Re: Magnetic Field in a Flat Spiral

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

Original poster: "Paul Nicholson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

David Thomson wrote:
> what is the formula for calculating the Q of a coil by taking the
> two voltages on either side of the resonant frequency?

Detect the coil's resonance with a distant pickup, or by measuring
the base current.  Turn down the output of your signal generator so
that it is below half of its maximum drive voltage. Tune the signal
generator for a maximum reading on your detector and mark this level.

Now turn up the generator to exactly twice the original output level.
The reading on the detector will go up. Then tune the generator either
side of resonance to find the two frequencies at which the level on
the detector falls to its original at-resonance value.  If these two
frequencies are f1 and f2, then the Q is given by

 Q = sqrt(3) * sqrt(f1 * f2)/|f1 - f2|

This test measures the Q of the whole resonator, which includes the
output circuit of the signal generator.  Therefore you must either
pad the generator down to a very low impedance with a shunt resistor
or a transformer, or drive the coil via a low-Z buffer.  This method
doesn't require linearity of the detector, only repeatability. 

A signal generator with a good fine tune is a prerequisite, as is a
frequency counter.  You need to make sure that the drive voltage can
be turned up by exactly a factor of two at the coil base. Use a sine
wave drive voltage.  Even with care the method might only be 5% or 10%
accurate due to the sensitivity to the small difference |f1-f2|.  Day
to day variation of the Q is to be expected, for reasons which remain
unexplored, I think.
--
Paul Nicholson
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