Inductors, inductors. The sophisticated looking “donut rings” that taunt electronics hobbyists. You wnat to get beyond the basics and get into building your own switched-mode power supplies, and this requires an inductor, ideally a “donut ring” inductor. Okay, so how do you approach getting one of those? Some people buy their toroidal inductors, others wind their own. That being said… I want to know how you wind your own.
The Wikipedia article on inductors contains some good equations for calculating inductance based off of geometry.
20200325/https://en.wikipedia.org/wiki/Inductor
So, let’s try out an example with the dimensions of one toroidal inductor ferrite core that I found on Digi-Key.
20200325/https://www.digikey.com/product-detail/en/tdk-electronics-inc/B64290L0618X038/495-3861-ND/1830191
rectangular cross section
diameter = 22.6 mm = 0.889764 in
thickness, 1/3 total diameter (1/6 edge) = 3.8 mm = 0.149606 in
inside diameter = 22.6 - 7.6 = 15 mm = 0.590551 in
height = 11 mm = 0.433071 in
30 AWG wire diameter = 0.25 mm
Work out the area into turns, single layer...
One turn = 2 * (3.8 mm + 11 mm) = 29.6 mm
Surface area: pi * 11 mm * (15 mm + 22.6 mm) +
2 * pi * ((22.6 mm/2)^2 - (15 mm/2)^2) = 1748.233 mm^2
1748.233 mm^2 / 0.25 mm = 6992.932 mm length wire @ 30 AWG single layer
Number of turns: 6992.932 mm / 29.6 mm = 236.248 turns
L = 0.00508 * 236^2 * 0.433071 * ln(0.889764 / 0.590551)
= 50.226 uH
Wow! That’s quite a bit of inductance… too much for my particular
application, actually. That assumes air core,
apparently… calculating with the ferrite core inductance factor
A_l is 617758.919 uH… gosh that’s big.
Okay, better method to compute inductance, now that I am better educated.
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Find “effective length” (l_e) that states a measure of inner diameter that you can use with the diameter of your wire to compute the number of turns you can put on the coil. Worst comes to worst, you can compute this yourself by looking at the geometry.
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Compute the number of turns (N) on a single layer by dividing effective length by the diameter of your magnet wire.
N = l_e / wire_diam -
Find the “inductance factor” (A_l) and compute inductance as follows:
L = A_l * N^2
Okay, let’s try calculating on a smaller toroidal ferrite core.
20200325/https://www.digikey.com/product-detail/en/tdk-electronics-inc/B64290P0037X038/495-3873-ND/1830203
Smaller inductor, 61 turns single layer, inductance factor 2.53 uH. Result: 9414.13 uH. Okay, still too big.
Let’s solve for the ideal, then.
L = 22 uF
22 uF = 2.53 uF * N^2
N = sqrt(22 uF / 2.53 uF) = 2.949 turns
Whoa… I must be doing something wrong here. Or maybe it’s just that those donut rings are bound to have very high inductance.
Okay, how about a small cylindrical coil about the size of the ones in doorbell ringers.
4 * 3.14 * 10^-7 * 1 * 200^2 * 0.000314 / 0.08
= 197.192 uH
Okay, that’s pretty good. So we know a doorbell ringer solenoid must have a couple hundred micro-Henries of inductance.
One turn = one circle around the core, not a complete surface coverage of the donut ring. Remember, we started with the straight cylinder inductors, and there it makes quite a bit of sense to count in terms of turns around the cylinder. So one turn, that’s like one circle, yes.
But hey, one point that I must make. About air core versus ferrite core inductors. Why are ferrite core inductors recommended for specific applications? The key is that the core material itself is non-conductive so that it resists the formation of eddy currents and the core losses that result. This allows ferrite core inductors to be efficiently useful at high frequencies. Air is also, of course, non-conductive so it is applicable to that particular use. The only disadvantage of an air core is that the physical size of an equivalent inductor must be much larger than a ferrite core inductor. However, if you only need a low inductance value, say around 20 uH, and you calculated that a resonable size geometry can deliver that inductance, then definitely go with the air core inductor. It will save you money when it works well.
So, in case I didn’t state the conclusion concisely enough… are you building your own switched-mode power supply? Don’t worry about hunting around for the ideal readymade inductor to buy. Just 3D print (or even paper mache) your own toroidal core, and wind your own coil with enamel-coated magnet wire. You’ll easily be able to create the needed air core 22 uH inductor, and by virtue of being an air core inductor, it will be efficient switching at high frequencies without core losses.
One important thing to state about cylindrical cores, though. It’s easier to buy readymade bobbins to wind a cylindrical core inductor upon, probably because it’s just simply easier to wind a cylindrical core than a toroidal core, so the market is that much bigger.
Here is another source for information on building your own inductors, but it appears to focus exclusively on cylindrical inductors. Not bad, but it could be better.
20200326/DuckDuckGo build your own 20 uf inductor
20200326/https://hackaday.com/2017/06/12/design-a-coil-for-a-specific-inductance/
20200326/https://rimstar.org/science_electronics_projects/coil_design_inductance.htm
Ah… but maybe I spoke too soon on that one, about winding your own inductors. Why was I earlier having trouble finding an inductor on Digi-Key for my switched-mode power supply? I was too restrictive in my search and didn’t fully understand the requirements for the inductor. Here is a good readymade toroidal air core inductor.
20200326/https://www.digikey.com/product-detail/en/signal-transformer/HCTI-22-16-4/595-1721-ND/7362972
It’s cheap, it’s toroidal, it’s air core, it’s high current, it’s low DC resistance, but it’s rather large. If you’re willing to exchange for a smaller size at a higher price, you have options.
First pick, I assume this must be an air core inductor since its design is identical to the other one that explicitly said it was air core. Less current, higher DC resistance, but otherwise still pretty good.
20200326/https://www.digikey.com/product-detail/en/bourns-inc/2105-V-RC/M8850-ND/775389
And if you want horizontal mounting, you can use this one. Vertical versus horizontal is the compromise between minimizing required board height versus minimizing required board surface area.
20200326/https://www.digikey.com/product-detail/en/bourns-inc/2105-H-RC/M8804-ND/775343
Interestingly, if you look at the inductors, they have exactly the same geometric appearance in number of turns, inner diameter, and outer diameter regardless of the physical size. Indeed, this is correct. If you look at the inductance equations, the inner and outer diameters factor into the equation in a proportional relation, so the inductance is pretty much independent of the physical size of the inductor provided that the geometric proportions are persevered. This is why those tiny canned inductors on the Raspberry Pi zero board can have a surprisingly high inductance value.