RE: K Factor & Mutual Inductance

            RE: K Factor & Mutual Inductance
            Fri, 11 Apr 1997 09:10:15 +1200
            "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
            Wellington Polytechnic, NZ

Heinz, John, all,

> John,
>         You state that the R is effective, not DC or AC. Why can't you
> measure the R of the coil, calculate the XL, at the
> expected frequency of operation, and use the result to find a ballpark
> Q? Could you elaborate on effective R?
> Heinz
> >
> >
> >Hi John, All,
> >Have you ever tried the formula Q = sqrt( L / C ) / R.
> >
> >Barry
> >
> > ----------------------------------------------------
>   Barry -
>   I have never seen the above Q factor equation before. What would you
> use
> for R? In the usual equation   Q = X/R   where X = 6.283 F L  the R is
> an
> effective resistance, not DC or AC.


    The "R" in the equation is the ESR (effective series resistance)
as it is for wL/R etc. ESR is measured at the frequency of operation
since it is frequency dependent due to skin effect.

Here is the derivation for the equation above:
Start with Q = wL/R = 1/wCR
=> Q^2 = wL/R x 1/wCR
=> Q^2 = L/C x 1/R^2
Therefore Q = SQRT(L/C)/R

(the => means "implies" for those without the math background)
The above formula appears in The Radiotron Designer's Handbook among
    Lastly, the ESR can be converted to an equivalent shunt resistance
by: shunt R = (1+Q^2) x ESR