A QCW coil throws a discharge that looks nothing like an ordinary Tesla coil's: one straight, smooth channel that visibly grows instead of appearing all at once. Builders call it a sword, as against lightning.
The reference coil used in these articles has never been switched on, so every length and ratio below is read off other people's builds. It is an example, not a reference. Work the numbers against your own coil.
Why it comes out straight
The reason is timing, not anything clever in the geometry.
A DRSSTC's bang lasts about 300 microseconds and reaches only about ten centimetres. Divided by the cycles in that window at the 50 to 150 kHz such a coil runs, that is 2.2 to 6.7 millimetres per RF cycle [derived], and the metre-and-a-half sword is fifteen such bangs laid end to end on a channel that stays lit. That much charge arriving that fast lets the channel break out in several directions at once, and it does.
A QCW's ramp lasts 6 to 25 milliseconds and its channel gains 0.13 millimetres per cycle, seventeen to fifty times slower [derived]. At that rate one channel grows, and it grows more or less continuously.
The 6 ms is the shortest converter ramp on file. Gao Guangyan's QCW 1 ran its first light at a "Pulse length around 6.2 to 6.5ms to peak of ramp, total ramp time just over 7ms", and the same page specifies the machine at "10 - 20ms ramp time" (loneoceans). His QCW 1.5 lists "Up to 20+ms ramp time to ~320V" and runs a burst of about 22 ms with the rise about 16.5. The 4 to 5 ms figure that also gets quoted belongs to the mains-ramped coils, where it is the rising quarter of a mains period and nobody chose it. That is a different machine, and the buck's page keeps it separate.
The 0.13 hides a band. A metre and a half over a 25 ms ramp is 0.06 mm per microsecond, and dividing by the frequency turns it into millimetres a cycle: 0.13 at 460 kHz, 0.20 at 300 kHz, 0.30 at 200 kHz [derived]. That makes 0.13 the fast end, and it needs a frequency near the top of the band below rather than in the middle. Nothing on file runs a metre and a half at 460 kHz either. The machine that ran there is Gao's QCW 1, which made one metre. The page that owns this division uses CJ's 2.39 m over 23 ms instead and gets 0.23 to 0.24, so the band across the two builds on file is 0.13 to 0.24, and the seventeen to fifty above is the ratio at the fast end of it.
The two machines differ in the rate of charge delivery rather than in shape, and everything else about a QCW follows from arranging that rate.
Why the other kinds do not do this
Put every sort of coil on one axis, how often charge arrives at the tip, and the shapes sort themselves out along it:
50 to 150 kHz thick branched lightning
200 to 500 kHz the long straight sword
1 to 4 MHz a thin straight warm flameHigher up that axis the channel is reheated more often, so it stays hot between deliveries and has no need to find a new path. Lower down it cools between them, and a cool channel tends to go looking for an easier way.
A spark gap coil sits near the bottom and has a second problem as well. It hands over its energy in about eighty microseconds and is then done, so its arc is thrown rather than grown. A DRSSTC fixed that half of it, so a longer on time does get a DRSSTC more length, but its charge still arrives in bursts fast enough for the head to break out sideways. A single channel only wins the whole way up when delivery is both slow and continuous.
Straighter is not simply better either, and that is why the useful range is a band. Push the frequency higher and branching keeps falling, but the channel starts to curl instead. A ramped tube coil at 2 MHz throws loops tens of centimetres across. Branching and curling are two different defects and frequency moves them in opposite directions, so the window sits in the middle rather than as high as the electronics can reach.
The only figure on record next to the bands is Uspring's, that sword arcs "seem only possible at frequencies of 400kHz or above".
He offers a mechanism there and says plainly that it is a hypothesis. A higher frequency moves the arc's space charges back and forth more often, which gives a higher current and so a hotter channel. A hotter channel conducts better, and a better conductor needs less voltage for a given length. That puts a high frequency arc in the same class as a slowly ramped one, a low voltage arc, and in his sideways-breakout hypothesis it is the low voltage, not the heat, that suppresses branches.
We do not stand behind even that last step, and a hot channel being straighter was never part of it. Straightness and branching are two defects, and frequency moves them in opposite directions. Why the sword bends withdraws frequency as a branching cause outright, and points out that the band table above calls 1 to 4 MHz a thin straight flame while a 2 MHz ramped tube coil throws loops tens of centimetres across. Read the bands as shapes that have been seen, not as a trade that has been measured.
Do not read length off the bands either. Uspring's "therefore longer" is length for a given voltage on one channel. The longest arcs anyone throws come off powerful low and mid frequency machines, where the length comes from power. A QCW is after the shape.
Whether a slow ramp can stand in for a high frequency is not established. No test of it by davekni has been found, on the forum or in these notes, and the one low frequency experiment of his that is on file cuts the other way. His 100 kHz QCW gave an initially straight arc path that then went zigzagged, which the discussion put down to the channel repelling itself rather than to branching (HVF 3140). Treat the lower end of the band as untested rather than ruled out.
The ceiling comes from the switches. The bridge commutates at the working frequency, and at megahertz the switching loss plus an IGBT's current tail kills the device. Hundreds of kilohertz is about the limit for IGBTs. Above that it is SiC or a valve.
The builds spread across that window rather than sitting at one end of it. Gao Guangyan's QCW 2 is laid out around a 273 against a secondary measured near 308 kHz unloaded, and his QCW 1 ran from 465 kHz down to 434 kHz between the start of the ramp and its peak on first light. That is about 270 to 465 kHz on one builder's own machines, a band rather than a threshold.
The low end of that band is an outlier in a second way too, and the two are one fact. QCW 2's own page gives a 2.41 by 3.52 inch secondary of about 610 turns of 38.5 AWG under an 8 by 2.09 inch spun toroid. That winding is 117.3 m of wire, so a bare quarter wave would sit near 639 kHz and its 308 is 52 per cent below it [derived]. Its toroid is 2.27 times the winding length, the most oversized ratio on file [derived]. A topload that large is what drags a resonator that far down, so the bottom of this band and the extreme topload ratio are one machine showing the same thing twice.
Another build page (thaumati) treats the ramp and the frequency as one thing: the ramped power cycle, "in combination with a high operating frequency", is what lets the arc grow much longer than a DRSSTC's. Read as frequency adding metres, that contradicts everything above. Read as frequency deciding how many channels the energy is split between, it agrees, because one channel that keeps all of it is longer than several that share it. That second reading is ours, not the source's.
In short, frequency sets the arc's character and power sets its length. The straightness comes from up the axis and the metres from power down it. Whether a slow ramp can substitute for the frequency has not been tested.
There are other explanations in circulation
None of them is a variant of the rate argument. One points at which half of the cycle the growth happens on instead of at the rate charge arrives, and it has a name on it. It is Steve Ward's, from September 2017 on HVF 117, and he marks it as a guess in the sentence that makes it: on QCW coils he expects all the streamer growth to happen "during the negative voltage portion of the oscillation", which he calls "my 'theory' for un-branching streamers", while for ordinary DRSSTCs he bets it happens on both. Nothing on file has tested it since. Hydron offered on the same thread to look for it once his own QCW was finished, and no result followed. One argument that rested on it has already been dropped, on the overcurrent page: that holding energy in the bridge lengthens an arc by stretching the sustaining half.
Two more are on HVF 973, a thread started to ask for the physics rather than to report it, and they compete with each other as much as with anything above. Uspring's first is sideways breakout. A slowly ramped arc is in effect a low voltage arc, the field across the channel is weaker, and a branch leaving sideways is that much less likely. His second is a random walk. The direction the tip takes next is statistical, and slower growth shrinks the region in which an avalanche can start, so forward is what is left. On the same thread k42 asked something else, whether the frequency at which the sword appears is a characteristic frequency of the spark plasma itself. Uspring answered it in the last post on the thread, and the answer is no. The plasma frequency follows the free electron density. 400 kHz corresponds to about one free electron per cubic millimetre, and a Tesla coil arc carries a great deal more than that, so the two frequencies are nowhere near each other.
One thing the slow ramp does is not in dispute. Anders Mikkelsen ramps to let the arc form early and clamp the secondary voltage to a low value, which lets a short resonator throw long sparks without flashing over and lets the coupling go as high as it does (HVF 3140). That explains the coil. It does not explain the straightness, and the two questions are easy to run together.
That makes four mechanisms for one observation, and no experiment yet that tells them apart.
What the ramp has to do
Ideally the arc grows at a constant speed, and constant speed means a constant voltage at the tip relative to ground. Any jerk in the supply is a jerk at the tip, and the arc answers a jerk with a new branch.
That is why the bus is ramped rather than switched, why the ramp comes from a converter rather than from skipping pulses, and why a corner anywhere in the curve shows up as a branch. The shape wanted is linear in the bridge's voltage. Because the load is resistive, that makes power rise as the square of time.
How long it gets
Length goes as the cube root of the energy in the bang. No number matters more in a QCW, because it is what makes upgrades disappointing:
L ~ E^n, n = 0.31 to 0.33Eight times the energy for twice the arc. Raising the bus from 325 to 440 V is 1.35 times the energy and about 18 to 20 centimetres on a 188 cm arc, not the 67 that a linear guess promises.
The ratio it reaches, arc over the length of the winding that threw it, runs from about 7 to 25 across published builds. That spread comes from technique, not size, and the records page is laid out to show it. The cleanest demonstration uses a narrower set than the whole list, though.
The cleanest case holds size fixed by accident. Gao Guangyan's QCW 1.0 and QCW 1.5 carry near enough the same winding, 14.0 and 14.1 cm, and reach 7.1 and 12.6. Same builder, same size, and 1.8 times apart. Widen it to the seven builds on the wall between 12.4 and 18.0 cm, a size range of only 1.45 times, and the ratios still run 7.1 to 25.0, a spread of 3.5 times, with a correlation against coil length of -0.04 [derived]. Within that group, size explains none of it.
Do not run that test across the whole wall, and be careful which way its answer points. Over the full range, ZakW's 5 cm winding to CJ's 25 cm, the correlation between coil length and ratio is -0.52, which invites you to say the ratio falls with size. Ask instead what that figure would be if arc length had nothing to do with coil length at all. Shuffle the arcs among the coils twenty thousand times, leaving the lengths where they are, and the same correlation averages -0.67 [derived]. Coil length is the denominator of the ratio, so the ratio falls with size on arithmetic alone. The measured -0.52 is weaker than that, not stronger, so all it supports is that arc length does grow with coil length, which the direct figure of +0.36 shows without the detour.
Nine coils will not carry more than that. The shuffled figure spreads over a band 0.35 wide, so -0.52 and -0.67 cannot be told apart here. The whole-wall correlation is indistinguishable from pure arithmetic, and its sign, if anything, points away from the reading it invites. That is why the seven coils of one size class are the test and the nine are not.
What limits it
- The overcurrent detector, if the energy piles into the end of the ramp. The bang tears and you hear a pop instead of seeing a sword.
- The frequency. Below about 200 kHz the channel runs cooler and branches. Whether a slow ramp can make up for that has not been tested.
- The channel's own charge. Space charge repulsion in the channel is about 0.01 newtons per cubic centimetre against 10⁻⁵ for the buoyancy of hot air, three orders of magnitude apart, and that sets the useful upper limit on ramp time rather than anything in the electronics. Both figures are Uspring's, quoted on the shape page. The post they came from has not been found again by either page, so they are named here rather than linked.
What happens when it reaches something
A QCW is built for reach, and a metre and a half of reach is a metre and a half of things it can touch. Touching one is a different event from a DRSSTC drawing to an earthed object, and again the difference is timing.
A DRSSTC throws its arc and the bang is over in about 300 microseconds. Whatever the arc touched, it touched at the end of something that was ending anyway. A QCW's channel is continuous for the whole ramp, so a touch happens in the middle of a burst that has milliseconds left to run, and the rest of that burst goes into a load the coil did not choose. What that does to the secondary, the poles and the bridge is on its own page. Read it before running a coil this size anywhere near earthed metal.
What belongs here is what the protection should do about it, because the ramp decides that, and it decides it the opposite way round from an ordinary coil.
Pulse skip drops a single bridge oscillation and comes straight back. On a DRSSTC that costs almost nothing, because the bus is flat and the machine returns to the conditions it left. On a ramp there are no such conditions. The buck voltage has moved on, the arc has grown, and the pole structure the driver was tracking is not the one it comes back to. Skipping does not pause the problem. It resumes into a different machine, and keeps doing so for the rest of the ramp.
A latching detector ends the burst instead, and on a ramp that costs exactly one flash, because the next interrupter pulse is the next bang anyway. The arithmetic that makes pulse skip attractive on a long bang is reversed here. QCW builders run ordinary overcurrent for this reason, and what the detector is actually for has its own page.
The two resonances above move as the arc loads the secondary, and how far they move rests on an arc capacitance of 4.14 pF per metre. That figure is one coil's arc, not a property of arcs, and it sits below the published measurements that hold up to checking. Treat the direction as the claim and the kilohertz as an illustration.
What the strike then does to the rest of the machine, the feedback, the poles and the mode the coil comes back on, is covered in five consequences on a page of its own.
What the channel is made of, and which clock it runs on
Two questions get asked together on HVF, and only one of them has a firm answer.
The first is how hot and how dense the channel is. Uspring answers it from a measurement rather than a guess: "Tesla coil arcs are relatively cold arcs, as e.g. compared to arc lamps", and putting a conductivity measurement against a table gives "about 5000 K". Pressure is ambient, and he notes why it stays that way on a QCW in particular: "These QCW arcs grow slowly and don't compress the air. They don't bang as loud as the non QCW arcs" (HVF 973).
The second, k42's question to him, is whether the frequency where the sword appears is a plasma frequency. His answer is no, and it rests on arithmetic rather than opinion: "Plasma frequency is related to the free electron density. For e.g. 400kHz that would be about 10^9/m^3 or about one per cubic millimeter. TC arcs generate a _lot_ more free electrons."
The arithmetic checks out. The electron plasma frequency is f_pe = 8980·√n_e with n_e in cm⁻³, so 400 kHz calls for 1984 cm⁻³, or 1.98 × 10⁹ per cubic metre, about two free electrons per cubic millimetre [derived, and it lands on his figure]. Published streamer measurements put the real channel near 10¹⁵ cm⁻³, which is five hundred billion times more [derived]. The plasma frequency of a real arc is in the hundreds of gigahertz. Nothing a coil does at 400 kHz can be resonating with it.
Which leaves a clock that does fit, and it is a time rather than a frequency
If the plasma's own frequencies are six orders too high, the thing to compare with a half period is how long the channel stays conductive after the current through it reverses. The pulsed-discharge literature measures exactly that, and the numbers land in the right decade:
half period at 400 kHz 1.25 µs
half period at 350 kHz 1.43 µs
half period at 100 kHz 5.00 µsAgainst those, published work on repetitively pulsed streamers reports that with an interval under a few hundred nanoseconds the next streamer reignites the channel the last one left, while at intervals of several microseconds it does not reuse the old trail and starts new channels at the edges of it instead (review of streamer discharge physics, memory effect in repetitively pulsed discharges).
That boundary falls right across the band where coils change behaviour. A sword is reported above 400 kHz, a half period of 1.25 µs at the fast end of that transition, and davekni's 100 kHz QCW at 5 µs went zigzagged instead, which is what "new channels at the edges of the old one" looks like from two metres away. The self-repulsion account further up and this one do not compete. Repulsion says why a fresh channel is pushed sideways, and this says why a fresh channel gets started at all instead of the old one being reused.
That last paragraph is our own hypothesis, not a result. The measurements quoted are single pulses into a gap, not a resonant coil driving a leader for twenty five milliseconds, and nobody has reported the interpulse-time experiment on a Tesla coil. It is written down because it is cheap to falsify. It predicts that the sword threshold should move with anything that changes channel decay, not with anything that changes voltage. Humidity is the obvious knob, since it is documented to speed up recombination and it is already the variable davekni blames for day to day scatter.
So is a lower frequency coil better, which is asked as one question and is two
It gets posted in that form on the Chinese forums, 频率越低越好吗, and its two halves go opposite ways.
On arc character the frequency matters and the direction is known. A longer half period gives the channel more time to decay, and what is seen is the zigzag at 100 kHz against the sword above 400. Lower is worse on that axis, and it is the axis a QCW is built for.
On arc length the common belief is backwards. Steve Ward measured it in 2011, and the result is rarely quoted. On the Tesla Coil Mailing List:
In my experiments with quasi-CW spark production, i found that my 360khz setup was far superior in converting primary amps to spark length than was a 280khz or 125khz resonator. And not just some 10-15%, but it was better easily by a factor of 2! So basically, same amount of amp-turns in the primary, but huge difference in spark output.
Three resonators, the same amp-turns in the primary, and the highest frequency turns those amps into arc twice as efficiently as the lowest (TCML, 17 May 2011). The folk claim never comes with a controlled comparison like that, and this one points the other way.
In the same message he also says where the folk claim comes from, and it has nothing to do with spark length:
Some day i need to do similar testing with a regular DRSSTC and see if winding low frequency secondaries (to keep the silicon switching slower) is not shooting ourselves in the foot in order to make long sparks. In the QCW case it certainly appeared that way.
Low frequency secondaries are wound for the switches, to give the silicon more time per cycle, and the habit gets repeated as if it were for the arc. Ward suspected in 2011 that the two goals pull against each other, said the QCW case certainly looked that way, and flagged the DRSSTC test as undone. We have not found anybody who has done it since.
As asked, then, the question has three answers. Lower frequency costs straightness for certain. It costs arc per primary amp by a factor of two on the one QCW comparison on record. It also gives you an easier time in the bridge, which is a real thing to want, but not what the question assumed.
And the part nobody can explain
Whether the sword comes out straight or curls over depends on the room more than on the coil: temperature, humidity, atmospheric pressure, and what is standing nearby. Two people with the same machine get different results and go looking for a fault that is not there. No single factor has been isolated, and that is worth its own piece.
The arc on the QCW department page is drawn to match: one channel, grown rather than thrown, with its length following the ramp slider at the cube root of the energy.