A buck converter can produce any ramp curve you like, and the curve you choose is the main setting on a QCW. Most branching problems are fixed in the ramp shape rather than in the hardware.
The shape control is easy to misread as one axis with a good end and a bad end. Arc length against shape is a hump instead: both ends branch, for opposite reasons.
The reference implementation
The standard set of knobs comes from Finn Hammer's Arduino code: amplitude, duration, a shape control, bangs per second, and a wick, which is a starting shelf before the ramp proper. No one has counted how many generators descend from it, and we will not guess. The generators we have read do carry that set. Gao's splits the window between rise and fall, rb_sama's has a single rise-over-total control, and the controller on our bench has all five of the knobs above plus two more.
There are usually two shape knobs, one in time and one in amplitude, called tscale and uscale in most implementations. Those two bend the curve.
One practical detail that can cost you an evening: if the controller reads two of those pots on A6 and A7, an Arduino Uno will not work. It has the same ATmega328, but the DIP package does not have those pins. Use a Nano or a Pro Mini.
The axis, written down
V(t) = V_max · (t/T)^p
p < 1 concave: fast start, early shelf <- half sine lives here
p = 1 linear <- "normal", the best one
p > 1 convex: slow start, sharp peak <- "exponential" lives hereThe physics is straightforward. A concave ramp brings the voltage to maximum before the arc has grown. Full power hits a short channel and it breaks out in every direction. At that point it is less a ramp than a long DRSSTC bang.
A convex ramp does the opposite: the arc lights gently and grows, and the power follows it up. ZakW removed the starting shelf entirely for this reason and used a non-linear rise instead, which does the same job without a corner in the curve.
The concave end is the worse end, even though it feels like the softer one when you move the control.
What shape is right
Two separate statements turn out to be the same one under one condition:
Jan says the ramp should be close to linear in the bridge's voltage, not in power. Steve Ward says the power into the arc should rise as the square of time.
The load is resistive, so P = V²/R. If R stays constant, a linear voltage gives quadratic power:
V ~ t => P ~ t^2 => L ~ E^(1/3)R does not stay constant. The resistance the bridge sees climbs steeply while the arc is short, and at low enough coupling it turns over and falls again before the ramp ends. While the load is still climbing, the power grows slower than the square, and past a turnover it grows faster. The two statements agree over the flat stretch and diverge early in the ramp. The curve is on the primary's page.
In practice, tune for linearity in voltage and let the power follow the load. Do not try to build a linear rise in power; that is a different curve.
Combining the axis and the rule, the right curve is an S. Convex at the start, which lights the arc gently and replaces the wick. Linear in the bridge's voltage through the middle and the end, so the power goes as t² on its own. And no corners anywhere, because the two-state shape branches exactly at its step. That is Jan's statement and Ward's combined, with a soft nose on the front.
What has actually been compared
There is one direct comparison, from MS.Lab, best to worst:
- Normal, close to linear. Best overall.
- Exponential. Fewer flashovers on the secondary, better on long ramps.
- Two-state. Branches.
- Half sine. Worst of those tried.
The exponential shape, shallow first and then steeper, makes sense as a defence against flashover and as the option for long ramps, not as a replacement for linear. A shallow start does not drive the voltage up while the arc is still short and all the field is on the secondary.
We cannot link that ranking, because we have not found the page we read it on again. Treat the order as reported, not as citable.
The shapes themselves are easy to show. These are the three MS.Lab put on his own scope while testing his ferrite-cored QCW, at 2 ms a division. We do not know whether they are the runs behind the ranking above.
A later comparison seems to point the other way, though the disagreement is only apparent. On kechuang, rb_sama reports that a slow enough rise never puts in enough energy to open a branch, so the arc grows along its own ionised channel and comes out the longest of the shapes tried, thin at the tip. This comes from photographs of his own machine, not from his LTspice model: three ramp shapes on one coil at 160 A off a 350 V bus with a 14.5 ms on-time (kechuang t/80477, read through the Internet Archive because the live site answers a fetch with a captcha). It comes from his build thread, not his modelling thread, and as a measurement it is stronger evidence than a simulation would be.
His three shapes, in his order:
- An equilateral triangle, steep rise and long fall: the arc has energy enough to open branches and splits into several strands, and because energy keeps arriving it keeps growing after it has branched.
- Steeper again: "由于上升沿更加陡，所以直接从breakpoint分出两束电弧", because the rising edge is steeper still it splits into two arcs straight off the breakout point.
- Slow: "由于上升速度较为缓慢，而电弧能量不足以打开分叉，从而沿着原有的电离通道不断 生长，最终能量下降，表现为电弧尖端细小", the rise being slow the arc's energy is not enough to open a branch, so it grows along the ionised channel it already has, and at the end the energy falls away and the tip comes out thin.
A reader in the thread turned the three into a rule that rb_sama had not stated. Branching happens when the voltage the channel carries crosses a threshold. The three rise rates reach that threshold at different times, so the branch sits at different distances along the arc: "达到阈值越快，【分叉点】距离【起弧点】越近", the faster the threshold is reached the closer the branch point is to the point the arc started from.
That is a sharper prediction than "steep ramps branch", because it says where. Anyone with a camera and two ramp settings can check whether the branch moves toward the breakout point as the slope steepens. We have not found anyone who has.
MS.Lab, on the other hand, found linear best overall. Both are right about what they measured, and a number neither of them gives reconciles the two. An exponential start delivers only 54 to 66 per cent of a linear ramp's energy over the same window, a third to a half less, 341 J against 594 on one load model. Fewer branches and less energy nearly cancel out. The slow shape wins the single longest arc and loses the overall ranking, and that matches the split the two reports describe. The energy figure is ours; the shapes and the ranking are theirs.
A step at the start of a ramp is different from the two-state shape below, and it does a second job that rarely gets mentioned. Besides the early, soft breakout it is usually fitted for, it leaves about five times more room to recover if the switching stumbles during the handover: nineteen cycles of ring against three and a half. That matters because losing the upper pole is a failure to recapture from noise, not a slow drift, so the margin is counted in cycles. There is also a third, stronger effect. A wick loads the coil before the ramp starts, and a loaded coil has already lost its lower lock point and the watershed next to it. The driver then does not just get more cycles to climb back; it gets a coil with nowhere else to lock. The reason is that the lock points go before the poles do. The arithmetic is with the driver modification.
The threshold model also says where the corner branches, not just that it does. A branch leaves when the voltage at the channel tip reaches a threshold, and a steeper rise reaches it sooner, so the fork lands nearer the breakout point instead of further along. It is the same tip voltage the next section holds constant. A corner crosses the threshold faster than anything else, so the two-state shape forks, and a tiny change of rate at the tail moves the fork instead of only causing it. The threshold model was proposed on kechuang; linking it to the tip voltage is our addition.
A builder who read all of that thought he had a counterexample
abc555 built his first QCW from rb_sama's threads and posted the objection that occurs to anyone who reads the mechanism quickly (kechuang t/87930):
如果剑弧形成原理是ontime时间内缓慢增加输入能量，导致电弧能量不足以打开分叉，从而沿 原来方向生长。那么为什么在ontime一开始就达到了限流点，却仍然有剑弧效果？
If the sword arc comes from raising the input energy slowly across the on-time, so the arc has not enough energy to open a branch and grows along the direction it already has, then why is there still a sword when the current limit is reached at the very start of the on-time?
The settings in his own post answer it. That run used a pulse-skip current limit of 50 A, a peak bus of 200 V, a 7 ms on-time and a rising edge taking up 90 per cent of it. The current was clipped from the first cycles, while the bus climbed for the whole ramp. Power is the product of the two. With the current held at its limit and the bus going from nothing to 200 V, the power rises just as gently as the bus does, so the rule still holds.
His question is useful because the substitution he made is an easy one to make. Read the rule in terms of current instead of power, and a current-limited machine looks like a counterexample. It is not. The ramp is a power schedule, and on a current-limited coil the bus carries all of it.
His own answer gets to nearly the same place by another route. During the transfer to the secondary, "由于拍频现象，初级电流峰值减小", the beat drops the primary current peak, and while it is down the bus can push energy across, so a higher bus moves more. That explains how a climbing bus keeps delivering into a primary that is already at its limit: the same conclusion, with the beat providing the mechanism.
He also proposes a test that is interesting in its own right: "所以如果用PLL把开关频率 固定在一个谐振峰，这时没有拍频现象，还会有剑弧效果吗？", if a PLL fixes the switching frequency on one resonant peak so the beat does not happen, is there still a sword? That would not decide whether the ramp works, but it would show how much of the delivery is due to the beat. No one in this corpus has run it.
The hump, and the tail that decides it
Plotted against the exponent, arc length is a hump, not a slope. It rises from about p = 0.4, peaks somewhere between linear and slightly convex, p = 1 to 1.5, and falls away past p = 2.5 into the pop.
The left side falls because full power arrives too early and the short channel branches. The right side falls because all the energy is in the tail, the overcurrent detector fires, and the bang tears; that is the pop.
Branching rises at both ends, by different mechanisms. A model that makes it monotonic has left one of them out.
The useful measure is the tail, not p. What actually trips the protection is how much of the energy arrives at the end. The bridge's voltage goes as (t/T)^p and the load is resistive, so power goes as (t/T)^2p and the share landing in the last fifth is 1 - 0.8^(2p+1) [derived, every row below]:
p= 0.4, strongly concave, near half sine: 33 per cent in the last fifth of the ramp.p= 0.7, concave: 41 per cent.p= 1.0, linear: 49 per cent.p= 1.5, slightly convex, near exponential: 59 per cent.p= 2.5, sharp peak: 74 per cent.p= 4.0: 87 per cent.
Set the overcurrent threshold against that share, not against the amplitude. Then a model of the shape control breaks in the same place the hardware does, and the model is only useful if it does.
It is absurdly sensitive at the end
This is the nastiest property of the ramp.
Tiny differences in ramp rate right at the end either cause branching or remove it. The tail is that sensitive, so the right-hand side of the hump is steep and somewhat unpredictable, not a gentle curve.
Tune the shape finely and last, after the pole, the detuning and the phase lead are all set. Change one parameter at a time, or you will not know what worked.
There is a diagnostic that goes with this, with a limit. A dip in current raises the losses in the channel and a new branch leaves, so a branchy arc points at the ramp. A crooked arc does not necessarily have the same cause. davekni's 100 kHz QCW went from a straight arc path to a zigzagged one, and the discussion settled on the arc repelling itself, adjacent sections of one channel pushing apart, with higher frequency reducing it (HVF 3140). That is the same space charge that limits ramp time further down, and it gives a zigzag with no branching at all. So count the branches before you blame the shape. Why the sword bends collects what is known about a channel that is crooked rather than forked. A squealing arc is often a shape problem, from the ramp or from the buck skipping cycles, but not always. davekni traced one on ZakW's coil to a beat instead, between the operating third harmonic and the secondary's second mode, and says what pointed him at it, that "your capture of squeaking/screeching sound shows that third harmonic in secondary current periodically" (HVF 3425). Scope the secondary current before you change the ramp.
Why smoothness matters at all
The ideal is growth at constant speed, and the shape has to deliver that. Why constant speed is the target, and why a jerk at the tip produces a new branch, is covered in what a QCW arc is. The ramp's part is to have no jerk in it.
The rest of the modulator ties in here. The buck sets the smoothness of the ramp. That is why pulse skipping never produced a sword, and why ripple and the discontinuous-mode threshold matter for shape, not just for efficiency.
What breaks first, in order
- Overcurrent, and the bang tears. Immediately, as soon as the tail puts the current over the threshold. This is the pop: the bang breaks near the top, the arc never finishes growing, and you hear it.
- Racing sparks. When the amplitude or the coupling goes up. Flashover across the secondary, visible in the dark.
- Tank capacitors overheating. Cumulative, over minutes. Calculated from RMS current.
- Bridge
dTfatigue. Latent, thousands of cycles, and the bridge dies weeks later for no visible reason.
The top of the shape control is limited by the overcurrent protection, not by heat. Heat limits the rate and the duration. They are two separate limits and should not be modelled as one.
Racing sparks limit the coupling, not the shape. The k of 0.185 that has been quoted as a ceiling value is one coil's JavaTC figure, BrOdin's, and on that coil it was too high to live with. The secondary he wound at 0.185 gave massive racing sparks at 2000 A, and he brought the coupling down until they stopped. No single number is the ceiling. What ends the experiment is the geometry of your own winding, and a coil that ran fine at 0.18 tells you nothing about the one on your bench.
What the ramp cannot buy you
All of the above is about the shape you set. There is a separate question about the shape you get, which the ramp does not reach. davekni asked it on HVF about his own machine: "With more refinement of ramp parameters, is there likely a setting where arcs behave more similarly from one pulse to the next?" (HVF 2397). No one in that thread answered it.
He answered it himself further down the same thread, apparently without noticing, when he reported a session where the arcs changed character:
Also, arcs were much straighter (much less curved) on average today. Expect that is related to somewhat higher temperature and humidity, as there is little intentional difference in ramp characteristics.
The ramp was essentially unchanged and the arcs were visibly different, so what changed was the room. That answers his question, and the answer is no. If temperature and humidity move the arc while the ramp stays the same, refining the ramp cannot give you shot to shot repeatability, because the biggest factor is outside the ramp.
Linking the two posts is our step; he connects neither. It does not mean ramp shape is unimportant, only that repeatability and shape are separate goals. The shape axis controls what the average arc looks like, and the scatter around that average comes from the weather.
Three axes that get mixed up
- Branching is set by the ramp shape, the pole, and residual voltage on the bus, and falls as frequency rises. Zigzag falls with frequency too, but because of the channel's own charge, not anything in the ramp.
- Channel thickness is set by frequency and power. Thicker at low frequency.
- The whole channel bending is set by the surroundings and the toroid's field. It rises as frequency rises.
Ramp time has three walls, and this coil meets the bank before the physics
You cannot stretch the ramp indefinitely. One limit is in the channel itself:
Uspring: the space charge repulsion in the channel is of order rho^2/(4·pi·e0), about 0.01 newtons per cubic centimetre, while the buoyant force from heating is about 10^-5. Three orders of magnitude apart.
The channel is pulled apart by its own charge rather than floating away on heat. That sets the upper bound on a sensible ramp time, past which the arc stops holding straight.
The energy side points the same way. We give no figure for it, because the only one we had was scaled from an arc length we could not source. Returns fall off on both counts together.
There is a nearer limit than the physics, in the reservoir. A 25 ms flash already draws about 495 J from the bus, and a 12000 µF bank at 440 V gives up about 528 J before it sags to 325 V, so the limit is at about 27 ms [derived], not somewhere comfortably past 30. The physics sets where the arc stops holding straight, but on this coil the bank runs out first, a limit in microfarads rather than in newtons per cubic centimetre. Check the bus sag. If the rail drops hard across a flash, the ramp is already up against the bank, not the arc, and the bank is what to size next.
A third limit is in the bridge, and it is not at a fixed ramp length, because what the switches can handle depends on both how long each pulse lasts and how often it comes. There is one case on record: flyglas ran 18 ms ramps at 10 Hz, 18 per cent duty, and lost all eight devices in the bridge, shorted internally and partly disintegrated. Duty alone does not decide it either. A long pulse heats the die right through, while a short one at the same duty gives it time to cool between shots. So a ramp length that is safe at a few bangs a second may not be safe at ten, and the 30 and 35 ms windows below are costed against the bank, not the bridge.
The blunted top, a shape nobody has tried
There is one shape the published generators cannot make: an ordinary rise with a blunted top, a plateau held before the fall. Gao's controller splits the window 80 to 20 between rise and fall, rb_sama's has a single rise/(rise+fall) control, and neither has a plateau parameter. The trapezoid has not been tried in anything published, so the arithmetic below is ours.
At a fixed window the plateau is a trade-off. It takes time from the rise, which steepens the front, and by the threshold model above a steeper front branches early. Window 25 ms, 20 per cent fall, 440 V peak:
plateau rise front slope energy vs flat
0 % 20.0 ms 20.0 V/ms 495 J 0
10 % 17.5 22.9 557 +12 %
20 % 15.0 26.7 619 +25 %
40 % 10.0 40.0 742 +50 %If you hold the slope and lengthen the window instead, the plateau adds energy with no penalty on the front, but you pay for it in the reservoir:
plateau window energy bank to stay above 325 V
0 ms 25 ms 495 J 11 260 µF
5 ms 30 ms 720 16 361
10 ms 35 ms 944 21 463Five milliseconds of plateau needs half as much bank again, and this machine's 12000 µF at 440 V already sits near the plain flash's 495 J, so there is little spare before you need another capacitor. The cost of the blunted top is in microfarads, not in slope.
The ramp on the QCW department page is drawn the way the modulator makes it: a wick, an even climb, a fall, with the primary current standing up inside the envelope. Its three sliders are the rate, the ramp's length and the wick. None of them is the exponent. The arc responds to the length at the cube root of the energy, and to the wick by splitting. The exponent is the one you set once, carefully, and last.