Circuit Duals and Magnetic Circuits - Page 1
Forum section: electronics / projects

author: freemo
author_rank: Contributor
timestamp: September 29, 2020, 09:47:14 pm
content: First post here, I really didnt know where else to go where I might be able to get feedback from people more advanced in EE than your typical hobbyist. I would have used Stackexchange but I dont have a specific question.I'd love to ask for feedback, any technical corrections, or just impressions or opinions about a rather indepth tutorial I spent the last week researching and writing. All criticism, the harsher the better is most welcome.It is a tutorial/article on the idea of Duality in math, how it applies to circuits, how to calculate duals for systems of equations as well as circuits, and a few examples of circuit duals. It also goes indepth on magnetic circuits as a dual of electric circuits, this is the part where I need a critical eye. There is an interesting blurb at the end about how to extract energy from permanent magnets as well, but dont get any crackpot ideas about infinite energy or anything!Ideally I'd prefer you to review it at my blog since this is the "official" version and the PDF has a few known rendering issues. Also the blog adds relevant coloring that I think is relevant to any feedback. The link for that is here:http://jeffreyfreeman.me/an-indepth-look-at-duals-and-their-circuits/However if you really must I also share a PDF version your welcome to share here. It doesnt have the table comparing dualities and has known rendering bugs, so I do not recommend it unless you have no other option to review. I will also attach the pdf here for redundancy or if someone doesnt wish to follow a link.https://drive.google.com/file/d/1fECh_IeFYBHoFuaw08zO2dkluZPunkP7/view?usp=sharingThanks in advance to anyone who puts the time in to help with this.

author: dmendesf
author_rank: Frequent Contributor
timestamp: September 29, 2020, 10:27:42 pm
content: Figure 4: Capacitor Low Pass Filter -> make that inductorThe link to your website goes for a different article than the PDFJust glazed over the PDF but seems very well written. Will read carefully when I get to the computer.

author: freemo
author_rank: Contributor
timestamp: September 29, 2020, 10:35:05 pm
content: Quote from: dmendesf on September 29, 2020, 10:27:42 pmMy apologies, you are right I put the wrong link in. I have just updated the post with the correct link.Quote from: dmendesf on September 29, 2020, 10:27:42 pmThanks for that catch, that error is only in the PDF, but I will correct it there. Now that i updated the link I suggest you read from the blog link if you can.

author: freemo
author_rank: Contributor
timestamp: October 01, 2020, 12:22:25 pm
content: Bump, I'd really like some feedback. As a tutorial I think its important I get at least one person who knows the subject to verify my wording and equations.Thanks.

author: mag_therm
author_rank: Frequent Contributor
timestamp: October 01, 2020, 03:39:37 pm
content: Hi Freemo.At (104) it could be clarified that a lower Re(u) does not directly mean higher core loss,although it would mean a higher copper loss in a wound inductor of same inductance, compared to an inductor with a "good" core.At (105) and the impedance plane, I think your u' and u'' are for the case of a series core loss R :Thevenin(there is another reciprocal set for the case of shunt core loss R: Norton)It is a good tutorial, Thanks

author: freemo
author_rank: Contributor
timestamp: October 01, 2020, 04:16:19 pm
content: Thank you so much for your feedback. I may be misunderstanding you so let me dig a little deeper into what you mean in each case.Quote from: mag_therm on October 01, 2020, 03:39:37 pmSo on this point one of us is confused, and it could very well be me. Let me explain my understanding of the equations and what your trying to say here, and either you can correct me, or perhaps you are mistaken, let me know. So the equation in (104) as stated there should represent the core loss of an inductor if the copper windings had 0 resistance. If the copper windings had a non-0 resistance then the equation would look like this: (u'' + P)/(u'), where u'' is the imaginary part of permeability (though with a 1/j term dropped), u' is the real part, and P is rho, which is the resistivity of the copper wires. Since the (104) form of the equation would be loss in a core-based inductor with 0-resistance wires, I think it's fair to argue that a lower u' (real part), presuming u'' and P dont change, **will** result in higher core loss. however a higher u'' (imaginary part), presuming u' and P, remains the same, does not guarantee higher core loss, perhaps this is what you meant and said real component by mistake? All of this is core loss though (since it applies to 0 resistance windings) and can not be avoided except by picking a material with better complex permeability. Now that isnt to say that the loss from the copper windings wont also be magnified by a lower u', it certainly will, so the copper windings do not present a simple loss as a dc resistance on its own, the loss increases from the resistivity of the copper with lower u' as well. But because there is a loss even with 0-resistance copper windings, and because a lower u' implies greater loss everything else remaining the same (even with a P of 0), I think it is safe to say that your statement is not correct, a lower Re(u) **does** directly mean higher core loss regardless of the copper resistivity, but with copper resistivity the extent of that increased core loss may be even more so.I believe I explain this in the paragraph that immediately follows equation (104), though I am going to reread it now and make sure I didnt misspeak. Assuming you have changed your opinion and now agree with me (if not please lets discuss so I can explore who is wrong and why), do you feel the paragraph following (104) is not clear and might need rewording to express what I just said?Quote from: mag_therm on October 01, 2020, 03:39:37 pmEquation (105) simply defines the meaning of u' and u'' as the imaginary and real parts of the complex permeability. It also shows that the imaginary part is multiplied by -1, which is the consequence of a reciprocal imaginary number relationship (basically 1/j is dropped). Obviously how you pull imaginary and real numbers out of a complex number wouldnt change based on circuit configuration. So not really following what you are trying to say here.Thank you again for your feedback and I look forward to hearing your response.

author: freemo
author_rank: Contributor
timestamp: October 01, 2020, 05:16:58 pm
content: By the way your comment did cause me to realize that a few statements I made in the article were incorrect.. I stated that higher imaginary component meant more loss, and while that wasnt the correction you made (you spoke of the real component) this was incorrect. A high imaginary component means less energy stored, and thus a larger ratio of loss, but not any additional loss in absolute terms. I have corrected it in three spots in my article.

author: mag_therm
author_rank: Frequent Contributor
timestamp: October 01, 2020, 05:30:30 pm
content: Hi Freemo.I think you are using the series loss model.Can you confirm?In that case Re(u) called u', your upper graph, sets the reactance component (jwL)( with 1 * j = +jAnd Im(u), called u'' your lower graph, sets the loss resistance R( with ( j * (-j) ) =1The loss angle relative to +j axis ( pure inductance ) isdelta = atan( R/wL)In series case, where usually R ( real part) is unwanted and smaller that jwL, delta is small angle.Your (104) Tan( delta) is just a ratio of the core effective Rs to the reactance jwL. Lower is better, and u'' << u'as your graphs showFor examplecore A : u' = 100 and u'' = 10core B : u' = 50 and u'' = 10If they both have same dimensions and turns, they will both have same core loss, even though core A has a lower tan(delta) .In the shunt case ( which I think you are not using) unwanted component is large, being in parallel wth the wanted jwL.In that case u'' >> u', tan( delta) = wL/Rp, and tan(delta) as figure of merit is same as the series case.I found a reference here: Snelling E.C. "Soft Ferrites" article 2.2.1

author: freemo
author_rank: Contributor
timestamp: October 01, 2020, 06:03:38 pm
content: Quote from: mag_therm on October 01, 2020, 05:30:30 pmI am not sure if I am using the "series loss model", I havent heard that exact terminology. but that does sound correct since I am using the same equations that could potentially used to calculate "effective series resistance". I'm just not sure if we are really talking about the same thing here or not as I havent heard it called "series loss model" specifically.I think it might clarify what I'm saying, and the implication of the terms u' and u'' if you take a look at my article at equation (120) which shows what the magnetic impedance would look like for a material with a specific u' and u'', keep in mind this equation is for the ferrite material itself and as such would only apply to inductors where the copper has 0-resistivty.As you can see in equation (120) the imaginary component solely dictates the reactance of the inductance such that a larger value of u'' means a smaller magnetic reactance, and a smaller value means a larger magnetic reactance. Likewise u' solely dictates the real component of the magnetic reactance, and therefore the magnetic energy loss is solely dictated by the real component. This all assumes I calculated equation (120) correctly and that I didnt make a mistake somewhere, which is entirely possible.Keep in mind u'' != Im(u), notice the negative sign in (105), that makes a slight but important difference between u'' and Im(u).Quote from: mag_therm on October 01, 2020, 05:30:30 pmI agree with the above statement, if the real resistance (the part that causes loss) is small, then the loss tangent angle, delta, will also be small.Quote from: mag_therm on October 01, 2020, 05:30:30 pmOn this point I dont agree (though I could be wrong, so if you can show me how I am wrong or why your statement is right I'd appreciate it. For an inductor of the same turns using core B there would be more loss (twice as much) as the same inductor using core A. The real component dictates actual loss and translates to the real part of the impedance. If you were to make a similar statement, however, and u' were fixed and u'' were the part varying then I would agree with you, in that case you would be right in stating that while the loss tangent might be higher the actual loss itself didnt change. Because u'' would effect the imaginary part of the impedance and thus would indicate less energy stored, but since u' didnt change there would be the same amount of energy lost in that case and thus the loss tangent would go up despite no additional loss taking place.But no, as you state it I beleive you are incorrect, a change in u' **does** mean both a change in actual absolute loss, and as such, also a change in the loss tangent (the ratio of lost energy to stored energy).. it is only with u'' that a change in u'' will not effect the amount of energy lost and only effect the loss tangent itself.To pull from other sources to confirm that the real component is the lossy component and not the imaginary component as you suggest see the following wikipedia article which states: "Both refer to the phasor in the complex plane whose real and imaginary parts are the resistive (lossy) component of an electromagnetic field and its reactive (lossless) counterpart." --https://en.wikipedia.org/wiki/Dielectric_lossQuote from: mag_therm on October 01, 2020, 05:30:30 pmThis part seems confusing to me, and perhaps where our disconnect is. I am not talking about an inductor in the shunt case or in a series case. this would be the loss tangent of the inductor itself it will directly hooked up to a power source with no other components. So im not sure referring to it as a series or parallel component really applies, its kinda either/both when its the only thing in the circuit.

author: mag_therm
author_rank: Frequent Contributor
timestamp: October 01, 2020, 06:54:26 pm
content: I'll try to send a message later.

author: freemo
author_rank: Contributor
timestamp: October 01, 2020, 07:18:11 pm
content: No rush, take all the time you need. I'm not going anywhere. But this is the first serious math/EE critique the paper got so I am eager to see where this goes. Like I said it is entirely possible I made a mistake and I am either unaware of it or am not seeing what it is now.I will say this if you are correct then it means most of my subsequent math leading up to equation (120) must also be incorrect.

author: freemo
author_rank: Contributor
timestamp: October 02, 2020, 12:03:15 am
content: Me and mag_therm took this to personal messages and then realized it better belonged here so others could contribute and discuss. With his blessings I will copy-paste our dialogue here and then leave my comments here rather than in direct message.Quote from: mag_therm on October 01, 2020, 11:34:05 pmAt this point I cant see the message I replied with anymore, but I basically asked why he moved to a private message and pointed out that I was familiar with the notation he was using but I usually see it using the angle symbol instead of <. I asked if he would mind if we move back to the forum post as I want to encourage other people to add their input and either correct one of us or add their own perspectives to help the conversation along. I also mentioned I would wait to respond on the main forum unless he indicated he wanted to keep it private still. He responded as follows.Quote from: mag_therm on October 01, 2020, 11:34:05 pmI will respond in a second post, dedicate this one to copy and pasting what he said and leave my own comments in the next post.

author: freemo
author_rank: Contributor
timestamp: October 02, 2020, 01:45:17 am
content: QuoteI agree with all that, I would call what you refer to as a "notational resistor" as a "virtual resistor" when I do my modeling,, but I would refer to it as "real resistance" or simple "resistance" and I rarely would refer to it as a "resistor" I would say something like "The resistance of the inductor's impedance is 5" or just "The resistance of the inductor is 5". Typically when adding a resistor to a component such as a capacitor or inductor I would refer to the virtual resistor more specifically as the "ESR" which means "Equivalent Series Resistance"QuoteI see what you were trying to say by Shunt resistor now, you meant instead of putting the virtual resistor in series with the inductor to calculate its ESR you put it parallel with the inductor instead and calculate it. But as you pointed out series virtual resistors are always used to model inductors, and you are correct I was using series here. In fact I'm not sure how shunt resistance would even work well, since the point of the ESR is to simulate the resistance caused loss of the inductor it would have to go in series . If it were in parallel since the ideal inductor has not ESR itself and the modeled ESR is parallel to it then if you model how it would respond to DC voltage applied across it it would appear to the model as there is no series resistance at all. I havent seen shunts dont to model inductors, though I could see how you might to model other things.. regardless that is not what I used here, so yea we can ignore the idea of modeling it as a shunt and move ahead.QuoteThat equation is roughly correct (the Area/Length part is a big oversimplified but that's not too important here). and yes I agree that the vacuum permeability u0 would be a real number positive value with no j there for an ideal inductor.However not that the Ideal equation for an inductor, as you have it, is a different beast entirely from the non-idealized one that uses a complex value of u. The real-world version would use a complex value u and therefore the inductance, L would also become complex valued if you take that approach. Its also important to note that if you wanted calculate an ideal inductor using the real-world form of the equation (which again behaves very differently despite looking similarly) you cant just subsubsitute in the complex form and treate it as the same equation. The reason for this is because an ideal inductor will have u' that is infinite For example to do what your doing there, to represent an ideal inductor using the non-ideal formula youd have to do the following:L0 = (infinity - u0 j) * (N^2) * Area/length ... of course infinities are not nice to work with or put in your equation so we can and do use the idealized form as you state it in which case L0 is not complex, where in the non-idealized form then L0 would become complex (and a proper value for u' other than infinity selected).The important part to realize though before I go on, is u0 (as a real number) in the equation you mentioned is the imaginary part of the complex permeability, not the real part. We just drop the j and the negative sign when using it in its idealized equation form as you just did.QuoteI agree with that so far as well, particularly when you are using u0 in its idealized form (as a real number representing the absolute value of the imaginary part of the complex permiability). Bear in mind also that even though ur here that you added in is also a real valued number the value (ur*u0) is the absolute value of the imaginary part of the new inductor you just mentioned as well. It is u'' from earlier. Same applies as i said earlier, if you used the non-dealized form of this equation then you would have to represent it as (infinity - ur*u0 j) and plug that in instead and youd get a complex inductance for dealing with the real world version of this, but since your doing ideal so far I agree.QuoteThis is where you loose me and it may just be me misunderstanding the way your speaking.. for starters lets keep things easy and talk in terms of absolute permeability not relative permeability. So u'' = ur * u0, the absolute is easier to work with.. now as we covered the ur you were using was real-value (idealized form) and u0 was idealized form as well (u0 is always in its idealized form though as vacuum permeability has infinite real component and finite imaginary. In other words u0 and ur were real u0'' and ur'', the lossless inductive part is the imaginary part u'' not u', you havent used u' in your rquations yet only u'' as an absolute (u0) and as a relative (ur), both are imaginary parts.So first thing you got wrong is where you say in the idealized form you are left with u' or Re(u) at 0 degrees. Though I suppose if you want to measure it from the real axis that is true. But since we are talking in terms of tangent loss angel it is measured from the positive inductive axis, so u'/Re(u) would be 90 degrees not 0 degrees loss tangent angle.QuoteI think you meant to say ur' in that statement or u' .. ur is not a real value anymore it is a complex value since we are talking about u' as its real component. But i do agree ui is a scalar real number, it is the negated real part of the complex permeability.QuoteAgain this compounds on your earlier mistake.. ur'' (or u'' to make things easier, the absolute form) was already used earlier its the imaginary component of complex u and up until this point that is what you were using. The only way to achieve R here would to introduce u', not u'' as the loss parameter.QuoteThis compounds the earlier mistake and adds additional mistakes if you want to represent an inductor with a lossy core but lossless copper windings the equation wouldnt look like that at all, it would be the following, assuming your using the idealized form of the equations you've been using, not the complex form.Z = [(u'')/(w*L0*u')] + [1/(w*L0) j], where L0 is the idealized real-valued inductance (imaginary part of the complex value when not-idealized), and u'' is the negated imaginary part of complex permeability, u' is the real part of complex permeability, and w is angular frequency.See my derivations from (108) to (120) to see how that is derived. At this point since your equations have diverged significantly from the actual questions I am not going to comment further on this section until you had a chance to remark since we have to agree on yoru earlier derrivartions before we can talk about the additional equations you base on that farther down.QuoteI usually just copy and paste in the unicode or memorize the unicode code like : ∠Wont always work on the web and you may not see it, could show up as a brick for you.QuoteEven today they rarely teach about complex permeability, or complex reluctance. But what they taught you years ago was the ""dominant imaginary part" not the dominant real part. It is just represented as a real value since the j is dropped (it is also negated and as the imaginary part is negative usually but presented as positive). So you've actually been learning about the imaginary part all these yearsQuoteNo that is not a typo. the electric and magnetic sides do not, in fact, have the same symbols, not exactly. The convention when talking about magnetic duals (magnetic regime analysis) is to use the same letters for say, magnetic capacitance, as you would for electric capacitance however you change the magnetic capacitance, in this case letter C, to its Cursive form.. so if you look closely you will see they are both the same letter but all the magnetic letters are in their cursive form (called Mathcal) and the electric ones are in their non-cursive form. I hate to be rude but did you actually read the text of the paper or did you just look at the equations. Because if you just looked at the equations I could see why you might be confused and very lost and why you may have gotten a lot of points wrong in trying to understand the writing. Magnetic Capacitance, and Electric Capacitance are different things, they both behave like capacitors but one is a capacitor for magnetic energy and the other is a capacitor for electric, the electric capacitor is the one you know of, magnetic capacitors might be new to you. Likewise magnetic inductors and electric conductors also aren't exactly the same thing (they are reversed mirror images of each other, but the math becomes reversed as well as a result of this). Similarly Magnetic impedance is not the same as electric impedance, though related.. Hell Magnetic DC is not even similar to Electric AC.The math for a magnetic capacitor will look just like the math for an electrical capacitor, except the capacitance is in heneries and not farads. Also the units for the impedance of a magnetic capacitor is in siemens and an electric capacitor is in ohms. I think you may have missed the part where we are talking about magnetic circuits, not electric circuits.. Though I am using electric circuits in order to describe and explain how to get to magnetic circuits.

author: freemo
author_rank: Contributor
timestamp: October 02, 2020, 12:48:21 pm
content: By the way for more clarification on the differences and how to calculate capacitance from a real-valued permeability value (what your used to), and a complex valued one (which result in a complex value for capacitance). As well as how the complex vs real-valued capacitances are used differently. See equations (82) to (86) and read the text between and around those equations. on the blog from here:http://jeffreyfreeman.me/an-indepth-look-at-duals-and-their-circuits/#the-magnetic-inductor-and-gyratorAlso if you want to see how complex permeability ultimately determines magnetic impedance (which is very similar to electrical impedance except for the difference in units) see equation (120) which i show the derivation for throughout that section.I think it will help explain the errors (or at least what I think are errors) in your equations better than I did here.

author: freemo
author_rank: Contributor
timestamp: October 02, 2020, 05:03:01 pm
content: Oh and one other quick note. Equation (120) which I describe as Magnetic Capacitance, and which it is (in the magnetic domain) would be equivalent to electrical capacitance, not electrical inductance. So earlier the equation I cited you for finding the impedance of inductor given permeability, that was incorrect on my part, that would have been the equation for a capacitor given permittivity OR for a magnetic capacitor given permeability, but not for an electrical inductor as I stated. Would have to take the inverse for that. My mistake, I've been working on magnetic circuits all week so got my domains mixed up in that response.

author: freemo
author_rank: Contributor
timestamp: October 15, 2020, 03:04:34 am
content: Quote from: mag_therm on October 01, 2020, 06:54:26 pmHey never heard back on this, did you get a chance to look?