[ §1 · resonator ]

Soft or hard switching, and why an SSTC couples tight

Whether a coil switches softly comes down to k squared Q. A loose primary at k = 0.15 never gets there, and its switching loss is nearly five times its conduction loss.

CommonGnd4 August 202613 min read

There is a short answer to whether an SSTC switches softly, and it is davekni's: an SSTC has no primary resonant capacitor, so the primary switches at maximum current, and zero current switching is a DRSSTC thing (HVF 1355).

He went back and edited that post himself. The edit points four replies down the same thread at Uspring, who says the opposite is possible and gives the condition for it. So the short answer is right about the coil in front of most people and is not the end of the subject, and the man who wrote it is the one who says so.

What soft switching would buy

Richie Burnett sets out what follows on his driver theory pages, with a precondition on all of it: the current passes through zero at the switching instant only when the driver is perfectly in tune with the resonator. Given that,

switching losses are greatly reduced, because no current flows at the switching instant and the heating left is conduction;
spikes and ringing are greatly reduced, because di/dt is the slope of a sinusoid rather than many amps interrupted in tens of nanoseconds;
paralleled switches share better, because the current is near zero for some time around each switching instant, so a mismatch in switching times matters less.

The condition

Uspring, in the same thread, answering davekni's question of whether an 80 cm arc leaves the secondary any Q to work with:

Q needs to be about 1/k^2 or more.

Q is the secondary's loaded quality factor and k is the coupling. His mechanism is in the next sentence and is worth more than the inequality: the secondary current has to be large enough to cancel the primary inductance, which takes a high Q to produce that current and a high coupling to make the primary feel it.

Burnett's reflected model gives the same thing as an angle. He shows the secondary's series resonance appearing across the primary winding as a transformed load, so the bridge's current is the sum of two components. The magnetising current is triangular and ninety degrees behind the voltage, and flows whether or not anything is coupled to the winding; the resonant current is in phase, and is the part doing work. His reflected resistance at resonance is Rs' = Rs·Lp/(k²·Ls), and he gives the magnetising current as inversely proportional to both the frequency and Lp, which is V/(2·pi·f·Lp). So

I_resonant / I_magnetising = k² · Q     [derived, from those two expressions]
phi = arctan( 1 / (k² · Q) )

which is Uspring's condition read as a phase rather than as a threshold. The exact two-port form of a coupled pair gets there by a different route and agrees: at the secondary's resonance the bridge sees 2·pi·f·Lp·k²·Q in series with 2·pi·f·Lp, whose ratio is the same k²Q [derived]. One expression, two models, which is the second route this corpus asks for before a figure travels.

Worth naming the boundary, because it is not zero. k²Q = 1 is a lag of exactly 45 degrees [derived, arctan 1]. The condition does not promise switching at the current zero. It promises the current is more in phase than in quadrature.

This is not Lenz's condition, which is written on the same two symbols and says something else. Qsec < 1/k is where the pair of poles collapses, and it lives on there is no secondary frequency. One asks whether the resonances survive the load, the other whether the bridge current is in phase with the bridge voltage. At k = 0.5 they sit at Q = 2 and Q = 4 [derived, 1/k and 1/k²], so a coil above 4 is on the safe side of both, and nothing here contradicts that page.

What the condition costs in coupling

1/k² moves fast, which is the whole argument for winding an SSTC primary tight:

k       Q the condition demands
0.15    44.4       a DRSSTC's coupling
0.35     8.2       Burnett's floor for an SSTC primary
0.40     6.3       his project coil
0.55     3.3       his design page coil

Those couplings are somebody's rather than illustrative. The 0.15 and Burnett's three figures, with his own hedges on the last two, are carried on an SSTC primary is a different part.

Now put a Q beside them. This corpus publishes exactly one secondary with a loaded figure and it is a QCW's rather than an SSTC's: unloaded Q 199, and 7.59 under a metre and a half of arc, on the secondary is a resonator. Running that one coil at the three couplings:

k       no arc              1.5 m of arc
        k²Q     lag         k²Q     lag
0.15    4.48    12.6°       0.171   80.3°
0.35    24.4     2.3°       0.930   47.1°
0.55    60.2     1.0°       2.30    23.5°

[derived throughout, arctan(1/k²Q) on that page's 199 and 7.59]

Every entry on the left clears the condition, and the arc decides the right one. That is one coil with the winding moved, which is the lever, rather than three different machines. Read down the left and even a DRSSTC's loose primary is switching nearly softly before breakout. Read across and the arc takes the same coil to 80 degrees, which is switching at the current peak. At 0.55 it survives the arc at 23 degrees.

Break-even is k = 0.363 [derived, the square root of 1 over 7.59], and Burnett's stated floor for the method is above 0.35. An empirical floor a builder gives for power transfer and a phase condition worked from a different model land within four per cent of each other, and neither man was arguing for the other's number.

The coil in the thread, and why it could not

Rapy2's machine is the one davekni and Uspring were talking about, and it is the only SSTC here with enough published to check: a 40 cm secondary of 0.35 mm wire on a 110 mm form running about 240 kHz, a primary of 10 turns at 125 mm, a bus to 390 V, 80 cm sparks, and a full bridge of FGA60N65SMD. He posts the secondary's inductance as 37.6, in microhenries.

The unit is a slip, and correcting it is worth more than dropping the figure, because impedance is the term Uspring's advice is written on. Wheeler on the geometry Rapy2 states returns 28 to 35 mH [derived, 110 mm on 400 mm close wound, the spread being whether the 0.35 mm is measured over the varnish or under it], so millihenries it is, and the spread is a reminder that a turn count is not the wire's bare diameter and nothing else. Take 37.6 mH against his own 240 kHz and the resonating capacitance is 11.7 pF, so √(L/C) is 57 kΩ [derived].

Which is the number Uspring says is too high. In the post carrying the condition he adds that for an 80 cm arc the secondary impedance wants to be below the typical 50k, "maybe 15 or 20k", because under an arc the loaded Q is the arc's resistance over that impedance and very little else. Rapy2's coil sits above the typical figure rather than below it.

What that costs him: this corpus publishes 210 kΩ for a metre and a half of arc, from Hydron's measurements of his own toroid currents (HVF 117), and scales it as one over length, which is 394 kΩ at his 80 cm [derived], and 394 over 57 is a loaded Q near 6.9 from the arc alone, 6.7 with the winding's own 199 beside it [derived]. The condition then wants k above 0.38, which is Burnett territory. At Uspring's 15 to 20 kΩ the same arc gives 20 to 26 and the demand falls to k above 0.20 to 0.23 [derived]. Rapy2's own coupling is not published, which is where the check stops: what can be said is what his impedance demands, not whether his primary supplies it.

The obvious objection is that the 210 kΩ and its scaling come off a different machine, and they do. No SSTC here has a measured arc resistance. The direction of the borrow is the safe one, because a shorter arc is a higher resistance and so a higher loaded Q, which makes these figures kind to the SSTC rather than harsh. What they cannot be is a specification for a particular coil.

How well established this is

Not very, and the man who wrote the condition says so first. In the same post Uspring adds that he had never seen a working ZCS SSTC and that his was speculation on theoretical grounds; that the cancellation of the primary inductance is usually very incomplete, because either the Q or the coupling is not large enough; and that what a real coil usually shows near the secondary's resonance is a dip in the primary impedance rather than a null.

davekni's own reaction, once Rapy2 posted the design he had copied, was that it looks to have high coupling and that ZCS with large arcs was still surprising to him.

And it does not arrive at once

Uspring's second caveat, in the same post. Even with the condition met the secondary current has to build up, so soft switching does not appear at the start of a burst, and he files the whole option under CW or QCW rather than short bangs.

How long is arithmetic on the same Q. A resonator's envelope rises with a time constant of 2Q over the angular frequency, which is Q/pi cycles [derived], so on the figures above it is 63 cycles with no arc, about two once a metre and a half of arc is loading it, and about four at 80 cm. The bind is the useful part: the Q that satisfies the condition is the Q that makes the coil slow to reach it.

The other question, which looks like a contradiction

The numbers

The condition: Q > 1/k², Uspring's, on the secondary's loaded Q.
The lag it produces: arctan(1/k²Q), with k²Q = 1 at 45 degrees [derived].
What it demands in Q: 44.4 at k = 0.15, 8.2 at 0.35, 6.3 at 0.40 and 3.3 at 0.55 [derived].
The one loaded secondary in this corpus: 199 unloaded and 7.59 under a 1.5 m arc, and it is a QCW's, not an SSTC's.
Break-even coupling on it: 0.363 under that arc [derived], against Burnett's stated floor of above 0.35 for an SSTC primary.
Secondary impedance Uspring asks for at an 80 cm arc: below the typical 50 kΩ, and he suggests 15 or 20.
What switching costs when the condition fails: davekni prices Rapy2's bridge off the datasheet, 0.78 mJ of turn-off energy at 60 A, which at 240 kHz is 187 W of switching against about 40 W of conduction, 227 W per device. Switching is 4.7 times conduction [derived].
And his conclusion is not that the devices are wrong. He puts continuous operation within reach of those IGBTs given thermal compound and cooling for about 900 W across all four, and separately notes that most SSTC designs he has seen use FETs, with fast IGBTs working in spite of the high current switching, especially where the enable duty is low. The choice itself is IGBT or MOSFET, which gives the reason as an SSTC's modest current. The two readings are one: the current is modest beside a DRSSTC's tank, and it is at its maximum at the switching instant, which is the quantity switching loss is written on.

What goes wrong

Setting the driver for ZCS and losing the bridge. Rapy2's actual failure, and Uspring's reading of it: with the condition unmet, what sits near the secondary's resonance is a dip in primary impedance rather than a null, and the dip was deep enough to raise the current until the devices went. Moving the frequency towards resonance raises current before it straightens phase.
Hard switching on a coil that calculated as soft. Check k²Q on the arc's Q and not the unloaded one. The condition holds comfortably before breakout and can fail after it, and on the coil above the swing is 12.6 degrees to 80.3.
A DRSSTC primary geometry reused on an SSTC. At k = 0.15 the arc-loaded Q would have to stay above 44.4, which no loaded figure published here approaches.
Paralleled devices that share badly only at high power. Same cause. Soft switching was carrying the sharing and the arc took it away.
Devices that survive the bench and die on the arc. The bench had no load to ruin the Q. It is the same trap as reading a hard-switched datasheet pulse as a rating, which IGBT or MOSFET has.
Soft switching that appears late in the burst and not at the start. Working as described. The secondary current has to build first.

Where next

An SSTC primary is a different part, the winding this condition asks for, and where Burnett's coupling figures and his magnetising current live.
The secondary is a resonator, where the loaded Q comes from.
There is no secondary frequency, for Lenz's Qsec < 1/k, a different condition on the same two symbols.
IGBT or MOSFET, the choice this prices.
Switching at zero is the failure case, the second question.

The SSTC department diagram draws the primary standing beside the secondary on one axis, because being near it is the only way they are coupled at all, and this is the department where near means near.

Soft switching puts k²Q against the threshold and says which side of it a given coil is on.

ZCScouplingMOSFET