Demystifying the meaning of leakage inductance of transformers and coupled inductors

[@faissalmataich7490]

4 years later, this is absolutely spot on professor! We can't thank you enough for your efforts and your never ending willingness to share knowledge!

[@sambenyaakov]

Thanks Faissal. This video may stay relevant forever as the leakage does seem to stay for ever

[@tangy1181]

@@sambenyaakov especially designing LLC or CLLLC

[@edecaldeira2229]

I'm a 13 years experienced power electronics engineer and still learning from you. Thank you very much.

[@sambenyaakov]

Thanks for kind note

[@ivanperezs]

You actually made it seem simple. Great presentation. Thank you very much.

[@sambenyaakov]

Thanks

[@fmendoza711]

Thank you a lot professor , your videos on mutual inductor and differences between transformers are helping me a lot with understanding very old railway technology in my job , best regards from Mexico

[@sambenyaakov]

Thanks

[@sanghyeonpark7226]

Thank you for another excellent video! Really enjoying your channel.

[@sambenyaakov]

👍😊

[@asifimranemon9096]

So vivid and detailed. Hats off.

[@sambenyaakov]

Thanks

[@Electromowls]

Sir what motivates you from uploading these videos ? I am inspired by your passion. Your videos are the top class resources that are available in power electronics. Thank you sir

[@sambenyaakov]

Thanks Mouli for nice words. The Egyptians built pyramids to be remembered. I am uploading videos😊😊And more seriously, I reached an age at which one realizes that it is more rewarding to give than to receive.

[@heinrichhein2605]

Yes i have also to say that your Videos are amazing in detail and accuracy, you cant and will not find any better things online. Maybe in a book and in a good lecture but even then this is just amazing! Imaging if more where doing such amazing work!

[@ezranoam]

Great intuitive video.. I wish I could go back in time and see that before designing my first DAB converter

[@sambenyaakov]

Thanks

[@sambenyaakov]

Thanks

[@Stelios.Posantzis]

Very nice expositions of the derivation of mutual and leakage inductance. The transformed voltage ratio being equal to the turns ratio assumption is a useful shortcut as its already known from basic physics and can be found easily elsewhere. The practical illustration of a Spice model simulation, however, is an awesome addition as for many Spice beginners it's not quite obvious how to model a non-ideal (or even an ideal!) transformer.

[@sambenyaakov]

Thanks. Good points.

[@kraftrad7840]

great explanations! greetings from Germany

[@sambenyaakov]

Thanks, Merry Christmas

[@RaananL]

Great presentation professor! As always i'm inspired by your unique talent of simplifying concepts and presenting them in an intuitive way.

[@sambenyaakov]

תודה רענן. מה שלומך?

[@RaananL]

מצויין תודה. עוקב אחר מרבית ההרצאות שלך ומשתף עם המהנדסים בצוותים שלי. כולם נהנים!

[@sambenyaakov]

👍

[@tangy1181]

Great video as always! thank you!

[@sambenyaakov]

Thanks

[@cherev]

Very detailed and intuitive explanation I appreciate it and very grateful to you for all lessons.I am impressed by the way of teaching approach you have. Keep going professor maybe it's the way of build an open access-online university with your valuable know-how. Thanks a lot...

[@sambenyaakov]

Thanks. Yes, I think this is the wave of the future. This and certainly future generations will not have the patient nor the motivation to go over pages and pages pf analytical derivations which are in fact superfluous today.

[@TheTallGirl]

Great presentation as usual Wish all school and university presentation was so good explained

[@sambenyaakov]

Thanks. Just had a peek at your channel. Repairing cars? Wow

[@TheTallGirl]

@@sambenyaakov It is relaxing to kick and smash things with hammer and it will in fact repair them

[@elvismao3924]

Excellent explanations! Thank you very much!

[@sambenyaakov]

Glad it was helpful! Thanks

[@htchtc203]

Thank you professor Ben-yaakov. Presentation was very clear and informative indeed. Also, very useful for the task I am currently my hand on. If I only could ask how to add or treat the magnetization inductance here. Obviously it is not the same as the mutual inductance but it appears to manifest itself quite the same way as the mutual inductance.

[@sambenyaakov]

Thanks. There are many related videos in my KZbin channel. e.g. kzbin.info/www/bejne/p33SiYKip9aNebc

[@htchtc203]

@@sambenyaakov So, after all, the mutual inductance and magnetization inductans are one and the same manifestation of reluctance of the core material. Lo and behold, I said to myself :D

[@ny6u]

Beautiful presentation 👏🏻👏🏻👏🏻

[@sambenyaakov]

👍😊

[@cuchulainkailen]

My bud, Sam. The mythical magic demystifier.

[@sambenyaakov]

👍🤔

[@robson6285]

Thís is a lesson i needed. We learned (often as kids) to use transistors and when opamps came it got really understandable. But transformers i only used when bought, with the input and output voltages printed on the case, because there is indeed some mystique when missing the deeper insights of the why of their unintuitive precise workings. My understanding of how&why transformers maintain that voltage/turnsratio i only became from your video's and answers, but thís lesson added most needed thus valueable insights. (But intuitive, i mean using a self designd&winded one, that will take me long time because for so long they felt a little "unelectronic" to me)

[@sambenyaakov]

Thanks Rob.

[@frunsebischkek1050]

Thank you very much for such a short and understandable summary. How would you model a magnetic amplifier? Or just a transformer with strong non-linear saturation, maybe asymmetrical around the working point of the magnetizing curve? Or if the hysteresis effects of most magnetic substances would have to be taken into account? For these two cases, is M1 = M2 = M too?

[@sambenyaakov]

See www.ee.bgu.ac.il/~pel/pdf-files/jour112.pdf

[@HamzaAhmad-m9q]

Thanks for the excellent intuitive explanation, Professor. Just one question. While choosing a resonant capacitor for LLC, which value of inductance should I consider for series resonance. In other words, will the capacitor resonate with La, or Lkg1 or Lkg2?

[@sambenyaakov]

The reflected leakage inductance to the primary.

[@thomassorensen7907]

Hi In 18:06 how do we come from the circuit OUT2 to OUT3? I just dont get how we get the component values in OUT3. To me it seems that Lkg2 is reflected to the primary side. But just dont get why k is used and not n.

[@sambenyaakov]

The generic SPICE does not include a transformer only coupled inductors defined by L1, L2 and K (n= sqrt(L1/L2). You emulate an ideal transformer by making L1 and L2 large.

[@ripamontiangelo6097]

Good morning Professor, congratulazions! very very interesting lecture, You are getting me back 50 years! Question... You know Eurobalise Railway train comunicaton? Lot of these concepts are used.... I'm trying to understand its fuctioning using Your tutorials... Angelo from Italy

[@sambenyaakov]

Thanks Angelo

[@arthurm7846]

Hi professor Sam, in power systems when we are calculating short-circuit current at the secondary of the transformer it is common to model it as a inductor which inductance is a percentage of the Zbase of the system (i.e. 1.0 MVA 4.16 kV 5% Impedance => L = 2.3 mH ) . Where this inductance comes from? Is it correct to state it all comes from the leakage inductance? Thanks again for all your videos, all of them are fascinating and helpful. 😄

[@sambenyaakov]

I am not familiar with this. I guess this is derived from leakage.

[@Life64644]

Dear sam, Thank you for the great help. In one of the final models, you have divided the LT2 by (k*k) to creat an ideal transformer. Could you please give me a clue about this derivation. I don't know how to drive that.

[@sambenyaakov]

Please help me out by pointing to the slide number or minute in the video you are referring to.

[@Life64644]

@@sambenyaakov the slide number is 22, time is 20:05. On the left, upper model, you have divided LT2 by (k*k). Please let me know why is that and how it resembles an ideal transformer. Thank a lot

[@sambenyaakov]

k (defined in PARAM) is the coupling coefficient between the original coupled inductors. You can check the validity of the division by k^2 by working out the inductance seen at the secondary with the primary open. Should be L22.

[@soderdaen]

I think at 13:55 on the top left image the inductor on the right ( K*L22 ) should be ( 1 - k ) * L22 or did I get something wrong? Plus I dont't understand where K*L22 went at 12:37 from the left image to the right.

[@sambenyaakov]

At 13:55 I say in recorded video that this is a mistake and it should be (1-k)L22, you probably did not listen😊 In all other points: you seem to be confused between inductors and reflected value of inductors. For example in 8:55 there is no L2*K .Rather, L1*k is seen from the secondary with a value L2*K . That is with a transformer you DO NOT put two inductors.

[@zihangao7385]

Totally agree that different models should have the same performance, or otherwise they cannot be stated as correct models and would lead to catastrophic problems for design and analysis. But I guess that the meaning of different models is that with some of them you might have different resolution and perhaps easier loops to analyze, e.g. for DAB ZVS current estimation using pi-type transformer model, and for CLLLC gain curve using T-type model, right? Since you mentioned the leakage inductances seperated for both sides, are there any proper ways do you think to theoratically estimate or experimentally measure correctly?

[@sambenyaakov]

Yes, different models are different visualization and can make perhaps easier the analysis (by hand) but you will end up with exactly mathematical expressions.

[@sujoybha]

While measuring leakage inductor of a transformer, I shorted the secondary and tertiary windings but the reading went from 10mH to 7mH. Is 7mH the leakage inductance of the transformer or am I measuring wrong. Transformer - Epcos EE13/6/6.15 core, Primary 8uH gapped core 256 turns, secondary 9 turns, tertiary 24 turns. When I did this for a larger transformer with ungapped core, I got about 5% leakage inductance but in gapped cores, I feel that I have to measure leakage inductance in some other way.

[@sambenyaakov]

Primary 8uH gapped ? mH?

[@sujoybha]

@@sambenyaakov 10mH gapped. Sorry not 8uH.

[@JacquesMartini]

@@sujoybha The question is also, at which frequency are you measuring? Going too high will case the parasitic capacitances take over and your transformer becomes resonant, fooling many measurement devices. Try the lowest frequency that makes sense, 1-10kHz is very common, even if the frequency of application is much higher. Only very low inductance transformers in the micro henry regions are measured with 100kHz and above. If you want to be sure and see more, get a low end vector network analyzer. They measure over a very wide span of frequencies and show you all nasty resonances and other parasitic effects. They are available at reasonable prices as small bench top USB devices. Something like this. www.digikey.de/de/products/detail/trenz-electronic-gmbh/29069/9460077?RF%20Evaluation%20and%20Development%20Kits&Shopping_Product_RF%2FIF%20and%20RFID&productid=9460077&gclid=CjwKCAiAsNKQBhAPEiwAB-I5zSTMmW0dWNbqu4tWWGwLPSeyI8bDnKKtzDmLZSWZi6WteYdxaYRNChoCcWwQAvD_BwE www.sdr-kits.net/DG8SAQ-Vector-Network-Analyzer-3-Series?gclid=CjwKCAiAsNKQBhAPEiwAB-I5zXDY8vuXURT-gx1d0v1QT3CHqHqCY66yvBMGOAGOcwBKZ5LEDEmx4RoCaDoQAvD_BwE The E13/6/6.15 has no gap, you have to add it using a spacer. If you have 10mH with 256turns, this yields an AL of ~150nH/N^2. This is much lower than the ungapped 900-1300nH/N^2. And sure, a gapped transformer will have more stray inductance than an ungapped. How much, depends on the size of the gap and the position of the windungs (both windings on center leg inside one chamber, two chamers or even different legs of the core).

[@j1112-q1w]

If I want to use primary leakage inductance Lp for output LC filter, does that mean I should use reflected value of Lp for 1/(2pi * sqrt(Lp Cout) )

[@sambenyaakov]

Not sure I am following. Where is the turns ratio? What kind of filter, no rectification?

[@j1112-q1w]

@@sambenyaakov a pwm filter for inverter. Np/Ns is 5.

[@sambenyaakov]

Using leakage inductance for filtering may not be a good idea. For one thing you get a rather small inductance so you will need very large capacitance.

[@j1112-q1w]

It's about 5mH primary leakage ( by shorting secondary). But I'm a bit confused about the value of L in the expression 1/(2pi sqrt(LC)). If I use 5mH, a C of 20uF would give about 600hz -3dB.

[@j1112-q1w]

Professor I think I got it now. The value for L is ( Lp/N^2 + Ls). Ls is small (uH) so I ignore. So all leakage reflected to secondary is 5mH/25. If I use 40uH, the value for 1/2pi sqrt(LC) is 1.7kHz. Thanks for the good explanation of equivalent circuit reflected to secondary side.

[@pbaemedan]

Professor, in your parameters definition you have LT1 = (L11 x 1K), does 1K mean 1000? Thank you for your time and effort. This is a great practical explanation.

[@sambenyaakov]

Hi, thanks. Please point to the minute in the video you are referring to.

[@pbaemedan]

@@sambenyaakov the time mark is 19:14, it's the definition of parameters in the pspice models listed on slide 22. I'm assuming all of the K's are the coupling coefficient, I don't understand what 1K means.

[@sambenyaakov]

@@pbaemedan Thanks for pointer. Sorry for the confusion. K is indeed the coupling coefficient but...when you write in LTspice 1k (not 1*k) this is interpreted as 1000.

[@pbaemedan]

@@sambenyaakov thank you for the information. Your series on coupled inductors provides large amounts of information and understanding. Again, thank you.

[@ziyangli5109]

Thanks a lot professor. It helps me to better understanding the power transformer. I have a question regrading to the slides 22, the first simulation schematic (on the left-top side). Could you please explain why La = L11*k^2 and the corresponding ratio is k*n1/n2? I don't understand how this is derived. Wish you all the best. Kind regards.

[@sambenyaakov]

La=L11*k^2? left top side ? on slide 22?

[@ziyangli5109]

@@sambenyaakov Thanks for your kind reply, professor. I have figured the derivation. WIsh you all the best in work and life.😀

[@tanvimahajan1019]

Can you help me with this I2= -jI2 , why was this done ?

[@sambenyaakov]

Please indicate the minute in video you are referring to.

[@tanvimahajan1019]

@@sambenyaakov 6:18

[@sambenyaakov]

@@tanvimahajan1019 This is an independent source used to carry out the analysis. This definition of the test source simplifies the math.

[@RaedMohsen]

@@sambenyaakov Still, this doesn't explain to me where this equation (I2=-jI2) comes from. Is there a typo here ? I understand that to get the output instantaneous power you would multiply v2 by i2.

[@sambenyaakov]

@@RaedMohsen Long time since we communicated. I arbitrarily define a source jI2 (90 degrees with respect to I1) and the minus is due to the direction (positive is into the terminal)

[@mustafeezulhassan8604]

Hello Sam Ben-Yaakov, Thanks for very informative video. Can you please share some thesis or textbook or paper explaining these concepts in more detail? Thanks in anticipation

[@sambenyaakov]

This way of explanation is original. You can find relevant videos in my KZbin channel. Go to You tube and search "Ben Yaakov + a relevant keyword, such as leakage, transformer, coupled inductors..."

[@mehtabhussain4961]

Thanks Sam ,🙏

[@sambenyaakov]

Thanks

[@seandafny]

Good talk

[@sambenyaakov]

Thanks

[@TabletopWargamer]

kzbin.info/www/bejne/nmrCk62vaJirgLc Next video in the series

[@sambenyaakov]

👍🙏

[@poll1986]

Dear professor, many many thanks for such a great video. Do you use any software simulation for your magnetics design (arranging windings, selecting core )? Recently I saw a video from SIMPLIS kzbin.info/www/bejne/jHWthmyjrLVrrac. They have acquired Gecko Circuits Magnetics design software and embed it into their spice simulation which seems to me also very interesting.

[@sambenyaakov]

Thanks Huseyin. No I am not using magnetic design packages. Have not found one that really saves me time. I will look into the software you indicated. Thanks for pointer. Sam

[@hoch5707]

Sir, I replied to your gmail. Thank you.

[@sambenyaakov]

Did not see it. [e-mail] or try [e-mail]

[@hoch5707]

My email is [e-mail], and I think you received it. I wrote to gmail account. Thank you sir.

[@JacquesMartini]

Hehe, the schematics expose you as israeli, the input is on the right, the output on the left 😂 (your native language form your way of thinking)

[@sambenyaakov]

Hi Falk, I am afraid that the joke is on you. 1. The majority of people on the plant that write from right to left are Arabs, so how come you came to the conclusion that I am an Israeli? 2, You really do not need to play Sherlock Holmes, Look up my profile in LinkedIn or just google "sam ben-yaakov" 3.In the majority of my published work, papers, tutorials, videos, etc. I am usually drawing the inputs on the left. Which shows, again, that statistics that is based on one case is nonsense. 4. Drawing the input on the right or left has nothing to do with the language that a person speaks but on his educational path - what he saw when he was a student. 6. You wrote :"the input is on the right, the output on the left 😂 (your native language form your way of thinking)", so I understand that you think that I am a right thinker while you are probably a wrong thinker😀.