# Re: Tesla Coil Q Factors

```X-Envelope-From: couturejh-at-worldnet.att-dot-net  Wed Aug 26 16:35:34 1998

Bert, All -

Please excuse the omission of R in the equation
Q = 6.283 x F x L/R
This is the same R that I also mentioned with Q and Vs that could not be
found by tests. This R can only be found after Q is found. Q is calculated
from the log dec which can be found by tests. However, finding the log dec
by the use of waveforms is not a simple matter. Several conditions must be
maintained that complicates the test. I made these types of tests several
years ago when writing my books.

After finding the true Q factor the secondary voltage can be found by the
equation
Vs = Q Vp  and   Q = Vs/Vp
This is a fundamental equation in the concept of Q factors. The
derivation of this equation and the best article I have seen on the Q
factor is in the Booton Radio Notebook of spring 1954. Boonton made a Q
meter that was the standard of the world. The meter uses a test circuit
that utilizes the above equation. I use this circuit in one of my books to
show a coiler how he can test a coil for the Q factor. It should be
understood that these are not TC operation Q factors. It is interesting to
compare Q factors obtained from this meter or a bridge meter with the Q
factors obtained using the half power test.

The Q factor is used in many ways. With iron core transformers the
secondary voltage is equal to the primary voltage times the ratio of
winding turns. With a Tesla coil which is a resonant air core transformer
the secondary voltage is equal to the primary voltage times the Q factor.
Note that the resonant rise in voltage of a resonant circuit is the Q factor.

The TC output voltage is directly related to the input wattage by the
equation
Vs = sqrt(2W/(CsxBKS))
The W is equal to the input watt seconds times an efficiency at a
particular point in the secondary circuit (this is not the overall
efficiency). This is one of several reasons why the Vs increases with an
increase in the input wattage.

The history of Q factors is a little known but interesting story. The
story begins with Kenneth Johnson about 1914 when he was working on
telephone circuits for the Bell Telephone Labs. In his calculations he was
working with a ratio of reactance to resistance (Q = X/R) and needed a
letter to represent this ratio. Q was not selected to represent the quality
of a coil. It was the only letter of the alphabet that wasn't already being
used by electrical engineers. Note that Q is the reciprocal of the
dissipation factor.

It appears that no one (including myself) has been able to coordinate the
seven key equations that I show and that are involved in the operation of
Tesla coils. I have been working on this for several years. The present
literature is of little use. I am still reseaching the problem.

Does anyone have any ideas?

John Couture

------------------------------------

At 05:26 PM 8/25/98 -0600, you wrote:
>Tesla List wrote:
>>
>> ----------
>> From:  John H. Couture [SMTP:couturejh-at-worldnet.att-dot-net]
>> Sent:  Monday, August 24, 1998 11:57 AM
>> To:  Tesla List
>> Subject:  Tesla Coil Q Factors
>>
>>   To All -
>>
><SNIP>
>
>Q = 6.283 x F x L    Q = Vs/Vp       Q = 3.1416/ Log Dec
>
><SNIP>
>>   With real coils the secondary voltage Vs increases when the input wattage
>> is increased. This means that in the equation Q = Vs/Vp the Q Factor would
>> increase with an increase in wattage. However, with real coils just the
>> opposite happens. The Q Factor decreases as the wattage increases. I show a
>> graph in one of my books of this relationship where the Q Factor decreases
>> with an increase in the wattage. To my knowledge there is nothing in the
>> present literature that shows why there is this apparent discrepancy with
>> the equations.
>>
><SNIP>
>
>John,
>
>The first equation is not quite right - it should be:
>       Q = (6.283 * F * L)/Reff
>where Reff is the combination of AC resistance in the circuit due to
>resistance, skin effect, winding proximity effects. As you indicate,
>determining the Q's of the primary and secondary circuits in a sparking
>coil is tougher, but can be estimated by looking at waveforms and
>back-calculating.
>
>However, output voltage is not directly relatable to input wattage,
>although you will see a degree of correlation: larger systems tend to
>use larger tank caps and higher primary voltages, and need more power to
>achieve similar breakrates. Output voltage is more directly a function
>of bangsize and system losses, since disruptive coils do not build-up
>secondary energy from bang to bang. Sparklength is another matter...
>
>I'm not familiar with Q = Vs/Vp - how was this equation derived?
>
>-- Bert --
>
>
>

```