Simplest Way to Measure Bs, Br and Hc of an Unknown Iron Core? - Page 1
Forum section: electronics / projects

author: KerimF
author_rank: Frequent Contributor
timestamp: June 12, 2023, 08:49:20 am
content: Hi all,Lately, the local retailers offer various iron E_I laminations of unknown type (for 50Hz). So, I had to find out a simple test to measure their non-linear parameters:Bs, saturation flux Br, saturation remanent flux Hc, coercive force [A/m]These three parameters could be used in simulation (as for LTspice) and in the transformer design (mainly the saturation flux, Bs).I ended up with a practical simple test as in the well-known saying “Necessity is the mother of invention (or innovation, in the least)”. Although the test is simple, its theory is not. And there is a possibility that it is known already but I missed finding it on the internet.Before sharing it here for discussion, could you please point out the simplest method to measure those three parameters that you had the chance to know or heard of? Thank you.Kerim

author: moffy
author_rank: Super Contributor
timestamp: June 12, 2023, 09:57:31 am
content: If I had to do it myself I think I would use the identity V= L*(di/dt) = N*(dphi/dt). I guess I would place some turns around the core and slowly inject DC current while low level modulating the turns and see how the inductance changes with bias current, reach saturation/low inductance value, and start reducing the current to measure the hysteresis. It would not tell what the actual B was unless there was a small gap in the core to place a hall sensor or such. Just thinking out loud, haven't pondered or researched the question previously I look forward to your solution.P.S. B = (L(i)*i)/(N*Ae) : 'L(i)', 'L' is a function of 'i'; 'i' is current; 'N' is the number of turns; 'Ae' is effective area; 'B' is the magnetic field.

author: Kleinstein
author_rank: Super Contributor
timestamp: June 12, 2023, 10:02:13 am
content: The is an old way of plotting the BH curve to a scope in XY mode. One would need 1 coil to drive the core with an AC (e.g. mains frequency) and than ideally a 2nd winding to measure the voltage (a 2nd coil is a bit easier and avoid the winding resistance to interfere). The voltage signal goes through an interegrator to gets B. The current with a shunts gives H.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 12, 2023, 12:30:25 pm
content: Quote from: moffy on June 12, 2023, 09:57:31 amYou gave good ideas. Thank you.On my side, I was looking for numerical results, besides making the test simple.I usually design transformers for my products, as inverters and mains stabilizers. And knowing these 3 parameters, even approximately (less than 2% error) also helps me simulate my transformers using LTspice.I hope you don't mind I delay my solution till I will get a few replies.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 12, 2023, 12:47:16 pm
content: Quote from: Kleinstein on June 12, 2023, 10:02:13 amYou are right.In fact, since I test always my designs using a scope, plotting the BH curve, as you described, was the usual way which I applied every time I needed to get numerically the parameters Bs, Br and Hc of an unknown core.I will look for your comments when I will present a somehow simpler way that I started to apply lately for such measurement.

author: TimFox
author_rank: Super Contributor
timestamp: June 12, 2023, 02:03:32 pm
content: The method involving an integrator is the modern version of the "Rowland Ring" measurementSee section 33.3 ofhttps://digitalcommons.unl.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1168&context=physicskatzThe old-fashioned measurement involves a ballistic galvanometer to measure the charge by mechanical integration.

author: jonpaul
author_rank: Super Contributor
timestamp: June 12, 2023, 02:32:24 pm
content: Hallo: Commodity laminations for mains trsansformers are well characterized. In decades of magnetics and PSU desng we never had to measure such data.There is not much variation in the silicon steel used (grain oriented) and the lam thickness of 14 mils (0.014", 0.356 mm) for all 50/60 Hz mains.The steel manufacturese eg Siemens, Arnold, ARMCO supply all info needed and have the Al, Ac and other needed paramters for any commmon lam sizes.Tradeoffs are Pfe losses vs Bmax.Try this calculatorhttp://www.dicks-website.eu/coilcalculator/Jon

author: KerimF
author_rank: Frequent Contributor
timestamp: June 12, 2023, 03:13:44 pm
content: Quote from: TimFox on June 12, 2023, 02:03:32 pmThank you for the interesting PDF on "Magnetic Properties of Matter".I couldn't notice the parameter Br (the saturation remanent flux) in the method which is presented in section 33.3. Perhaps I missed it since I read the section rather quickly.I guess it is time for me to start presenting on my next post the simple method which I was referring to.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 12, 2023, 03:50:18 pm
content: Quote from: jonpaul on June 12, 2023, 02:32:24 pmI agree with you fully.But it happened that I was born and live where the privilege of buying well-known brands of iron laminations doesn't exist anymore since about 15 years ago. In the past golden years, I was able to get, for example, French laminations with Bs in the range 1.7 to 1.5 Tesla. Now, most offered ones have Bs about 1 Tesla only (I have no idea from which source the local traders import them). Yes, a few years ago, I personally was really surprised when I discovered first this unexpected low Bs (1 Tesla with Hc~=100 A/m). To be on the safe side, I started assuming that Bs=1 Tesla in my all designs. Lately I decided to test each lot which I may receive and design its transformers according to the test's results. So, I needed to find out a very simple way to measure Bs, Br and Hc by using a scope. For instance, I am also designing a BH meter based on this simple method (using ATmega8) so that the measurement could be made by my assistances without the need of a scope.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 12, 2023, 04:19:30 pm
content: The basic idea I started with is that getting the traces of the coil voltage and current during one cycle (actually half, because of symmetry), on a scope, should be enough, as they are, to extract the Bs, Br and Hc parameters. But my brain had to know how this could be done.Step 1:On the scope’s screen, only 4 points need to be read (as absolute values) on the coil voltage and current traces, as illustrated on the attached image:V_max, the coil peak voltageV_Izero, the coil voltage when the coil current is zero, i(t)=0I_max, the coil peak current when the coil voltage is zero, v(t)=0 (the flux B is maximum)I_Bzero, the coil current when the coil voltage equal Vmax, v(t)=V_max (the flux B is zero)Step 2:The following mechanical parameters need to be known too:N = the number of wire turns of the coilTW= the E lamination Tongue Width (E length/3), in cmCW= the Core Width, in cmFrom TW and CW we can deduce:Lm = 6*TW/100, the Magnetic Length (no gap), in meter.A = TW*CW/10000, the cross-sectional area of the core, in m2We will see later how Bs, Br and Hc could be calculated from the above 7 values which are:V_max, V_Izero, I_max, I_Bzero, N, Lm and A.Note:Since, by definition, Bs is at I_max = infinity (or very high), we will also see how to determine the practical top of I_max in a test so that the results will have errors less than 2%.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 12, 2023, 09:12:43 pm
content: Step 3: (Please see step 1 and step 2 on my previous post #9)Calculating the value of a parameter means there is a formula for it.So, there are 3 formulas for Hc, Br and Bs.Hc = Kh * I_BzerowhereKh = N/LmBr = Kb * V_max * cos(wt_zero) / wwhereKb = 1/N/Awt_zero = arcsin(V_Izero / V_max)w = 2*pi*FBs = (Mh - Hc) / (Mh / Mb - Hc / Br)whereMh = Kh*I_max + HcMb = Kb*V_max/w-μ0*Kh*I_maxμ0=1.25664E-06Step 4:I had to check the validity of the above 3 formulas.Unfortunately, I don’t have a known iron core to test it and verify that the results of these formulas are indeed very close to the ones which could be deduced from its datasheet.Again, necessity is the mother of...For fun, could anyone here guess how I was able to check their validity?Hint: The answer could be found on my previous posts.(To be continued)Cheers,Kerim

author: moffy
author_rank: Super Contributor
timestamp: June 13, 2023, 02:03:39 am
content: To verify the equations I would first do a dimensional analysis just to make sure nothing silly slipped in, a sanity check.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 13, 2023, 04:47:26 am
content: Quote from: moffy on June 13, 2023, 02:03:39 amThis is indeed the first crucial step to verify a formula. Thank you for pointing it out.In fact, I try always not to forget to do this verifyat every stepwhile I work to get/deduce a technical formula and be sure that the unit(s) on both sides are the same.But, as you know, we have to verify those three formals also numerically, based on a good reference.Do you think you can guess the valid reference which helped me get a practical idea on the accuracy of their results?

author: jonpaul
author_rank: Super Contributor
timestamp: June 13, 2023, 08:18:27 am
content: Hello again: You are killing flys with atom bombs! WAY too complex...Silicon steel materials properties Bsat, Pfe vs B, temps. etc are the same regardless of vendor and location!Bmax ~ 18..22 k GaussVariations are % Si (see standard % for lams ) and thicknessDepending on application, ambient, load, and safety class Bmax are normally derated below Bsayt.Suggest you find a basic magentic design text book and lear about it.Kind Regards,Jon

author: Hydron
author_rank: Super Contributor
timestamp: June 13, 2023, 08:48:46 am
content: Sounds like there is no guarantee of him being able to get grain orientated silicon steel (or possibly anything better specified than "flat bits of ferrous metal"!) so maybe not so helpful assuming that testing isn't required?

author: KerimF
author_rank: Frequent Contributor
timestamp: June 13, 2023, 09:23:53 am
content: Quote from: jonpaul on June 13, 2023, 08:18:27 amIn theory, you are right.And since I can't give you samples of the iron laminations I have to work with, you cannot, even if you want to, agree on anything I say.In fact, most engineers around the world are fortunate, as you said, for being able to work with iron laminations whose Bs is the range of 1.8 to 2.2 Tesla (surely not 1 Tesla as in my case).Kind Regards,Kerim

author: KerimF
author_rank: Frequent Contributor
timestamp: June 13, 2023, 09:37:42 am
content: Quote from: Hydron on June 13, 2023, 08:48:46 amEven the human race lives on the same planet Earth, humans on it have to live in totally different worlds. We like or not, this is how the world runs since always and till the end of time.

author: Kleinstein
author_rank: Super Contributor
timestamp: June 13, 2023, 09:59:20 am
content: Older grades of transformer steel can vary quite a bit. The theoretical Bs is still about the same, but the usalble magnitzation can be lower. EI cores are usually not grain oriented, but more isotropic (at least in the plane) material. Br and Hc can vary quite a bit with details, though these are usually less relevant for the use in a transformer. It gives a little more standby loss, but this is usually more like a nice to have part and not essential in most uses. The design of a transformer would not be that mich difference if Br or Hc changes - just somewhat different performance at light load.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 13, 2023, 12:06:19 pm
content: Step 4: (continued)I guess most of you agree that a professional simulator (as LTspice) could be used as a valid reference.The attached “NL_50x5_280_10diz_v1.zip” is a test made for LTspice.The assumed core parameters under test are:Bs = 1 TeslaBr = 0.85 TeslaHc = 100 A/mBy applying their 3 formulas after simulation, we get:Bs = 0.993304 TeslaBr = 0.844313 TeslaHc = 99.8267 A/mTherefore, the calculation errors are:Bs_err = -0.669571%Br_err = -0.669072%Hc_err = -0.173262%This proved, to me in the least, that my simple test is indeed valid.Step 5:I noticed that when I_max is increased, I_Bzero increases a little unlike I_avg and I_rmsTo get practical low errors, I_max needs to be about 3.5 to 5 times I_Bzero.In the attached LTspice test, I_max = 4.80391 * I_Bzero @V_rms=150V.Conclusion:This novel simple test for the non-linear iron cores is simply a new pearl added into the scientific bag though a few engineers around the world may appreciate it.Salut,Kerim

author: jonpaul
author_rank: Super Contributor
timestamp: June 14, 2023, 10:55:43 am
content: Hello again:all parameters of transformer steel eg Bm are easily found for every type, % silicon and lam thickness.There is no need for any novel measurements of questionalbe utilityKind Regards,Jon

author: KerimF
author_rank: Frequent Contributor
timestamp: June 14, 2023, 01:03:08 pm
content: Quote from: jonpaul on June 14, 2023, 10:55:43 amSorry, how long should one live to realize that what could be easy for him to get or do, it may not be so to everyone around the world (and vice versa).Where is the problem?! If this novel method is not important to you, just ignore it.Me too, when I learnt, in 1979, about the novel Costas Loop to demodulate a DSB-SC (Double Sideband Suppressed Carrier) signal, I also forgot about it soon after I designed and built (as an MS thesis) a much simpler reliable demodulator using one PLL only. And for many years in the 80's, I used my novel DSB-SC demodulator in my short-range RF voice links (between house and workplace, 3km distance), first on MW band then on FM band. I will talk about this in details (as for why I did it and how) on the RF board.Very Kind Regards,Kerim

author: Kleinstein
author_rank: Super Contributor
timestamp: June 14, 2023, 04:06:59 pm
content: I don't see much novel in the method. It is more or less the standard method used in the last 100 years or so, just with digitial integration instead of the old style low pass filter to do analog integration.

author: TimFox
author_rank: Super Contributor
timestamp: June 14, 2023, 05:05:59 pm
content: I am of that generation that used a ballistic galvanometer to integrate the charge required for a Rowland Ring measurement.Does anyone still sell such galvanometers?In my college lab, they were bolted to the wall and used a telescope to follow the scale reflection through the moving mirror.I believe they were made by Leeds and Northrup.I have found table-mounted devices from India, but I haven't located any that are wall-mounted.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 14, 2023, 06:23:56 pm
content: Quote from: Kleinstein on June 14, 2023, 04:06:59 pmYou may be right.In this case, I surely missed the source, you know, which also provides 3 formulas whose electrical parameters could be known by a simple reading of 4 points on the coil voltage and current traces on a scope.Directing me to that source will be much appreciated. Thank you in advance.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 14, 2023, 06:31:05 pm
content: Quote from: TimFox on June 14, 2023, 05:05:59 pmI wonder if the method, you mentioned, is simpler than what I described.

author: TimFox
author_rank: Super Contributor
timestamp: June 14, 2023, 06:40:43 pm
content: The method was tedious, involving manual reversal of the coil current and noting the maximum excursion of the galvanometer.The next student to do the lab experiment used a rudimentary analog computer to do the integration.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 15, 2023, 03:00:21 pm
content: I am surprised that no one liked to ask me about the known basic formulas from which the 3 formulas on post #10 were derived and let the measurement be simple (relative to the conventional known methods).Perhaps no one here is ready to believe they are valid because they are not known or approved by any scientific site.The irony is that a new idea, by definition, starts always from one person in the world, unless a few individuals may think of it in the same period of time, in different regions on earth.

author: Conrad Hoffman
author_rank: Super Contributor
timestamp: June 15, 2023, 04:57:04 pm
content: I have never seen one of these in the wild, and the photo of the head isn't very good, but the manual may offer some useful information:https://www.ietlabs.com/pdf/Manuals/GR/1670-A%20magnetic%20test%20set.pdfThe patents can also be looked up but I don't know if they offer more info.

author: TimFox
author_rank: Super Contributor
timestamp: June 15, 2023, 05:23:25 pm
content: Note the wide range of units discussed in the "Introduction" of the G-R manual.Present-day SI units for magnetic variables are listed there as "MKS, rationalized (MKS-R)".Rationalized vs. non-rationalized involves a factor of 4 pi, besides the orders of magnitude from cm vs m, etc.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 15, 2023, 11:39:09 pm
content: Quote from: Conrad Hoffman on June 15, 2023, 04:57:04 pmSorry, I am not sure what I am supposed to learn from reading this PDF. Does it explain a simpler method than the one I use?

author: Conrad Hoffman
author_rank: Super Contributor
timestamp: June 15, 2023, 11:45:31 pm
content: GR was very good at explaining the fundamentals underlying the designs of their equipment. They were usually rigorous in accounting for subtle errors. I've found I always learn something from them though many people are smarter than me and don't need more information.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 15, 2023, 11:58:51 pm
content: Quote from: TimFox on June 15, 2023, 05:23:25 pmThe units I am familiar to are of MKS, Tesla (for Bs and Br), A/m (for Hc), Weber (for ‘Φ’, the Magnetic flux) and H/m (for μ0=4*pi*1e-7).

author: TimFox
author_rank: Super Contributor
timestamp: June 16, 2023, 01:47:56 am
content: Those are SI, and our voltmeter calibrations agree with it.However, there are many more sets of units that have been or are in use in physics and engineering, even English units (line/in2, etc.) and one should be aware that they exist.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 16, 2023, 02:00:45 am
content: Quote from: Conrad Hoffman on June 15, 2023, 11:45:31 pmThe needs of an adult determine his professional knowledge in life. The different needs of humans let their knowledge complement each other.In other words, the lack of knowledge about something is simply the lack of interest about it, for one reason or another, no matter if the person, in question, is genius or not.In my case, I like to learn (or discover) what I can apply in real and be useful to me in a way. But I may like to hear some other things just to pass my free time or for fun.

author: johansen
author_rank: Super Contributor
timestamp: June 16, 2023, 02:07:20 am
content: I have found that cheap microwave oven transformers start to saturate at 1.2T but they run them at 1.7 to 1.9.They are gain oriented, allegedly. The I piece comes from two E pieces.As such most of the core is oriented correctly but the short segments are not, hence the soft saturation.Anyhow just wind a coil and measure the power consumption after subtracting copper losses

author: KerimF
author_rank: Frequent Contributor
timestamp: June 16, 2023, 02:10:13 am
content: Quote from: TimFox on June 16, 2023, 01:47:56 amI work with the MKS units, but I am also aware of all sorts of other units since, once a while, I need to convert them to MKS ones while solving new equations and getting new formulas at work.

author: TimFox
author_rank: Super Contributor
timestamp: June 16, 2023, 02:12:46 am
content: @KerimFAnother common unit for magnetic flux densityBis the Gauss.1 Tesla = 104Gauss.However, Gauss is a unit in non-rationalized cgs, so the corresponding unit of magnetic fieldHis the Oersted, but in vacuumB=H, different from in rationalized units.You will find Gauss used often, since the Tesla is rather large and the Earth's field is very roughly a Gauss.Tabulations of magnetic materials often use Gauss and Oersted, so you should understand them as well as Tesla and A/m2.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 16, 2023, 02:26:43 am
content: Quote from: johansen on June 16, 2023, 02:07:20 amGood remark, thank you.I will try to test a coil whose core is made by the E pieces only and see the difference. Obviously, its new structure will not be practical at all. It will just help verifying your remark.And the power consumption (real power) can be measured rather easily by a scope having the Ch1*Ch2 function (which I have).

author: KerimF
author_rank: Frequent Contributor
timestamp: June 16, 2023, 02:43:35 am
content: Quote from: TimFox on June 16, 2023, 02:12:46 amI am sorry for giving you the impression that I don't understand well all the other units you mentioned.You are right that most tabulations of magnetic materials are given in Gauss and Oersted. And I used to convert them to Tesla and A/mIf I am not wrong, you give me the impression that I have to make another version of my 3 formulas and let it be suitable for Gauss and Oersted (what about the length unit?).

author: TimFox
author_rank: Super Contributor
timestamp: June 16, 2023, 02:54:13 am
content: Technically, Gauss should be used with cm.Note that Gauss and Oersted form a non-rationalized system, so the equations are different from the rationalized system such as rationalized MKS (SI) using meters, where there is a dimensional difference betweenBandH.

author: KerimF
author_rank: Frequent Contributor
timestamp: June 16, 2023, 03:13:04 am
content: Quote from: TimFox on June 16, 2023, 02:54:13 amTo check if the new 3 versions are right, their results, for the same coil, should be:New Bs, Br (Gauss) = 10000*old Bs, Br (Tesla)New Hc (Oersted) = 4*pi*1e-3 * old Hc (A/m)

author: KerimF
author_rank: Frequent Contributor
timestamp: June 16, 2023, 04:25:21 pm
content: The 3 formulas of Hc, Br and Bs on post #10 are for the MKS units (A/m, Tesla and m).The following 3 formulas are for the non-rationalized cgs units (Oersted, Gauss and cm):HHc = Khh * I_BzerowhereKhh = 4*pi*N/LLm/10LLm, in cmBBr  = Kbb * V_max * cos(wt_zero) / wwhereKbb = 1e8/N/AAwt_zero = arcsin(V_Izero / V_max)w = 2*pi*FAA in cm2BBs  = (Mhh - HHc) / (Mhh / Mbb - HHc / BBr)whereMhh = Khh*I_max + HHcMbb = Kbb*V_max/w - Khh*I_max

author: KerimF
author_rank: Frequent Contributor
timestamp: June 17, 2023, 07:23:12 am
content: To complete the topic of this thread professionally, I will answer the question that no one asked me:What is the well-known work on which your 3 formulas were based and derived?Its answer is simple to those who are familiar with LTspice simulator.They are derived from the work of John Chan in modeling a non-linear coil.To those who don’t have LTspice, I attached a PDF of the LTspice help page which is related to John Chan model.His two formulas, one for the positive BH branch and the other for the negative one, are the Bup(H) and Bdn(H) respectively.Obviously, if someone will be able to prove that any of my 3 formulas is not valid, he simply proves me that John Chan model is also not valid.Regards,Kerim