Taming Capacitor Inrush: How to Size an NTC Thermistor for Your Power Supply

The Inrush Current Problem

Every engineer who has designed a power supply with a bulk electrolytic capacitor on the front end has heard the dreaded "thunk" at power-on — or worse, watched a fuse blow or a bridge rectifier fail. The culprit is inrush current: the momentary surge that flows when you connect a discharged capacitor to a voltage source through near-zero impedance.

At the instant of switch-on, a discharged capacitor looks like a short circuit. The peak current is limited only by the source impedance, the wiring resistance, and any series elements you deliberately place in the path. In a typical offline power supply with a 330 µF bulk cap behind a bridge rectifier, the peak inrush on a 325 V peak mains line can easily exceed 100 A for a few milliseconds — enough to weld relay contacts, trip breakers, or stress components far beyond their ratings.

The simplest and most cost-effective fix is an NTC (Negative Temperature Coefficient) thermistor in series with the AC line. When cold, it presents a relatively high resistance that limits the surge. As current flows and the thermistor self-heats, its resistance drops to a low "hot" value, minimizing steady-state power dissipation. Sizing it correctly is the engineering challenge.

Key Relationships

The peak inrush current through a series resistor into a discharged capacitor charged from a DC-equivalent peak voltage $V_{pk}$ is:

where $R_{cold}$ is the NTC resistance at ambient temperature (typically 25 °C). This is the worst-case scenario — power applied at the peak of the AC cycle with the capacitor fully discharged.

The charging time constant is:

This tells you how quickly the capacitor charges and, critically, how long the thermistor must absorb energy before the current decays.

The energy the NTC must absorb during the inrush event is approximately:

For a fully discharged capacitor ($V_{cap,0} = 0$), this simplifies to:

Note that this is a simplification — the NTC and the capacitor each absorb roughly half the total energy delivered by the source during an RC charging event, so the thermistor absorbs approximately $\frac{1}{2} C V_{pk}^{2}$ of energy. This value must stay below the NTC's maximum rated single-pulse energy; exceed it and the thermistor can crack or fail open.

Worked Example: 230 VAC Offline Supply

Let's size an NTC for a common scenario:

• Supply voltage: 230 VAC RMS → $V_{pk} = 230 \times \sqrt{2} \approx 325\,\text{V}$
  • Filter capacitance: $C = 330\,\mu\text{F}$
  • Target peak inrush current: $I_{target} = 15\,\text{A}$
  • NTC hot resistance: $R_{hot} = 0.5\,\Omega$ (from datasheet at operating temperature)
  Step 1 — Required cold resistance:
  $$R_{cold} = \frac{V_{pk}}{I_{target}} = \frac{325}{15} \approx 21.7\,\Omega$$

  You would select a standard NTC value of 22 Ω at 25 °C.

  Step 2 — Verify peak inrush with selected value:
  $$I_{peak} = \frac{325}{22} = 14.8\,\text{A}$$

  Comfortably under our 15 A target. Good.

  Step 3 — Time constant:
  $$\tau = 22 \times 330 \times 10^{-6} = 7.26\,\text{ms}$$

  The inrush event is essentially over within $5\tau \approx 36\,\text{ms}$ — about two full mains cycles. The thermistor will begin self-heating during this window, but the cold resistance dominates the limiting.

  Step 4 — Energy absorbed by the NTC:
  $$E_{NTC} = \frac{1}{2} \times 330 \times 10^{-6} \times 325^{2} \approx 17.4\,\text{J}$$

  You need an NTC rated for at least 17.4 J of single-pulse energy. A device like the Ametherm SL32 2R522 (22 Ω, 2.2 A steady-state, 45 J max energy) would be a suitable candidate with comfortable margin.

  Step 5 — Steady-state dissipation check:

  At full load, suppose the supply draws 2 A RMS through the NTC. The hot resistance dissipation is:

  $$P_{hot} = I_{rms}^{2} \times R_{hot} = 2^{2} \times 0.5 = 2\,\text{W}$$

  That's manageable but not negligible — it affects efficiency. In higher-power designs (above ~200 W), engineers often switch to an active inrush limiter with a relay that bypasses the NTC after startup.

  Practical Design Considerations

  Worst-case timing: The absolute worst case is power applied at the AC peak with a fully discharged capacitor. If your product can be power-cycled rapidly, the NTC may still be warm (low resistance) from the previous cycle and won't limit the next inrush effectively. Datasheets specify a cool-down time — typically 30–60 seconds. If your application demands rapid cycling, consider a fixed resistor with a bypass relay or an active limiter IC. Derating: NTC energy ratings are specified at 25 °C ambient. In a warm enclosure (say 50 °C), the thermistor starts at a lower resistance and absorbs more energy per event. Derate accordingly — a 30% margin on energy is a sensible minimum. Multiple capacitors: If your design has several capacitors across different rails that all charge simultaneously, sum their $\frac{1}{2}CV^{2}$ contributions to get the total energy the NTC must handle. Placement: The NTC goes in series with the AC line, before the bridge rectifier. This way it limits current on both half-cycles during the initial charge.

  Try It

  Rather than running these calculations by hand every time you spec a new power supply, open the Inrush Current Limiter (NTC) Calculator and plug in your supply voltage, capacitance, target inrush current, and NTC hot resistance. The tool instantly returns the required cold resistance, peak current, time constant, and absorbed energy — giving you the numbers you need to pick the right thermistor on the first try.