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RE: K Factor & Mutual Inductance

Subject: 
            RE: K Factor & Mutual Inductance
       Date: 
            Tue, 15 Apr 1997 17:08:44 +1200
       From: 
            "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
Organization: 
            Wellington Polytechnic, NZ
         To: 
            tesla-at-pupman-dot-com


Hi John,

> >> Apparently we both agree that the R is not the DC or AC 
resistance. It > >> must
> >> be determined by calcs after finding the Q and the X of the coil.
> >
> >Whoa! It is the resistance at the frequency of interest (effective 
> >AC resistance). The rho of the material is factored in. The only 
> >reason it is difficult to calculate is the many-bodied problem. The 
> >surroundings affect it. You can test this for yourself. Try mounting 
> >a primary and cap close to ground and measure its Q without the gap. 
> >Then sit it up a few feet and measure again. This should be of 
> >interest to anybody wanting to couple more primary power to the 
> >secondary than ground etc.  You can also see the effect of doing this 
> >on the secondary.
> >
> >Malcolm
> >
> >---------------------------------------------------
> 
>  Malcolm -
> 
>  I assume when you say "the rho (a greek letter) of the material" you
> mean the resistivity of the material.

Yes.

>  When you say "reason it is difficult to calculate" what equations are
> you using?

None. How do you allow for proximity to floor, ceiling, walls etc. 
Any attempted calculation of secondary Q is going to be valid for 
only one set of loading conditions (shunt impedance in other words).

>   I am working on a graph for effective resistance. Do you have any
> suggestions?

You could reduce shunt impedances by positioning the coils you are 
measuring well away from the abovementioned fixtures. In fact, 
knowing Zo (easy) you can actually arrange for the shunt impedance to 
be the same for each coil by simple measurement of Zbase despite the
differences in Zo for each coil.

Zshunt = Zo^2 x Zbase  (where Zo = SQRT(L/Cdistr) approx.)

The table then has a constant in the form of Zshunt built in. This 
will be a pretty high value. With the coil so arranged, measure Q in 
the usual manner and use that to calculate ESR using either Q = wL/R
or Q = SQRT(L/Cdistr)/R. At least that's the way I'd do it. Any use?

Malcolm