# Re: K Factor & Mutual Inductance

```Subject:
Re: K Factor & Mutual Inductance
Date:
Thu, 3 Apr 1997 07:05:34 +0000
From:
"John H. Couture" <couturejh-at-worldnet.att-dot-net>
To:
Tesla List <tesla-at-pupman-dot-com>

At 01:45 PM 4/2/97 +0000, you wrote:
>Subject:
>            Re: K Factor & Mutual Inductance
>       Date:
>            Wed, 2 Apr 1997 14:08:26 +1200
>       From:
>            "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
>Organization:
>            Wellington Polytechnic, NZ
>         To:
>            tesla-at-pupman-dot-com
>
>
>John,
>       I'm going to have to throw all my textbooks away :( after
>
>> One equation for the mutual inductance of air core concentric solenoids
>> is
>> shown in Terman's "Radio Engineers Handbook". Once the mutual inductance
>> Lm
>> is found the K Factor can be found by the equation
>>           K Factor = Lm/(sqrt(LpLs))
>> where Lp and Ls are the inductances of the primary and secondary coils.
>
>That equation is good for any coil - air-cored, iron cored or
>whatever? There are no conditions stated by Terman or anyone else to
>my knowledge (except JHC perhaps ;)
>
>> Note that the K Factor or coupling is not only dependent on the physical
>> location of the coils but also on several other parameters such as
>> resonant
>> frequency, Q Factor, log decrement, etc.
>
>Where is the frequency dependence in that equation? Lp? Ls? M? k? I've
>not observed any frequency dependence in Lp or Ls from DC to TC
>frequencies in all the measurements I've done. So it must be in k or
>M, right? But what defines either of those? Is the number of flux
>linkages between two coils frequency dependent? Why?
>
>Malcolm
>
>> Also, the critical coupling can
>> be
>> found when these parameters are coordinated to give Rp = Rs where Rp and
>> Rs
>> are the primary and secondary effective resistances.
>
>>
>> The JHCTES computer program determines the K Factor and other parameters
>> in
>> this manner. The results have been found to agree closely with tests of
>> actual coils. To my knowledge this is the only computer program
>> presently
>> available that utilizes this method of finding these parameters.
>>
>>  John Couture
>>
>>--------------------------------------------

Malcolm -

I hadn't consudered iron core coils because the classical TC is an
air
core coil.

The K factor is dependent on the Q factor, log decrement, and coil
effective resistance but not the frequency. The frequencies in the Lm,
Lp,
Ls equations cancel out when used in the K factor equation.

You are correct in that the number of flux linkages between the coils
are
not frequency dependent. I checked the JHCTES computer program and it is
correct in that the K factor does not change when the frequency changes.
Like you, the program does not always agree with what I say.

Thank you for bringing this to my attention. Please do not throw your
textbooks away.

John Couture
>

```