How it works
When a rectifier charges a large DC-link capacitor directly from the mains, the only things limiting the current are the line impedance and the capacitor's ESR. The resulting surge can reach hundreds of amperes, stressing the rectifier diodes, tripping breakers and welding relay contacts. A precharge (inrush limiting) resistor in series with the DC link keeps that first current pulse within a safe value.
This calculator sizes the resistor from the worst case: the capacitor is empty and the input is switched on at the voltage peak. The peak current is then roughly the peak line voltage divided by the resistance, so the minimum resistance follows directly from the allowed peak current.
When a capacitor is charged from a fixed DC voltage through a resistor, the resistor dissipates exactly the energy that ends up stored in the capacitor, ½·C·V², regardless of the resistance. With a rectified AC input the loss is somewhat lower, but ½·C·V² is the safe upper bound to design for. That energy arrives in a short pulse, so the resistor must be rated for pulse energy (or an NTC for its energy rating), not just continuous power. The temperature rise is estimated adiabatically from the resistor mass and heat capacity.
The time constant τ = R·C sets how long precharge takes. After about 3τ the capacitor reaches 95% of its final voltage, which is a common point to close the bypass relay. Cement and wirewound resistors must be bypassed after precharge; NTC thermistors heat up and drop their resistance on their own but still benefit from a bypass in high-power designs.
Design procedure
- 1Find the worst-case peak line voltage. For a 230 V line with +10% tolerance the peak is about √2 · 253 V ≈ 358 V; for a 400 V three-phase line it is about 622 V line-to-line. Use the high-line value, because it gives both the largest current and the largest energy.
- 2Choose the peak current the rectifier, fuses and relay contacts can tolerate. The diode's non-repetitive surge rating I_FSM and the fuse's I²t are the usual limits. Divide the peak voltage by this current to get the minimum total resistance in the charging path.
- 3Check the charging time. With τ = R·C the capacitor reaches 95% after about 3τ. If that is longer than your start-up budget, the only options are a higher allowed peak current (lower R) or a smaller capacitor.
- 4Select the resistor by single-pulse energy, not by continuous power. Each charge dumps roughly ½·C·V² into the resistors; compare that with the pulse-energy or short-time overload curve in the datasheet, with margin for repeated power cycles.
- 5Decide how the bypass closes. A relay or contactor should close after 3τ to 5τ, when the remaining voltage step across the resistor is small, so the contact does not see a second current spike.
Formulas
- Peak line voltage
- V_pk = √2 · V_line
- DC-link voltage
- V_dc ≈ 0.9 · V_pk (single-phase), 1.35 · V_LL (three-phase)
- Minimum resistance
- R ≥ V_pk / I_max
- Energy per charge
- E = ½ · C · V_dc²
- Time constant
- τ = R · C, t₉₅ ≈ 3τ, t₉₉ ≈ 5τ
- Adiabatic temperature rise
- ΔT = E / (m · c_p)
Worked example
A 230 V single-phase drive with a 2200 µF DC link and a 50 A peak-current limit needs R ≥ 325 V / 50 A ≈ 6.5 Ω. Each power-up dumps about ½ · 2200 µF · (293 V)² ≈ 94 J into the resistor, and τ ≈ 14 ms, so the bypass relay can close after roughly 45 ms.
Common mistakes
- Rating the resistor by its continuous wattage. A 5 W resistor can survive a 100 J pulse if its pulse curve allows it, and a 50 W resistor can fail if it does not. Always read the pulse or overload rating.
- Forgetting the bypass. Cement and wirewound resistors left in circuit carry the full load current and overheat quickly.
- Ignoring repeated cycles. If the equipment can be switched off and on several times in a row, the resistor does not cool between pulses, so multiply the energy by the expected number of back-to-back cycles.
- Using the nominal instead of the maximum line voltage. Energy grows with V², so a 10% higher line voltage means 21% more energy in the resistor.
Frequently asked questions
Why is the energy in the resistor independent of its resistance?
For an RC charge from a fixed DC voltage, the energy lost in the resistor equals the energy stored in the capacitor. A larger resistor lowers the peak current and stretches the pulse, but the total stays ½·C·V². With rectified AC the loss is a little lower, which the interactive explorer shows.
Should I use an NTC thermistor or a fixed resistor with a relay?
NTCs are simple and cheap for low and medium power, but they need time to cool down between power cycles and still dissipate some power in operation. A fixed resistor with a bypass relay handles repeated power cycling and high power better.
What pulse rating do I need?
Choose a resistor whose single-pulse energy rating comfortably exceeds ½·C·V² at the highest DC-link voltage, including any mains overvoltage. The calculator applies a safety factor and shows the required rating.
When should the bypass relay close?
Typically after three to five time constants, when the capacitor is at 95–99% of its final voltage, so the relay closes with very little current step.
Results are engineering estimates. Verify your design with datasheets, simulation and measurement.