"Method to Find Coupling Coefficient"
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
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)
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%.