Answer to ‘inductor saturation riddle’

[@brendanzotto1239]

As always professor Ben-Yaakov your explanations are enlightening and concise. I have watched dozens of your videos at this point and you have helped me solidify my understanding of power electronics enough that I want to pursue a graduate degree in it! Thank you so much!

[@sambenyaakov]

Excellent! Go for it. Good luck.

[@beiwujin5959]

I am an electronic engineer from China, I am really appreciate your lectures. Thank you!

[@sambenyaakov]

Thanks

[@SuperHal2k]

That's a beautiful lecture. More riddles ! :D

[@sambenyaakov]

👍

[@ebarbie5016]

Thanks. This was actually my original answer: "The simple answer is that this is a trick question, as the given energy expression does not apply to varying or non liner inductance. There should be another term involving L^2 and i. Coil energy is derived by integrating instantaneous power vi, but L is a function of i, so derivative should be according to chain rule using two parts... This is similar to energy stored in a moving coil, both i and L are functions of the displacement parameter (x or theta). In this case, some of the energy dissipates as core losses, due to the change in current leading to dipole movement..." If the L(I) dependence can be approximately formulated, one can derive an analytic stored energy expression. As for the second part, while core saturation and hysteresis losses are two different phenomena, any change in current in a saturatable inductor will lead to some power loses. The energy is obtained by integrating iv as i*d(Li)/dt = i*[(di/dt)*L+(dL/dt)*i] and so on...

[@sambenyaakov]

Well not exactly. Your derivation: ______________ The energy is obtained by integrating iv as i*d(Li)/dt = i*[(di/dt)*L+(dL/dt)*i] and so on... _________________ Is incorrect . Write to [e-mail] if you need an explanation why.

[@ebarbie5016]

@@sambenyaakov Thanks. I'll have to dig into it more deeply, but the interesting thing is that I was able to get correct analytical results when I modeled a simple electromagnetic machine in PLECS, where I had a variable inductance L(theta) and thus L(i). But is was linear dependence. Using the obtained energy expression, I was able to calculate the correct torque of the machine... So, it seems that my assertion for calculating energy as stated above does work for some scenarios, or was it the bad clock that shows the correct time once a day concept? :-)

[@michaelk.1108]

Thank you for this video, Prof. Ben-Yaakov. Very good explanation. The truth can be found in the known equations.

[@sambenyaakov]

Indeed. Thanks

[@cuchulainkailen]

Wow. That Sam. What a sneaky guy.

[@sambenyaakov]

🙂

[@rayachotybharathkumar268]

Honestly, This was a very difficult one for me. Thanks professor

[@sambenyaakov]

Well, You have bee with the majority😊

[@tingranwang4199]

Hi professor, this video is amazing! would you mind posting the video where you talked about this riddle? so we can have some more context when watching the answer to the riddle :) thank you!

[@sambenyaakov]

It's posted in my KZbin channel. I have now added the link to the riddle at the description section of the answer video.

[@tingranwang4199]

@@sambenyaakovthank you!

[@monguskooklord7867]

So the core is able to store relatively less energy per dI once it passes the knee? Do you already have a video on the macro effects of inductor saturation within a switching converter?

[@sambenyaakov]

1. Yes. 2. Good subject. Will consider.

[@cuchulainkailen]

@@sambenyaakov ... I've read that proper output L selection for smps is needed to avoid sub-harmonics when smps is at 50% duty cycle - but no explanation was given. Could you do something on this? What is "proper" there? Sounds like some kind of modulation issue, no?

[@martinmartinmartin2996]

An important point :where is this energy dissipated? my_guess: NOT external to the the inductor OR transformer but in the core material and the copper losses of windings ; in the case of the transformer the , primarily in the primary winding when the core is saturated.

[@sambenyaakov]

Indeed

[@sam7901]

Excellent and useful analysis 👍

[@sambenyaakov]

Thanks

[@saivedavyaschowdarychintaa5668]

Learning new things which we won't get to know in our universities thank you very much sir ❤️❤️❤️

[@sambenyaakov]

Thanks for kind words

[@Greg_Chase]

When the core's bulk (majority) of electron spins are aligned, the magnetic field *_of the core_* has reached its max level of magnetization (aka it is saturated). HOWEVER. Since there is a coil of wire still present around the magnetic core, and since current in the coil can still be increased beyond the point of saturation of the core, the increase in energy past the core saturation cannot be stored in the core. The additional magnetic field created by the increase of current in the coil, admittedly, can no longer increase the B field in the core, since the core is saturated. But the additional magnetic field of the coil can easily increase in volume it occupies in space. *EXAMPLE* 1) a coil is capable of 100,000 amps 2) its (non-gapped) core saturates once the coil current reaches 1 amp 3) as the coil current is increased from 1 amp to 100,000 amps, the coil's magnetic field grows, but the core remains saturated, at its max B field (maximum magnetization) So the additional energy IS NOT stored in the core once it attains saturation. The additional energy must therefore be 'stored' in free space, in the vacuum, in the form of an increased "coil only" magnetic field .

[@sambenyaakov]

Thanks for comment, but all this is very well known and taken into account. It is generally assumed that at core saturation the relative permeability approaches 1 (not zero) and the vacuum or air permeability is left. So basically what is left is an air coil.

[@Greg_Chase]

@@sambenyaakov right, I was trying to re-state what you presented. There are two devices at opposite ends of the spectrum related to core saturation: A 'magnetic amplifier' purposely saturates the core at a chosen time by way of a DC-powered winding to create the huge drop in inductance/permeability, so as to bring about an amplification of the AC or RF running through a second coil winding; as the core saturates, the permeability drops and the AC current then increases. This is also known as a 'saturable reactor' At the opposite side of the core saturation game is the gapped core, used in for example a flyback transformer. It allows much higher input signal to the primary winding while preventing the core from saturating, using a 180 degree phase shift and a blocking diode in the secondary winding to de-couple the primary's energy from the secondary until the huge magnetic field in the gapped-core primary is allowed to collapse, which forward-biases the blocking diode and couples the large collapsing primary field to the secondary. CRT monitors used high power flybacks as the cheapest way (a gap in the core and a diode!) to create the large voltage in the secondary used to accelerate the electron beam toward the view screen. I liked your video because it clarified the math and operation of core saturation and change in permeability and self-inductance when saturation occurs. It was well done, and enjoyable - thank you!

[@sambenyaakov]

@@Greg_Chase 👍

[@jessstuart7495]

How are transformers designed so they can tolerate small DC currents without going into saturation?

[@sambenyaakov]

Small air gap

[@jessstuart7495]

@@sambenyaakov, Ah, so the air gap reduces the magnetic flux around the core for a given mmf. I suppose powdered iron torroids have a "distributed" air gap due to the space between the iron particles. Makes sense. Thank you.

[@sambenyaakov]

@@jessstuart7495 👍

[@yingzhang8493]

Dear Prof. I really like your channel and videos. This is a very interesting riddle. Thanks for sharing. Just one quick question, at 1:48 in the video, I was wondering if feeding a current source to an inductor legit. Thanks.

[@sambenyaakov]

A problem would arise only in there is an abrupt change in current e.g. di/dt=infinity, which is not the case here.

[@mohalothman99]

Thanks ❤️

[@sambenyaakov]

Thanks

[@pedrocasique7352]

¡No entendí bien todo estimado profesor! Pero voy a verlo más veces y preguntarle. ¡Muchas gracias!

[@sambenyaakov]

Don't hesitate to ask. Better in English😊

[@anshaggarwal2060]

Hi Sir, a question that arises whenever i wind inductors, which makes sense here, is: How is the saturation magnetic flux density related to saturated current. As B = uH; and H is a function of I. For Isaturation there would be a Hsaturation and hence from the B-H curve a Bsat. Can it be also derived with equations to get a more exact approximation of Isat from the value of Bsat. This problem occurs when u have datasheets that only give you Bsat. Thanks for your reply in advance!

[@sambenyaakov]

Have you seen kzbin.info/www/bejne/g2SydoBsodOZiKc ?

[@anshaggarwal2060]

@@sambenyaakov no sir. Thanks for the suggestion

[@raviselvans1963]

Dear sir, Can you please create play list for your videos...

[@sambenyaakov]

I really don't kno whow to organize play lists (im plural). You can easily look for a subject by searching in KZbin search window e.g. "sam ben-yaakov sic"

[@tomg8069]

Hello, i have question due to my test circuit. I measure coil saturation current by observing voltage on 0.0125Ohm resistor in series to coil on B1 area when it is still linear. I use good pulse gen. I have test transformer from 3kw inverter on 24v so i expect to have 50 or more Amps....on one of push pull coils. I have scores of 10..15A !? When i measure singe coil (no transformer) i get proper values with even 40A scores so it is not issue with my test circuit (big capacitors and gel battery)....maybe it is by the fact i use 12v in test circuit and trafo coil has ~50v p-p ??? Thanks in advance :) regards

[@tzi-9047]

Thank you professor . It’s very interesting! I think L(i) is similar Coss(v) of MOSFET. In cace of Coss(v), Energy is stored like L(i)?

[@sambenyaakov]

Indeed very similar see kzbin.info/www/bejne/r3SuYpuwnLiSo7c and part 2 and 3

[@tzi-9047]

Thank you very much for introduced movie. I learn much from your movie! Regards,

[@tamaseduard5145]

🙏🙏🙏❤️🙏🙏🙏

[@sambenyaakov]

👍😊

[@mohamadjneidi7021]

Hallo professor, i know you can help me with this, to calculate the number of turns "N" i am confused between (L = AL*N^2) formula (AL value from datascheet of a EE-core "N97" for example) and (N = (L*I)/(B*Ae) formula (L,I,B are given and Ae from datasheet). in each formula i get an another value of "N" . thank you

[@sambenyaakov]

There is a difference between formulas. The first states the L you will get (this will be for a given gap). The second ensures that a given B will be reached at a given I

[@mohamadjneidi5761]

@@sambenyaakov thank you 👍👍

[@justinn771]

Thank you sir.

[@sambenyaakov]

Thanks.

[@Uko_]

Professor, using differential permeability and inductance is a clever way to abstract its nonlinearity. But, I want to know the analytical expression of the permeability and inductance itself. For example, Vectorial Incremental Nonconservative Consistent Hysteresis (VINCH) model, it is the latest research that describe its nonlinearity as far as I found it on the internet. And also being vectorized model, makes it better compared to fundamentally scalar of Preisach and Jiles-Atherton models. Although the conclusion section stated that it's only consider the special case of rate-independent isotropic material. vincent.francois-l.be/VINCH_model.pdf Would you like to please explain it from theory till simulation perhaps, in the future videos? Thank you very much.

[@sambenyaakov]

There are a number of ways you can study permeability: the phenomenological (B/H, Maxwell equations), the model fitting (Atherton, VINCH) and the material aspect. Each has its own place.

[@_Jkobson]

so. after watching this video i don't understand, what wasn't resolve at my answer for this riddle. " energy doesn't go anywhere and doesn't appear out of nowhere. the expressions given in the middle of the video are valid separately from each other for two different inductors that have a constant inductance over the studied current interval in them. In reality, the energy storage process can be divided into several stages( for ease of integration): 0) energy consumption in heat from the winding resistance ( including eddy currents and skin effect) and core heat for the remagnetization of dipoles 1) the current increases from zero to the inflection point of magnetic induction, energy accumulates in the dipole moments of the core as long as the dipoles are able to rotate freely in a certain direction, then different behavior is possible for different materials, two or three inflection points are possible, etc. and different slopes between them 2) after the inflection point, there is a long section of current that ends with constant magnetic induction through the core(only through it), at this point all the dipoles are aligned along magnetic lines. During this entire interval, the energy accumulation in the inductance formed only by the wire( an inductor without a core, only air) also continues. 3) then there is accumulation only in the inductivity formed by the wire up to the theoretical limit, if there is one. I have never asked myself whether there is a maximum magnetic induction for a particular volume of space On the interval 1-2, the inductance remains in the "nominal" on the interval 2-3, the inductance "decreases" according to the law depending on the core material, which can be divided into its own sub-intervals on the interval 3-infinity, the inductance is equal to the inductance of the coil winding without a core using splitting into these intervals, we can use the formula from the middle of the video separately for each interval to calculate the energy by summing the energy of each interval. As a consequence of the non-decreasing sum of the series, we have E1

[@sambenyaakov]

Hi , I do not understand the reason for your grievance. Following your first reply I responded: "Thanks. You have a good gut feeling but the explanation does not resolve the the question as asked" Then you added more explanations showing the equation L(i)(I)di/dt but without explaining which L(i) is it, derivative or total. Also "energy accumulates in the dipole moments of the core as long as the dipoles are able to rotate freely in a certain direction" , is not exactly correct. What about a core with air gap? And what is: " because there is always a winding from the diode, which also accumulates energy". So why the complaint?