Mutual Inductance (was Flat Primary Winding - next question)
To: "'Tesla List'" <tesla-at-pupman-dot-com>
Subject: Mutual Inductance (was Flat Primary Winding - next question)
From: Tesla List <tesla-at-stic-dot-net>
Date: Sun, 21 Jun 1998 23:46:14 -0500
From: terryf-at-verinet-dot-com [SMTP:terryf-at-verinet-dot-com]
Sent: Sunday, June 21, 1998 12:13 AM
To: Tesla List
Subject: Re: Mutual Inductance (was Flat Primary Winding - next question)
Just for clarity,
The coil in case A has the following parameters:
15,000 volt 60 mA neon input (variac controlled)
17.05nF primary cap
8.84 inch avarage radius flat spiral primary of 1/4 inch tubing.
5.67 inch wide coil section
Lp = 118.4 uH
Fo = 112.0 kHz
5.13 inch radius
33.33 turns per inch
0.02002 bare wire diameter
Ls = 75.4 mH
Cself = 16.68 pF
Ctop = 10.10 pF
The JHCTES program gives a K of 0.21 and m = 602.04 uH.
Mark's program gives a K of 2.01 and m = 635.96 uH.
The actual K is 0.2069 and m is 618.19 uH.
The thing I really like about Mark's program is that it predicts K for
various coil heights.
My coil will not quench well with a K of 0.21. I have to raise the coil
about 2 inches to get a clean quench.
Mark's program very accurately predicts the K at various heights. The
JHCTES program omits this input because of "lack of emperical data" (page
11-1 Tesla Coil notebook). Perhaps John could add this feature to JHCTES??
At 08:09 PM 6/20/98 -0500, you wrote:
>From: John H. Couture [SMTP:couturejh-at-worldnet.att-dot-net]
>Sent: Saturday, June 20, 1998 3:01 PM
>To: Tesla List
>Subject: Re: Mutual Inductance (was Flat Primary Winding - next question)
> All -
> The mutual inductance of a Tesla coil is important because it is the major
>parameter that connects the two magnetic circuits of the primary and
>secondary tank systems. Mutual inductance can be used to find other
>parameters including the important K factor or coupling of the coils.
> K = Lm / sqrt(Lp x Ls)
> It is always interesting to compare different methods of finding TC
>parameters like the mutual inductance. Mark has listed below the mutual
>inductance he has found for different primary coil arrangements. To compare
>his data using the JHCTES program I came up with the following for System A:
> Pri cap = .031 uf Pri spiral avg rad = 9.0 ins Width = 5.7 ins
> Sec rad = 5.14 ins Turns = 1000 TPS = 33.33
> Bare wire dia = .020 Sec term = 40 pf
> Some of the outputs
> Pri ind = 135 uh Pri turns = 15
> Sec ind = 76.3 mh K Factor = .20
> Op Freq = 77.86 KHZ Mut Ind = 656 uh
> Keep in mind that small changes in the inputs can make large changes in
>the outputs when solving for mutual inductance. The pri cap in the inputs
>can be used to change the pri turns. Coilers who have the JHCTES program may
>want to try other changes to see how they affect the mutual inductance.
> To my knowledge the only TC program available today for the coiler that
>solves for the mutual inductance is the JHCTES program. The Corum program
>has mutual inductance as an input not an output. The JHCTES program uses an
>algorithm based on an equation in Terman's Radio Engineering Handbook.
> One advantage of Mark's program is that it provides more detail of how the
>primary bathes the secondary as you go up the sec coil. To do this with the
>JHCTES program requires additional calculations on the part of the program
>user. If much of this work was to be done it would be better to write a new
>program and incorporating Terman's equation.
> John Couture
>At 07:29 AM 6/18/98 -0500, you wrote:
>>From: Mark S. Rzeszotarski, Ph.D. [SMTP:msr7-at-po.cwru.edu]
>>Sent: Thursday, June 18, 1998 2:49 AM
>>To: Tesla List
>>Subject: Re: Flat Primary Winding - next question
>>Steve Young said in part:
>>>I am wondering just how
>>>primary diameter affects coupling to the secondary. I envision the
>>>magnetic flux from a larger diameter primary will intercept more of the
>>>secondary than will a more compact primary, but I don't know the practical
>>>significance of such an effect. I would assume we should couple to as much
>>>of the secondary as possible to even out the secondary volts per turn
>>>distribution (implies large diameter primary).
>>Consider three flat spiral primaries:
>>System A: inside diameter 12", outside diameter 23.34", N=15.125 turns
>>(Terry Fritz's primary)
>>System B: inside diameter 12", outside diameter 36.00", N=15.125 turns
>>System C: inside diameter 12", outside diameter 36.00", N=14.000 turns
>> Assume each is coupled to a secondary which is 1000 turns of .02"
>>wire on a 10.25 inch diameter by 30 inch tall secondary, positioned such
>>that the bottom turn of the secondary is in the same plane as the flat
>>Results of mutual inductance calculations:
>>System A: Lp=131 uH Ls=76.3 mH M=636 uH K=.20
>>System B: Lp=151 uH Ls=76.3 mH M=614 uH K=.18 (same # turns as
>>System C: Lp=132 uH Ls=76.3 mH M=569 uH K=.18 (tried to match Lp of
>> Conclusion: you get slightly better coupling with the smaller
>>diameter primary. The current in the secondary is directly proportional to
>>M, so the small diameter primary may be advantageous. Of course, you could
>>wind a solenoidal primary and get even higher M, if you can hold off the
>>>This leads to another thought. If the primary effectively couples mainly
>>>to the lower part of a 1000 turn secondary (e.g. the first 100 or so
>>>turns), then do we in effect have a 100 turn secondary feeding a 900 turn
>> One can examine the degree of coupling between the primary and
>>secondary by looking at the mutual inductance M between the primary and a
>>one inch tall segment of the secondary. In the example below, I looked at
>>the coupling between the primary and a secondary 10.25" diameter, 1" height
>>with 33.33 turns. The secondary coil is moved from 0" above the primary to
>>28" above the primary, near the top of the actual secondary. Here are the
>>results for System A and System C (which have the same Lp and Ls):
>>Position M for System A M for System C
>> 0" 93 uH (100%) 64 uH (100%)
>> 2" 71 uH ( 76%) 53 uH ( 83%)
>> 4" 50 uH ( 54%) 42 uH ( 66%)
>> 6" 35 uH ( 38%) 32 uH ( 50%)
>> 8" 25 uH ( 27%) 25 uH ( 39%)
>> 12" 13 uH ( 14%) 15 uH ( 23%)
>> 16" 7 uH ( 8%) 9 uH ( 14%)
>> 20" 4 uH ( 4%) 6 uH ( 9%)
>> 24" 3 uH ( 3%) 4 uH ( 6%)
>> 28" 2 uH ( 2%) 3 uH ( 5%)
>> It is clear that the larger diameter primary bathes the secondary a
>>little higher up than the smaller diameter primary. Still, most of the
>>coupling is accomplished in the lower 1/4th of the coil height or so. So,
>>to answer your question, no, not 100 turns, more like 200 turns!
>> There are striking similarities between the magnifier configuration
>>and the conventional two coil system. Unfortunately, you generally lose
>>with the magnifier, unless you can build a really fast quenching series type
>>rotary spark gap to handle the higher coupling coefficient.
>>Mark S. Rzeszotarski, Ph.D.