Analytical Optimization of Solid–Round-Wire Windings

In this paper, an analytical optimization of solid-round-wire windings conducting sinusoidal current is performed. New closed-form analytical equations are derived for the normalized solid-round-wire diameter to achieve minimum ac winding losses for sinusoidal current. Approximations of Dowell's equation are used to derive expressions for normalized diameter at the local minimum of winding ac resistance and normalized critical diameter. An equation for the winding ac resistance at the local minimum is derived. Additionally, equations for the normalized diameter at the local maximum of ac resistance and the normalized boundary diameter between low- and medium-frequency ranges are given. The formulas enable inductor and transformer designers to minimize winding loss without utilizing finite-element method analysis. Experimental verification of the presented theory is given.

[1]  Rafal Wrobel,et al.  Contribution of End-Winding Proximity Losses to Temperature Variation in Electromagnetic Devices , 2012, IEEE Transactions on Industrial Electronics.

[2]  Marian K. Kazimierczuk,et al.  Pulse-Width Modulated DC-DC Power Converters , 2008 .

[3]  Phoivos D. Ziogas,et al.  A novel approach for minimizing high-frequency transformer copper losses , 1988 .

[4]  D. Schroder,et al.  A contribution to the design optimization of resonant inductors for high power resonant DC-DC converters , 1992, Conference Record of the 1992 IEEE Industry Applications Society Annual Meeting.

[5]  Rafal Wrobel,et al.  Performance Analysis and Thermal Modeling of a High-Energy-Density Prebiased Inductor , 2010, IEEE Transactions on Industrial Electronics.

[6]  A.M. Pernia,et al.  1D/2D transformer electric model for simulation in power converters , 1995, Proceedings of PESC '95 - Power Electronics Specialist Conference.

[7]  F.C. Lee,et al.  Computer-aided design for high-frequency power transformers , 1990, Fifth Annual Proceedings on Applied Power Electronics Conference and Exposition.

[8]  William Gerard Hurley,et al.  Optimized transformer design: inclusive of high-frequency effects , 1998 .

[9]  P. L. Dowell,et al.  Effects of eddy currents in transformer windings , 1966 .

[10]  M. Kazimierczuk,et al.  Model of laminated iron-core inductors for high frequencies , 2004, IEEE Transactions on Magnetics.

[11]  Marian K. Kazimierczuk,et al.  High-Frequency Magnetic Components , 2009 .

[12]  Marian K. Kazimierczuk,et al.  High-frequency small-signal model of ferrite core inductors , 1999 .

[13]  M. Kazimierczuk,et al.  Resonant Power Converters , 1995 .

[14]  Marian K. Kazimierczuk,et al.  Maximum drain efficiency class F3 RF power amplifier , 2011, 2011 IEEE International Symposium of Circuits and Systems (ISCAS).

[15]  Marian K. Kazimierczuk,et al.  Winding losses caused by harmonics in high-frequency flyback transformers for pulse-width modulated dc-dc converters in discontinuous conduction mode , 2010 .

[16]  Marian K. Kazimierczuk,et al.  Minimum copper and core losses power inductor design , 1996, IAS '96. Conference Record of the 1996 IEEE Industry Applications Conference Thirty-First IAS Annual Meeting.

[17]  Marian K. Kazimierczuk,et al.  Stray capacitances of single-layer solenoid air-core inductors , 1999 .

[18]  Hiroo Sekiya,et al.  Design of AC resonant inductors using area product method , 2009, 2009 IEEE Energy Conversion Congress and Exposition.

[19]  Marian K. Kazimierczuk,et al.  Self-capacitance of inductors , 1997 .

[20]  Marian K. Kazimierczuk,et al.  Modelling Winding Losses in High-Frequency Power inductors , 1995, J. Circuits Syst. Comput..

[21]  P. Mathys,et al.  Ohmic losses calculation in SMPS transformers: numerical study of Dowell's approach accuracy , 1998, 7th Joint MMM-Intermag Conference. Abstracts (Cat. No.98CH36275).

[22]  Marian K. Kazimierczuk,et al.  Harmonic winding losses in the transformer of a forward pulse width modulated DC-DC converter for continuous conduction mode , 2012 .

[23]  J.-P. Schauwers,et al.  A closed-form formula for 2-D ohmic losses calculation in SMPS transformer foils , 2001 .

[24]  Marian K. Kazimierczuk,et al.  Proximity‐effect winding loss in different conductors using magnetic field averaging , 2012 .

[25]  M. Albach.  Two-dimensional calculation of winding losses in transformers , 2000, 2000 IEEE 31st Annual Power Electronics Specialists Conference. Conference Proceedings (Cat. No.00CH37018).

[26]  M. Swarnalatha,et al.  A Switched-Capacitor Inverter Using Series / Parallel Conversion with Inductive Load , 2013 .

[27]  M. Kazimierczuk.  Pulse-Width Modulated DC-DC Power Converters: Kazimierczuk/Pulse-width Modulated DC-DC Power Converters , 2008 .

[28]  Rafal Wrobel,et al.  Thermal Design of High-Energy-Density Wound Components , 2011, IEEE Transactions on Industrial Electronics.

[29]  Marian K. Kazimierczuk,et al.  Foil Winding Resistance and Power Loss in Individual Layers of Inductors , 2010 .

[30]  E. Snelling.  Soft ferrites: properties and applications , 1969 .

[31]  Marian K. Kazimierczuk,et al.  Inductor winding loss owing to skin and proximity effects including harmonics in non-isolated pulse-width modulated dc-dc converters operating in continuous conduction mode , 2010 .

[32]  J. A. Ferreira.  Analytical computation of AC resistance of round and rectangular litz wire windings , 1992 .

[33]  Johann W. Kolar,et al.  Implementation of a Transformerless Common-Mode Active Filter for Offline Converter Systems , 2010, IEEE Transactions on Industrial Electronics.

[34]  J.W. Kolar,et al.  Implementation of a transformer-less common mode active filter for off-line converter systems , 2006, Twenty-First Annual IEEE Applied Power Electronics Conference and Exposition, 2006. APEC '06..

[35]  M. Kazimierczuk,et al.  Modelling iron-powder inductors at high frequencies , 1994, Proceedings of 1994 IEEE Industry Applications Society Annual Meeting.

[36]  M. Kazimierczuk,et al.  Comparison of various methods for calculating the AC resistance of inductors , 2002 .

[37]  F. Lee,et al.  Proximity effects in coils for high frequency power applications , 1992 .

[38]  Marian K. Kazimierczuk,et al.  Winding resistance of litz-wire and multi-strand inductors , 2012 .

[39]  Sidney C. Larson,et al.  Effective resistance to alternating currents of multilayer windings , 1940, Electrical Engineering.

[40]  Jan Abraham Ferreira,et al.  Improved analytical modeling of conductive losses in magnetic components , 1994 .

[41]  M. Bartoli,et al.  Modeling Litz-wire winding losses in high-frequency power inductors , 1996, PESC Record. 27th Annual IEEE Power Electronics Specialists Conference.

[42]  M. Kazimierczuk,et al.  Harmonic winding loss in buck DC-DC converter for discontinuous conduction mode , 2010 .

[43]  M. Perry,et al.  Multiple Layer Series Connected Winding Design for Minimum Losses , 1979, IEEE Transactions on Power Apparatus and Systems.

[44]  Marian P. Kazmierkowski.  Inductors and Transformers for Power Electronics , 2008 .

[45]  Marian K. Kazimierczuk,et al.  Transformer winding loss caused by skin and proximity effects including harmonics in pulse-width modulated DC¿DC flyback converters for the continuous conduction mode , 2011 .