Re: Maggies and such

["Malcolm Watts" <M.J.Watts-at-massey.ac.nz> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)]

Hi Antonio,

On 18 Aug 00, at 20:31, Tesla list wrote:

> Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 
> 
> 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!).

That is really interesting!!!  My first shot at making sense 
of maggies several years ago made me jump to the conclusion 
that all one had to do was tune the primary to the extra coil 
and bingo.  I later realized that was in error and the error 
arose because L2 was quite small relative to L3. I may have 
serendipitously hit upon a k12 that worked.
    Two years ago I then had a shot using the method I 
outlined above with two identical resonators and a rather 
loose k12 and that seemed to work fine. In that particular 
case I couldn't ignore the effects of C2. 

> 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!

Wow - I have to try that!!!
 
> 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)

Are you saying that L1 doesn't even figure?? I guess you are.

> 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.

I love it!  It won't be tonight but it will be very soon I try 
this.

Regards,
Malcolm