Re: Coupling Coefficient

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Barton B. Anderson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <tesla123-at-pacbell-dot-net>

Hi CJ - 

Don't let our past thread confuse you. Coupling is the ratio of inductance the
primary and secondary have upon one another (mutual inductance) due to the fact
the coils are in close proximity. Yes, changing proximity by repositioning
primary or secondary does change the ratio of mutual indutance or coupling (K).


As far as measuring Mutual Inductance, here's a post from 1997 that as far as
I'm concerned, is still the easiest and as accurate as to the stability of the
current load being used. Of the list below, I have found hair dryers to apply a
pretty stable current at around 10 amps. Let it run for about 1 minute (to
stabilize heat coils with output air) and the change in current will be
minimal. Resistors of low value are no good as they heat up and current changes
dramatically. High value resistors don't apply a lot of current (but it can
stabilize well). Heat elements have the same problem as low value resistors (I
even tried a 3000W 10ohm - no good). Hair dryer is still #1 in my book. 

Terry's 97 post follows. 

Take care, 
Bart 
  

From:   Terry Fritz 
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. 
  

Tesla list wrote: 
>
> Original poster: "CJ Moore by way of Terry Fritz <twftesla-at-qwest-dot-net>"
> <wizard1234-at-home-dot-com> 
>
> I have been doing some searching trying to find a test to find k, however I 
> have only been able to find vague descriptions. I have two questions about 
> it, 1) Does anyone know of a good site with explanation of the test/why it 
> works etc, and how to do it and 2) (This is probably a very simplistic 
> question), but what effects the Fo and Fs, if I were to do the test and came 
> up with an undesirable result, what do I need to do I change. I had thought 
> that it was the position of the primary and secondary, but now I am not so 
> sure. 
>
> Thanks for your help, 
>
> CJ