Re: Maggies and such

["Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)]

Tesla list wrote:
 
> Original poster: "Malcolm Watts" <M.J.Watts-at-massey.ac.nz>

> Without looking at how you've done it I discovered that the
> following works well:
> 
> - calculate C2 (Medhurst)
> - calculate C3 (    "   )
> - sum Ctot = C2+C3
> - sum Ltot = L2+L3
> 
> Fr = 1/[2.PI.SQRT(Ltot.Ctot)]

I made some tests to verify if your relation corresponds to mine.
Unfortunately, it doesn't, but I found some very interesting relations:

Selecting a mode that doesn't require a too large C2 (modes n,n+1,n+4
are ok):

Mode 2,3,6:
L1=44 uH
L2=14 mH
L3=30 mH
C1=10 nF
C2=12 pF
C3=10 pF
k12=0.56

Ctot=22 pF
Ltot=44 mH
Fr=162 kHz
But the primary resonates at 1/(2*pi*sqrt(L1*C1))=240 kHz

Note that in this case, it's better to ignore C2, since the
relation L1*C1=(L2+L3)*C3 matches (perfectly!).

Observing this, I looked at the equations of the optimal design
(http://www.coe.ufrj.br/~acmq/tesla/magnifier.html),
and saw that the relation:

L1*C1=(L2+L3)*C3 (1)

-Always- matches exactly!

And more: The coupling coefficient of the transformer, if expressed 
in terms of the circuit elements, depends -only- on L2 and L3!

k12=sqrt(L2/(L2+L3)) (2)

The ratio L2/L3 depends on the chosen mode as in the original
equations, and C2 can be calculated from C3 and the mode (k,l,m) as:

C2=C3*2*l^4/((l^2-m^2)*(k^2-l^2)) (3)

A design can then be made in the following way:

Choose L3 and C3, from available third coil and terminal:
L3=20 mH
C3=10 pF 
Choose the mode and compute L2 from the original formula:
Mode 3,4,5 (k,l,m)
L2=L3*((l^2-m^2)*(k^2-l^2))/(2*k^2*m^2)=2.8 mH
>From (1), and a given C1 compute L1:
C1=10 nF
L1=(L2+L3)*C3/C1=22.8 uH
Compute k12 from (2):
k12=0.35
Compute C2 from (3):
C2=81 pF

The result is identical to what is obtained from the original formulas,
but this design is simpler.

Antonio Carlos M. de Queiroz