Re: Bart's Coil

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <twftesla-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>

Hi:

I am accompaining this discussion, although may have missed how it
started.

Some considerations that may be useful:

In a Tesla coil modeled as two coupled LC tanks, L1-C1 and L2-C2,
with coupling coefficient k12 between L1 and L2 and losses ignored,
the following relations are valid:

-The two tanks must be tuned to the same frequency, if optimum
 energy transfer is desired.
 L1*C1 = L2*C2
-The complete system has always two natural oscillation frequencies,
 f1 = a*f0
 f2 = b*f0
-Perfect energy transfer happens when a and b are integers
 with odd difference (as 1,2, 2,3, 1,4, 2,5, etc.)
-The coupling coefficient for this ("magical values") is given by:
 k12=(b^2-a^2)/(b^2+a^2)
-If the difference b-a=n there is zero energy at the primary
 at the nth notch of the primary voltage.
-Complete energy transfer occurs after b/2 full cycles of the
 primary voltage, or b semicycles of the secondary voltage.
-f0 (that multiplies a and b) is related with the elements by:
 f0=(1/(2*pi*a*b))*sqrt((a^2+b^2)/(2*L2*C2))

So, looking at the primary or at the secondary voltages it's
possible to count b (number of semicycles until complete energy
transfer). If the system is properly adjusted, a=b-1, and k12 
can be calculated as:
k12=(2*b-1)/(2*b^2-2*b+1)

Antonio Carlos M. de Queiroz