A Tesla coil's secondary is a long single layer of thin wire on a plastic tube. It works as one half of a resonator, and most secondary problems come from winding it as if it were a transformer winding, where the turn count is what matters.
What a secondary actually is
The secondary does not receive energy in proportion to its turns. It is rung, and the high voltage comes from a resonance building up, not from a turns ratio. The rest of this article follows from that.
The wire picks the frequency
Take a close-wound single layer on a former of fixed length. It is tempting to make the turn count length ÷ wire diameter, and nothing else, but two things hide in that. The first is which diameter. What goes on the former is the insulated wire, not the bare copper, and on fine wire the enamel is a real part of the thickness. The second is that close winding is itself a choice. Finn Hammer's Energimuseet secondary, 1680 turns of 0.224 mm wire, is space wound by its builder's own description. So the count carries a packing factor, and builders rarely state it.
At a factor of 0.9, taken for illustration, the turn count falls 10 per cent, the inductance falls 19 because it goes as N², and the frequency rises 11.1 [derived]. That shifts every absolute turn count and frequency below. It does not change the shape, because a constant packing factor is a constant multiplier, so the rule below still holds.
Inductance goes as N², and the capacitance barely moves because the toroid supplies most of it. That gives a simple result:
The resonant frequency is directly proportional to the wire diameter. Double the wire, double the frequency.
On one real coil, 150 mm of winding, 90 mm former, Ces 14.03 pF:
wire turns L frequency Z
0.15 mm 1000 39.7 mH 213 kHz 53.2 kΩ
0.20 mm 750 22.3 284 39.9
0.238 mm 630 15.8 338 33.5 the copper rule
0.30 mm 500 9.9 426 26.6 this coil
0.40 mm 375 5.6 569 19.9
0.50 mm 300 3.6 711 16.0Changing the wire moves all four numbers, and not all in the same direction. The coil is the same height in every row: 500 × 0.30 mm is 150 mm, the length of the winding.
You can use the same check on someone else's build page. Turns, winding length and wire gauge over-determine one another, and the length of wire on the former is then N × π × D, so you can check a published secondary against itself before using any of its numbers. Thaumati's QCW closes: 750 turns over a 6″ winding is 125 turns to the inch, and 1/125″ is 0.008″, the bare diameter of the 32 AWG it states; 750 × π × 3.5″ is about 209 m of wire against the 200 m it states. Neither check is in the write-up; both are arithmetic on what it does state. Run the other way, the same identity fills gaps: an 8 kW continuous DRSSTC never gave a turn count, and its stated inductance and frequency put the winding near 1440 turns, which is also where close-winding its stated gauge lands. If a page's pitch works out finer than its own wire is thick, it was written from memory, and the rest of it deserves the same suspicion.
Two marks on that axis, and they are not in conflict
0.211 mm → 300 kHz, the edge of the straight-sword band
0.238 mm → where a rule of thumb says the copper is best used
0.232 mm → a built QCW
0.300 mm → this coilThe copper rule is wire diameter about twice the skin depth, so the current reaches the middle of the wire instead of hugging the surface. Below that you are wasting copper cross-section; above it, the middle carries almost nothing.
Solved properly, the two marks sit close together, both below this coil. The copper-optimal wire on this former is 0.238 mm and it lands at 338 kHz, well clear of the sword edge. There is no cliff between them.
The mistake is to solve it only once. The skin depth depends on the frequency, and the frequency depends on the wire, so picking 2δ at the old frequency gives an answer about 10 % off.
And the copper rule matters far less than it looks
The skin-effect calculation gets quoted a lot, but it is rarely followed through to what it actually changes.
this coil 0.300 mm = 2.79δ R_ac/R_dc 3.92 unloaded Q 199
a built QCW 0.232 mm = 1.94δ R_ac/R_dc 2.58 unloaded Q 231The built QCW is on the rule. Ours is 1.4× over it in skin depths and 1.3× in diameter, and the QCW's copper really is better.
Now put an arc on both. The arc sits in parallel with the copper, so it sets the loaded Q, and you need an arc resistance to say by how much. We use 210 kΩ, which Uspring worked out of Hydron's measured toroid currents in his own words, "a strong resistive load of about 210kOhm" at the point of maximum current 180 µs into the burst. We also give a Terry Fritz SPICE fit from about twenty years earlier, at around 220, but it has no link on that thread or anywhere else. Treat the agreement as our claim, not as a second source you can check:
Q under arc to the copper
this coil, unloaded Q 199 7.59 3.82 %
the built QCW's wire, unloaded Q 231 7.63 3.31 %Both lines use our coil's 26.6 kΩ, because the other coil's impedance is not published and making one up would decide the answer [derived from 210 kΩ, that impedance and the two unloaded Q]. So the two lines compare only the wire.
The difference is half a percentage point of the power. Arc length goes as the cube root of energy, so that is under a fifth of a per cent of arc, under three millimetres on a metre and a half [derived, 0.177 per cent of 1500 mm].
The loaded figure depends on impedance, and the wire table at the top shows it. Uspring computes a Q of about 4 under that same 210 kΩ, on Hydron's coil rather than his own (HVF 117), and a coil at 53.2 kΩ, the first line of the wire table, computes to 3.9. Twice the impedance gives half the loaded Q, because under an arc the number is R_arc over Z and very little else.
The reason to care about the wire is the frequency it forces, not the resistance it saves. Through the frequency it sets the impedance, the detuning margin and the pole structure. Pick the frequency first and let the wire follow.
The copper still matters for heat. 3.82 per cent of a 27 kW peak is about 1.03 kW in a winding weighing under a hundred grams. That is a heating question, not an arc-length question, and here the two wires do differ. The built QCW's wire puts 3.31 per cent into the copper against 3.82, so it runs about 13 per cent cooler for the same burst. That is negligible on a short bang and not negligible on a machine running pulse skip, which exists to make the on-time longer. Builders of long-on-time coils say the same from the other side: use thicker wire to carry a load closer to continuous.
Q is the impedance divided by the resistance
Both numbers are already in the JavaTC output:
Z = sqrt(L/C) = 26 596 Ω JavaTC prints "Reactance at Resonance" 26596
Q = Z / R_ac = 199 JavaTC prints "Secondary Q" 199And the same Z works under the arc, the other way up
no arc Q = Z / R_ac = 199 the copper, in SERIES
under arc 1/Q = 1/199 + Z/R_arc = 7.6 the arc, in PARALLEL, on 210 kilohmsZ appears once on top and once underneath. Lower impedance means a worse unloaded Q and a better tolerance of arc loading. So there is no single right answer to "what should the secondary impedance be". It depends on which of those two matters more to you.
It also means the unloaded Q that calculators print is close to irrelevant once there is an arc. 199 and 231 become 7.59 and 7.63, half a per cent apart on a sixteen per cent difference in the unloaded figure. Under the arc the number is set by the impedance and the arc, and the copper has almost dropped out.
A QCW secondary is not a DRSSTC secondary
The secondary a DRSSTC is usually built with is tall and thin, at a higher impedance than a QCW wants. Built QCW coils sit elsewhere:
The Z and L of that built QCW, below, are our own numbers, not from a formula. We entered its published geometry into JavaTC and fitted the turn count until it reproduced the published 340 kHz; it lands at 342.95, within 0.9 %. The second constraint is the wire pitch that makes 603 turns fit the winding. Neither number was published.
Fitting the turns is normal practice, not a dodge for this one coil. In a build report the turn count is the least reliable figure, and builders often write it with a tilde. dr. kilovolt's SiC coil gives a 125 mm former, a 150 mm winding, about 400 turns and 19 mH. Wheeler's formula over that geometry returns 11.9 mH, and 19 mH would want nearer 505 turns. Everything else in the report is consistent: 19 mH at its measured 251 kHz needs 21.2 pF across the coil, its 6 × 25 cm toroid is about 10.8 pF of that, and what is left is an ordinary self-capacitance for a coil that size. The inductance, the frequency and the coupling all hold up. Only the turn count should not be quoted. Those figures are ours, from its published geometry.
The plot shows three QCW aspect ratios: 1.49:1 and 1.58:1 built, and 1.28:1 on a machine not yet built. The two built DRSSTCs whose ratios we have sit at 2.06 and 3.43, one and a third to two and a half times higher. That gap is too large to be scatter. A low aspect ratio gives coupling, and a QCW depends on coupling to get a long arc from a small resonator.
A builder running 1.5:1 (HVF 3140): "A low aspect ratio secondary is definitely a good way [to raise coupling]… but even going below 1:1 could be practical for larger coils."
There is a price. A lower aspect ratio means more field inside the winding, and that is what causes racing sparks. It also lowers the impedance. In the last few years that has come to be seen as a feature, but it was not always.
The ramp is what makes the price affordable. An arc allowed to form early holds the secondary voltage down for the rest of the ramp. Because of that clamp, a short resonator throws a long arc without flashing over, and the coupling can go where it would have arced over on a coil driven the ordinary way. Ramp rate, high coupling and a short secondary are really one decision described three ways (HVF 3140), so you cannot take a QCW's aspect ratio from a DRSSTC's.
The field is moving down
Built QCW secondaries are moving towards lower impedance. There is no single right value, only a direction. The lever is coupling. Raising it moves the primary-impedance turnover out past the end of the ramp, so a growing arc no longer crosses the peak. That is what "flatter" means here. It does not mean a smaller spread; at a fixed primary tap the spread does not even change steadily with coupling. What matters is that the turnover leaves the ramp, so the load keeps rising instead of turning over halfway up. A low aspect ratio raises the coupling and lowers the impedance at the same time, which may be why the two get confused.
That does not make existing coils wrong. A 28 kΩ coil in that range makes three metre arcs. Take this as which way to move if you have a choice, not as a sign that anything in the middle of the range is wrong.
The topload owns the coil
Ces total 14.031 pF
of which the toroid 10.879 pF = 78 %
the winding itself 3.152 pF = 22 %The toroid sets most of the frequency, the impedance and the tolerance of arc loading, and the winding sets the remaining 22 per cent. In practice, "tuning the secondary" means "choosing the toroid".
Bare, this winding would ring at about 900 kHz. With its toroid it rings at 426, less than half.
What a toroid costs is on its own page.
One built coil shows the toroid's effect on its own, across two of its builder's pages. Gao Guangyan wound one 32 AWG secondary, 5.55 inches of winding, and measured it standing alone under two toroids a year apart:
the same 32 AWG, 5.55 in winding, measured standing alone
8 in toroid, 2014 408 kHz
11.25 x 3.4 in toroid, 2015 339.3 kHz
16.8 per cent lower [derived]The first reading is on QCW 1.0, the second on QCW 1.5, where he writes that he went back to that original 32 AWG coil for the experiment. Both are his own readings of the resonator standing alone, so the new primary that came with the fat toroid affects neither. What does differ between them is a year, two rooms and two supports, the second a floating wooden plank. Take 16.8 per cent as the rough size of the effect, not as a controlled repeat.
What the arc does to it
The arc hangs off the topload as a capacitance and a resistance at once.
- The capacitance adds to the coil's own, so the resonance moves down, badly, in a QCW.
- The resistance drops the Q from 199 to about 7.6. The sharp peak becomes a low hill.
→ the frequency slides down the ramp
Why the upper pole, seen from the winding
Three reasons, none of them about the driver:
- The secondary's field is lower inside the winding on the upper pole, so bringing the coils closer is less dangerous there.
- The lower pole changes the voltage distribution along the winding in a way that makes a primary-to-secondary flashover more likely.
- The upper pole follows the detuning downward; the lower one runs into the primary and stops.
loneoceans' first-light report on his first QCW: "primary set at turn 7.5 (392kHz) but coil oscillates itself to the upper pole" A plain UD2.7, no modification, the primary tuned below the secondary, which he measured alone at 408 kHz, and the driver goes to the upper pole on its own. That is a measurement, and it answers the worry that the upper pole needs a special driver.
→ there is no secondary frequency
How to wind it
- Tight turns, one layer. Winding with a space between turns raises the frequency, which is usually the opposite of what you wanted.
- No bubbles in the varnish. Every bubble is a corona site and a future puncture.
- Ring out topload to ground before power. Continuity, with a meter, every time.
How to ground it
The ground is the other plate
The toroid's capacitance is capacitance to ground, and at 426 kHz its reactance is about 34 kΩ. Every bit of displacement current that leaves the topload has to arrive somewhere and get back to the bottom of the winding, and it gets back through the counterpoise. So the ground connection is one plate of the capacitor that sets your frequency.
Without a counterpoise the room becomes the other plate. The coil still resonates, but against a capacitance you cannot repeat. The evidence, from the calculator you probably already use, is on what RF ground is.
It is also why the lead to the counterpoise shifts the measured frequency (see Measuring it, below).
- Not to mains earth. Not ever.
- A counterpoise: a large metal sheet under the coil. Roofing aluminium beats foil, and round the corners off.
- A short lead, not run alongside anything else.
- The bottom of the secondary goes to both the counterpoise and the strike ring.
There is a calculator for how big it should be on the page that owns it.
Bigger is not always better, and when it goes wrong the damage is to the coil. A ground of low enough impedance lets the topload discharge faster than charge can move in the winding, and the reflected front punches through the turn-to-turn varnish and takes out the bottom fifth of the winding. Why that happens, and why no one can give you a settled impedance without field measurements, is on the same page.
What will get you: two layers, unchecked varnish, and ferrite you did not design around
A gap that is nearly closed is worse than one that is open. If you sleeve the secondary, get the space between the winding and the sleeve right. davekni describes what goes on in a tight one: "A tight space between secondary and insulation sleeve often creates corona discharge between secondary windings and adjacent insulation, at least in normal (non-QCW) SSTCs and DRSSTCs" (HVF 3522). He puts two costs on it and they are on different timescales:
One is slow degradation of secondary wire enamel insulation. Other is ionized air provides a conductive path that may initiate arcs along secondary surface
The first eats the coil over months and the second ends a run, and both come from the same millimetre. He says this about ordinary SSTCs and DRSSTCs, and says plainly that he does not know how much of it applies to a QCW at its lower secondary voltage. So it is an open question. The safe choice is a sleeve that either stands well clear of the winding or sits tight against it with nothing in between.
A cheap fix comes from a builder who lost a secondary before finding it. After a winding was destroyed by a primary-to-secondary flashover on first power up, "原来那个次级因为耦合太大，在170几v上电时初次火导致次级被玩坏掉了", because the coupling was too large and it flashed over at a bus of about 170 V, the replacement was wrapped in a layer of mica insulation paper, bought at 30 yuan for a one by five metre sheet. His report on it afterwards: "这个次级玩坏2个管子也没打火", this secondary has destroyed two transistors and still has not flashed over (hvdiy 33610).
That second report is a real result. He is not saying the coil got better. The failure moved: the bridge now dies before the winding does. That is the right order, because you can replace a bridge in an evening and a secondary takes a lot longer.
Ordinary electrical tape is not an insulator at these voltages. This comes from a spark gap coil, a different class of machine, so take the mechanism and not the numbers. Once the stress across it is high enough, tape stops behaving as a dielectric and starts behaving as a conductor, so a wrap that looks like insurance can become the path. On those machines builders use epoxy between windings, high voltage silicone compound, or potting the whole thing in oil. There is no figure to carry over, only the general point: a material rated for mains has no useful rating here.
Ferrite inside the secondary is a trade, not free coupling. Ferrite conductivity rises with temperature, so a warm core starts loading the resonator it sits inside, and a coil not designed around that gets worse the longer it runs. It can be done, though. davekni's oversized QCW is built on ferrite deliberately: a floor and a centre post, the top of the post NiZn "for low conductivity", no potting, k = 0.71 on an 11.8 mH secondary over a 300 mm core (HVF 2397). Choose the material and the cooling along with the rest of the machine, or leave the core out.
Metal closer than half the secondary's diameter kills the Q. A chassis, a case, a rack or a radiator loads the resonator and loses energy to induction heating, and nothing on a scope tells you it is happening.
Measuring it
Whatever the calculator said, the coil you wound has a different resonant frequency. The topload moves it, the bench moves it, the wall behind it moves it, and the lead down to the counterpoise moves it. Three ways to find out what you actually have:
- A signal generator through a resistor. Start at 1k and go to 10k when you want the dip sharp enough to read.
- Ring it down. A nanofarad into the scope, and watch it decay.
- An antenna near the topload, looking for the peak in the field.
Measure it assembled, with the topload on. A bare winding is a different resonator and its number is no use to you.
What goes wrong, and what each symptom means
Where the winding is damaged tells you most of what you need, because the mechanisms that damage a secondary act at different heights and need different cures.
- The measured frequency is well above the calculated one. Instruments floating, or the coil measured bare without its topload.
- Flashover across the winding, low down. Racing sparks: a strike rail too close to the primary, defects on the toroid, humidity, or coupling simply too high. The usual advice that tight coupling is survivable holds on the upper pole, where the secondary's field is lower inside the winding; on the lower pole, bringing the windings together is noticeably more dangerous.
- Inter-turn arcing in the bottom fifth, with nothing jumping to the primary. This is the whiplash failure, not racing sparks, and it needs the opposite treatment. The ground impedance is too low; the coupling is not too high.
- Flashover across the middle, level with the top of the primary. A different mechanism entirely: the second mode.
- Damage at the top of the winding, and no arc leaving the topload. Nothing broke out, so the voltage up there climbed until something else gave. Give the arc somewhere to leave from: what a DRSSTC breakout point is for.
- Damage spread the length of the winding rather than gathered at one height. Running on the lower pole.
- The coil performs worse than an identical one with no visible difference. Something metal is inside half a diameter of it.
- The frequency walks down as the arc grows. That is normal. The arc's capacitance adds to the coil's, and on a QCW it does so catastrophically.
- The topload voltage stops responding to more power. It clamped. Current, not voltage, is the better indicator of arc length from there on.
Where the edge of this is
The largest QCW being designed at the time of writing does three things to the secondary that no hobby coil does yet: litz instead of solid wire, a secondary MMC of C0G ceramics to add capacitance without adding winding, and an aspect ratio of 1.28:1. All three point the same way, towards lower impedance and higher coupling.
Where next
- What a topload costs, the trade at the top of it.
- What RF ground is, the connection at the bottom.
- There is no secondary frequency, which pole the winding wants and why.
- The second mode, the flashover that is not about coupling.
The figures here come from published measurements, not from our bench. Our own coil, used throughout, is not switched on yet. Its numbers are from JavaTC, and a cold-coil sweep will replace them with measured ones.