NTC Thermistor Sizing for Capacitor Inrush

The Inrush Current Problem

If you've ever designed a power supply with a big electrolytic cap on the input, you know that satisfying "thunk" when you flip the switch — or the much less satisfying sight of a blown fuse or a dead bridge rectifier. That's inrush current doing its thing: a massive surge that happens when you slam a discharged capacitor onto a voltage source with basically no impedance in the way.

Here's what's happening. At the exact moment you close that switch, your discharged cap looks electrically identical to a dead short. The only thing limiting current is whatever resistance exists in the path — the source impedance, maybe a few milliohms of wire, and whatever you've deliberately added. Take a typical offline supply with a 330 µF bulk capacitor sitting behind a bridge rectifier. Connect that to 230 VAC mains (325 V peak) and you can easily see 100 A or more for a few milliseconds. That's enough to weld relay contacts together, blow circuit breakers, or stress your semiconductors way past what they signed up for.

The fix most of us reach for first is an NTC thermistor — that's Negative Temperature Coefficient for anyone keeping score — wired in series with the AC input. When it's cold, it acts like a moderately high resistance that chokes down the surge. Then, as current flows through it, the thermistor heats itself up and its resistance drops to a much lower "hot" value. This keeps steady-state power loss reasonable. The trick is sizing it properly, and that's where things get interesting.

Key Relationships

When you're charging a discharged capacitor through a series resistor from a DC-equivalent peak voltage $V_{pk}$, the peak inrush current works out to:

Here, $R_{cold}$ is the NTC's resistance at room temperature — usually specified at 25 °C. This represents the absolute worst case: power applied right at the peak of the AC waveform with the capacitor completely empty.

The time constant for this RC charging circuit is:

This tells you how fast the cap charges up, and more importantly for our purposes, how long the NTC has to sit there absorbing energy before the current dies down to something reasonable.

Now for the energy calculation. The NTC thermistor has to absorb energy during the inrush event, and the amount is approximately:

If you're starting with a fully discharged capacitor where $V_{cap,0} = 0$, this simplifies nicely:

I should point out that this is a bit of a simplification. During an RC charging event, the energy delivered by the source gets split roughly in half — the capacitor stores half, and the resistor dissipates the other half as heat. So the thermistor ends up absorbing approximately $\frac{1}{2} C V_{pk}^{2}$ worth of energy. This number absolutely must stay below the NTC's maximum rated single-pulse energy specification. Go over that limit and you're looking at a cracked thermistor or one that fails open, which is not the kind of excitement you want in your power supply.

Worked Example: 230 VAC Offline Supply

Let's walk through a real sizing exercise for a pretty common scenario:

• Supply voltage: 230 VAC RMS, which gives us $V_{pk} = 230 \times \sqrt{2} \approx 325\,\text{V}$
  • Filter capacitance: $C = 330\,\mu\text{F}$
  • Target peak inrush current: $I_{target} = 15\,\text{A}$ (a reasonable limit for most designs)
  • NTC hot resistance: $R_{hot} = 0.5\,\Omega$ (typical value from datasheets at operating temperature)
  Step 1 — Figure out the required cold resistance:
  $$R_{cold} = \frac{V_{pk}}{I_{target}} = \frac{325}{15} \approx 21.7\,\Omega$$

  Standard NTC values don't come in 21.7 Ω, so you'd pick the nearest standard value of 22 Ω at 25 °C.

  Step 2 — Double-check the actual peak inrush with that selected value:
  $$I_{peak} = \frac{325}{22} = 14.8\,\text{A}$$

  That's comfortably under our 15 A target, so we're good to go. A little margin never hurt anyone.

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

  The inrush event essentially wraps up within about $5\tau$, which is roughly 36 milliseconds — that's about two complete mains cycles. The thermistor starts heating itself up during this window, but the cold resistance is what's doing the heavy lifting for current limiting.

  Step 4 — Work out the 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. Something like the Ametherm SL32 2R522 would work here — that's a 22 Ω device rated for 2.2 A steady-state current and 45 J maximum energy. Plenty of margin, which is exactly what you want.

  Step 5 — Check the steady-state power dissipation:

  Let's say your supply pulls 2 A RMS at full load, and all of that flows through the NTC. The hot resistance dissipation works out to:

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

  That's manageable, but it's not nothing — it'll definitely show up in your efficiency calculations. For higher-power designs pushing above 200 W or so, most engineers switch to an active inrush limiter that uses a relay to bypass the NTC after startup. You get the current limiting when you need it, then you short it out for normal operation.

  Practical Design Considerations

  Worst-case timing matters more than you think: The absolute worst-case scenario is when you apply power right at the peak of the AC waveform with a completely discharged capacitor. But here's something that catches people — if your product can be power-cycled quickly, the NTC might still be warm (meaning low resistance) from the previous power-up cycle. In that state, it won't limit the next inrush nearly as effectively. Check the datasheet for cool-down time — you're typically looking at 30 to 60 seconds. If your application needs to handle rapid power cycling, you'll want to consider a fixed resistor with a bypass relay or switch to an active limiter IC instead. Derating is non-negotiable: Those NTC energy ratings in the datasheet are specified at 25 °C ambient temperature. Stick that thermistor in a warm enclosure — say 50 °C, which is pretty typical — and it starts at a lower resistance and ends up absorbing more energy per inrush event. Always derate. I usually aim for at least 30% margin on the energy rating as a bare minimum. Some designs warrant even more if thermal conditions are tight. Multiple capacitors complicate things: If your design has several capacitors across different rails that all charge up at the same time during power-on, you need to sum up all their individual $\frac{1}{2}CV^{2}$ energy contributions. That total is what the NTC has to handle. This is one of those details that's easy to miss if you're only thinking about the main bulk cap. Placement is simple but critical: The NTC goes in series with the AC line input, before the bridge rectifier. Position it there and it limits current on both half-cycles during that initial charging surge. Put it anywhere else and you're probably not getting the protection you think you are.

  Try It

  Rather than grinding through these calculations by hand every single time you're specing a new power supply — and let's be honest, nobody enjoys that — you can open the Inrush Current Limiter (NTC) Calculator and just plug in your supply voltage, capacitance, target inrush current, and the NTC's hot resistance. The calculator instantly spits out the required cold resistance, actual peak current, time constant, and absorbed energy. It gives you everything you need to pick the right thermistor on the first try, which beats the alternative of ordering three different parts and testing them all.