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Re: Calculation of Q?



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At 12:11 AM 3/9/97 +0000, you wrote:
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>X-Envelope-From: sfalco-at-worldnet.att-dot-net  Sat Mar  8 14:37:57 1997
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>Date: Sat, 8 Mar 97 20:53:45 +0000
>From: Steve Falco <sfalco-at-worldnet.att-dot-net>
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>Subject: Calculation of Q?
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>I came across an equation for calculating the Q of a solonoid coil in
>the ITT book "Reference Data for Radio Engineers". The formula is:
>  Q = A * d * sqrt(f)
>where A is a coefficient that varies with the ratio of Length/Diameter,
>d is the diameter in inches, and sqrt(f) is the square-root of the
>frequency in megahertz.
>
>-------------------------------------------  Snip

>	Steve Falco
>	sfalco-at-worldnet.att-dot-net

------------------------------------------------->

  Steve -

 Finding a reliable formula for  the Q factor of a Tesla coil is not easy.
There are several equations for radio use like the one you show but they do
not work with Tesla coils. The Q factor for Tesla coils is an indication of
the ability of the secondary coil to ring down, that is, the time it takes
for the dampened sine wave to attenuate to a certain percentage of the
maximum amplitude. 

The wave attenuation involves the equation  Q = X/R = 6.283 L F / R  where L
is the coil inductance, F the frequency, and R the effective resistance. The
6.283L is a constant for a particular coil, but the F and R vary greatly
depending on how the Q factor is calculated and how the coil is tested. 

Commercial meters like the Boontoon 260A use 1000 HZ for the test frequency
and a correction factor R that appears to work for radio use. But when it
comes to Tesla coils it is a whole new ball game. One test is Q = Fc/(Fh-Fl)
where Fc is the resonant frequency of the coil with Fh and Fl the .707
voltage point frequencies. This gives a Q factor that will get you in the
ballpark and near the true value for Tesla work.

Another test which is the only way to find the true Q factor of an operating
Tesla coil is  Q = 3.1416/Log Dec .  The method of finding the Log Dec is
shown in my Tesla Coil Notebook. This Q factor is always much lower than the
.707 voltage point tests. This is an easy test to make if you have an
oscilloscope.

There is still another problem with finding the Q factor of a Tesla coil.
The Q factor involves the effective resistance R of the coil. This R
involves several other parameters. All of these parameters must be
coordinated for a complete solution of the Tesla coil system. The JHCTES
computer program does this job and is the only program that shows a Q factor
where all of the parameters are coordinated and work in the equations. In
the past coilers have said the theoretical equations did not work. Now with
the JHCTES program you can find the Q factor and you do not even have to do
the calculations.

John Couture






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