Approach of copper losses determination in planar windings
2016; Institution of Engineering and Technology; Volume: 52; Issue: 12 Linguagem: Inglês
10.1049/el.2016.0919
ISSN1350-911X
AutoresA. Abderahim, Ahmat Taha Mahamat, J. P. Chatelon, David Piétroy, S. Capraro, Jean Jacques Rousseau,
Tópico(s)Electronic Packaging and Soldering Technologies
ResumoElectronics LettersVolume 52, Issue 12 p. 1050-1052 Power electronics, energy conversion and sustainabilityFree Access Approach of copper losses determination in planar windings A. Abderahim, A. Abderahim LabHC, Université Jean Monnet Saint-Etienne, 18 Rue Professeur Benoît Lauras 42000, Saint-Etienne, FranceSearch for more papers by this authorA.T. Mahamat, A.T. Mahamat LabHC, Université Jean Monnet Saint-Etienne, 18 Rue Professeur Benoît Lauras 42000, Saint-Etienne, FranceSearch for more papers by this authorJ.P. Chatelon, J.P. Chatelon LabHC, Université Jean Monnet Saint-Etienne, 18 Rue Professeur Benoît Lauras 42000, Saint-Etienne, FranceSearch for more papers by this authorD. Pietroy, D. Pietroy LabHC, Université Jean Monnet Saint-Etienne, 18 Rue Professeur Benoît Lauras 42000, Saint-Etienne, FranceSearch for more papers by this authorS. Capraro, S. Capraro LabHC, Université Jean Monnet Saint-Etienne, 18 Rue Professeur Benoît Lauras 42000, Saint-Etienne, FranceSearch for more papers by this authorJ.J. Rousseau, Corresponding Author J.J. Rousseau rousseau@univ-st-etienne.fr LabHC, Université Jean Monnet Saint-Etienne, 18 Rue Professeur Benoît Lauras 42000, Saint-Etienne, FranceSearch for more papers by this author A. Abderahim, A. Abderahim LabHC, Université Jean Monnet Saint-Etienne, 18 Rue Professeur Benoît Lauras 42000, Saint-Etienne, FranceSearch for more papers by this authorA.T. Mahamat, A.T. Mahamat LabHC, Université Jean Monnet Saint-Etienne, 18 Rue Professeur Benoît Lauras 42000, Saint-Etienne, FranceSearch for more papers by this authorJ.P. Chatelon, J.P. Chatelon LabHC, Université Jean Monnet Saint-Etienne, 18 Rue Professeur Benoît Lauras 42000, Saint-Etienne, FranceSearch for more papers by this authorD. Pietroy, D. Pietroy LabHC, Université Jean Monnet Saint-Etienne, 18 Rue Professeur Benoît Lauras 42000, Saint-Etienne, FranceSearch for more papers by this authorS. Capraro, S. Capraro LabHC, Université Jean Monnet Saint-Etienne, 18 Rue Professeur Benoît Lauras 42000, Saint-Etienne, FranceSearch for more papers by this authorJ.J. Rousseau, Corresponding Author J.J. Rousseau rousseau@univ-st-etienne.fr LabHC, Université Jean Monnet Saint-Etienne, 18 Rue Professeur Benoît Lauras 42000, Saint-Etienne, FranceSearch for more papers by this author First published: 01 June 2016 https://doi.org/10.1049/el.2016.0919Citations: 7AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract A new approach is presented in order to determine copper losses from measurements or simulations of planar inductors. Copper losses are modelled with a series resistance r(f) that depends on the frequency. Measured or simulated admittances of the inductors are used to determine the model parameters of the inductors. The resistance r(f) is determined in three frequency domains: (i) at very low frequencies (or DC); (ii) at low frequencies (capacitive couplings are negligible); (iii) at resonant frequencies, i.e. high frequencies. The presented approach is different as those encountered in literature and allows the series resistance from measured or simulated Sij parameters to be determined. Introduction Embedded equipments are more and more numerous and require small distributed power supplies to supply specific circuits. High efficiencies are required for such power supplies. In order to reach high efficiencies, both losses in active and passive components have to be reduced. This Letter deals with the determination of copper losses against frequency in planar magnetic components. Copper losses are modelled by using a resistance r(f) that depends on the frequency. The resistance r(f) takes into account both skin and proximity effects. In the past, numerous works were devoted to the determination, to the calculation of copper losses for wound windings using round wires, Litz wires or foils [1-3]. Papers related to planar inductors are not so many. In order to take into account both skin and proximity effects, some authors have shown how to determine from simulation [4] or from measurement [5] copper losses by using a series resistor. Harburg et al. [6] have modelled AC losses and compared them with 3D simulations. A new approach to calculate copper losses by using a 2D distribution of the magnetic field was also developed [7]. Our specific approach is different from the previously mentioned methods and allows the series resistance from measured or simulated Sij parameters to be determined. In this Letter, coreless inductors are considered as shown in Fig. 1, but the proposed method can be used for inductors with magnetic layers. Fig 1Open in figure viewerPowerPoint Coreless inductor Copper losses are usually taken into account by a serial resistor which depends on the frequency. Fig. 2 shows a coreless inductor model, the copper spiral has been deposited on a lossless substrate: L is the inductance, C1 and C2 represent the capacitive coupling between the spiral and the ground plane and C12 takes into account the capacitive coupling between turns. The only resistance r(f) is dependent on frequency in order to model both skin and proximity effects. Fig 2Open in figure viewerPowerPoint Coreless inductor model Determination of the model parameters Four constant elements (L, C1, C2 and C12) and one frequency-dependent parameter have to be determined. L, C12, C1 and C2 are not frequency dependent (L is constant because no magnetic material is used for this inductor; capacitances are also constant because the substrate permittivity is constant on the entire frequency range), only r(f) depends on frequency. By using four-terminal network y-parameters which can be obtained either by simulation (3D finite-element analysis software such as HFSS) or by measurement (impedance meter or vector network analysers), the model parameters L, C1, C2 and C12 can be determined (1) (2) (3)Constant parameters are determined as shown in Fig. 3: Fig 3Open in figure viewerPowerPoint Y12 admittance curve Fig 4Open in figure viewerPowerPoint Y12 equivalent circuit model Fig 5Open in figure viewerPowerPoint How to determine r value at resonant frequency? In the linear portion of the curve that represents the evolution of the y12-parameter against frequency, one can state that y12 is purely inductive, then (4)and (5)The resonance frequencies of Y12, Y11 and Y22 admittances allow the capacitances C12, C1 and C2, respectively, to be calculated. The frequency resonance of an LC network is related to L and C values (6)In these conditions, capacitances are expressed as below (7) (8) (9) are parallel resonance frequencies of Y12, Y11 and Y22. The resistance r(f) is frequency dependent and has to be determined in three frequency domains: at very low frequencies (or DC), at low frequencies (capacitive couplings are negligible), at resonant frequencies, i.e. high frequencies. At very low frequencies (or DC) The very low frequency resistance can be either calculated or measured. Fig 6Open in figure viewerPowerPoint Series resistance r(f) against frequency Fig 7Open in figure viewerPowerPoint Comparison between extracted resistances from simulation and measurements for inductor 5 turns – 400 µm ribbon width – 200 µm space width Fig 8Open in figure viewerPowerPoint Comparison between extracted resistances from simulation and measurements for inductor 5 turns – 400 µm ribbon width – 100 µm space width If the 3D finite-element analysis software is not able to give an accurate value at low frequencies, the DC resistance can be calculated using the following equation: (10)LCR meter or impedance meter are suitable equipment to measure a low frequency resistance by using a four-point probes method. At low frequencies Fig. 4 shows the equivalent circuit model for Y12 parameter. At low frequencies, capacitive couplings are negligible. From (2), the real part of this expression is equal to (11)The physical solution of this single-variable quadratic equation (r is the variable) is given by (12)This approach cannot be used for very low frequencies because measurements with a vector network analyser (VNA) and simulation with HFSS are impossible or not accurate. At resonant frequencies, i.e. high frequencies At high frequencies no parameters can be neglected. In these conditions, it is very difficult to extract the r value except at the resonant frequency of each Y-parameter. Indeed at the resonant frequency, the magnitude of the Y-parameter curve only depends on r value as shown in Fig. 5. By using a curve fitting procedure, the r value at the resonant frequency can be determined. By using the presented approach, the evolution of the resistance against frequency was determined for a coreless inductor which exhibits the following characteristics: number of turns: 5 – square spiral – copper thickness: 5 µm – ribbon width: 400 µm – space width: 50 µm named 5_400_50. Results are shown in Fig. 6. Results Comparisons between extracted resistances from either simulation or measurements are shown in Figs. 7 and 8. The dashed curves show the ratio r(f)/rDC determined from measurements while the solid curves show r(f)/rDC determined from simulation (HFSS). There is a good agreement between extracted resistances from simulation and measurements. Conclusion A new approach to determine copper losses from measurements or simulations of planar inductors has been presented. Copper losses are taken into account by means of a series resistance which depends on frequency. Simulation and measurements have been carried out. There is a good agreement between the results. 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