Re: How to rise the secondary? (fwd)

---------- Forwarded message ----------
Date: Sun, 05 Jul 1998 23:50:47 -0500
From: Bert Hickman <bert.hickman-at-aquila-dot-com>
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: How to rise the secondary?

John and all,

Sorry for the late response - I was away on a 3-day minivacation. John,
you ask some very interesting questions. My responses are interspersed

-- Bert --

Tesla List wrote:
> -----Original Message-----
> From: John H. Couture <couturejh-at-worldnet.att-dot-net>
> To: Tesla List <tesla-at-pupman-dot-com>
> Date: Wednesday, July 01, 1998 2:58 PM
> Subject: How to rise the secondary?
>   To Ed, Antonio, Bert, and Malcolm -
>   Many thanks for all the information regarding the raising of the
> secondary. It is gratifying to know that with the Internet and Tesla List it
> is possible to ask technical questions of this nature and be able to receive
> immediate replies from around the world. Coilers of only a few years ago
> were at a tremendous disadvantage without this type of resource.
>   As is typical with TC design, answers to a technical question sometimes
> brings up more questions.

Well, besides the pretty sparks, this is also part of what makes coiling
so interesting!

>   1. Doesn't changing the coupling (K) only change the time of energy
> transfer for a tuned TC system regardless of frequency? For example with K =
> .20 the energy will transfer for all coils and operating frequency:
>    Transfer time = 1/K = 1/.20 = 5 half cycles.

Mostly... however gap losses significantly influence the "effective"
transfer time lossy systems with low k. The effective transfer time can
viewed as the time at which you have no remaining "bang" energy left in
the primary circuit -  you've transferred part of it, and dissipated
the rest. A lossy gap, combined with a low k, can result in zero primary
energy being reached long before the predicted time for a complete
Primary:secondary transfer. Terry's excellent post shows this very
phenomonon occuring for low values of k and different gap styles. The
1/k estimate is reasonably close for relatively high k, low-loss

>   2. The total amount of energy transferred will occur when the TC system is
> in tune.
>        That is when  LpCp = LsCs
>        What are the equations relating the amount of energy transferred to
> special coupling coefficients?

The so-called "Magic values" of K are derived assuming NO system losses.
These are values of K that would result in 100% efficiency in energy
transfer (i.e., where primary I and E will simultaneously be 0 after "n"
half-cycles if there are no system losses). Magic values of K versus the
number of half-cycles ("n") can be found by:

      K = (2n-1)/(2*n^2-2n+1)

      K(1) = 1.000
      K(2) = 0.600
      K(3) = 0.385
    * K(4) = 0.280 (tough to achieve in a quenched 2-coil system)
    * K(5) = 0.220
    * K(6) = 0.180
    * K(7) = 0.153
    * Range of K's that work best for typical 2-coil systems
Voltage and energy relationships are discussed in a following section.

>   3. If the primary is designed with enough clearance to prevent sparkovers
> between the pri and sec coils, raising the secondary would be unnecessary?
> In other words the coupling is determined only by the sparkover clearance
> limitation. Using insulation instead of air to separate the pri/sec coils
> could be used to reduce the clearance and increase the coupling. But this
> would not change the amount of energy transfer or the length of sec term
> spark.

Overcoupling breakdowns cause flashovers between various portions of the
secondary winding itself, not between the secondary and the primary.
Improving the insulating strength (using an overcoat of Glyptol, Behr
Build50, Red Insulating Varnish, or using heavier vinyl insulated wire)
may permit a higher coupling coefficient to be used.

>   4. What are the equations relating the quenching characteristics to
> coupling and output spark lengths?

There is probably no closed-form equation(s) that can adequately predict
spark-length to quenching (other than you get maximum spark if you can
quench once all primary energy has been transferred to the secondary).
There are some closed-form equations which approximate secondary voltage
as a function of time, Rp, and Rs. One form, which assumes linear Rp and
exponential damping, is shown in Sargent, "High Power Electronics",
pages 284-285. This assumes that LpCp=LsCs, and that the primary
resistance is dominated by an "equivalent" gap resistance of Rp.

 Vout =   [Vx] * [e^(-t/T)] * [Cos(Wt/Sqrt(1-K))-Cos(Wt/Sqrt(1+K))]
      = Vmax term * Loss term *  Oscillatory Beat Response term      

        Vx = 0.5*(Vgap)*Sqrt(Ls/Lp)
         e = 2.718281828
         T = 4*Lp*Ls*(1-K^2)/(RsLp+RpLs)
        Fo = 1/(2*Pi*Sqrt(LpCp))
         W = 2*Pi*Fo = 1/Sqrt(LpCp) = 1/Sqrt(LsCs)

Practially speaking, we can probably assume that maximum sparklength is
concurrent with maximum energy transfer efficiency. This will occur if
we can maximize K while still being able to successfully quench at the
first point of zero primary energy. For K's in the 0.18 - 0.23 range,
the energy transfer efficiency can be shown to be in the 75-85% range
respectively. Modern air-coupled resonant charging transformers with
k=0.6 (sometimes used to generate high voltages for research) have
demonstrated efficiencies of 95% including gap losses.   

>   5. In #1 above the number of half cycles required to transfer all of the
> energy of a tuned TC from pri to sec coils can be found. However, how many
> half cycles are required to properly charge a suitable sec terminal so there
> will be a sec output spark and quenching time is not important?

For efficient coil operation, a good quenching gap is always desirable,
since streamer loading (except for power arcs to ground) may not always
be sufficient to guarantee quenching... and failure to quench always
results in poorer coil performance. A fully-loaded secondary, under
heavy streamer loading, will typically show a 10:1 drop in effective Q
(a Q of >150 before breakout may drop to 15 or less under heavy streamer
loading). The appropriate answer to your question is: "the MINIMUM
number of half cycles while still being able to quench at the first
notch under full streamer loading". A well insulated secondary, combined
with a good quenching gap can permit higher K, less gap losses, and more
"trapped" secondary energy. Since predicting gap and streamer quenching
performance ahead of time is quite difficult, "tweaking" K is an
essential part in maximizing a coil's performance.  

>   6. The point of over/under coupling (critical coupling) is determined when
>        Rp = Rs  How are these two parameters calculated at the time of
> design?
>       The equation  R = Xl/Q   cannot be solved because both  R and Q  at
> high voltage operation are unknowns at time of design.
>   John Couture

Disruptive coils rely on rapid energy transfer to the secondary to
minimize gap losses, and upon streamer loading and gap quenching to
block secondary:primary energy backfeeding. Disruptive coils run best at
K's MUCH higher than classical critical coupling. Classical critical
coupling has no meaningful place in modern day disruptive coiling...