# RE: K Factor & Mutual Inductance

```Subject:
RE: K Factor & Mutual Inductance
Date:
Fri, 11 Apr 1997 09:10:15 +1200
From:
"Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
Organization:
Wellington Polytechnic, NZ
To:
tesla-at-pupman-dot-com

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.

What???

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:
=> 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
others.
Lastly, the ESR can be converted to an equivalent shunt resistance
by: shunt R = (1+Q^2) x ESR

Malcolm
<snip>

```