A buck can produce any curve you like. Which curve is the main setting on a QCW, and the most underrated one: most branching problems are fixed here rather than in the hardware. It is also tempting to read the shape control as one axis with a good end and a bad end. It is a hump, both ends branch, and they branch for opposite reasons.
The reference implementation
Finn Hammer's Arduino code is where the standard set of knobs comes from: amplitude, duration, a shape control, bangs per second, and a wick, a starting shelf before the ramp proper. Nobody has counted how many generators descend from it, and this page will not guess. What it can say is that the generators this corpus has read carry that set: Gao's splits the window between rise and fall, rb_sama's carries a single rise-over-total control, and the controller on this bench has all five of the knobs above and two more.
There are usually two shape knobs rather than one, in time and in amplitude, called tscale and uscale in most implementations. Those two are what bend the curve.
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 direct. A concave ramp brings the voltage to maximum before the arc has grown. Full power arrives at a short channel and it breaks out in every direction. That is not really a ramp any more, it is a long DRSSTC bang.
Convex does the opposite: the arc lights gently and grows, and the power follows it up. Which is why ZakW removed the starting shelf entirely and used a non-linear rise instead, doing the same job without a corner in the curve.
What shape is right
Two independent statements, and under one condition they are the same statement:
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. Hold that R still and linear voltage gives quadratic power:
V ~ t => P ~ t^2 => L ~ E^(1/3)R does not hold still. The resistance the bridge sees climbs steeply while the arc is short, and at a low enough coupling it turns over and falls again before the ramp ends. Where the load is still climbing the power grows slower than the square, and past a turnover it grows faster, so the two statements agree over the flat stretch and part company early in the ramp. The curve is on the primary's page.
Putting the axis and the rule together, the right curve is an S: convex at the start, which lights the arc gently and replaces the wick; linear through the middle and the end in the bridge's voltage, so the power goes as t² by itself; and no corners anywhere, because the two-state shape branches precisely at its step. That is Jan's statement and Ward's being the same statement, with a soft nose on the front.
What has actually been compared
One direct comparison exists, 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.
Read that as: "shallow first, then steeper" is the exponential shape and it makes sense. Not as a replacement for linear, but as a defence against flashover and as the option for long ramps. The logic is direct: a shallow start does not drive the voltage up while the arc is still short and all the field is sitting on the secondary.
A second comparison since points the other way, and only looks like a disagreement. 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. That is the not from his LTspice model but from photographs of his own machine, 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). This page previously credited that observation to the modelling thread and it belongs to the build thread; it is a measurement rather than a simulation, which makes it better evidence and not worse.
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.
And a reader turns the three into a rule the thread did not state. 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, and "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 prediction, and it is a sharper one than "steep ramps branch". It says where. Anybody with a camera and two ramp settings can check whether the branch walks toward the breakout point as the slope steepens, and this corpus has not found the check. MS.Lab had linear best overall. Both are right about what each measured, and they reconcile on a number neither states: 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, and the two nearly cancel. The slow shape wins the single longest arc and loses the overall score, which is exactly the split the two reports describe. The energy figure is ours; the shapes and the ranking are theirs.
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 anybody 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?
It is not a counterexample, and the line above his question says why. The settings on that run were a pulse-skip current limit of 50 A, a peak bus of 200 V, a 7 ms on-time and a rising edge occupying 90 per cent of it. So 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 exactly as gently as the bus does, and the rule was never broken.
Which makes his question the most useful thing on this page, because the substitution he made is the one the mechanism invites. Read it as current rather than as power and a current-limited machine looks like a refutation. It is not. The ramp is a power schedule, and on a current-limited coil the bus is carrying all of it.
His own answer reaches 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 is a mechanism for how a climbing bus keeps delivering into a primary that is already at its limit, which is this section's conclusion with the beat supplying the how.
And he proposes a test worth running for its own sake: "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 does not decide whether the ramp works, but it measures how much of the delivery the beat is responsible for, and nobody in this corpus has run it.
The hump, and the tail that decides it
Arc length against the exponent is not a slope, it is a hump. It runs up 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.
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.
It is absurdly sensitive at the end
This is the nastiest property of the whole thing.
Microscopically different ramp rates right at the end either give branching or take it away. The tail is that sensitive, which also means the right-hand slope of that hump is steep and slightly unpredictable rather than a gentle curve.
Which means: tune the shape finely and last, after the pole, the detuning and the phase lead are all set. And change one parameter at a time, or you will not know what worked.
Why smoothness matters at all
The ideal growth is at constant speed, which is what the shape has to deliver. Why constant speed is the target, and why a jerk at the tip is answered with a new branch, is what a QCW arc is. What this page owes it is a ramp with no jerk in it.
Everything else about the modulator connects here. The buck sets the smoothness of the ramp, which is why pulse skipping never produced a sword, and why the ripple and the discontinuous threshold matter as shape rather than as 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.
What the ramp cannot buy you
Everything on this page is about the shape you set. There is a question about the shape you get that the ramp does not reach, and it was asked on HVF by davekni looking at 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). Nobody in that thread answered it.
He answers it himself further down the same thread, without appearing to notice, reporting a session where the arcs changed character on him:
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.
Read the second clause. The ramp was essentially unchanged and the arcs were visibly different, so the variable that moved was the room. That is the answer to his own question and it is a negative one: if temperature and humidity move the arc while the ramp holds still, then refining the ramp cannot buy shot to shot repeatability, because the dominant term is not in the ramp.
The connection between the two posts is ours; he draws neither. And it does not say ramp shape is unimportant, only that repeatability and shape are different targets: this page's axis controls what the average arc looks like, and the scatter around that average is 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 by the channel's own charge rather than by 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 wall 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.
So 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 simply stops holding straight.
The energy side agrees in direction, and this page no longer puts a figure on it: the centimetres it used to quote were scaled off an arc length that the page carrying them could not source, and both went together. Returns fall away on both counts at once.
And there is a nearer wall than the physics, in the reservoir. A 25 ms flash already asks about 495 J of the bus, and a 12000 µF bank at 440 V gives up about 528 J before it sags to 325 V, so the wall is already at about 27 ms [derived] and not somewhere comfortably past 30. So the physics sets where the arc stops holding straight, and the bank sets where this coil runs out first, in microfarads rather than in newtons per cubic centimetre. The check is the bus sag: if the rail drops hard across a flash the ramp is already against the bank rather than the arc, and the bank is what to size next.
A third wall is in the bridge, and it does not sit at a fixed ramp length, because what the switches budget is the pair: how long each pulse lasts and how often it comes. One case is on the 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 on its own does not decide it either: a long pulse heats the die through, while a short one at the same duty leaves it time to cool between shots. So a ramp length that is safe at a few bangs a second is not safe at ten, and the 30 and 35 ms windows on this page are costed against the bank, not against the bridge.
The blunted top, a shape nobody has tried
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 carries a single rise/(rise+fall) control, and neither has a plateau parameter at all. The trapezoid is untried in the published corpus, so the arithmetic below is ours.
At a fixed window the plateau is a trade, not a gift. It steals time from the rise, which steepens the front, and a steeper front is what branches early by the threshold above. 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 %Hold the slope instead and lengthen the window, and the plateau is pure gain in energy, but it is bought 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 wants 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 to spend before the next capacitor. The cost of the blunted top is measured in microfarads, not in slope, which is the honest way to offer a shape no generator yet makes.
The ramp on the QCW department page is drawn as 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, and none of them is the exponent: the arc answers the length at the cube root of the energy and answers the wick by splitting. The exponent is the one you set once, carefully, and last.