:: how to find Max Flux of ferrite core? (partially solved) - Page 1
Forum section: electronics / beginners

author: 3roomlab
author_rank: Frequent Contributor
timestamp: December 21, 2014, 05:47:18 pm
content: hello folksi am mucking about with ferrite cores and other misc coresi am using this software tool to help with some numbershttp://www.electronicecircuits.com/electronic-software/mini-ring-core-calculator-programdue to my lack/low-level of theoryi need help to find out how does the software determine a certain core at certain frequency can only contain X amount of max fluxexample :using the AL/ui tool inside the softwareif i have a JOHNDOE core 20mm x 10mm x 10mm (coating 0.1mm) and if we obtain (example) 100uH from 10 turns (say by measuring off a LCR meter)we get AL = 1000nH/n^2 and ui = 769.2. but it does not have a facility to determine what max flux saturation could be.(i have made some inductor with known core characters, and measuring with LCR and compare with this tool, they are very very close, like 5% or less error)so with a known ui (permeability), known operating voltage and frequency, we could calculate peak AC flux. but i dont understand how does the software determine max flux in its iron powder/ferrite tabs(in the same software tool, under the tabs of iron-powder/ferrite, inside there is a section where it can tell you if you have over-saturated the core by inserting an operating voltage, i am trying to understand how to apply this to unknown cores)

author: T3sl4co1l
author_rank: Super Contributor
timestamp: December 21, 2014, 07:20:08 pm
content: Bmax = Vsq / (4 * Ae * F * N)Bmax in T is Vsq in volts (squarewave), Ae in mm^2, F in MHz, N in turns. Or Ae in m^2, F in Hz, etc.Ae is core cross sectional area, which you can measure or at least estimate (if the cross section is round or square).Bmax is peak flux density, if Vsq is a full square wave, such that flux density starts at -Bmax, the square wave rises, and for half a period, Bmax rises through 0 up to +Bmax, then the square wave falls, and so on. Change accordingly if you have a single-ended waveform (e.g., single or two-switch forward converter, flyback converter). Or instead of 4 in the denominator, use 4.44 (~= pi * sqrt(2)) for a sine wave.Tim

author: 3roomlab
author_rank: Frequent Contributor
timestamp: December 21, 2014, 08:03:37 pm
content: thanks tim, i ventured to this equation as well. using this i found certain useful values too, relative to voltage appliedhave you seen the software? they do it without using voltage... by material specs? because i cant find anything else on web except for those higher level mathsor have to use this?http://info.ee.surrey.ac.uk/Workshop/advice/coils/BHCkt/index.htmlscope + osc and manually drive to get saturation scale ?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: December 22, 2014, 12:37:32 am
content: Are you making transformers or inductors?Transformers are concerned with voltage (and flux, and flux density), so you don't need to know anything about permeability or inductance, as long as they are large enough to meet the requirements.Inductors are still concerned with voltage (and flux), but they are designed to draw current due to a low average permeability. So they are often specified in terms of current. The conversion is simple: Phi = Ipk * L.Phi = Vsq / (4 * F) in the earlier equation.If you have a cut core, you can vary the gap with shims. The design process is then only concerned with getting enough turns on the core to satisfy the flux requirement (for both transformers and inductors, the wire size is determined by current flow). The gap is then adjusted for the desired inductance.If you have pre-gapped cut cores, or distributed gap (e.g., powdered iron) cores, you do not have this degree of freedom, and you can approach the design process from either direction: flux or current. It doesn't matter which, because they are both equivalent, the proportion between them being set by the core properties. Design is then not so much a matter of "the equations say I need permeability W in size X by Y" (there are far too many degrees of freedom to be able to calculate all core parameters from the design information), but applying the requirements to a listing of parts and seeing which ones are most suitable.Tim

author: 3roomlab
author_rank: Frequent Contributor
timestamp: December 22, 2014, 03:37:14 am
content: nope im not experimenting with customable cores, they are all fixed toroid inductors/transformer.hmmm im not familiar with -- Phi = I(peak) * L... i think i will look for more examples in the interweb about this equation

author: T3sl4co1l
author_rank: Super Contributor
timestamp: December 22, 2014, 04:23:57 am
content: Phi = Ipk * L is the definition of inductance. You might've seen it in voltage form as V dt = L * dI, or even more often, V = L * dI/dt.Tim

author: nixfu
author_rank: Unknown
timestamp: December 22, 2014, 04:29:11 am
content: Usually you need to know what "mix" the ferrite is eg, type 43, type 77, etc.. and then you can look up the standard values for that mix. Each mix will have different curves based on frequency.Here is some data for various mixes from a company I have purchased from in the past:http://palomar-engineers.com/Downloads/Fair-Rite%20Material%20Specifications.pdfhttp://www.fair-rite.com/newfair/materials.htm

author: 3roomlab
author_rank: Frequent Contributor
timestamp: December 24, 2014, 12:40:04 am
content: hmmm iam going no where because i dont understand the di/dti am trying to find a relation between permeability of a material vs max flux per cross section permissibleif using the mini ring software toolif say i can establish these numbersunmarked toroid = 20mm OD, 10mm ID, 5mm thick20 turns of wire gives me 500uH (measured using LCR)the software calculates that the core has a material property of (AL) 1250nH/N2and (permeability) ui= 1803.4Wb/A.m-1(H/m)but with these data taken/measured, how do i calculate the maximum theoretical flux this particular core is capable of? (so that i can avoid saturation)edit :: i think i am discovering how hard is the question i am asking, as permeability is a variable subject to B and H intensities. and it is the B approximate variable that i am trying to grab off the permeability approximation offered by the mini-ring software ... gee wheeez ... wth did i get myself into lol

author: 3roomlab
author_rank: Frequent Contributor
timestamp: December 24, 2014, 02:38:13 am
content: yes indeed, so practically, it seems i have answered my own question in my first post, when i said ... there is an experiment to find the hysterisis loop, which offers the saturation point answer LOLbut then again, w/o the practical probing, the uinumber offered by the mini ring calculation is a permeability ratio vs uo. with that, i think an estimation can be doneif the value offered by the mini ring calculator is ... ui= 1000the actual permeability at the point of calculation is = uix uo= a fixed value in tesla = 0.0012 Tor with the equation m = B/H and looking at nixfu's fari-rite pdfby using an arbituary magnetizing force of say 10Oe, it seems the resulting value B can be helpful in giving an idea of what to avoid. B = 0.012Tand so it seems a material with higher ui, requires lesser oersteds, but a lower material will need more oersteds.then using the toroidal flux calculation, B(peak)= (Vrms*10000)/(4.44*F*N*A)if V = 1v, N = 200, F = 1kHz, A =1.B = 0.0113 Tbut this estimation is so raw lol...edit :: and youtube is the boss

author: T3sl4co1l
author_rank: Super Contributor
timestamp: December 24, 2014, 07:21:57 am
content: Ah, I see.. it's more elementary. Then...dI/dt is the time rate of change in current. If everything stays constant over the time period dt, then you can change ds to deltas and the calculus is trivial:V = L * deltaI / deltatFor a constant voltage and constant inductance, current rises linearly with time (or falls, if voltage is negative... more importantly, it's always in the same direction as the voltage is).This is very handy, because pretty much all switching supplies have some part of the waveform where we hold the inductor voltage constant -- so we immediately know the current must be rising linearly during that time. Cool!Notice the mean value of current does NOT depend directly on voltage, as it does in a resistor (V = I*R). The mean value can be anything -- the inductor only cares that the current changes. So, to get a certain amount of current (like the output current from a buck converter, to supply a load), it's the duty of the circuit to control the voltage, on and off, to keep current in the right range.When working with magnetism, there are always two complementary aspects at work:- Voltage and current change- Flux and current (or more accurately, magnetomotive force, MMF -- amp-turns)- Flux density and magnetic field strengthFlux is the time integral of voltage: although you measure voltage directly with a voltmeter or oscilloscope, you can also measure flux, too (of course, voltmeters aren't any good at measuring small flux... but scopes are great). Flux is in units of volt-seconds, the weber (Wb).Volts and amps are the most important in circuit, because we have instruments to measure them. Both flux, amps and volts are all measured in circuit, between points.So, flux is the time integral of voltage, and current is the time integral of, well... the change in current. Or voltage is the derivative of flux, and dI/dt is the derivative of current. Same thing, different direction. (If all this calculus is throwing you for a loop, do look up a basic explanation of calculus -- it's actually very simple and intuitive, concerning how variables change with respect to others. It's about curves and slopes and such. There are many good videos and websites out there that do a good job. Sadly, I don't have any to recommend offhand.)Flux density (variable usually B, units tesla T == Wb/m^2) and magnetic field strength variable usually H, units A/m) are the fields-in-space, bulk equivalents to the others. Just as resistivity is the bulk equivalent of resistance (a circuit property, measured between two terminals), and so on. (Again, if fields are throwing you for a loop -- there are many great videos explaining what fields in space are, maybe even including vector fields, and some vector calculus -- yes, merely how directional variables change with respect to others! There's probably some good E&M tutorials too, hmm...)Inductance is the conversion factor between flux and current, or between voltage and current rate-of-change. 1H == 1 Wb/A == 1 Vs/A.Permeability is the conversion factor between flux density and magnetic field strength: mu_0 = 4pi x 10^-7 H/m.So, permeability is the bulk equivalent of inductance.By the way, any time you see a bulk property, it's usually that it's in units of "something-meters", or "something per meters" -- these usually use a times-two-divide-one sort of ratio to bring the "something" out. Like, resistance goes up with length and down with area, so resistivity is ohm-meters, and resistance (the circuit value) = resistivity (the bulk parameter) * length / cross-sectional-area. Other times, you see "something per cubic meters", which is a density. Ah, but sometimes you don't see either, like pressure, which is a force per area. Ah, but if you break down the units, you get 1 Pa == 1 N/m^2 == 1 J/m^3 -- pressure is actually energy density! Which is why it takes work (with a capital 'W') to pressurize something -- you're putting energy into some volume.There are just a few bits missing before you can design magnetics from scratch:mu = mu_r * mu_0mu is the permeability of the core (H/m). mu_r is the relative permeabilty, typically 1 (vacuum, etc.), 10-100 (powdered irons, gapped ferrites), or up to ~10,000 for ferrites, or even more for special materials.Since we have core materials of reasonably high relative permeability, we can make the approximation that, instead of flux flying around through all the damn space around a winding (needless to say, integrating over that space would be painful!), it's entirely confined to the core. This isn't true, but the value of an approximation is in its usability: as long as the permeability is more than 10, we can expect it's true to within an error of maybe 1/10th (10%). Or over 100, 1/100th (1%), and so on. So it's an approximation, but it's very reasonable for engineering purposes. And since your average powdered iron is around 75, or ferrite around 2000, it's probably a better approximation than the mechanical measurements of the cores themselves, so it's lost in the noise. Good approximation indeed!Now that we have a core, which traps "all" the flux from the winding, we know where all that flux is going. Aha, now we can calculate things easier.How long of a path does the flux travel?How much is its cross sectional area?You might guess from the units that flux density is flux per area, so we need to know the area. A_e is the effective area of the core. l_e is effective length. These, together with mu_r, are all we need to describe a core to reasonable accuracy. Now we can design inductors and transformers.And now that we can completely simplify the geometry into a cheesy diagram, ALL the equations that are left are nothing more than dumb, easy ratios. Bitchin'.Those are...dB = V*dt / A_e (increase in flux density, in a core of cross section A_e, after applying a flux V*dt)B = mu * H = mu_r * mu_0 * H (bulk inductivity)H = N*I / l_e (magnetic field strength: N = number of turns around or through the core -- N*I is amp-turns or MMF)A_L = mu * Ae / l_e (circuit inductivity -- the inductance you get from a single turn. Note the "times area per length" conversion from bulk inductivity mu into pure circuit inductance!)L = A_L * N^2 (inductance for a winding of N turns)How about some more complicated ones? Sadly, all our core materials saturate, so we don't want to force them to run at excessive flux density. Even then, we don't usually want to go very high, because core losses (heating) go up with B as well. You determine Bmax (the peak operating flux density) in this way, either based on saturation (less a safety factor) or how much heat you can allow in your core.The peak flux of a square wave is V / (4*F). (Note that F in Hz == 1/s, so V/F is Vs = flux.)- The 4 appears because, if flux starts at zero, and the square wave starts in the middle of a flat top, then for the remaining half a flat, flux rises to peak, then the wave's flat bottom drops flux through zero to -peak, then the next flat top raises it back up through zero (where we started in the cycle) up to +peak, and so on.- If you're working with a sine wave, instead of 4, you use 4.44 (~= sqrt(2)*pi), and Vrms. (For the square wave, Vpk = Vrms so I don't need to specify for that case.)- If you're working with a single switch type converter (like a flyback, boost, buck, etc.), flux starts at zero and goes positive, then back to zero; it never goes negative. So you have to use 2 instead of 4. Or, just take t_on * VCC, and that's that.Smushing together a few more, and you get...N = V / (4*F*Bmax*Ae)The number of turns you need for a transformer*, to support a square wave (balanced, not "single switch") voltage, at frequency F, peak flux density Bmax, and cross sectional area Ae.Note that current and permeability don't appear in this equation. Ideally, transformers do not draw magnetizing current at all (permeability is infinite). So that's a good thing.*Or inductor...But, for an inductor, we WANT to draw current. How? By using a small permeability.In the above equations, whenever you see mu, you can put in whatever the effective permeability is, as seen by the flux flowing through the loop. If you happen to put air gaps in that loop, you get a lower effective permeability.So the last bit that's missing is, how lengths and gaps work together.l_e is the effective length of the core. But the core has a very high permeability (ferrites and such). We can do two equivalent things: translate everything into terms of air gap alone, or in terms of average core alone.If we think of the core as "air gap equivalent", this is simply l_c = l_e / mu_r. A core with A_e = 100 mm^2, l_e = 100 mm and mu_r = 2000 has the same inductivity as an imaginary wafer of air, with cross section 100 mm^2 and thickness 100/2000 = 0.05 mm (about the same as tissue paper). This isn't an imaginary quantity, though; it's very real. It would be fantastic to build a winding so it drives a really tiny volume of air, but this is impossible, so we use cores effectively to focus the magnetic field down to smaller volumes of air, so that we can get higher energy density!(And guess what: as I said before, energy density is also pressure. In fact, the attractive or repulsive force you feel with magnets is precisely this pressure, which is the energy density of the fields around the magnets. The energy density is e = B^2 / (2*mu). If you run the numbers for mu_0 and 1.5T (typical of an NdFeB magnet at the face), the pressure's not bad at all -- which is why they can be so dangerous to handle!)Note that you don't get much air to store energy in, if you just use an ungapped core. You can add more, by simply gapping it (shimming the core pieces apart, or grinding down the center peg -- note that, if you use shims, you must count them double! The gap length l_g is the total gap around the loop, not necessarily the physical gap length.)Powdered iron cores already have fairly low permeabilities (10-100), and they're usually offered in formats (like solid toroids) that are inconvenient to gap. The explanation is that they're made up of powdered materials (which have high permeability, in and of themselves), which doesn't pack very well, so the air gap is distributed between particles, rather than concentrated at one gap.Whatever the case, whether it's a distributed gap or an explicit one, you can find the air gap equivalent l_eff = l_c + l_g = (l_e / mu_r) + l_g. Since this length equivalent is also an air equivalent, use mu_r = 1 (or mu = mu_0) in the earlier equations.The alternate view is to find the average permeability. Given the resistivity of copper, and typical core properties, it seems the best values are in the range of mu_r = 10 to 30. (I haven't yet evaluated why this is, but it's certainly the empirical case. The resistivity of the copper winding is important -- because, if we could just send infinite current through a teensy bit of wire, we wouldn't need cores at all!) Too low and you need so much wire that you incur more winding losses; too high and you end up needing way more core than you should (high mu --> low energy density!) and thus incur more cost and core losses.In this view, we are calculating the average permeability by assuming l_eff = l_e. We already know l_eff (the mu_r = 1 equivalent, I'll call it l_eff* now) from above, so mu_eff = mu_r * l_e / l_eff* = mu_r * l_e / [(l_e / mu_r) + l_g] = mu_r / [(1 / mu_r) + (l_g / l_e)]. The last form is neat, because it's dimensionless: it's the reciprocal of the sum of reciprocals of mu_r (already a ratio of mu) and l_e/l_g (which is how many times longer the core path is than the air gap path).Finally, selection.Ferrite cores can be gapped to order (or ground or shimmed by hand), so it's best to design by flux density first. Once you know how many turns you need, you can calculate the required gap l_g by working backwards first from inductance, then from A_L, and then from l_eff or mu_eff.Alternately, if you're working with gapped ferrites in a catalog, or powdered iron toroids that you can't gap, you can ignore the last, oh, ten paragraphs or so -- because, the Ae, l_e and mu_eff are what you get, end of story. You can design based upon required inductance (N = sqrt(L / A_L)) or flux density (the 'transformer method', if you will?), running the calculations for every part that's likely close enough for use, and finding the one the most suitable. Once you have some choices narrowed down, you can refine further: check the core losses, adjust turns for exact inductance (or as exact as possible), stuff like that.Sadly, there is no formula to suggest an ideal core -- or perhaps fortunately, because physics would be really weird if that sort of thing were nailed down from so little information. You can make guesses based on typical geometries (an EE core is going to have certain ratios of l_e and Ae, etc.), you can include copper losses in the calculation (and how much area there is for winding the copper, the winding area Aw), and so on. Mostly, you're just cranking numbers over and over, because there isn't a comprehensive spreadsheet across manufacturers from which you can run all the calculations at once to pick the best parts. Alas, that's where engineers have to pick up, it seems.Tim

author: miguelvp
author_rank: Super Contributor
timestamp: December 24, 2014, 07:46:50 am
content: Quote from: T3sl4co1l on December 24, 2014, 07:21:57 amWow, I'm glad it was more elementaryBut a question about all that, and I'm still trying to digest it.Can someone say that electricity travels only because of magnetic flux? even on a wire and if so it's electricity mostly magnetic more than what we call electrical?Edit: and I mean it as a question I almost have no clue of what I just asked

author: T3sl4co1l
author_rank: Super Contributor
timestamp: December 24, 2014, 09:00:16 am
content: Not only because of magnetism, because of electric..ism too. Whether it's DC or light, energy flows as a vector (Poynting vector) along the surface. Which is the product of magnetic and electric fields.It's a little different for DC, because a minuscule electric field drags electrons through the conductor itself, rather than just along the surface. But for AC, it's pretty effective to look at current as electrons humping around sympathetically (like waves on the sea) as the wave propagates through the space around the conductor. Very little energy flows actually within the conductor itself.When you're talking about magnetic or electric fields more or less exclusively, it's that you're working at a low enough frequency, or high or low impedance, or short distance, to be in the near field regime (all equivalent factors).Noteworthy: at frequencies where the electrical length of the ferrite core is significant, you get propagation and interference phenomena. Which is why you get different kinds of impedance peaks for different dimensions of ferrite beads. To put it another way, the index of refraction is quite high (velocity of propagation quite low), because mu_r is large (velocity of light goes as 1/sqrt(mu)).Tim

author: 3roomlab
author_rank: Frequent Contributor
timestamp: December 24, 2014, 08:31:26 pm
content: hmmmm air gap equivalent ... that will take some time for me to digest ...*goes to meddle with numbers in opencalc*