Calculate inductance of hollow rod - Page 1
Forum section: electronics / projects

author: Mike007^2
author_rank: Newbie
timestamp: May 24, 2023, 09:46:06 am
content: Hello,I'm working on a FMICP coil and want to calculate/design the inductance of a hollow rod. We all know how to calculate the inductance of a simple rod wound inductor, so I thought this was going to be a walk in the park. But I stubbed my toe and need your help.Inductance of a wound rod can be calculated as explained on the Coil32.net site here:https://coil32.net/online-calculators/ferrite-rod-calculator.htmlBut I can't find a formula or example of a hollow rod (tube?)Does anybody know where to start?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 24, 2023, 10:27:05 am
content: Is this for the ICP itself, or a separate (resonator?) coil? In other words: does it matter for any other purposes that it's hollow?For the inductance of a (hollow) rod core with winding, the rod is simply averaged out. Effectively Ae is smaller thus Bsat is smaller, but the same outer dimensions are had. I suppose the better effective equivalent is, mu_r is reduced by the cross sectional difference. Which is a small effect (for mu_r >> 10) so it won't matter much for the calculation.Also note that these formulas (or at least, I'm guessing so) are all approximations, likely due to Weeler or Terman. Don't expect to get much better than 10% agreement with them: good enough to be in the ballpark, but plan on either iterating the (mechanical) design, or including some means of adjustment to tune it in.Tim

author: Mike007^2
author_rank: Newbie
timestamp: May 24, 2023, 11:43:44 am
content: Dear Tim,Unfortunately i can't say why it needs to be hollow, but it does need to be hollow. With the coil a plasma will be generated.So if i understand correctly, I need to correct the mu_r as a ratio of area between rod and tube and i can use the same formula as the rod?so, let's say i have a outer diameter of 50mm, inner of 25mm, length of 100mm and a material magnetic permeability of 1000I use the 50mm al outer diameter in the rod calculation with a adjusted permeability, so: 1000 * (Aouter-Ainner)/(Aouter) => 1000*(1964-491)/(1964) = 750 ?And because there is less overall ferrite area it will saturate faster?thanks in advance

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 24, 2023, 01:13:18 pm
content: Yeah, that's what I would figure.I ask about other reasons, because keep in mind the field inside the hollow will be, if not zero, then very close to it, and having considerable leakage to the winding outside it. The ferrite is an effective shield. So don't expect to do very much with the space inside there.As I understand it, ICP is normally done with an air cored inductor, at high enough frequencies and reduced pressure where breakdown in free gas is possible. Or maybe plasma is ignited elsewise (a spark generator or something). Hence, plasma develops, and it's inductively coupled. I don't see offhand what a rod core is going to help with this, unless it's to increase the Q factor of a matching inductor or something. Which might be helpful, I don't know. FYI.Tim

author: Mike007^2
author_rank: Newbie
timestamp: May 24, 2023, 02:17:27 pm
content: Aah i think you just caught my error, i must have used the right hand rule with my left hand or something.I'm trying to create something similar than , see Figure 28 of 10.1088/0022-3727/46/28/283001 (paste inhttps://www.sci-hub.se/to see for free)And you are correct, you can see they wound in not axially as a rod, but as a toroid. I imagined the ferrite of figure 31 sideways , but in figure 32 its clearly visible that is nog the case.At least other folk can find now how to calculate a hollow rod

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 24, 2023, 03:02:31 pm
content: Ah, that makes more sense then. CheersTim