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Re: K Factor & Mutual Inductance

Subject: 
        Re: K Factor & Mutual Inductance
  Date: 
        Wed, 9 Apr 1997 07:16:05 +0000
  From: 
        "John H. Couture" <couturejh-at-worldnet.att-dot-net>
    To: 
        Tesla List <tesla-at-pupman-dot-com>


At 10:15 PM 4/7/97 +0000, you wrote:
>Subject: 
>            Re: K Factor & Mutual Inductance
>       Date: 
>            Mon, 07 Apr 1997 06:49:31 -0700
>       From: 
>            Bert Hickman <bert.hickman-at-aquila-dot-com>
>Organization: 
>            Stoneridge Engineering
>         To: 
>            Tesla List <tesla-at-pupman-dot-com>
> References: 
>            1
>
>
>Dr. Resonance:
>
>I agree with your assessment that coupling coefficient should be
>independent of power level. Coupling coefficient defines the portion of
>magnetic flux that is shared between the primary and secondary, and is a
>function only of relative geometry and spacing between the two for air
>cored coils. Although optimal primary running frequency seems to lower a
>little bit under high power operation, this is not attributeable to any
>changes in the coupling coefficient, but more likely in effective
>secondary:toroid loading capacitance after the region around the top
>becomes heavily ionized. Also, estimating optimal quench-time as a
>function of fr and k requires adjustment - but this is a function of gap
>energy losses and k.
>
>-- Bert H --
>
>
>Tesla List wrote:
>> 
>> Subject:
>>         Re: K Factor & Mutual Inductance
>>   Date:
>>         Mon, 7 Apr 1997 04:57:32 -0700
>>   From:
>>         "DR.RESONANCE" <DR.RESONANCE-at-next-wave-dot-net>
>>     To:
>>         "Tesla List" <tesla-at-poodle.pupman-dot-com>
>> 
>> To: John Couture
>> 
>> Hi John:
>> 
>> We normally think of coeff. coupling being independent of system power,
>> ie,
>> if you ignore the effects of additional electric field capacitance above
>> the sec. coil (usually on 5% or less anyway) then the coeff. coupling
>> measurements should be the same with a sig. generator and scope vs. a
>> powered up system.  Does your equations somehow tie "power" into the
>> coeff.
>> coupling equation??
>> 
>> I know the relationship between mutual inductance, coeff. coupling, and
>> Q,
>> but was wondering how power fits into the system with regard to
>> calculations?  Any comments greatly appreciated in this area.
>> 
>> We normally tune up systems using a sig. generator (vacuum tube type for
>> higher output) and scope, and then make an adjustment for actually power
>> up
>> operation.  There seems to be a direct linear relationship between these
>> two primary tap positions.  A small extrapolation is usually necessary
>> for
>> high power systems operating over 5 KVA.
>> 
>> We plan to do some more direct research in this area this summer and try
>> to
>> develop an exact difference so as to develop a simple equation or simple
>> ratio/proportion which can be applied to most coil systems.  Richard's
>> systems with high coeff. coupling might respond differently.
>> 
>> Any comments -- John or Rich H., et al   -- on your thoughts and
>> observations.
>> 
>> DR.RESONANCE-at-next-wave-dot-net
><SNIP>
>
>----------------------------------------------------------

 DR.RESONANCE -

 Note in all of the K factor equations that the units cancel out and the
K
factor ends up as a dimensionless quantity. This means that the K factor
is
only a ratio like pi. The K factor, however, is a variable ratio
depending
on the parameters. Pi is a constant.

The K factor can be dependent on many parameters. For example, flux
linkages
are dependent on the currents in the coils. These currents vary with the
frequency, impedence, etc.

As for how power fits into the system you can use the equation shown in
the
Tesla Coil Construction Guide   
                         Watts = .5 Cp Vp^2 BKS/EFF
This equation tells us that more rotary gap breaks (BKS) will give
longer
sparks provided you have enough power and high enough efficiency.
Coilers
have difficulty understanding how to apply this equation properly. Note
this
is a standard equation not mine.

I have never tried to tie power and coupling coefficient into one
equation.
It should be possible because the K factor is a ratio of impedences. The
impedences affect the flow of currents thru the Tesla coil system which
in
turn affects the flux linkages, etc. There may be coilers on the Tesla
List
that have done this.

 John Couture