# coupling coefficient - Best Method

```Hi Dan,
In late November of last year, the methods of measuring coupling was
discussed.  We went on and on, but in the end, I think this one post summed
it all up.  There must have been 50 posts on this subject then!!  I
remember it, because I started it :-))

BTW - At:

www.pupman-dot-com

are the stored archives of all the previous posts to this list going back
many years.  You can get them in zip format and such.

Terry Fritz

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From:   terryf-at-verinet-dot-com[SMTP:terryf-at-verinet-dot-com]
Sent:   Thursday, November 27, 1997 9:14 AM
To:     Tesla List
Subject:        Best Method to Find Coupling Coefficient

All,
I have tried all the suggestion I have received (Thanks Malcolm, Fr.
Tom, John C., Mark Rzeszotarski).  The best method I have found that does
not require expensive equipment or great theoretical challenges consists of
the following.

Apply a heavy 60 Hz AC current to the primary coil.  This is best
done by placing a space heater, hair dryer, etc. in series with the primary
to limit the current to about 10 amps.  Measure this current with a
multimeter.  Note that the space heater gives a fairly stable resistance.
Light bulbs have a non-linear resistance through the AC cycle and distort
the measurement (they must cool down substantially at the nodes of the AC
cycle).  Of course, use great caution with the live AC on the primary so as
not to kill yourself. Only the isolated primary need be connected to the AC.
The capacitors, transformers, and other wiring should be disconnected from
the primary for this test.  Be cautious of the AC finding its way on to the
secondary!

Place a 10k ohm resistor and a 1uF capacitor across the secondary and
measure the AC voltage.  It will be on the order of say 100 mV AC.  The
resistor and capacitor will eliminate stray noise picked up by the secondary
and swamp any resonance which is significant at these low levels.

The mutual inductance is found by:

M = V / (w * I)

Where:

M = Mutual inductance in Heneries.
w = the line frequency in radians per second (377 for 60Hz or 314
for 50 Hz).
I = The measured current in the primary in amps AC.
V = The measured secondary voltage in volts AC.

As an example:
If the current in the primary is 10 amps and the frequency is 60Hz
and you measure 0.100 volts AC, you would get:

0.100 / (377 * 10 ) = 26.52 uH for the mutual inductance.

k can then be found by using the formula:

k = M / sqrt(L1 * L2)

Where L1 and L2 are the inductances of the primary and secondary coils.

This method is rock solid in theory and easy to do.  The accuracy is
excellent.  There is little that can go wrong compared to other methods and
you don't need anything special other than a multimeter to do the test.  The
accuracy is dependant on the accuracy of your multimeter.  My tests could
easily get within 1%.

Thanks again for all the great suggestions and do be careful with
the AC if you try this.

Terry

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