Couple a primary to a secondary and the resonance splits in two. The driver sits on one of them, and that choice decides most of what the coil does. It also means the frequency you carefully measured on the secondary is a mode that no longer exists.
Where the two come from
The resonance condition for the coupled system is
(1 - w1^2/w^2)(1 - w2^2/w^2) = k^2and solving it for w gives
w±^2 =
[ w1^2 + w2^2
± sqrt( (w1^2-w2^2)^2
+ 4k^2 w1^2 w2^2 ) ]
/ [ 2(1 - k^2) ]Tuned to each other, that collapses to the familiar form:
f± = f0 / sqrt(1 -+ k)Tighter coupling drives them apart. Worked on the QCW this corpus keeps its figures for — primary 349.9 kHz, secondary 426.49, both from JavaTC — using the general form above rather than the tuned one, because that machine is deliberately detuned:
k lower upper apart
0.30 328.9 475.7 146.8
0.39 320.0 506.5 186.5
0.421 317.0 519.1 202.1 <-
0.45 314.2 531.9 217.7
0.50 309.5 556.8 247.3
<- as builtOurs is the marked row. The trajectory those two poles then follow as the arc grows is its own page.
Which one you land on
davekni and Uspring arrived at the same rule independently:
Applied to the loaded coil, not the bare one
The rule is right and it is easy to apply to the wrong state. A published build looks at first like a flat contradiction of it: loneoceans runs an ordinary UD2.7A, no PLL and no self-oscillation, with the primary tapped at 392 kHz — and reports that the coil oscillates itself to the upper pole.
Work it in both states and the contradiction dissolves.
primary tapped at 392
no arc, secondary 408
lower 42 below
upper 87 above -> lower
under arc, secondary 320
lower 91 below
upper 45 above -> upperWith no arc out the primary is nearer the lower pole, and with the arc loading the secondary it is nearer the upper. His coil settles where the rule says it will once the arc is out, which is the state that matters. The rule is not wrong; applying it to a bare coil is.
And the criterion is the midpoint, not the loaded secondary
Which sharpens something this corpus had been using in a weaker form. "Primary above the loaded secondary" is necessary and not sufficient — what decides which pole the primary is nearer is the midpoint between the two poles, and because coupling is not symmetric about the secondary those are different tests.
On the coil this corpus keeps its figures for:
arc midpoint primary 349.9
1.5 m 379.5 30 below
2.0 m 370.4 20 below
2.81 358.1 8 below
3.46 349.9 levelThe primary only reaches the midpoint at 3.46 m, and the pole structure comes apart at or before 2.81. So on this machine the upper pole is never the nearer one at any arc length it can reach — the forcing is required for the whole ramp, not merely until the arc grows enough to take over. Anders' criterion is satisfied from about 1.65 m onward and it is not enough.
And the mechanism underneath both is gain
The proximity rule describes the outcome without giving the cause, and the cause is worth having because it is what a modification has to overcome. Anders Mikkelsen states it directly:
[a self-oscillating UD2.7 and similar driver] would need more gain at the upper pole, which means that the primary needs to be tuned above the loaded secondary frequency. This is not possible for a plain self-oscillating driver, as the lower pole would have more gain without spark detuning.
He puts the excess the upper pole needs at "maybe 6 dB?".
That is checkable on a coil with known numbers, by working out the primary current each pole would draw at the same bridge voltage:
arc lower is stronger by
0 +5.5 dB
0.5 m +9.4 dB
1.0 m +5.5 dB
1.5 m +1.9 dB
1.8 m crossover
2.0 m -1.0 dBThe crossover at about 1.8 m arrives at the same place as Anders' tuning criterion, by a different route. His condition — primary above the loaded secondary — is met between 1.65 and 2.0 m on this coil, since the primary sits at 349.9 against a loaded secondary of 355.1 at 1.5 m and 338.2 at 2.0. Two independent calculations, one through currents and one through tuning, landing on one point.
So across the whole useful part of a ramp the lower pole holds an advantage of roughly 2 to 9 dB, while the upper one needs a 6 dB excess to be chosen. The total deficit is 8 to 15 dB, and it is why feedback left to itself goes down rather than sometimes going down. What that deficit means for a driver that starts from noise — and why a modification can beat it anyway — belongs with the modification.
So there are three strategies, not two
- Primary below the loaded secondary, upper pole forced. The detuning rule is satisfied and the driver has to be modified. davekni calls this the ideal and says plainly that it requires either a PLL or self-oscillation.
- Primary above the loaded secondary. The upper pole comes free, with no starting oscillator and no PLL, and the detuning rule is given up to get it. loneoceans sits 22.5 per cent above his loaded secondary and takes about a metre of arc for it.
- Lower pole, unmodified. Which is where an ordinary DRSSTC lives happily and where a QCW loses the linear ramp it exists for.
The corpus had the first and the third and treated the second as a mistake. It is a trade: the pole for the tuning. Which one is right depends on whether you would rather modify a driver or give up matching under the arc's load.
And the first of the three is the common one rather than the exotic one, which is worth saying because "the ideal, requiring a PLL or self-oscillation" reads like a fringe position:
builder primary vs secondary
Lucasww 244 < 300
CJ 395-420 < 430-450
ours 349.9 < 426.5Lucasww draws 1.30 m on a UD2.9 in pulse-skip mode; CJ draws 2.39 m and is the only one of the three with both frequencies measured rather than computed. All three sit with the primary below the loaded secondary and work the upper pole. So the configuration this page spends its length on is the one builders actually end up in.
Two external checks of the pole equation
The first is the sharper of them, because nothing in it comes from a description: davekni's oversized QCW in HVF 2397 is specified by component values, and he states the pole he measured.
primary 5.6 uH · 64.8 nF
-> 264.2 kHz
secondary 11.8 mH · 32 pF
-> 259.0 kHz
k = 0.71
equation -> upper 485.8
he measured 485
+0.17 %From parts to a measured frequency with nothing adjusted in between, and at k = 0.71 — twice as tight as this corpus's coil, so the agreement is not the equation being fitted to one case. It also puts his lower pole at 200.0 kHz: at that coupling the two are a factor of 2.43 apart, which is what the QCW habit of tight coupling looks like taken further than most people take it.
And one against a coil described rather than specified
MS.Lab publishes enough to do it: primary 313 kHz, k = 0.5, and a working frequency reported as 480 to 490 kHz.
secondary measured in place
356 -> upper 476.0 -0.8 %
secondary measured on a bench
411 -> upper 525.2 +9.4 %This one agrees to within a per cent, and only with the secondary measured where the coil actually stands. That is a second lesson at no extra cost: the number that goes into this equation is the resonance in situ, not the one from the bench, and the two differ here by 55 kHz.
Which one a ramped coil can actually use
Everything above is true of any coupled pair. This is the part that is only true of a machine with a ramp, and it is the reason the choice matters at all: the frequency slides the whole way down, so the question is not which pole is better but which one is still doing the job at the end.
Coupling splits the resonance in two and the driver holds one of them for the whole ramp. It is usually put as a preference, and put that way the lower pole wins most of the comparison. That is the wrong question. The question is which one still does the job, and on this machine there is only one answer — and, worse, it is not the one the coil goes to by itself.
Start with where the driver lands if nobody stops it. With plain feedback off the primary's current zero, it settles on the pole nearest the primary's own frequency, and the primary is at 349.9:
distance from the primary's 349.9
to lower to upper lands
no arc 32.9 169.2 lower
1.5 m arc 54.2 113.4 lowerBoth ends of the ramp, and not close. So forcing the upper pole is not a refinement — without it the machine runs in the mode it was not built for, and that is what the starting oscillator or PLL is for. Which changes to make to an ordinary board, in the words of the people who made them, is converting a DRSSTC driver.
Then the reason it matters. The first one is not frequency at all, it is that the lower pole breaks the ramp, which is the entire machine:
Anders Mikkelsen: Lower pole operation leads to the tank drawing more power as the secondary gets additional capacitive loading from the arc, making it hard to slowly ramp the power up. Most people prefer to run QCWs on the upper pole as it gives a more linear response of power vs bridge voltage.
A QCW exists to raise power smoothly and predictably. A pole on which power rises by itself as the arc grows does not degrade that job, it cancels it. An ordinary DRSSTC does not care, because it has no ramp — which is exactly why the lower pole is ordinary there and wrong here.
And the same answer arrives from the band. Straight swords need 300 kHz and up, which is Anders' threshold, and the lower pole leaves that band almost immediately:
arc sec lower upper
0 426.5 317.0 519.1
1.0 374.8 302.9 477.2
1.2 366.1 299.9 471.0 band
1.5 355.1 295.7 463.3
2.0 338.2 288.4 452.4
band = lower leaves 300 kHzThe lower pole is out of the band at about 1.2 metres. The upper one does not leave it at any arc length this coil can reach — which is the honest way to put it, since the page has just spent a warning saying the 4.14 pF/m calibration cannot be stretched past two metres, and quoting a figure at eight would be spending a number this page has already voided.
The two do not sink the same way, and the difference is not the one this page used to claim. Differentiate the pole equation along the ramp and the lower track runs at a near-constant rate the whole way — 13.4 kHz per metre at the start, 14.6 at its steepest around 1.5 m, 13.7 by three metres. It never accelerates. What changes is the upper one, which starts at 54.7 kHz per metre and is down to 12.4 by three metres: a factor of four of braking. The two rates only meet at 2.73 m.
Be honest about what the lower pole does give, because it is not nothing and it is not only efficiency. It reaches its own pole unaided, it drifts less with a spread in coupling, and it is easier on the hardware: copper loss follows skin depth and goes as the square root of frequency, and the gate supply's average current goes as Q_g·f. With no arc that is 1.28 times less copper loss and 1.64 times less gate current; under a 1.5 m arc, 1.25 and 1.57. If heat ever appears as a mark against the lower pole, the sign has been flipped.
And the upper pole has one numerical advantage of its own, which belongs here for the same reason the lower one's do: 12 dB more power into the arc in davekni's simulation. Twelve decibels of power is a factor of 16, not the factor of four this corpus used to print — four is what you get by applying the amplitude form, 10^(dB/20), to a quantity that was stated as power.
Count them. For the lower pole: it reaches itself unaided, it drifts less with a spread in coupling, it moves a smaller fraction across the ramp, and it costs less in copper and less in gate current. Five. For the upper: the ramp stays linear, the band stays above the sword threshold, and the arc gets more power. Three. And still the upper, because two of those three are not about quality at all; they are about whether the machine does its job. Efficiency in a mode that will not ramp and makes a branching discharge instead of a sword is efficiency in the wrong machine.
The trap
The secondary frequency you measured is the resonance with the primary taken away. In the assembled system there is no such mode.
The same machine makes the point without a hypothetical: 426.49 kHz is what the secondary measures on its own, and with the primary beside it the real working points with no arc out are 317.0 and 519.1. Neither of them is 426.5, and nothing in the assembled coil is.
One asymmetry that is not about power
The lower pole is where the system lands unaided and is easier on everything, and it carries a higher flashover risk when the windings come together. On the upper pole the secondary's field is lower inside the winding, which is why the usual advice about tight coupling being survivable holds there and not on the lower.
The frequency falls, the pole does not change
The arc adds capacitance and pulls the secondary's frequency down, and both poles come down with it. Same mode. You stay on whichever pole you landed on at the start, for the whole bang.
Until they stop existing
Which is the other half of the same subject rather than a separate one: a pair of resonances that can be moved can also be destroyed, and the condition for it is exact rather than a vague "eventually". Udo Lenz, on the Tesla Coil Mailing List in February 2013:
system loading makes the center frequency and one pole go away, leaving only one frequency near the primary resonance… That will happen when Qsec drops below 1/k.
Near the primary's resonance, not the secondary's — which this page had backwards until the source turned up. It also has to be that way round: the condition is written on the secondary's Q, so the secondary is the resonator being damped out, and a frequency cannot be set by the resonator that was just killed.
Sweep the coil with no arc out and there are two sharp peaks, one at 317 kHz and one at 519, with a dip between them. Now load it. The secondary's Q is what the load spends: 199 with nothing drawn, and down around 4 with a metre and a half out. As it falls, both peaks get broader and lower, and they slide towards each other. The dip fills in. Past Q = 2.375 there is no dip left and no two peaks — one broad hump remains, near 349.9 kHz, which is the primary.
The secondary stops being a resonator, the primary never stopped being one, and what is left is the primary's own resonance with a lossy load hung on it.
Two things follow that are easy to miss. It arrives sooner than the arithmetic says — Lenz adds that a large split between the primary and secondary resonances brings it on earlier, and this coil's split is 21.9 per cent measured against the primary, so any arc length computed from Qsec < 1/k alone is a ceiling rather than an estimate. And past that point there is no pole to choose: "for large system loads, you'll have just one ZCS frequency, so there is no choice between poles at this point." Everything on this page belongs to the start and the middle of a bang.
An arc reaching an earthed object does the same thing, but only across a band of strike resistances, and it does three other things besides. That is its own event rather than a property of coupled resonators.
And past it is a place you can work, not a place you have failed
Which this page had implied without ever saying, and it is wrong to imply. Anders Mikkelsen took 3.18 m operating beyond the collapse, and describes the regime rather than apologising for it: only one ZVS frequency, and arc loading with minimal effect on the operating frequency.
That last clause is the diagnostic, and it is a better one than any threshold calculation, because it needs no capacitance model:
poles alive
frequency tracks the arc
past collapse
frequency stops caringA machine whose frequency stops responding to arc length has not drifted. It has left the two-pole regime, and every argument on this page about choosing between poles stopped applying at that moment.
The argument nobody should flatten
Uspring's position is that on the lower pole the arc pulls the secondary towards the working frequency and the transfer improves, while on the upper it pulls away and the coil detunes. davekni's is that the upper pole is worth 12 dB of arc power at one simulated load. Both observations are real, and the temptation to declare a winner should be resisted.
What the community does in practice is a compromise: tune the primary below the secondary, and force the upper pole from the driver. Then the arc brings the frequencies together as the ramp goes on instead of separating them. davekni puts it as being able to force upper pole operation even with the primary tuned lower, so that arc loading lowers the secondary resonance and keeps the frequencies close over the whole of the arc's growth.
Getting the inputs without trusting a model
Every number on this page comes out of k and the primary's resonance, and both are usually taken from a simulator. One sweep of the cold coil measures them instead, and it needs nothing running.
Checking which one you are on
Look at the frequency at the very start of the arc, at minimum load. It tells you immediately.
A sharp jump of about a factor of two in the middle of a ramp might be a real transition. A smooth slide downwards is normal.
The two poles are why a QCW's timing has to be tracked the whole way up the climb, and why the department diagram draws a driver with a lead in it rather than a box marked driver.