envproduction·api/api-origin/v1·backendcommongnd.org·checking…buildde577045
[ §7 · calculators · primary tank ]

Tesla coil MMC and primary tank

calculators

Published MMC calculators size the bank and its voltage rating. This one adds two things a DRSSTC depends on: the primary resonance, which feeds the coupled poles calculator, and the current each capacitor carries. Current usually kills an MMC before voltage does.

current through a burst

per capacitor24.4 A113 A at the peak, 10S1P at 14.0 % duty

bank12.00 nF20000 V rating against 4331 V peak

primary resonance353 kHzwith L 17.0 µH

bank capacitance 12.00 nF (10S1P)bank rating 20000 Vprimary resonance 353 kHz (L 17.0 µH + this C)primary impedance 37.6 Ω (√(L/C)) MMC reactance 27.1 Ω at 490 kHzMMC voltage 4331 V peak at 160 AMMC current 113 A RMS at the peak per CAPACITOR 113 A RMS at peak, 24.4 A averaged each, at the peak 160 A, 1333 V/µs, 433 Vstored energy 112.532 mJ Voltage margin ×4.62. 24.4 A RMS per capacitor is a lot.Film MKP of this class usually takes single-digit tolow-tens of amps. Add PARALLEL strings: the currentdivides and the capacitance rises, so shrink eachcapacitor at the same time.Current usually kills an MMC before voltage does.
formula
C = C₁·P/S      U_bank = U₁·S      f_pri = 1/(2π√(L·C))
U on MMC = I_pk/(2πf·C)      I_RMS = I_pk/√2      E = ½·C·U²
ring-up, lossless: +2·U_bus a half cycle (full bridge), +U_bus (half)
rating allows I = U_bank / (1/(2πf·C))
duty = burst length × bursts a second   (cannot pass 100 %)
per capacitor = I_RMS/P,  averaged ×√(duty · e)
  e = ½ rings up (Conner's I_RMS = ½·I_pk·√(t_on·BPS)), ⅓ QCW ramp, 1 steady
heat = I_averaged² · ESR a capacitor     rise = heat · R_th
limits

f_pri here is the resonance of the uncoupled primary. The frequency a coil actually runs at is a pole of the coupled system. Compute that in the coupled-poles calculator and bring it back here.

MMC voltage is given for the steady state. Transients run higher.

The ring-up shown is the fastest case: the primary on its own, no losses, no secondary, the bridge switching on every current zero. A real coil rings up more slowly, and a QCW, whose bus ramps, behaves quite differently. Use it for the current the bank's rating allows, which is where the overcurrent limit belongs, and the shortest burst that could reach it.

“Rings up” is typical, not a bound. Steve Conner's rule fits about four bursts in five in our circuit simulation. With a heavy arc load on long bursts the current sits near its peak for most of the burst and the capacitors take up to half as much heat again, so pick steady for a safe figure. The ring-down after the bridge stops, through the diodes, is not counted either, and it added 5 to 77 % to the bank's heating in the same simulation, more at light load.

The per-capacitor current assumes the burst current divides evenly between parallel strings. Pick your capacitor from the list and the page checks its dV/dt, peak and RMS current against the datasheet. With your own capacitor, compare the “each, at the peak” line with its datasheet, because dV/dt or peak current can be the limit before RMS is.