Tesla coil is a quarter-wave resonator I’snt it ?

[VNTC]

US Patent No. 645576, Nikola Tesla, System of transmission of electrical energy, filed September 2, 1897; granted March 20, 1900 "The length of the...coil in each transformer should be approximately one quarter of the wave length of the electric disturbance in the circuit, this estimate being based on the velocity of propagation of the disturbaiice through the coil itself..."
I don’t know why? Mr. Steve Ward, a very successful coil man not mention about that.
Let’s look at a SRSSTC. The resonance frequency decide only by L2C2 so with an available L2 coil depend on the value of C2 we have many difference resonance frequency, and it will work OK at any resonance frequency? I don’t think so. I have seen a L2C2 coil give highest voltage at the middle of the coil height and none at the top because it runs at double frequency that it should be.
And until now I not yet knows is it the true in DRSSTC? (My small DRSSTC is progress)
Hello guys let’s tell us your mind.
Thank you all.

[Mads Barnkob]

The quarter wave design as the most optimal Tesla coil has not been proved by any of the old spark gap coil builders and even less by the modern DRSSTC/QCWDRSSTC builders.

Especially the QCW where very long sparks are achieved from shaping the voltage envelope more, which gives a better result than any other factor.

The quarter wave design was properly the best theory to practise that was possible in Tesla's days, but it can also bring us to another question.

What is the best Tesla coil?

We build Tesla coils to make sparks to have fun with it, Tesla wanted to power the entire world wireless, its two completely different end goals.

[Uspring]

The quarter wave condition is just another way of saying that the secondary is run at the lowest resonance. You can drive the secondary at higher frequency modes, but they will put antinodes somewhere along the winding. You don't want arcs to originate there. If you want to use higher frequencies it is better to wind less turns since that reduces losses.

[Mads Barnkob]

The quarter wave condition is just another way of saying that the secondary is run at the lowest resonance. You can drive the secondary at higher frequency modes, but they will put antinodes somewhere along the winding. You don't want arcs to originate there. If you want to use higher frequencies it is better to wind less turns since that reduces losses.

I found my DRSSTC4 to be very hard to understand, as it would perform the same or better at a wide range of frequencies away from the lowest resonance.

https://highvoltageforum.net/index.php?topic=24.0

[Teravolt]

any body correct me if I am wrong, yes a tesla is a 1/4 wave length however with distributive capacitance and top load and arc capacitance that changes. the reson I know I have tried to build teslas to a desired resononant F. the more turns the mor diributive capacitance. I think that you can figure it out with java tesla coil. why do you ask?

[Mads Barnkob]

I remember where I had "the old guys denounced it" from, it might just have been that it was read mistakenly. I was referring to this:

The length of the secondary coil is used to calculate the wire weight. In the past it was thought that the secondary coil wire length should match the quarter wave length of the Tesla coil's resonate frequency. However, it has since been determined that it's unnecessary.

From: https://www.teslacoildesign.com/design.html

[Uspring]

The length of the secondary coil is used to calculate the wire weight. In the past it was thought that the secondary coil wire length should match the quarter wave length of the Tesla coil's resonate frequency. However, it has since been determined that it's unnecessary.

If you think of the secondary being just a long straight wire of length l pointing upwards, its resonance frequency would be given by the quarter wave condition

l = lambda/4 and
lambda = c/f

->

f = c/(4*l)

c being the speed of light and f the frequency. That's the quarter wave antenna model.
A wound coil has a different geometry, making the above equations unsuitable, and when you add a top load, the resonance f drops considerably.

I found my DRSSTC4 to be very hard to understand, as it would perform the same or better at a wide range of frequencies away from the lowest resonance.

Generally, a coil works best if run at the secondary resonance. For a DRSSTC, though, you usually want to run at a frequency, which is given by the zero current switching condition in order to avoid hard switching. There are 3 such frequencies, the lower pole, the upper pole and a middle frequency. The lower and upper poles are located below and above the secondary resonance, so the zero current switching condition is in conflict with the desire to run at the res frequency. Particularly at high coupling, the frequency difference between the poles and the secondary fres can be considerable. The high coupling compensates for this drawback, though.

The middle frequency is in principle the best, but it suffers from instability issues and cannot be obtained by the usual feedback mechanism.

[T3sl4co1l]

Quarter wave is approximately correct, yes.  The wave velocity is lower due to geometry, and the characteristic impedance is much higher (which is mainly what we're after, as the impedance of corona and sparks as your only load is quite high).

If you enter typical dimensions here,
https://hamwaves.com/inductance/en/index.html (which was updated like just last week!)
you'll find the waveguide impedance figure, which is related.

Unfortunately it seems to give poor results for low frequency, tight wound coils (negative RS?), but the inductance is probably not too bad.

Wide range tuning is probably a sign of low Q and high coupling.  The minimum coupling is ~1/Q (less, and power is lost in the primary or recirculated in the supply, rather than coupled over), and if Q is limited by corona discharge, it can be pretty high (I'm not sure how much it actually is, and I'm sure it depends on breakout geometry and everything else).

Tim

[joabel1971]

The quarter wave design as the most optimal Tesla coil has not been proved by any of the old spark gap coil builders and even less by the modern DRSSTC/QCWDRSSTC builders.

Especially the QCW where very long sparks are achieved from shaping the voltage envelope more, which gives a better result than any other factor.

The quarter wave design was properly the best theory to practise that was possible in Tesla's days, but it can also bring us to another question.

What is the best Tesla coil?

We build Tesla coils to make sparks to have fun with it, Tesla wanted to power the entire world wireless, its two completely different end goals.

I am building device to generate resonant hydrogen plasma & have some suggestions that have not been offered - on how to make a better Tesla Coil (since the question was asked).    In my experiment - I am attempting multiple resonant conditions to create a non-thermal plasma that is 100% ionized (a non-flammable, room-temperature ICP jet). 

a.  I started my design with Tesla Patent #512,340 (showing the potential advantages of interleaved cone-coils).   I have tested this coil (without external capacitors) to find resonant conditions for AM electrolysis experiments.  This interleaved method apparently stores 250,000 times as much energy as a 1-wire coil winding method.   Interleaved coils also have the ability to cancel out their own reactance at their resonant frequency (based on overall wire length of the secondary). 

b.  To tune the coil & take advantage of superposition - I am using the rest frequency of hydrogen (1.42 Ghz @ 21 cm) and 6 more 1/4-wave wirelengths multilayered (lowest frequency is 346,778 Khz @ 865.104 meters).  The correct phase between frequencies to create constructive interference has been calculated at 3/2*pi, however, square-wave signaling appears to eliminate this requirement. 

The summation formula is:
f(x) = 8 + ∑ sin((5.291423766936 * 4^n * x) + 3/2 *pi)
n = 7 - 14

This superposition calculation has been mathematically proven with graphing software. 

FR @ 4^14 =   1,420,405,751.  766702882816 Hz   
FR @ 4^13 =      355,101,437.  941675720704 Hz   
FR @ 4^12 =        88,775,359.  485418930176 Hz   
FR @ 4^11 =        22,193,839.  87354732544   Hz   
FR @ 4^10 =          5,548,459.  967838683136 Hz
FR @ 4^9 =            1,387,114.   991959670784 Hz
FR @ 4^8 =              346,778.   747989917696 Hz

c.  To allow the use of 30 volt, 10 amp DC power supplies - I have ALSO added 1/4-length PRIMARIES (in relation to the secondary lengths) & positioned them below the secondaries (not layered, but adjacently below) to try to fix any impedance mismatch.  1/4-wave transformers are documented ways of eliminating impedance mismatch. 

d.  I am signaling the device with a new microcontroller that outputs 54 different frequencies at the same time (1 Hz - 25 Mhz) - called the Parallax Propeller 2.  It is tested.    The 3 highest frequencies will be generated using either Voltage Controlled Oscillators (VCOs) or output signals from a Vector Network Analyzer (NanaVNA-F V2 is capable of 1.42 Ghz).   

e.  I am using a slant angle that causes the slant height of the cone-coils to be equal to the circumference of the cone.   This simplifies calculations in a number of ways.  The slant angle that does this is around 80.842150 degrees (depending on the size of the nozzle hole at the top).

f.  My 3 output nozzles are nested and contain 4 materials - water (to generate steam), hydrogen & graphite, and hydrogen & silica.  Due to the self-organizing properties of complex (dusty) plasma, my overall goal to to create a new material - a graphene/silicene hybrid. 

g.  All non-hydrogen gasses (including ambient air) are being evacuated from the cone coil system using qty. 2 - 8" duct fans. The cones are internally bi-sected with a sheet of stainless steel to create a ducting system.  (1 fan to suck air in - 1 fan to suck air out).

h.  The entire frame is made of 304 stainless steel (non-magnetic & poorly conductive).  The coils are 18 AWG enameled copper for the primary & 30 AWG enameled copper for the secondary.

i.  No capacitors are being used - since the interleaving creates a certain amount of capacitance to reach resonant conditions. 

j.  The highest voltage used is 300 volts at 1 amp for the lowest frequency (since the resistance of the secondary wire is 292 ohms).   Each successive voltage is 1/4 of the prior, but current should remain 1 amp for all superpositioned wires.

k.  Design attached.