| Voltage Definition | Initial capacitor voltage, Vi | 800 V DC | The maximum normal operating voltage immediately before the pulse. Include charging tolerance, ripple, and expected voltage transients in the design review. |
| Minimum usable voltage, Vf | 600 V DC | The lowest voltage that still allows the load, converter, switch, or actuator to meet its required performance. |
| Usable voltage window | Vi − Vf = 200 V | A larger allowable voltage swing increases usable energy for the same capacitance, but may require a wider input-voltage range for the load. |
| Required voltage rating | Greater than the maximum applied voltage | The selected capacitor assembly should have a voltage rating above the maximum steady-state and transient voltage, according to the applicable safety standard and the system derating policy. |
| Voltage polarity and reversal | Unipolar pulse; no intentional reverse voltage | Many polarized capacitor technologies require protection against reverse voltage. Confirm polarity, switching behavior, and possible ringing in the complete circuit. |
| Capacitance Definition | Required pulse energy, Epulse | 1,000 J | Define the energy that must reach the load. Add the estimated losses of switches, cables, inductors, converters, and protection circuits when calculating stored energy. |
| Ideal stored-energy equation | E = ½CV² | This equation gives the total energy stored at a specified voltage. It does not represent the energy available between two operating voltages. |
| Usable energy between two voltages | Eusable = ½C(Vi² − Vf²) | Use this equation when the capacitor discharges from an initial voltage to a defined minimum voltage. |
| Calculated minimum capacitance | C = 2E / (Vi² − Vf²) ≈ 7.14 mF for the example | For 1,000 J delivered ideally from 800 V down to 600 V, the theoretical minimum is approximately 7.14 mF. Practical designs normally require additional margin. |
| Recommended design allowance | Typically add application-specific energy margin | Account for capacitance tolerance, temperature effects, aging, ESR losses, wiring losses, switching losses, and energy reserve. The final margin must be validated by testing. |
| Pulse Current and Power | Pulse duration, tp | 10 ms | Specify the complete current waveform, including rise time, peak duration, decay time, and any ringing or repeated sub-pulses. |
| Average pulse power | P = E / t = 1,000 J / 0.010 s = 100 kW | This is the average power during the 10 ms pulse. It is different from the long-term average power of a repetitive pulse system. |
| Approximate current at 800 V | I ≈ P / V = 100 kW / 800 V = 125 A | Use the actual load waveform for final sizing. A constant-power load draws more current as the capacitor voltage falls. |
| Approximate current at 600 V | I ≈ P / V = 100 kW / 600 V = 167 A | The lowest operating voltage can produce the highest current. Verify the capacitor, busbars, switches, fuses, and connectors against the peak current. |
| ESR voltage drop | ΔVESR = I × ESR | For a 10 V maximum ESR drop at 167 A, the total circuit ESR must be no greater than approximately 0.060 Ω. Include capacitor, interconnect, switch, and contact resistance. |
| Capacitive voltage drop for constant current | ΔV = I × t / C | Use this approximation only for a near-constant-current pulse. For a constant-power or converter-driven load, use a time-domain simulation or measured waveform. |
| Repetition and Thermal Requirements | Pulse repetition rate | 2 pulses per second | Define the repetition rate, burst length, duty cycle, and rest time. These parameters determine average heating and recharge requirements. |
| Long-term average load power | Pavg = E × repetition rate = 1,000 J × 2 = 2 kW | The average energy flow is 2 kW before system losses. The charger and thermal system must support the average power, not only the pulse power. |
| Approximate capacitor ESR loss | Ploss = IRMS² × ESR | Calculate RMS current from the real waveform. High peak current can create significant heating even when the duty cycle is low. |
| Recharge time | Specified by the next-pulse deadline | The charger must restore the required energy before the next pulse while respecting the capacitor charging-current limit and thermal conditions. |
| Operating temperature | Define minimum, normal, and maximum temperature | Capacitance, ESR, leakage current, service life, and allowable ripple current vary with temperature. Validate performance at the full specified temperature range. |
| Safety and System Validation | Stored energy at maximum voltage | Estored = ½CVmax² | Treat the capacitor bank as a hazardous energy source. Provide suitable discharge, isolation, labeling, access protection, and verification of zero voltage. |
| Balancing requirement for series capacitors | Required when voltage is shared by multiple series units | Use a validated balancing method to control unequal leakage-current effects and transient voltage distribution. |
| Measurement bandwidth | Sufficient for the fastest edge and ringing frequency | Voltage and current probes, wiring, and sensors must have suitable bandwidth and safety ratings so that peak values are not understated. |
| Waveform validation | Measure V(t), I(t), pulse width, repetition rate, and temperature | Confirm the actual waveform against the design assumptions. Pay particular attention to overshoot, reverse voltage, current sharing, and contact bounce. |
| Final selection criteria | Voltage rating, capacitance, ESR, peak current, RMS current, life, temperature, safety | Choose the capacitor assembly only after electrical, thermal, mechanical, environmental, and safety requirements have been checked together. |