Leakage inductance A brief study of the key feature of a transformer 3 key aspects of the leakage inductance 1. Introduction 2. Leakage inductance in transformers. 3. The influence of the transformation ratio and the winding strategy on the leakage inductance. 4. Leakage inductance calculation models comparison. 5. How do we work 6. About us & APEC 2020 www.spfrenetic.com Introduction In the magnetic elements design process, particular attention must be paid to the core and winding geometry, and the wire distribution in the available space for the winding. This affects the performance of the transformer parameters and the whole electronic system. One of the parameters that is affected by geometry is the leakage inductance. This is an inductive component caused by the imperfect coupling between the transformer windings. It causes an important effect in switchedmode power supplies, for example, the appearance of voltage peaks in the MOSFETs or electromagnetic interferences (EMI), which increases the switching losses and reduces the efficiency of the converter. The calculation of this parameter in the magnetic element design procedure is paramount to be able to perform simulations of the electronic system in conditions which are as close to reality as possible, and to avoid having to invest more effort and money in the case that the system does not behave as expected after it has been built. The Frenetic team presents three APP notes in this ebook, in which models for calculating the leakage inductance and experimental measurements are shown to see how this parameter fluctuates depending on the transformer construction. www.spfrenetic.com LEAKAGE INDUCTANCE IN TRANSFORMERS Designing a magnetic component with a specific leakage inductance can be challenging and difficult to predict as the theoretical results commonly differ form reality. T he objective of this App Note is to show how to control the leakage inductance, and check the theoretical knowledge with experimental results. LEAKAGE INDUCTANCE : HOW TO REDUCE IT: • Decreasing the number of turns and layers Leakage inductance is produced by the imperfect magnetic • Reducing the insulator layer thickness coupling between the transformer windings. The magnetic • flux generated in the primary winding is never transferred Using interleaving arrangement Less • Lowering the mean turn length 100% to the secondary winding. • • Increasing the core window width Decreasing the core window height losses This leakage inductance depends basically on:  The winding geometry From more than 3 W The reduction of the leakage inductance is important in order to obtain better  The core geometry to2.2 W power eﬃciency, but it goes as a expense of other parameters. For example,  Number of turns reducing the number of turns, will also produce higher core losses. Due to the fact that the winding geometry and arrangement On the other hand, it is important to have in mind the relationship between leakage have high influence on the leakage inductance, it gets really inductance and parasitic capacitance. Lower leakage inductances will lead in higher complicated to calculate it analytically and get reliable results. capacitances: C1= 1/w2lk1 However, if you know the eﬀect these parameters have on In cases where higher leakage inductance is required, a magnetic shunt can be the leakage, you will be able to control it. inserted between layers. Other possibility would be the use of fractional turns. EXPERIMENTAL RESULTS : In this section, 4 experiments are carried out with the purpose of showing the eﬀect of the diﬀerent options mentioned above, to reduce the leakage inductance.  Experiment 1: PQ26/25 tranformer with a turnS ratio of 2:1.  Experiment 2: PQ26/25 tranformer with a turns ratio of 2:1 but the number of turns is half than in the experiment 1.  Experiment 3: PQ26/25 transformer with a turns ratio of 2:1 and PSSP arrangement.  Experiment 4: PQ26/20 transformer with a turns ratio of 2:1 and a PSSP arrangement. Results for experiments 1 and 2 show how the reduction of the number of turns will lead in a decrease of the leakage inductance. Comparing experiments 1 and 3 it can be appreciated how the leakage changes when the primary and secondary wires are alternated. Experiments 3 and 4 show the eﬀect of the change in the height of the window; higher core windows will have higher leakages inductances. CONCLUSIONS Knowing the leakage inductance on advance can give you an idea of the total eﬃciency of the magnetic component before manufacture it. Theoretical calculations can give you an approach of the leakage inductance of a planar transformer, but when it is not planar, calculations become much harder and less accurate. This is the reason why it is thought planar transformers have lower leakage inductance, but the fact is that it is because the interleaving arrangement in this type of transformers is easier to be carried out. Not only is important to predict it, but also to be able to control it. The experiment results show how the tips to reduce the leakage inductance are easy and eﬀective. LEAKAGE INDUCTANCE THE INFLUENCE OF THE TRANSFORMATION RATIO AND THE WINDING STRATEGY ON THE LEAKAGE INDUCTANCE T he non linked f lux be t ween pr imar y and sec on dar y win d in g s of tra n sf or mer s lea d to what is co mmo n ly kno wn as t he leaka ge in ducta nce . Its ma gn it ude pla ys a key r ole in moder n switche d mode po wer sup p lie s. Whe th er it nee d s to be min imized o r max imized, the use of comp lex pred ict ion mo de ls, tha t are many t ime s far fr o m realit y, is req uired. T he objective of t h is paper is t o pro vide a genera l idea of t he leakage ind uctance ran ge va lue s f ou nd in different topologie s and turns ratios. CASES OF STUDY: As explained in previous application notes, two of the key parameters affecting the leakage inductance are the transformer turns ratio and winding arrangement. With the aim of having a reference when creating a design, a brief summary of the leakage inductance measured will be provided for different transformer designs measured at Frenetic’s Laboratory. Values of leakage inductance will be measured for Configuration 1 Configuration 2 Configuration 3 Configuration 4 different converters with four different winding configurations, from highpot winding arrangement (Conf. 1) to a two layers interleaving arrangement (Conf. 4) passing through simple PS configuration (Conf. 2) and simple interleaving (Conf. 3). Figure 1: Winding arrangement configurations used for for the measurements. EXPERIMENTAL RESULTS: Table 1 shows the converters used for this experiment for each topology with different configurations of windings. Results demonstrate how the smaller the difference between primary and secondary turns, and the better the interleaving arrangement, the smaller the leakage inductance achieved. RM8/I CASE 1: Figure 2 shows how the leakage inductance is reduced 50% from Conf. 1 to Conf. 3 in a RM8/I. The more is the winding interleaved, the lower the leakage. Minimization of the leakage inductance in flyback converters is generally a must. Otherwise high voltage spikes at the switching node would be present with the increased stress that this involves in the semiconductors. Interleaved planar transformer could be used in this case but taking special care of the parasitic capacitance that will create a path for common mode noise. PQ40/40 Figure 2: Leakage inductance in two RM8/I with a turns ratio of 5:1. CASE 2: In Figure 3, it has been used a PQ40/40 with turns ratio of 1:1. The Llk is reduced by a factorof 4. The decrease on the leakage inductance appears as a consequence of the division of the winding on higher amount of layers with interleaving arrangement, from PS to PSPS arrangement. Figure 3: Leakage inductance in two PQ40/40 with a turns ratio of 1:1. PQ40/40 CASE 3: Case 3 uses the same core shape than in case 2 but with 8 times higher turns ratio (8:1). Winding Conf. 1 and 2 does not seem very different, however, as we can see in the results, the Llk is reduced 2.6 times, form 5.2 to 2 uH. Comparing to case 2, it seems to have lower Llk change, but talking in absolute values it has higher impact, Figure 4: Leakage inductance in two PQ40/40 with a turns ratio of 8:1. as in Case 2 the leakage is reduce 0.6 uH, and in Case 3 is of 3.2 uH. CONCLUSIONS The design of a magnetic component is a very complex task to do it manually, which could produce a number of iterations due to problems find it during the test stage. Noisy signals are common during first testing stages, therefore the designs should Company consider it. Since the technology used by Frenetic is automatized for calculating partner due the losses of: to the harmonics, the users of Frenetic can verify the maximum THD that their magnetics could manage before rising maximum temperature. LEAKAGE INDUCTANCE MODELS LEAKAGE INDUCTANCE CALCULATION MODELS COMPARISON One of the keys to a good engineering design, indistinctly of the technical branch, is a high accuracy inter in predicting the result of such design. When the design is a transformer, one of the most interesting parameters, due to its positive or negative influence in the power topology, including the risk of several iterations, is the leakage inductance. The objective of this application note is to present two models for calculating the leakage inductance, highlighting when each of them can be used, and to compare them with experimental measurements done in our laboratory. Classical model StephensBoyajian (SB) model Conventional transformer configuration Interleaved transformer This model considers the magnetomotive force distribution and configuration requires detailed knowledge about the winding geometry for calculating the leakage inductance radial and axial components. a = winding height (cm) Axial component: b = winding width (cm) c = insulation thickness (cm) Radialcomponent: Model works for: Model does not work for: Model works for: Model does not work for: Simple winding arrangements.  Highfrequency effects.  Complex winding arrangements.  Layers with different height. (MMF) distributions.  Nonuniform MMF distributions.  Highfrequency effects  Nonuniform magnetomotive force  Layers with different height. L. M. R. Oliveira and A. J. M. Cardoso, "Leakage Inductances Calculation for Power Transformers Interturn Fault Studies," in IEEE Transactions on Power Delivery, vol. As found in the book “Transformer and inductor design handbook”, written by Colonel Wm. T. McLyman. 30, no. 3, pp. 12131220, June 2015. Results: A total of 5 measurements were done to verify the Classical and SB models, being the winding distribution the variable parameter. The results of the study are indicated in the table below and, analyzing the data, it can be seen that the Classical model has a 110% average error and the SB model a 51%, and in all the cases the error using SB is lower, so it can be concluded that this method gives better results due to its higher complexity regarding to the Classical one. At a more detailed level, and focusing on the SB model, the results using the conventional winding structure (CASES A, B and C) are not correlated at all, but it is shown a high error when there are a high number of layers, all of them far from the core. When an interleaved structure is used, thanks to consider the MMF distribution, the error is not too high compared with the Classical model. MODEL CASE A CASE B CASE C CASE D CASE E Transformer construction: WINDING Core shape: PQ40/40 DISTRIBUTION Core material: Ferroxcube 3F36 Number turns: 24 / 24 CLASSICAL METHOD 1.64 µH 6.87 µH 15.69 µH 1.71 µH 2.61 µH Wire: Round 12AWG/12AWG (+62.4%) (+34.7%) (+180.2%) (+74.5%) (+196.6%) (relative error) Gap: 0 mm SB METHOD 1.49 µH 5.65 µH 11.35 µH 1.44 µH 1.29 µH In the image at right, it can be seen the (relative error) (+47.5%) (+10.8%) (+102.7%) (+46.9%) (+46.6%) transformer used for the CASE C measurement. MEASUREMENTS 1.01 µH 5.1 µH 5.6 µH 980 nH 880 nH CONCLUSIONS A lot of models can be found in literature for trying to calculate the leakage inductance accurately, but in all of them assumptions are done, so differences between theoretical results and real measurements are almost always found, even in those in which a detailed study of the winding geometry is done. With all this, if all the parametersCompany of a transformer partner of: are wanted to be known before manufacturing a prototype for checking its performance in the converter in a simulation software, for example, other methods based on finite element analysis or artificial intelligence are needed. ARE YOU ON THE ROAD TO DESIGNING A COMPETITIVE PRODUCT ? Your products deserve the best magnetics. That’s why we would like to introduce you to Frenetic®. What can Frenetic® do for you? ACCELERATE YOUR PROJECT Frenetic’s AIbased technology has been designed to create the optimum design according to your specifications, after a free specs validation. Tell our team which preferences you have for your magnetics and our team will tell Frenetic ®. She can shape the magnetics according to your preferences! She knows how important the cost optimization and timing is, thus guaranteeing the best cost and time tradeoff to our partners www.spfrenetic.com The allinone magnetics solution Getting F renetic ®by your side includes 1. S tudy of the specifications . 2. Trans former design using Frenetic AI. 3. C omplete des ign report. 4. X sample(s ) of the designed trans former. 5. Trans former tests and characterizations . 6. Meas urement report. 7. Priority support from Frenetic’s magnetic experts. What does that mean for you Our engineering team as signed to your project is at your dispos al until you get the magnetic agreed to your specifications . Pleas e share with us at any time any ques tions or comments you may have about your project, we are here for you! We want you to forget about the magnetics , spend your time on the things that really matter to your project www.spfrenetic.com Tell us about your project Visit our website and tell us about your project. Our team will review your specifications or comments and get back to you to discuss what can Frenetic do for your project. Frenetic will also allow you to choose your own preferences for your magnetics, if there is a needed size or you want to improve efficiency, just let us know, Frenetic will take it into account and get the optimum result in days, job done. Alos, we are talking in APEC 2020 so make sure you write at miguel.delafuente@spfrenetic.com for any further info. about our conferences and available slots to meet us! Website: www.spfrenetic.com Our application notes archive: www.spfrenetic.com/applicationnote For any further info.: miguel.delafuente@spfrenetic.com Follow us on www.spfrenetic.com
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