although it does reach a minimum.


And besides, I need mathematical practice, unfortunately I don't need quite
this much of it...

Tim

What "quartic" ?:-) I keep harping at you guys to use Laplace
notation to avoid getting balled-up with "j".

...Jim Thompson
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