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Toroid inductors make sense to me. The magnetic circuit is closed. However, I do not understand inductors that just have a magnetic core in the center (like this one): enter image description here

Considering that the inductance for an inductor with an air gap is:

enter image description here

If the air gap is at least the size of the iron core, wouldn't the air gap define inductance way more than the iron core?

jsotola
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easox
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    Yes. Yes it would. –  Nov 10 '20 at 20:00
  • easox, Consider winding an air-core on a longish nylon bobbin. Measure its inductance. Now insert a laminated steel I bar (longer than the bobbin and fully filling the interior) into your bobbin. What do you predict will happen to the inductance? (And how does the B-field change?) Suppose you further lengthen the I? Then imagine taking a laminated U (or C) and attaching it to close the magnetic loop (eliminating the air path.) What do you predict? Of course the air path will dominate and fringes out so its also not a simple length to work out. – jonk Nov 10 '20 at 21:29

3 Answers3

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The air gap is significant and is the definer of the inductance but, the main thing about using an "open" ferrite core is that all the winding turns remain highly coupled to each other (unlike in a pure air core). This means that you can still take advantage of the relationship of inductance being highly proportional to turns squared.

So, there is a good "winding" benefit but, \$A_L\$ is much reduced because of the very dominant air gap. Nevertheless, being able to rely on \$L \propto N^2\$ is a useful thing especially if you wind your own.

And, of course, with such a massive (and dominant) air gap, temperature related variations in permeability are virtually non-existent (unlike a closed ferrite core). The ability to deal with large magnetic field strengths (ampere turns) is also another rich benefit compared to ungapped core designs.

Andy aka
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  • Hi, i have some difficulties to understand why an open core has a better coupling than an air "core" ? The flux is the same between the two isn it ? Do you have ans docs on the subject ? – Jess Jul 01 '22 at 20:12
  • It's as simple as I say: the main thing about using an "open" ferrite core is that all the winding turns remain highly coupled to each other (unlike in a pure air core) @Jess - that doesn't happen in an air core. – Andy aka Jul 01 '22 at 21:00
  • Thank you but I do not understand I will try again to get informations on the subject – Jess Jul 02 '22 at 06:56
  • Any windings on a ferrous core will be nearly 100% coupled to each other because the flux is concentrated in the core @Jess - maybe ask a new question and draw a picture to show what you mean. – Andy aka Jul 02 '22 at 08:58
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Yes the inductance will be much much lower than a closed toroid. However, there is still some benefit from the high permeability of the core material.

If you are interested in calculating the flux density (and therefore inductance) due to the magnetization of a particular coil, then I would suggest taking a look at this paper.

Kaverine, Evgueni & Palud, Sebastien & Colombel, Franck & Himdi, M.. (2017). Investigation on an Effective Magnetic Permeability of the Rod-Shaped Ferrites. Progress In Electromagnetics Research Letters. 65. 43-48. 10.2528/PIERL16110203.

Since we already know that $$L=\frac{N^2\mu_0\mu_rA_e}{l}$$

The effective relative permeability of the rod comes from its geometry and the permeability of the core material (again see paper above). I would recommend the simple calculation based on empirical data $$\mu_{rod}=\frac{\mu_{core}}{1+0.84\left(\cfrac{d}{l}\right)^{1.7}(\mu_{core}-1)}$$

Eric
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The size of the "air gap" of a straight iron-core inductor is the same order of magnitude as the core itself. The relative permeability of iron is, roughly, five orders of magnitude higher than air. Therefore, the air gap term in that equation is very small relative to the core.

vir
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    That's not entirely true - the air will dominate the magnetic reluctance formula. For instance, a closed ferrite core with a small percentage gap length takes the effective permeability down an order of magnitude very easily. If you look at core data sheets, they often tell you how much the effective permeability reduces. For instance an E38/8/25 in 3C90 material has an ungapped permeability of 1660 and an overall length of 44 mm but, with a 1.1 mm gap, the permeability drops to 45. Do you get what I'm driving at? Once you get to about a 0.5% gap, the original ungapped perm is a side issue. – Andy aka Nov 10 '20 at 20:42
  • Yes, I guess I was more considering small gap in comparison to large gap instead of small gap/no gap. – vir Nov 10 '20 at 20:58
  • It is OK to update (edit) your answer based upon Andy's comment. In the event Andy removes his comment, your answer will still show the new information. I would suggest that you leave your original content and add to your answer (perhaps giving attribution to Andy in your edit). I will delete this comment after a short while. – Marla Nov 10 '20 at 21:35
  • I didn't downvote btw. – Andy aka Nov 10 '20 at 21:43