This is probably the single most useful rule when choosing a tank, and it is the one that explains why a QCW runs single-digit nanofarads where a DRSSTC runs tens.
The two columns are not the same size
Things that grow with current:
- tank capacitor loss,
I²·ESR, quadratic; - primary copper,
I²R, quadratic; - device conduction: an IGBT goes as
I, SiC asI²; - the peak rating of the switches and the overcurrent threshold, which is a hard linear wall.
Things that grow with voltage across the tank: the capacitor's voltage rating, which you fix by adding series links for pennies, and the risk of a primary-to-secondary flashover, which you fix with geometry.
Jan's rule: better a tank that is too high impedance. The current can be turned down by tuning. Too low an impedance and the current cannot be brought down at all.
Why a QCW cares more than a DRSSTC
A low impedance tank accelerates the current too quickly at the start of the bang. The overcurrent detector fires before the end of the ramp, and instead of a sword you get a pop.
That is where the single-digit nanofarads come from. It is not a subtle preference, it is the difference between the machine working and not.
The other half of the same motive: a QCW's ontime is tens of times longer than an ordinary DRSSTC's, and the switches have to carry that current for milliseconds rather than hundreds of microseconds.
The free lunch in detuning downwards
At a fixed frequency L and C move as a pair, so:
Z = sqrt(L/C), current goes as C, power goes as Cand the voltage on the capacitor does not depend on C at all.
Adding primary turns to detune downwards, so that the frequencies meet under the arc, also raises the impedance. Lower current at the same power, from the same movement. One adjustment, two problems solved, which does not happen often.
The tank capacitor on the DRSSTC diagram is drawn as a matrix because the part count is the point, and on the QCW page you can take it out entirely and watch the arc fall to a bit over half.