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I'm designing a very simple circuit to enable a Raspberry Pi to power down safely in the event of a power outage.

It is comprised of a supercapacitor, a diode to prevent reverse current flow, and a PNP transistor to bridge two pins and send a shutdown signal to the Pi in the event of power supply loss. There is a boost converter on the output so I can provide 5 V to the Pi for as long as possible.

Currently, I have a 15 W, 2 Ω resistor in series with the diode to limit inrush current to the capacitor, but I understand that NTC thermistors are more commonly used for this purpose.

However, the specs provided for most NTC thermistors seem to be geared towards AC power supply usage. Everything here is operating at 5 V. My questions:

  1. Is a resistor an appropriate choice for inrush current limiting in this case, given that the power is relatively low (max supply power is 15 W), or is there some reason I'm missing that resistors as inrush limiters are a terrible idea?

  2. I'm finding the dissipation constant/heat calculation confusing for NTC thermistors. For example, if I want to limit the current to 2 A, it seems obvious to me that my minimum resistance value should be Vpeak/Imax, or 2.5 Ω. What I'm less certain of is how to figure out, based on dissipation constant, if my chosen NTC thermistor will heat up too much (overheat), or not enough (resistance remains too high during normal operation after inrush) at the power levels I'm working with.

Am I overthinking it, and should I just choose an NTC with a higher continuous current rating (say 5 A) than I need and an appropriate resistance at 25°C?

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No, or probably not.

Plain resistors are a poor choice, as the current decreases exponentially over time; charging eventually to say 99% is very slow compared to a current limiter of nominal value. Compare:

schematic

simulate this circuit – Schematic created using CircuitLab

enter image description here

You'd want a higher hFE part for practical use, or a PMOS and more control circuitry, and probably an enable so it's not idling with so much bias current once it's charged.

NTC thermistors:

Mains rated parts are designed for specific ratings. For example, a 20mm 10Ω part might be suitable for 120/240V use up to 1mF or so. They're not rated for, or at least I'm not aware of any for, low voltage use. Mind, I haven't exactly shopped in detail for them.

They will be usable at lower voltage, and proportionally higher capacitance, to give the same heating and thus charging curve, but I don't know that you'll have a combination for this particular combination of capacitor, inrush current, and charging time.

The tricky thing is, matching the resistance value and heat capacity to the power supply and capacitor. There may not be a part commercially available with the right combination of values.

And you may not want that solution anyway, because its operation depends on the temperature rising during a full-enough charge cycle to do the job. Otherwise it's just a slow resistor with little temp rise.

Best?

Of course, an SMPS. You can't use just any regulator here; what's required, is one with continuous current limiting (foldback may be acceptable, but hiccup/faulting isn't workable), and low dropout (ability to reach 100% duty). It can even be a synchronous buck-boost or "flying inductor" regulator that's bidirectional, supplying the 5V during discharge. You'll have to find a chip for that (or design the function yourself..!).

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  • \$\begingroup\$ Thanks for this very thorough answer. Your point about the exponential current decrease in resistors is well taken (and well illustrated). The upstream power for this whole thing is actually a switch mode power supply. I’ll have to check the specs, but if it has continuous current limiting, perhaps I will just let it do the work and not worry about inrush on my circuit. Otherwise I will think about a circuit like the one you've illustrated above. I’m not so concerned about getting the absolute maximum out of these capacitors; just enough for adequate shut down time. \$\endgroup\$
    – yeah
    Jan 23 at 9:18

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