Re........ Measuring Coupling Coefficients

From: 	Barton B. Anderson[SMTP:mopar-at-mn.uswest-dot-net]
Sent: 	Wednesday, December 10, 1997 8:12 PM
To: 	Tesla List
Subject: 	Re........  Measuring Coupling Coefficients

Tesla List wrote:

> > -------------------------------------------------------- snip
> >> The equation ( K = >1/sqrt(QpQs) ) will predict a K of 0.0527 but does not
> > take into account that the two coils are separated by 150 feet and thus have a K
> of  zero.

ok, I'm confused. I've been reading these posts and am become more confused by the
moment. In the above statement, what does "separated by 150 feet" mean? Is this just
an arbitrary view point? an exaggeration, a "what if"?

K is a "coefficient" of two values of magnetic flux which defines "what percentage (or
ratio) of flux from one coil is coupling another coil". If outside of coupling, (k =
0) then k is meaningless. K says "for this coil(Q) and that coil(Q), here is your
attainable coupling ratio of mutual inductance". The physical dimensions and
configuration (geometry) of coil to coil will either over couple, under couple, or hit
the mark.

> > ------------------------------------snip
> >    The K - 1/sqrt(QpQs) is for mutually coupled coils so the K would not be
> > zero. As Q depends on F it would appear that coupling depends on frequency. I
> > havn't seen an explanation for this contradiction with other K factor equations.
> >  JHC

Yes, if Q changes with frequency then k would "change with" frequency. But, changing
your frequency requires a geometric change to attain Xl = Xc at the new frequency
which will have a new k ratio. Therefore, geometry determines k as well as the

Here's a mood point: In an RF Coil, Q = 2 PI F L / re :::: where "re" is the ac
effective resistance, not the dc resistance measured with a 9v battery powered meter.
At low frequencies, the coils resistance should be ok to use in a calculation, but in
an RF Coil, as frequency increases the effective resistance(re) increases because "re"
is a "resistive" component drawing in-phase current from the ac source, and if "re"
increases then Q decreases. By how much would be dependent on the I^2R losses at the
operational frequency and that might be a bit hard to calculate if not impossible. It
will be interesting to see how Marks program performs this function.

I personally like Malcolm's measuring technique for k, because he is throwing high
frequency across the coil to make measurements which should effectively bring "re"
closer to "operational values". Throwing the same operational frequency across the
coil should be even more precise.

Just some thoughts,