Energy/magnetic field of planar vs solenoid inductor - Page 1
Forum section: electronics / rf-microwave

author: shridmaster
author_rank: Contributor
timestamp: June 17, 2023, 07:07:14 pm
content: A colleague and I got into a debate about inductors, and we realized neither of us knows enough EM/RF to answer this question.We have an air core solenoid inductor that resonates in series with a capacitive load. It's important that it be air because maximum linearity is an absolute must, however we're working in the 1-3MHz region, so it ends up being like 10cm tall and 1cm or so in radius, I think roughly 500 turns for 600uH. There's a copper disc inside we can adjust up and down to tune the inductor. The inductor is also inside an aluminum block with conductive coating and tied to ground to shield the outside electronics from its fields. We're looking to reduce its height and save space.One idea was to convert it from a solenoid to a planar inductor. I argued that if we do that, it would end up losing a lot more energy to the surrounding shielding. I said that with the solenoid, most of the volume of the field lines are within the solenoid. His argument was that only the field lines going directly through the surface normal to each winding affect it, so that's not a concern. I said that that's assuming lumped element model which I don't think we can do here.We're now completely confused about what the "storing energy in a magnetic field" for an inductor even really means. Is it only the field lines that are normal to the area enclosed by the windings that matter? I mean anything going through the windings has to go up around and come back through anyways, so if its going through then by definition it's in the entire space around it, but we only need to calculate what's going through.But the shielding around does warm up, I mean that's how inductive heating works right? Or is it that the magnetic fields are not blocked at all and maintain all their energy, but they induce currents in the shielding, and it's the varying electric fields that lose energy to the shielding?Are there any concerns here we should be thinking about when switching from solenoid to planar?Any guidance in our thinking would be very appreciated, trying to read through EM material is making my head spin.

author: radiolistener
author_rank: Super Contributor
timestamp: June 17, 2023, 07:47:07 pm
content: The best inductor Q-factor is achieved when it has the same length for all axis. If you flatten some side of inductor, it will increase losses.If Q-factor (energy losses) is not critical for your needs, you can use planar inductor.

author: shridmaster
author_rank: Contributor
timestamp: June 17, 2023, 08:02:27 pm
content: Quote from: radiolistener on June 17, 2023, 07:47:07 pmCan I ask why that is? I'm reading through Griffiths right now to get a better understanding. Is it because for a solenoid, each winding shares the same cross-sectional area as the one above, so they share all flux, while for a planar only some of flux of the outer loops are going through the inner loops?

author: radiolistener
author_rank: Super Contributor
timestamp: June 18, 2023, 12:19:13 am
content: shridmasterI don't know the exact reason, this is just a recommendation from manuals about inductor design from old literature. I think this recommendation just come from some practical experience instead of theoretical fabrications. Someone just performed some testing for different inductor geometry, found that dependency and shared it.As for the theoretical foundations, I think it may be because such a coil geometry is optimal to minimize energy loss for electromagnetic radiation and wire heating.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: June 18, 2023, 07:46:06 am
content: Q factors in the 2000 range are achievable, given good materials, and enough of them. What are you actually doing, what voltage/current, and why / in what way does it need to be tunable?Tim

author: shridmaster
author_rank: Contributor
timestamp: June 18, 2023, 09:09:24 am
content: We're looking at amplitudes of 350-500V or so depending on the system, passive resonant gain from 24V. The current is very small, on the order of few mA.The application is mass spectrometry. According to the mass spec scientists, the linearity of the sine waves is the most important part in getting an accurate m/z spectrum. In this specific mass spec system, the 1-3MHz sine wave is then also coupled to other parts, which means the total load capacitance is somewhat variable. Needs to be tunable to perfectly hit resonance, the system completely collapses otherwise.

author: LM21
author_rank: Regular Contributor
timestamp: June 18, 2023, 11:14:32 am
content: I can give some links where I found info about Q and coil inductance. Perhaps it helpsTheory firsthttps://www.g3ynh.info/zdocs/magnetics/part_1.htmlA little more practicalhttps://hamwaves.com/inductance/en/index.html#input

author: geggi1
author_rank: Frequent Contributor
timestamp: June 18, 2023, 11:42:35 am
content: Instead of the copper disc for tuning you should start looking into ferrite or powder iron cores.If you have a servo or something similar to adjust resonant frequency it is probably possible so fit the ferrite in the same way.When using a ferric core you will have a higher permeability and would be able to reduce the number of windings and get a more efficient inductor.If you find a core that have the correct frequency range and a permeability of for instance 10 you can get away with only 60 turns and a thicker wire that will get you a higher Q-value.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: June 18, 2023, 12:47:26 pm
content: Mass spec is a solved problem; what are you doing differently, say from published solutions, and why?I'm not terribly familiar with it myself, but I recall phase balance being a concern as well, as the quadrupoles need to be balanced with respect to their surroundings.Do you have an upper limit on harmonic distortion? Ferrite loading will be acceptable up to some amount depending on this.And if you don't have a limit -- I would simply conclude either your application doesn't care (and a traditional ferrite or powder core will do fine), or, the limit isn't really what you mean it to be: "as little as possible" has quite small bounds these days, as one could use a (type 1) superconducting resonator to achieve very good filtering indeed. Are you willing to buy the materials and cryostat to achieve that? At some point, there will be another controlling constraint.Shielding must be at an adequate distance, to allow magnetic field around the coils (and coupling between them, if applicable), keeping inductivity and Q high. Typically the shield diameter is 2-3 times the coil diameter, and a diameter or two taller than the length. Tune by capacitor. Keep metal away from the coils. Variable capacitors have much higher Q than variable inductors.Tim

author: shridmaster
author_rank: Contributor
timestamp: June 18, 2023, 08:28:30 pm
content: Thanks for the links guys!Mass spec is not a solved problem per se, but it is mature and quadrupole based mass spec especially has been very stagnant. I'm on an R&D team that's trying to redesign it for portability without sacrificing performance so we're trying to be innovative.I'd like to bring this thread back to the original topic, appreciate all the info on practical inductor construction, but I'm still curious about our question on how the magnetic fields radiate around the inductor. Are we only concerned with the field lines penetrating the loop surface normal? Is the shielding around affecting the magnetic fields in any way?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: June 19, 2023, 12:16:25 am
content: Ah, I see. Then compactness would be valuable, suggesting a permeable-loaded design?As mentioned, significant field extends out by a diameter or two. The coupling factor to a loop at such distance is roughly the ratio of areas, when on centers; and for a loop of same diameter but separated by some distance along the middle axis, it depends on the overall length as well of course, but it drops off particularly quickly when the distance is more than a diameter or two.So, a metal shield placed at such distance, causes only a modest decrease in inductance, say, 10 or 20%; or permeable shield, the same increase. Placed right up on the coil (minimal separation), the reduction will be considerable; in the extreme case (shield-coil spacing less than the spacing between turns, say), it starts looking more like a round-wire microstrip and the inductance is essentially due to wire length with no mutual inductance advantage.Tim

author: johansen
author_rank: Super Contributor
timestamp: June 19, 2023, 04:27:02 am
content: The ideal cross section and volume of an inductor is close to that of a crispy creme donut ratios. If you spend a few minutes googling this stuff you can find a relatively recent paper that describes how as the frequency rises, the optimal cross section for highest Q from a given length of wire changes from a circle, into an eclipse that thins out as the frequency rises, sort of like the beehive springs of a certain well known engine.As for mass spectrometers, they dont seem to have any inductors in the system. And i have access to a number of them. Currently a friend of mine is working on taking the hyperbolic ground stainless steel~25 cm long rods out of one system, and putting them in a different machine that has something like 15cm long 1cm diameter circular moly rods. We were concerned about the increased rf load...but then found out the same circuit board is used for both machines.With regard to shielding an inductor inside a copper cage, the optimal coil diameter to cage diameter likely has something to do with the skin depth in the shield, and how much energy you want to store in the inductor.The higher the q and lower energy stored, then the smaller the radius of the inductor relative to the cage.At some point it becomes worth it to cool the inductor and the cage with liquid nitrogen to get the q higher.

author: profdc9
author_rank: Frequent Contributor
timestamp: June 19, 2023, 05:13:04 am
content: Magnetic field lines are always closed (there are no magnetic monopoles). Because of this, the magnetic field lines in a solenoid must loop back around the outside so that it can be closed. Bending the solenoid into a toroid closes the lines between the two ends of the solenoid with the minimum gap which best encloses the magnetic field within the solenoid.The two main source of loss with inductors is the skin effect and the proximity effect. The skin effect confines the cross-section of the wire used for carrying AC current to near the surface. For this reason, sometimes coils use flat wires rather than round ones so that more of the cross-section carries current, and sometimes "Litz" woven wires are used, though usually not above 1 MHz. The second is the proximity effect. Two parallel currents in adjacent turns repel each other so that the copper between them is not used for conduction, also increasing resistance.The energy density stored in a magnetic field is given by 1/2 B dot H, or usually given as 1/2u B^2. This applies to inside the coil, outside the coil, and even inside the wires. Because air is u=1, and copper is diamagnetic so that u is slightly less than one, the energy is going to be both inside and outside the coil, but mostly inside as that is where the field strength is the highest.The aluminum shield is probably heating due to eddy currents. It is not heating due like an inductor cooker would heat a steel pot as aluminum is paramagnetic but the field is not really strong enough to cause hysteresis or saturation that heats the aluminum.Inserting a copper slug into the inductor is going to cause significant eddy current losses and dissipate your Q for sure. Basically anything that depends on Lenz's law to reduce the inductance is going to increase loss. You could use a slug made of a low-loss permeable iron powder core like MicroMetals Type 2 or 6. These are fairly linear materials at the 1-3 MHz region, though I am not sure what kinds of magnetic field strengths your application requires. It if is like 10 T, I am not sure there is any material that retains its linearity at that field (except vacuum).Thinking a bit outside of the box, you could try to vary the geometry of your coil. For example, if you wind the coil around a bendable form, then if you bend the form into a toroid, the flux leakage is minimized and the inductance is maximized. If you bend the form to be a straight solenoid, the flux leakage is maximized and the inductance is reduced. Alternatively, your coil form could be flexible and could be stretched out to reduce inductance, or compressed to increase it.Another possibility is to try to make a really tiny roller inductor. Making a roller inductor with a tiny wire and pitch might not be so easy.Another thing to consider is if you need such a large inductance in the first place. You need a certain resonance frequency 1- 3 MHz, and you're looking for a particular impedance sqrt(L/C) of the resonant network. For example, for 2 MHz, L=500 uH, this implies C=200 pF or Z=1600 ohms. L large and C small implies a high impedance. You could you use a pair of transformers to step the impedance down to low impedance, and then the inductance required might be 49 and 64 times less if a 7:1 or 8:1 turns ratio transformer is used. For example, the inductance would decrease by a factor of 8, and the capacitance would increase by a factor of 8. It would be much easier to make a low value tunable inductor around 60 uH and C=1600 pF. You would need to make a transformer with something like a 3:24 turns ratio which I have done for amateur radio use. A standard roller inductor could tune up to 60 uH.If you want to go even lower loss, have a fixed inductance and use a vacuum variable capacitor. This is not cheap, but it is low loss and tolerates high power and fields.

author: shridmaster
author_rank: Contributor
timestamp: June 19, 2023, 05:22:06 am
content: Quote from: T3sl4co1l on June 19, 2023, 12:16:25 amI think I'm starting to understand. Doing some more reading of Griffiths, especially his chapter "Magnetic Forces Do No Work". It really is purely a function of the flux lines through, which correlates 1:1 with the current in a vacuum, but when you've got shielding around as you say you're now looking at mutual inductance and back emf from other objects, so the flux lines through are no longer just a function of the current through the inductor, but also how external objects induce and react to it and change the magnetic field as well.In the case that there's conductive shielding close by, the magnetic field generated by running current through the inductor ends up inducing a current in the shielding which then produces its own magnetic field that opposes the one acting on it in the first place, thereby reducing the flux lines in the inductor in the first place, and thereby reducing its inductance because you now have fewer flux lines for a given current.Do I have that correct?Quote from: johansen on June 19, 2023, 04:27:02 amThey do not inherently need one, a quadrupole mass analyzer is almost entirely a capacitive load, but as I said the voltages are in the range of 350-500V and requires high linearity so we use a series LC tank to achieve passive gain. I work for a fairly major player in the market, all of our systems use LC resonant tanks to achieve this as far as I know.

author: shridmaster
author_rank: Contributor
timestamp: June 19, 2023, 06:47:28 am
content: Quote from: profdc9 on June 19, 2023, 05:13:04 amThanks for your reply, very informative!So here's something I'm confused on. I understand magnetic field lines are loops, they must return to the source just like a circuit. So when we talk about field lines, do we think of the whole loop as one entity, or do we have one large vector field, and the loops are just what we'd expect from like principle of least action or something?

author: radiolistener
author_rank: Super Contributor
timestamp: June 19, 2023, 06:51:53 am
content: Quote from: shridmaster on June 19, 2023, 05:22:06 amObjects placed close to the inductor is affecting it due to near field coupling. Near field consists of out of phase electric and magnetic fields. Since they are out of phase they're not create plane electromagnetic wave, so there is no energy flow from inductor into the space (actually a real inductor has some small amount of energy leakage through plane electromagnetic waves emission). Energy is stored around inductor coil as electric and magnetic fields. This is how inductor store energy. If you place some object within this near field zone these objects start interacting with electric and magnetic near fields of inductor, so it leads to a property change for inductor.This is the same as to place some vibrator or shielding plane near antenna, it affects antenna properties, include antenna impedance, Q-factor/loss and radiation pattern. The same thing happens with inductor, the only difference is that inductor is too small in comparison with wavelength, so it's radiation efficiency can be ignored.Note that both type of fields are present around inductor - electric and magnetic.

author: Marco
author_rank: Super Contributor
timestamp: June 19, 2023, 07:00:02 am
content: Why not getting a custom inductor wound on a gapped "air core" toroid? Then you can play with the copper insert at the gap. Can be placed much closer to a metal enclosure.

author: Kleinstein
author_rank: Super Contributor
timestamp: June 19, 2023, 01:17:26 pm
content: If close to the coil the conductive shiedling will also carry quite some current to force the magentic field to stay inside.Instead of a simple solenoid coil one could consider starting with 2 opposide direction coils or even a toroidial coild without a magnetic core. This way the main coil is already keeping the field local an reduce the stray field. This would need more copper for the main coil, but can save on the shield part.With enough air gap even a coil with some core material (e.g. ferrite) can be quite linear. The main part of the energy storage is still in the air gap, not in the ferrite. With a large air gap the field tends to be relatively weak anyway and the core material is usually far away from saturation in a relatively linear part of the magnetization curve.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: June 19, 2023, 05:13:01 pm
content: Quote from: shridmaster on June 19, 2023, 05:22:06 amYes, and a more subtle point is that the reflection has a slight phase shift, due to the resistance and self-inductance of the shield. The induced current has a small phase shift, which introduces a loss angle in the original coil. So the Q tends to go down as well. For reasonable dimensions and good conductors (aluminum, copper), it's a small difference (some percent?).I'm not sure offhand how to express the L/R of an induced current. Is it pure resistance combined with leakage inductance between the source and shield? Or is there additional phase shift due to the distribution (including phase shift) in the skin effect? So, it might vary with material/frequency.One note that's easy to conclude though: the skin depth is given by material and frequency, and presumably is localized to the, well, surface of the shield. Which means the volume the magnetic field can occupy, only varies by a small amount -- the mechanical inner dimension of the shield plus two skin depths or so. Which is roughly a mechanical explanation of why inductance decreases with increasing frequency: the volume available to the field shrinks (the effective boundary expands closer to the mechanical surface).A mechanical explanation is not actually required as this is a necessary property of a real 1-port having a lossy inductance characteristic (Kramers-Kroning relation). So there will be such a mechanism naturally. But it's nice to have both sides (theoretical expectation and mechanical explanation).Tim

author: T3sl4co1l
author_rank: Super Contributor
timestamp: June 19, 2023, 05:36:26 pm
content: Quote from: Kleinstein on June 19, 2023, 01:17:26 pmA typical geometry might be a 5-wall cubic shell of ferrite, around a "square" solenoid (i.e. length equal to diameter). If the shell is tight fitting, the effective permeability is still pretty low (maybe 5-10?), which is a convenient gain in inductance, not too much impact on linearity (but again, without a spec, who knows), and provides shielding to surroundings (you can surround the ferrite with solid metal, at almost no change in L or Q, for not needing much thickness of ferrite; amount depends on flux density and mu_r).For shield spaced probably half a diameter out from the coil, mu_eff will be particularly low, maybe 2 or less? And obviously, it approaches 1 as shield spacing / size goes to infinity, but it gets quite close after just a couple diameters.Conversely, mu_eff continues going up as you shrink the core closer to the winding, and put material inside the solenoid. Consider geometry like a pot core with some amount of airgap on the middle peg.Tim