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Re: [TCML] Critical Coupling?



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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