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Bulk Capacitor Calculator

Size the bulk capacitor bank of a motor drive fed through a harness. It checks the bank's ripple current, the real bus impedance at the PWM frequency, the harness LC resonance against the driver's negative input resistance, and simulates hot-plug and load-step transients. The model was first built for a small robot-joint driver.

Bus and load

Bus voltage, nominal18 VSupply voltage, max18 VPhase current, peak1 ADriver input power at that current10 WPWM frequency20 kHzCurrent-loop bandwidth160 Hz

Capacitor bank

Capacitors in parallel1 Nominal C each100 µFC left at bus voltage (DC bias)100 %ESR each150 mΩESL each (with vias)10 nHRipple-current rating each0.55 A rms

Damping branch (optional)

Damping capacitor (0 = none)0 µFIts ESR or series resistor100 mΩ

Harness to the supply

Length1 mLoop inductance800 nH/mLoop resistance50 mΩ/m

Protection and regeneration

TVS breakdown, or the clamp limit if none52 VDriver max operating voltage52 VInertia at the motor44 g·cm²Speed before an unbraked stop2000 rpm

Defaults: the MMC's current bench — an X-NUCLEO-IHM07M1 (L6230) shield with its single 100 µF / 63 V electrolytic, on an 18 V bench supply through about 1 m of leads, driving a maxon EC-i 40 at up to 1 A. The shield has no TVS, so the clamp limit is set to the L6230's 52 V supply maximum. ESR, ESL and ripple rating are typical for a low-ESR electrolytic of that size, not from the part's datasheet.

Check / quantity	Value	Criterion / note

Bus impedance seen by the driver

Bank ∥ harness (∥ damping branch), log–log

Below the current-loop bandwidth the driver regulates its power, so it looks like a negative resistance of −V²/P. If the bus impedance peak reaches that line inside the loop's bandwidth, the input filter and the driver can oscillate together (Middlebrook). Keep the peak at least 6 dB below it, or add damping.

Hot-plug

bus charged from 0 V in one step

Load step

0 to full input current

C_eff = n · C · retention · ESR_bank = ESR / n · ESL_bank = ESL / n

I_C,rms = Î · √(M (√3/4π + cos²φ (√3/π − 9M/16))) ≤ 0.46 · Î (worst case, M ≈ 0.61, cos φ = 1)

Z_bus(f) = Z_bank ∥ Z_harness ∥ Z_damp · ΔV_pp ≈ 2√2 · I_C,rms · |Z_bus(f_sw)|

f₀ = 1 / 2π√(L_h C) · Z₀ = √(L_h / C) · stable if |Z_bus|_peak ≤ ½ · V² / P

Optimal damping (n = C_d/C = 4): R_d = Z₀ √((2+n)(4+3n) / (2n²(4+n)))

Regeneration into an isolated bus: V_peak = √(V_max² + J ω² / C)

References

J. W. Kolar, S. D. Round — Analytical calculation of the RMS current stress on the DC-link capacitor of voltage-PWM converter systems (IEE Proc. EPA, 2006)
R. D. Middlebrook — Input filter considerations in design and application of switching regulators (IEEE IAS, 1976)
R. W. Erickson, D. Maksimović — Fundamentals of Power Electronics, ch. 10: Input filter design (optimal damping)