# Re: coupling coefficient - Best Method

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Terry, All -

The test that Terry shows for mutual inductance (Lm) and described below
is a good one and was shown in Tesla's Colorado Springs Notes. I show this
test in my Tesla Coil Design Manual complete with an example.

This type of test gives the mutual inductance so the coupling is found
indirectly. The test is somewhat novel in that it solves a differential
equation. Tesla obviously understood differential equations.

V = Lm di/dt          Lm = V dt/di

Lm = Vp/(6.283 F Is)      K = Lm sqrt(Lp Ls)

It is amazing that such a simple test can solve a differential equation.
Most diff equations require a lot more work to solve. The wiring diagram I
show gives the mutual inductance on the multimeter directly in microhenries.

I show a 12 volt light bulb for a ballast because I use a 120 to 6 volt
transformer for the test so the non linearity of the low voltage lamp is
less critical. This makes the test safer because of the low voltage. I
agree, however, that the proper linear resistance would be better.

This test is great for finding the mutual inductance. However, one fault
I find with using this test to determine the coupling is that two
additional tests are required to find Lp and Ls. This brings in more test
errors that affect the accuracy of the answer found for the coupling. I
believe the test I show for finding the coupling directly is simpler and
more accurate. An example is shown in one of my books.

John Couture

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At 06:53 PM 9/2/98 -0600, you wrote:
>Original Poster: Dan Kline <ntesla-at-ntesla.csd.sc.edu>
>
>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
>
>----------------------------------------------------------------------------
>
>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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