[ §7 · calculators · primary tank ]

Primary tank

Published MMC calculators size the bank and its voltage rating. This adds the two things that decide a DRSSTC: the primary resonance, which is the input to the coupled poles calculator, and the current each capacitor carries, which is what usually kills an MMC, not the voltage.

capacitance, each · nFvoltage, each · Vin seriesin parallelprimary inductance · µHprimary current, peak · Aworking frequency · kHzburst duty · %

per capacitor42.3 A113 A in burst, 10S1P at 14 % duty

bank12.00 nF20000 V rating against 4278 V peak

primary resonance310 kHzwith L 22.0 µH

bank capacitance 12.00 nF (10S1P)bank rating 20000 Vprimary resonance 310 kHz (L 22.0 µH + this C) MMC reactance 26.7 Ω at 496 kHzMMC voltage 4278 V peak at 160 AMMC current 113 A RMS in burst per CAPACITOR 113 A in burst, 42.3 A with dutystored energy 109.826 mJ Voltage margin ×4.67. 42.3 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, not voltage, is what usually kills an MMC.

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
per capacitor = I_RMS/P,  ×√duty for the average

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 per-capacitor current assumes the burst current divides evenly between parallel strings. dV/dt and the datasheet ripple current are not checked here and both can bite before the RMS figure does.