# Peak current of inrush limiting inductor?

I have this tricky question and I can't wrap my head around it.

There is this inductor to limit the inrush current that will be charging up a capacitor. I'm questioning the design of it, but I don't know how to calculate it.

The input voltage is 240 V AC (60 Hz), so probably the worst case is about 330 V peak when this thing is energized, and I want to treat it like a DC at that moment but I'm not good at math.

The second part is a series inductor of 1 mH and then a 22 uF capacitor that gets charged.

I know that at first the inductor will be much more limiting in the current when this thing is first energized, but at the same time the capacitor represents the highest load because it is completely discharged. Then the inductor (I imagine) will quickly lose its impedance, but at the same time the capacitor gets charged and draws less current.

The questionable thing is that this inductor is only rated for 330 mA. I can't figure out if this is more than enough or not enough. Is it pretty easy to calculate this (even an approximation will be great) or is this something that is better simulated? I had a feeling there was something wrong with this circuit. I drew a very much simplified schematic but just for reference let me include the actual thing: • Inductors are highly imperfect devices. Significantly, they exhibit wire resistance. Also, there will be an optimal external resistor to use (assuming you don't find a perfect fit with the inductor for this) as part of the design. Also, if you are using a transformer, you might consider inserting a resistor in the primary circuit, with a relay that eventually cuts out the resistor. The relay remains unpowered until the DC output voltage (assuming transformer and bridge rectifier plus filter capacitors, for example) reaches some design level. And yes, there is math to such a design.
– jonk
May 16 at 18:58
• Also, there are many current ratings for inductors: current at which they will heat up enough to lose 20% of inductance, temperature limit current and so on. So for a short period its very likely that the inductor can survive much more than 330mA. (I'm not telling you to ignore the ratings, but to pay attention to the scenarios and specs they apply to). May 16 at 19:18
• Hmm. Is this newly added schematic supposed to be a line-powered 330 VDC supply with current limiting using just these three parts? I guess I missed reading that detail, earlier. My mistake.
– jonk
May 16 at 19:23
• Can you calculate Zo and SRF? and thus peak current assuming you had a Triac with ZCS? or not with random phase turn on May 16 at 19:43
• @pgibbons - Hi, Thanks for adding the full schematic. The one thing that jumps out at me is that there is a resistor (not sure if its designator is R28 or R29) between "Phase" and the diode. It seems to be 100 ohms, 3 W if I'm reading the schematic correctly. That is very relevant and will likely affect all the answers :-( May 16 at 21:06

## TL;DR

Your initial question bears no resemblance to the actual design. The soft-start on the feedback will greatly reduce the stress on the components.

## This is a transformer and optoisolated forward converter with negative feedback on a series low-side switching FET with a soft-start cap to limit the target voltage for a slower rise-time. This C21 could be increased for more protection margin from the ~ 3ms time constant with more than the 1uF used, but a 20W transient on a 3W cement WW resistor is possibly safe (assuming that was done with the 1mH Air Cores. I'm not going to waste any more time on this question as it was presented poorly before the schematic with false assumptions.

For the simple answer consider series reactance and the exponential curve, time constant, T=RC and T=L/R with a step input and each part has some resistance (TBD)

What is T? then I max

I know that if a diode is say rated for 10Adc it's bulk resistance is less than the inverse of Imax or Rs <= 1/I or R <= 0.1 ohms, as an estimate.

Thus 340Vp/ 0.1 ohms would be 3400 Amps. Ooops L does not current-limit here.

SRF (LC) ~ 1 kHz
Zo (LC) ~ 7 ohms min @ SRF
Vin (60Hz) = 240 V rms & 340Vp
thus steady state impedance @ 60 Hz is dominated by diode bulk resistance and Xc(60Hz)

To limit SS current in L to 0.33A then add R = 240/0.33= 740 Ohms or reduce C and use an active PFC boost circuit. But always compute Pd in R and derate by up tp 50% and Imax by derated by at least 25% based on your Load R.

If you happened to turn on the switch at peak voltage what is the impedance for a UHF spectrum of an air gap power switch turning? basically it's limited by the diode bulk resistance and ESR of the cap and DCR of L. Above shows a 10A diode with an ideal L and C drawing 50A peak or over 20 kW for a few microseconds.

This is why I said unless you had a zero-crossing switch (ZCS) driving a Triac, your cap and switch would be severely over-stressed.

Bottom line is you cannot do this without further limiting the current.

With a ZCS switch it would look like this The cap. would still not like it (poof) with the 1 kVAR shown in plot as 1kW surge current, so even here you need a current limiting power resistor.

Even with a 1k resistor that is rated for 10W you get a large surge peak, so often in SMPS they use NTC ICL's with a timer bypass (opt.) to raise the cold resistance. • Anything doesn't make sense? Last one has a surge power of 91 Watts in 1k. May 16 at 20:35
• Thank you very much for this explanation. The inductor(s) are air-core I'm fairly certain. Apparently they fail from time to time, well your explanation makes a lot of sense. I'm not an electrical engineer but the person that designed this circuit has been known to make mistakes. May 16 at 21:04
• Worst case ESR of cap for 22 uF general purpose is 10 ohms and low ESR is 0.1 Ohms for electrolytic and lower for plastic film. The DCR of two 1 mH inductors air core will be around 0.5 Ohms each (L/R=2000) so the worst case surge Pmax is on the resistor but worst case temp rise will be on the capacitor if switched on at peak voltage. May 16 at 22:43
• It must also be low ESR film type to reduce heat rise and very large not electrolytic which will be the weak spot. The diode is if it is a 1N4005 1kV 1A diode around < 0.5 ohms or less at huge currents but only rated for 1 cycle at 30A. This would probably fail within a low number power cycles. -1 for insufficient info on question. May 16 at 22:45
• You can also simulate in Falstad's if you know how to draw schematics and specify Beta for RsOn , I used Beta=40. It also has TL431. With lots of practise, that only takes 30 minutes, without... days May 17 at 13:35

The maximum current will depend upon where in the AC cycle the power is turned on. simulate this circuit – Schematic created using CircuitLab

If the power switch is closed at the zero-crossing point of the AC cycle, or during the negative part of the cycle where the diode will not conduct, the current in the inductor will look something like this: Of course it won't look exactly like this because components are not ideal. In fact, it may look a lot different from this because the inductor core, unless it is an air-core inductor, may saturate.

If on the other hand, the switch closes while the power is at the positive peak of the cycle, the simulated current looks like this: The reality, again, will likely not look like this.

• Agreed That's a big IF for zero crossing and not realistic. May 16 at 20:26
• @TonyStewartEE75 who knows? The OP might use a zero crossing solid state relay. There are a range of possible outcomes. One possible outcome involves switching while voltage is zero or negative. May 16 at 20:31
• His inductor will still saturate and Pd may burn up and Cap explode even with ZCS May 16 at 20:36
• It's a tough call to say which would break first, the cap, the inductor or the diode on ZCS powerup. The one with the highest resistance is my guess at peak current. How big is a 1mH air core inductor? Perhaps you should add some realism to put things into perspective May 16 at 20:45
• @TonyStewartEE75 Here is a 1mH air core inductor. Is it too bulky, heavy, or expensive for the OP's purposes? We don't know, because those purposes are neither contained in the question, nor in comments. So the OP can look at the weight, the bulk and the price tag, and make his/her own decision on the matter. "Jantzen Audio 1.0mH 18 AWG Air Core Inductor Crossover Coil" parts-express.com/… May 16 at 21:23