Fringing Field Formulas and Winding Loss Due to an Air Gap

The paper describes a simple treatment for the fringing fields of an air gap in the core of a magnetic component such as an inductor or a transformer. It verifies the derived analytical formulas for the fields by using numerical (finite-element) calculations. It then applies these formulas to the calculation of high-frequency eddy-current losses for two types of winding arrangements, both of which employ thin rectangular conductors. The rectangular conductors are commonly used in flex circuit windings, printed circuit windings, and thin-film windings. The two types of winding configurations are flat and barrel wound. Each behaves in a different way as a function of the position of the conductor.

[1]  Jiankun Hu,et al.  Optimization of shapes for round-wire high-frequency gapped-inductor windings , 1998, Conference Record of 1998 IEEE Industry Applications Conference. Thirty-Third IAS Annual Meeting (Cat. No.98CH36242).

[2]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[3]  Fred C. Lee,et al.  Design of high-frequency hybrid power transformer , 1988, APEC '88 Third Annual IEEE Applied Power Electronics Conference and Exposition.

[4]  M. H. Kuo,et al.  Effects of air gaps on winding loss in high-frequency planar magnetics , 1988, PESC '88 Record., 19th Annual IEEE Power Electronics Specialists Conference.

[5]  F. C. Lee,et al.  Improved winding design for planar inductors , 1997, PESC97. Record 28th Annual IEEE Power Electronics Specialists Conference. Formerly Power Conditioning Specialists Conference 1970-71. Power Processing and Electronic Specialists Conference 1972.

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

[7]  D. A. Dunnett.  Classical Electrodynamics , 2020, Nature.

[8]  W. Roshen,et al.  Planar inductors on magnetic substrates , 1988 .

[9]  Charles R. Sullivan,et al.  Design of microfabricated inductors , 1996, PESC Record. 27th Annual IEEE Power Electronics Specialists Conference.

[10]  Deepak Divan,et al.  Optimal air-gap design in high-frequency foil windings , 1998 .

[11]  W. Joines,et al.  Air-gap reluctance and inductance calculations for magnetic circuits using a Schwarz-Christoffel transformation , 1995, Proceedings of PESC '95 - Power Electronics Specialist Conference.

[12]  Charles R. Sullivan,et al.  AC resistance of planar power inductors and the quasidistributed gap technique , 2001 .

[13]  Devendra K. Misra,et al.  Electromagnetic Fields and Waves , 2004 .

[14]  Jose A. Cobos,et al.  New modeling strategy for the fringing energy in magnetic components with air gap , 2002, APEC. Seventeenth Annual IEEE Applied Power Electronics Conference and Exposition (Cat. No.02CH37335).

[15]  H. Grotstollen,et al.  Improved analytical modeling of conductive losses in gapped high-frequency inductors , 1998, Conference Record of 1998 IEEE Industry Applications Conference. Thirty-Third IAS Annual Meeting (Cat. No.98CH36242).

[16]  Deepak Divan,et al.  Optimal air gap design in high frequency foil windings , 1997, Proceedings of APEC 97 - Applied Power Electronics Conference.

[17]  R. Fox,et al.  Classical Electrodynamics, 3rd ed. , 1999 .

[18]  P. Lorrain,et al.  Electromagnetic fields and waves , 1970 .

[19]  N. Takahashi,et al.  Study of modeling method of lamination of Reactor core , 2006, IEEE Transactions on Magnetics.

[20]  M. Albach,et al.  The influence of air gap size and winding position on the proximity losses in high frequency transformers , 2001, 2001 IEEE 32nd Annual Power Electronics Specialists Conference (IEEE Cat. No.01CH37230).

[21]  Hiroshi Tomita,et al.  A magnetic thin film inductor and its application to a MHz switching dc-dc converter , 1994 .

[22]  G. Claydon,et al.  High efficiency, high density MHz magnetic components for a low profile converter , 1992, [Proceedings] APEC '92 Seventh Annual Applied Power Electronics Conference and Exposition.

[23]  N. Takahashi,et al.  Study of eddy-current loss reduction by slit in Reactor core , 2005, IEEE Transactions on Magnetics.