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Re: [TCML] Critical Coupling?



Indeed I suspect too  "critical coupling" means 
something different for coilers than in radio theory.
I don't think it stands for "magic k" values either.
I guess you are right and that it denotes  the
highest coupling in practical SGTC designs before
insulation problems are faced.
In Tilbury's book "The ultimate TC design and
construction guide" (pp 108-113) he refers to the
value k=0.2 as the critical coupling.
Quote from the book:
"A dashed line appears at k=0.2 in the worksheet 
graphs and in the figures 4-19 through 4-24 denoting
the critical coupling fot spark gap tesla coils.
The worksheets can be used to design any type of coil;
however,the critical coupling threshold of k=0.2 
applies only to SGTCs."

Frankly,fixing value k=0.2 for all designs of SGTCs
,all primaries and secondaries has got no sense to me.
Moreover,insulation problems also depend on the bang
size.With k<0.1 the insulation problems can be induced
if the bang size gets too large for the coil size and
the various flashovers ,or if you are lucky ,just 
secondary racing sparks will happen.



Dex   




--- bert.hickman@xxxxxxxxxx wrote:

From: Bert Hickman <bert.hickman@xxxxxxxxxx>
To: Tesla Coil Mailing List <tesla@xxxxxxxxxx>
Subject: Re: [TCML] Critical Coupling?
Date: Thu, 14 Jan 2010 16:58:34 -0600

Dex,

Coilers really DO use a different definition. Most TC's do not operate 
in the steady state regime. The above definition for critical coupling 
defines maximum CW RF power transfer (as a function of primary and 
secondary Q) when the system is in _steady state_. This definition is of 
limited use for most Tesla Coils, since most TC's never reach steady 
state. They operate in the transient regime, and are best characterized 
instead by their transient response.

If you plug in typical TC primary and secondary Q's, you can easily see 
that the critical coupling predicted by the above formula is much too 
low. For example, the Q of a typical SGTC primary circuit is of the 
order of 10-15 (including the spark gap). The Q of a well constructed 
non-sparking secondary, with a good RF ground, is in the range of 
100-250. Plugging these values into the above formula, one gets a 
critical coupling value of only 0.016 - 0.03.

Most SGTC's and DRSSTC's actually operate with "optimal" k's that are in 
the range of 0.10 - 0.20, and VTTC's or SSTC's may run with k's in the 
range of 0.3 - 0.4 or higher. For TC's, optimal is defined as longest 
sparks for a given input power with no abnormal insulation problems. Now 
in the transient regime, there are a number of so-called "magic" k 
values that, in theory, result in the most efficient P <-> S energy 
transfers. Using a magic k value permits energy to be fully transferred 
between primary and secondary LC circuits over _an integral number_ of 
RF half cycles.

Magic k values for a coupled 2-coil system are 0.6, 0.385, 0.28, 0.22, 
0.18, 0.153, 0.133, 0.117, 0.105... and so on. For example, a k of 0.18 
would permit full transfer energy over 6 half-cycles, or three complete 
RF cycles. With SGTC's (and good performing - quenching - spark gaps), 
most coilers find that the higher the k, the better their performance... 
until they start getting racing sparks or other insulation failures. 
This tends to limit most air-insulated SGTC's to a maximum (critical?) k 
of about 0.22. The other limiting factor is the quenching capability of 
the spark gap itself. At present, there are no analytical tools to 
predetermine best k for a SGTC other than experimentally. Note that 
oil-insulated "air core" resonant transformers have been used in pulsed 
power applications with k's of 0.6.

Bert
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Dex Dexter wrote:
> In radio engineering critical coupling of 2
> tuned coupled LC circuits is defined as:
> 
> k=1/SQRT(Q1*Q2)
> 
> Q1,Q2 are quality factors of first and second
> circuit.
> 
> I notice that term "critical coupling" is 
> often refered to in the context of tesla coils
> and coiling as well.
> 
> Does it have the same meaning and definition
> like in radio engineering?
> 
> If not,please explain what it is and give definition
> of it.
> 
> Dex  
> 



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