Re: Overcoupling??

To: tesla-at-pupman-dot-com
Subject: Re: Overcoupling??
From: "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)
Date: Fri, 07 May 1999 11:44:03 -0600
Approved: twftesla-at-uswest-dot-net
Delivered-To: fixup-tesla-at-pupman-dot-com-at-fixme
Hello all,
             Here is an excerpt of a discussion I've been having 
lately with John Freau. It is just part of the conversation so gaps 
will exist but you'll get the gist. Terry's mention of turns ratio 
in regard to the topic spurred me to send this to the list. I hope 
John doesn't mind me sending this.

Regards,
Malcolm

 ------- Forwarded Message Follows -------

From:           Self <DIRECTORATE/MALCOLM>
To:             FutureT-at-aol-dot-com
Subject:        Re: Secondary Inductance (fwd)
Date sent:      Mon, 26 Apr 1999 11:45:46 +1200

Hi John,
          I thought I'd have a crack at doing a proof of the turns 
ratio idea.  To help decide the method of proof, I thought I'd have a 
look at a practical example where different aspect ratios give the 
same Cs which I failed to do last time.
     
     I'll take a Diameter of 10" and Height of 30" for both coils as 
a starting point. According to Medhurst, Cself for this coil is 
0.61*10*2.54 pF = 15.5pF close enough.  I'll choose a height for the 
new secondary coil of 10" and by knowing Cself = 15.5pF, arrive at a 
diameter of 13" for this coil (Cself comes out to 15.3pF which is 
pretty close).

Let Lp = 100uH which gives Np = 37 turns.
Let Ls = 10mH which gives Ns = 371 turns for the first secondary and 
the expected turns ratio.

For the new secondary, both Ls and Cs have to be the same so I need 
to find Ns to achieve this:  193 turns.

Interesting! That says I can do better than the turns ratio if the 
primary looks like a secondary and the secondary has the aspect ratio 
of a typical primary (sort of). 

Ns/Np = 193/37 = 5.21    and SQRT(Ls/Lp) = 10

Wow!  I hadn't expected that.  I simply have to try this. I expect 
that I'd get a reasonable if low coupling constant by overlapping the 
secondary on one end of the primary to a small degree.

The physical layout poses plenty of problems when it comes to 
generating high voltages in a small size but the argument is for 
academic interest. Let me try for a more moderate sized coil that I 
can whip up on the workbench:

Let Lp = 10uH, Dp = 4" and Hp = 5"   Then Np = 13 turns

Let Ls in both cases = 5mH and let me choose Ds = 2" and Hs = 10" for 
the first secondary. That gives me Cself = .71*2.54*2 pF = 3.6pF
That gives me Ns = 707 turns

SQRT(Ls/Lp) = 22.36   and Ns/Np = 54.4

Knowing Vout prop to SQRT(Ls/Lp) says that voltage step up falls 
short of the turns ratio which appears to be the usual scenario.

Now let me choose a second secondary where Ds = 3".  If Ls remains 
the same, then Hs is 3" to meet the Cs = 3.6pF requirement (I chose 
those based on getting the same capacitance or at least one of 3.5pF).
This forces the new Ns = 311 turns.

Now Ns/Np = 311/13 = 23.9  which is still slightly worse than 
SQRT(Ls/Lp).

So I conclude that there exists a configuration where one can do 
better than Ns/Np but also that I am unlikely to better Ns/Np for the 
normal coil geometries we employ.  Still not a formal proof 
unfortunately. In view of the finding, I'd now like to try the first 
configuration I came up with. It would be amusing to get a longer 
spark than the primary gap setting from the shorter coil than I could
get from the taller one.

Of course this all ignores that one would expect 4/PI times the 
step-up ratio from a distributed circuit. 

**NOTE TO LIST MEMBERS - that last statement is made on the 
assumption that the Corum's theory has some validity which might not 
be the case.**

Better check me out on all this. I may have gone off the rails 
somewhere.

Cheers,
Malcolm