Sizing a tank capacitor by RMS current

The tank capacitor is the part that makes a doubly-resonant coil doubly resonant, and it is the part people size wrong most reliably. Voltage and pulse rating usually pass with room to spare. What kills a bank is RMS current.

Averaged over time, not over the bang

I_rms(average) = I_rms(during the bang) · sqrt(duty)
duty = bang length × bangs per second

And the shape of the envelope inside the bang moves the answer by a factor of the square root of three:

• a flat top gives I_pk / sqrt(2), so 0.707 of the peak;
• a linear rise gives I_pk / sqrt(6), 0.408;
• a quadratic rise, which is what a QCW does, gives I_pk / sqrt(10), 0.316.

Dissipation is I_rms^2 · ESR. The catalogue current is quoted for a stated temperature rise, usually twenty degrees, which gives you the thermal resistance for free and lets you work out the real rise rather than guessing at it.

Check which edition of the datasheet you are reading

TDK's B32642B0333J was rated 70 V RMS at 400 kHz in the 2015 edition of its datasheet and 35 V in the 2018 edition. Exactly half.

The public capacitor tables everybody links to were built on the older numbers.

Small capacitors carry more current per nanofarad

This is the counterintuitive one, and it is why "I will fit bigger ones to be safe" is backwards. At a fixed bank capacitance, smaller parts give you more current. From one family at 1000 V:

• 10 nF: 1.3 A each, 130 mA per nF. A 12.2 nF bank as 9 series by 11 parallel is 99 parts and 14.3 A.
• 22 nF: 1.9 A, 86 mA/nF. 9 by 5, 45 parts, 9.5 A.
• 100 nF: 5.4 A, 54 mA/nF. 9 by 1, nine parts, 5.9 A.

Nearly a factor of three in current for the same capacitance, and the price is count: parts go up as the square of the current gain, because every extra parallel string needs its own series stack.

And on a QCW, small in the other sense too

A QCW wants a small bank outright, single-digit nanofarads to about fifteen. Forty-four nanofarads is a mistake somebody has made in public and said so: with that much capacitance the primary current climbs so fast that the overcurrent detector trips and cuts the ramp short. The sound of that is a pop instead of a sword.

The reason is the tank's characteristic impedance. At a fixed frequency L and C are tied together, and:

Z = sqrt(L/C),   primary current goes as C,   power goes as C

while the voltage across the bank does not depend on C at all. So the fix for too much current is more primary turns and less capacitance, and the fix for too little is the reverse: Landon Kageler went from 12 to 30 nF, dropped the inductance, and the arc grew.

And the current does not divide the way you think

Between parallel strings, the current divides in inverse proportion to ESR and path resistance, not to capacitance. At the frequencies a tank runs at, capacitance is not what decides it.

The same source disposes of the idea that small capacitors make a poor bank: a network's ESR does not depend on the size of its unit, and dividing the heat between more parts improves the cooling. What limits it in practice is the number of joints and the symmetry of the paths, not the physics.

One more thing that follows from where the heat goes: about two thirds of it leaves a film capacitor along its axis and one third radially. Cool the leads first, and space the parts so air can pass between them.

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The rig on the DRSSTC department page draws the bank as a matrix rather than one symbol, because the number of parts is the point. Take the tank capacitor out on the QCW page and you have a ramped SSTC, which is a different machine with a different set of problems.

Figures here are from manufacturers' tables and published builds. The arithmetic on them is ours.