# re: 3/4 wavelength secondaries

```>>From sgreiner-at-wwnet-dot-comTue Jul 23 21:59:58 1996
>Date: Tue, 23 Jul 1996 21:32:37 -0700
>From: Skip Greiner <sgreiner-at-wwnet-dot-com>
>To: tesla list <tesla-at-pupman-dot-com>
>Subject: re: 3/4 wavelength secondaries

Skip Greiner wrote,

>Thanks to Richard Hull, Robert W. Stevens, and John H. Couture for their
>answers to my query re the subject.

You're welcome. RWS.

>I have snipped all of the above responses since they virtually reiterate
>the same ideas, ie., it should be possible to wind a 3/4 wave coil and
>make it resonate somewhere near its 3/4 wave frequency, taking into
>account its cself, etc.

>Richard, I want to do this if its possible. I understand it "should break
>out 1/3 of the way up the coil. If it is a standing wave, maybe it won't.

>John, I have my own home-brewed program to design coils. It does
>approximately what you suggest as far as satisfying the numerous
>applicable equations. It uses Wheeler and various other accepted
>equations for L, wavelength and frequency.

>Robert, I have a coil in which the wire length is "fairly" close to the
>1/4 wave resonant frequency. This coil will put out discharges exceeding
>36" from a 4.5" insulator on top with only a 1/4-20 screw for the top
>terminal.

Skip,

The relationship between streamer length and terminal voltage is so
non-linear that the strike distance measured to a grounded target
cannot be used to accurately guesstimate voltage.  As I pointed out
earlier, once corona is formed in the air, the voltage becomes
clamped by the ionized atmosphere and will not rise appreciably with further
increases in the application of power.  The length of the streamer will however
grow from this point on,  in a direct relationship with increasing current.  Your
1/4-20 terminal is probably not yielding more that 60 or 70 kilovolts
(if that high) at the corona clamping level, but your system can push enough
current behind the leading edge of the output pulse to push the streamer to
36 inches.

> there is also a great amount of corona from the top several
>turns of the secondary.

Without any electrostatic field shaping/control at the top end of
your secondary (which is provided as a side benefit of a toroidal
topload), corona from the top winding is a common, coil damaging problem.

> Driving power is a 15kv 120ma neon.

>Why did I bring this all up?

>I have tried to design and wind both 1/4 and 3/4 wave coils to be run
>with none or very little terminal capacitance with the idea that given
>the same energy delivered to the terminal capacitance, and using the
>energy equal to 1/2 cv^2...then decreasing the terminal cap should lead
>to increasing the voltage.

If it were possible to put a large radius, smooth top terminal on top of a
secondary that by some magic not allowed by the laws of physics, did not also
contribute a substantial amount of isotropic derived capacitance then maximum
voltage could be achieved.  The metal shape would provide the corona holdoff
we desire (avoiding early corona voltage clamping effect) whil'st not adding the
capacitive component which causes a so equipped resonator to max out
considerably short of 90 electrical degrees.
terminal from an electrical perspective, you will see that the
resonator is less than a full 90 electrical degrees long, and therefore cannot
achieve maximum voltage swing.  In the real hardware world though, such
toploaded, foreshortened coils gain so much benefit from the corona holdoff
feature provided by a large toroid, that they still provide better
performance than those full length resonators without toploads.

I believe that the capacitance represented in the toroid also helps
because it becomes a local storage facility to provide energy behind
the discharge streamer where and when we need it most, at the moment of
breakout.  For example, consider a 100 pF toroid charged to 3
megavolts, (this is entirely within the range attainable with a large
homebuilt coil).  1/2CV squared yields 450 Joules!  If discharged in the first
180 degrees of a 100 KHz  damped sinewave, this stored energy from
just the toroid represents  a pulse power of  90 megawatts! Only with the storage and
holdoff attributes of a large topload could we reap the benefits of resonant rise
to build our power to such high levels.  Resonance makes a coil
function, resonant rise makes it function better!  Techniques to hold
off the formation of energy draining corona are the route to maximizing resonant
rise.

Richard Hull advises to employ a topload so large that you are
just able to break away from it in the upper reaches of your system's
power capability.  He's right.  This is another fine design balancing
act however in and of itself!  A system that takes 8 KW to form corona is going
to be an outstanding performer when running at its optimum design power
level of 10 to 12 kilowatts, but before producing corona it will  be beating itself to
an early death when there are just 7 kilowatts being put into it, no
corona yet, and nowhere for this power to go.  An analogy is a
powerful radio transmitter operated with the antenna disconnected.
It doesn't take long to let the smoke out of a 10 KW broadcast
transmitter under such conditions if there are no fast acting safety shutdown
circuits in place.  Ditto for Tesla coils.  There is much more smoke
stored in the really big systems, and this smoke is expensive!

> Although its been a couple of years since I
>read Tesla's CSN, I believe he thought he was winding 1/4 wave coils and,
>if memory serves, he used very small terminal caps. I understand about
>corona and the fact that a toroid should build up the energy before
>breakout, but is that really how a TC works? I should not be able to get
>36" discharges from a 1/4-20 bolt if that assumption is true.

I see nothing unexpected from the 36 inch discharge size you show in this
example from merely a 1/4-20 bolt as a top terminal.  A 120 MA neon
transformer represents a lot of power!  I'll bet you real money that if you add a
it back into tune, that you will add at least 25% to your streamer
length with no other changes.  That is a conservative estimate.
I have a 15KV-at-60MA powered coil that consistently exceeds 40 inches
with a 3 inch by 24 inch toroid perched on a 4.25 inch dia. coil
wound 24 inches long with #26 wire.  My system RF capacitor is a little on the
small size for this size neon at just 0.008 mfd.  With a considerably more massive
topload I have measured 52 inchers to a ground target. I'm sure this
would increase further with a bit of a capacitor size increase, as
the cap size (and the voltage it is charged to) sets the system energy.
I haven't tried to resonate this system without a topload.  Maybe I
will try it just for fun if I can tap my primary down enough to retune.

An example of a big coil that did achieve humongous size streamers
with a pointy discharge electrode (no topload) is Robert Golka's 150
KW magnifier.  I'd say the same story holds true.  If he had properly employed
a large holdoff toroid, his sparks would have been that much MORE humungous.

>In any event I do not believe a 1/4 or 3/4 wave coil can be wound in any
>"reasonable" configuration. In fact the resonant frequency of 1/4 wave
>coils is always about 40% higher than the 1/4 wave wire length and a
>toroid must be used to bring in the frequency even taking into account
>the increase in cself due to ionization.

That statement is counter to my experience.  I have found that when a
given freespace 1/4 wave wirelength is made into a coil, the resulting coil
operates at a longer wavelength (lower frequency) than its equivalent stretched
out wavelength.  For example, I have wound 753 feet of #22 enamelled wire
onto a 4.1875 inch diameter form to a length of 22.675 inches.  753
feet of wire represents a freespace 1/4 wavelength at 327.6 kHz.  The
actual measured Fres of this coil with no topload is 317.6 kHz. By
forming this length of wire into a coil the frequency dropped 3.1%.
Another way of looking at this is that by winding the coil into a
spiral, the velocity of propagation down the wire has slowed by 3.1%.

> The resonant frequency of a 3/4
>wave coil is always lower than the 3/4 wave wire length so the 3/4 wave
>coil cannot be tuned at all. I have tried configurations from 5" to 48"
>in diameter and heights up to 190"(absurd, but the program allows it).
>I have actually built coils up to 48"x48" just to prove the program and
>the designs usually come in close to 10%.

Oh, I see now what you meant all along.  You're stipulating that you start out
with 1/4 wavelength of wire measured off to the freespace wavelength
at some frequency.  Then, no matter what shape you wind it into, the
resulting resonator no longer represents a 1/4 wavelength resonator
at that given frequency.  You didn't come out and say this in your
original post.  Yes, you're absolutely right, and from what I hear it seems that
this particular anomaly is difficult to predict in mathematical models.
This is why, even after the computer CAD program tells you final
parameters to ten decimal places, you still have to build a Tesla
coil in hardware, and play around with it a bit to make it work.  I
don't even bother with computer models.  Several elementary
electrical formulas on the old scientific calculator and away I go to
the shop.  For me, a lathe, or a drillpress are more essential in Tesla coil design
than a computer!  This is not to say that computerized TC design programs
won't help save time by calculating tables quickly.  Ultimately, it
will determine your level of achievement with a  coil project.

>I would certainly appreciate any comments to this and I would especially
>like to hear from anyone who has built a 1/4 or 3/4 wave coil that comes
>in close to the correct frequency.

I cited an example above in 1/4 wavelength resonance that was just
3.1% off.   Now that I think I understand your definition of  'correct
frequency', I suspect that this may not actually be possible.  As
soon as you wind a straight wire into a coil you increase its total
inductance, and that combined with self capacitance will lower the
self resonant frequency of that piece of wire.  I've learned to live
with this minor guesswork factor in determining final secondary size, and my
coils always work just fine, even if they don't work at the 'correct' frequency.
This seems to be a bit of an art, the feel for which one only gets
after winding many, many coils.  I've read Tesla could merely look at a coil
and tell you right on what frequency it would resonate at.  Tesla had
'computers' available in his day.

A while ago I posted an idea of hanging a stretched out length of
straight wire as a secondary resonator with a ball topload (bottomload?) from
a  bridge.  Although this would be an interesting experiment, it would create an
efficient coupling transformer to the surrounding air, and bleed away much of the
energy generated in the form of an EM radio wave.  I suspect that with a given,
finite powered oscillator, there would be less energy available for making sparks
off the end when compared to a traditional, compact, helical resonator.

>Thanks for listening

>Skip

Happy Coiling!, regardless of freespace wirelength, rwstephens
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