
Marc T. Thompson,
Ph.D.
System Design
Consultant
ENGINEERING CONSULTING
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Bibliography of Inductance Calculation References
Note: Comments or additions to this list are welcomed at marctt@aol.com
Index
INDUCTANCE CALCULATIONS
INDUCTANCE HIGH FREQUENCY
CALCULATIONS
INDUCTANCE OPTIMIZATION
INDUCTION HEATING
SPIRAL COILS 
APPLICATIONS
SPIRAL COILS  IMPEDANCE
CALCULATIONS
SPIRAL TRANSFORMERS
FERRITE MATERIALS
[1] J. Bhagwan and F. Trofimenkoff, "Mutual Inductances of Coils on a Cylinder of Infinite Length," IEEE Transactions on Magnetics, vol. MAG16, no. 2, March 1980, pp. 477479
[2] S. Butterworth, "On the Coefficients of Mutual Induction of Eccentric Coils," Philosophical Magazine, series 6, vol. 31, (1916) pp. 443454
[3] M. Caulton, "The Lumped Element Approach to Microwave Integrated Circuits," The Microwave Journal, May 1970, pp. 5158
[4] H. Dwight, Electrical Coils and Conductors, McGrawHill, Inc., New York 1946 (QC645.D991). Proximity effect in wires, pp. 192, 224; mutual inductance of filamentary circles, pp. 228; mutual inductance of two thin disk coils, pp. 253; magnetic field from round coil of small rectangular cross section, pp. 292.
[5] M. ElDerini, "Mathematical model of a solenoid for energy and force calculations," Journal of Physics D: Applied Physics, 17, (1984) pp. 503508
[6] M. ElMarkabi and E. Freeman, "Electromagnetic properties of a circular cylindrical coil in a set of planar ferromagnetic regions," IEE Proceedings, vol. 129, pt. A, no. 8, November 1982, pp. 582589
[7] J. Ferreira, "Improved Analytical Modeling of Conductive Losses in Magnetic Components," IEEE Transactions on Power Electronics, vol. 9, no. 1, January 1994, pp. 127131
[8] Frederick Grover, Inductance Calculations: Working Formulas and Tables, Dover Publications, Inc., New York 1946. Inductance of a rectangle of round wire, pp. 60; inductance of regular polygons of round wire, pp. 60; inductance of an ellipse of round wire, pp. 65; inductance of single layer coils on rectangular winding form, pp. 70; mutual inductance of circular filaments, pp. 77; coaxial circular coils, pp. 88; self inductance of circular coils with rectangular cross section, pp. 94; inductance of flat spiral, pp. 167; high frequency effects, pp. 261.
[9] W. Hurley and M. Duffy, "Calculation of Self and Mutual Impedances in Planar Magnetic Structures," IEEE Transactions on Magnetics, vol. 31, no. 4, July 1995, pp. 24162422
[10] K. Iizuka, R. King, and C. Harrison, "Self and Mutual Admittances of Two Identical Circular Loop Antennas in a Conducting Medium and in Air," IEEE Transactions on Antennas and Propagation, vol. AP14, no. 4, July 1966, pp. 440450
[11] Yukikazu Iwasa, Case Studies in Superconducting Magnets, Plenum Press, New York 1994 (QC761.3.I9)
[12] A. Lofti and F. Lee, "Two Dimensional Skin Effect in Power Foils for HighFrequency Applications," IEEE Transactions on Magnetics, vol. 31, no. 2, March 1995, pp. 10031006. Approximate analytic result for foil with rectangular cross section.
[13] A. Lotfi, P. Gradzki, and F. Lee, "Proximity Effects in Coils for High Frequency Power Applications," IEEE Transactions on Magnetics, vol. 28, no. 5, September 1992, pp. 21692171
[14] T. Lyle, "On the SelfInductance of Circular Coils of Rectangular Section," Philosophical Transactions, vol. 213A, (1913) pp. 421435
[15] P. Murgatroyd and N. Walker, "The Frequency Dependence of Resistance in FoilWound Inductors," Electrocomponent Science and Technology, 1979, vol. 5, pp. 219222
[16] W. Odendaal, J. Ferreira, and W. Cronje, "Combined Numeric and Analytic Methods for Foil Winding Design," Proceedings of the Power Electronics Specialists Conference PESC '94, pp. 843849
[17] A. Rezzoug, J. Caron, and F. Sargos, "Analytical Calculations of Flux and Induction and Forces of Thick Coils with Finite Length," IEEE Transactions on Magnetics, vol. 28, no. 5, September 1992, pp. 22502252
[18] P. Ryff, P. Biringer, and P. Burke, "Calculation Methods for Current Distribution in SingleTurn Coils of Arbitrary Cross Section," IEEE Transactions on Power Apparatus and Systems, vol. PAS89, no. 2, Feb. 1970, pp. 228232
[19] W. Scott, The Physics of Electricity and Magnetism, 2d Edition, John Wiley and Sons, New York, 1966 (QC518.S431). Self inductance of circular loop, pp. 361.
[20] W. Smythe, Static and Dynamic Electricity, 2d Ed., McGrawHill, New York, 1950 (QC518.S668). Mutual inductance of circular loops, pp. 313; self inductance of circular loop, pp. 317.
[21] M. Stafl, Electrodynamics of Electrical Machines, Iliffe Books Ltd.k, 1967
[22] F. Terman, Radio Engineers' Handbook, McGrawHill, New York, 1943. Skin effect in round wire, pp. 30; skin effect in flat ribbon, pp. 34; proximity effect in adjacent wires, pp. 36, 77, 81; self inductance of circular wire loop, pp. 52; self inductance of rectangle of round wire, pp. 53; self inductance of flat rectangular coil, pp. 59.
[23] U.S. National Bureau of Standards, Radio Instruments and Measurements, Government Printing Office, 1924 (TK6550.U585). Self inductance of rectangle of rectangular wire, pp. 247; spiral coil, pp. 261; flat square coil, pp. 266; mutual inductance of two rectangles in the same plane, pp. 274.
[24] Harold A. Wheeler, "Formulas for the Skin Effect," Proceedings of the I.R.E., September 1942, pp. 412424
[25] Harold A. Wheeler, "Simple Inductance Formulas for Radio Coils," Proceedings of the I.R.E., October 1928, pp. 13981400. Approximate formulas for disk, solenoid, and pancake coils.
[26] D. Wilcox, M. Conlon, and W. Hurley, "Calculation of Self and Mutual Impedances for Coils on Ferromagnetic Cores," IEE Proceedings, vol. 135, pt. A, no. 7, September 1988, pp. 470476
[27] D. Wilcox, W. Hurley, and M. Conlon, "Calculation of Self and Mutual Impedances Between Sections of Transformer Windings," IEE Proceedings, vol. 136, pt. C, no. 5, September 1989, pp. 308314
[28] M. Zahn, Electromagnetic Field Theory: A Problem Solving Approach, Krieger Publishing Company, Malabar Florida, 1987 (QC665.E4Z32)
1.2. Inductance High Frequency Calculations
[29] R. Asensi, J. Cobos, O. Garcia, R. Prieto, and J. Uceda, "A Full Procedure to Model High Frequency Transformer Windings" Proceedings of the Power Electronics Specialists Conference PESC '94, pp. 856863
[30] F. Banzi, "Higher Q from Pot Core Inductors," IEEE Transactions on Parts, Hybrids, and Packaging, vol. PHP13, no. 4, December 1977, pp. 371377
[31] B. Carsten, "High Frequency Conductor Losses in Switchmode Magnetics," Power Control and Intelligent Motion, November 1986, pp. 3446
[32] M. Duffy and W. Hurley, "High Frequency Effects in Planar Magnetics: Inclusive of Skin Effect," Proceedings of the Power Electronics Specialists Conference PESC '95, pp. 645650
[33] D. Pollack, "The Design of Inductances for Frequencies Between 4 and 25 Megacycles," Electrical Engineering, September 1937, pp. 11691176
[34] P. Murgatroyd, "Some optimum shapes for toroidal inductors," IEE Proceedings, vol. 129, part B, no. 3, May 1982, pp. 168176. Optimum winding shapes.
[35] P. Murgatroyd, "The Brooks Inductor: A Study of Optimal Solenoid CrossSections," IEE Proceedings, vol. 133, part B, no. 5, September 1986, pp. 309314
[36] P. Murgatroyd, "The Optimal Form for Coreless Inductors," IEEE Transactions on Magnetics, vol. 25, no. 3, May 1989, pp. 26702677
[37] A. Rand, "Inductor Size vs. Q: A Dimensional Analysis," IEEE Transactions on Component Parts, 1963, pp. 3135
[38] M. Adler, "A FieldTheoretical Approach to Magnetic Induction Heating of Thin Circular Plates," IEEE Transactions on Magnetics, vol. MAG10, no. 4, December 1974, pp. 11181125
[39] R. M. Baker, "Design and Calculation of InductionHeating Coils," AIEE Transactions, part 2, March 1957, pp. 3140
[40] Samir Basu and K. D. Srivastava, "Electromagnetic Forces on a Metal Disk in an Alternating Magnetic Field," IEEE Transactions on Power Apparatus and Systems, vol. PAS88, no. 8, August 1969, pp. 12811285
[41] R. Dudley and P. Burke, "The Prediction of Current Distribution in Induction Heating Installations," IEEE Transactions on Industry Applications, vol. IA8, September/October 1972, pp. 565571
[42] L. Egan and E. Furlani, "A Computer Simulation of an Induction Heating System," IEEE Transactions on Magnetics, vol. 27, no. 5, September 1991, pp. 43434354
[43] D. Geselowitz, Q. Hoang, and R. Gaumond, "The Effects of Metals on a Transcutaneous Energy Transmission System," IEEE Transactions on Biomedical Engineering, vol. 39, no. 9, September 1992, pp. 928934
[44] William G. Hurley and John G. Kassakian, "Induction Heating of Circular Ferromagnetic Plates," IEEE Transactions on Magnetics, vol. MAG15, no. 3, July 1979, pp. 11741181
[45] A. L. Jones and K. F. Pezdirtz, "Nondestructive Eddy Current Testing," IEEE Transactions on Instrumentation and Measurement, vol. IM21, Feb. 1972, pp. 1115
[46] Sergio Lupi, "Planar circular coils for induction heating," Elektrowarme International, 37, (1979), pp. 319326
[47] N. R. Stansel, "Induction Heating  Selection of Frequency," AIEE Transactions, vol. 63, October 1944, pp. 755759
[48] Herbert F. Storm, "Surface Heating by Induction," AIEE Transactions, vol. 63, October 1944, pp. 749754
[49] C. Tudbury, "Electromagnetics in Induction Heating"
[50] J. Vaughan and J. Williamson, "Design of InductionHeating Coils for Cylindrical Nonmagnetic Loads," AIEE Transactions, vol. 64, August 1945, pp. 587592
1.5. Spiral Coils  Applications
[51] V. Franyuk and L. Ivankovich, "EddyCurrent Transducer Based on Flat Spiral Coils," Soviet Journal of Nondestructive Testing, vol. 24, 1988, pp. 235238
[52] X. Huang and K. Ngo, "Design Technique for a Spiral Planar Winding With Geometric Radii," IEEE Transactions on Aerospace and Electronic Systems, vol. 32, no. 2, April 1996, pp. 825830
[53] X. Huang, K. Ngo, and E. Bloom, "Design Techniques for Planar Windings with Low Resistances," Proceedings of APEC '95. Tenth Annual Applied Power Electronics Conference and Exposition, vol. 2, pp. 533539
[54] M. Ketchen, "DC Squids 1980: The State of the Art," IEEE Transactions on Magnetics, vol. MAG17, no. 1, January 1981, pp. 387394
[55] H. Lee, "A highbandwidth induction sensor coil," Journal of Physics E: Scientific Instruments, vol. 15, 1982, pp. 10171019
[56] Sergio Lupi, "The Calculation of Planar Circular Coils for the Induction Heating of Bimetallic Plates," Archiv fur Elektrotechnik, 60 (1978) pp. 313318
[57] T. Munsat, W. Hooke, S. Bozeman, and S. Washburn, "Two new planar coil designs for a high pressure radio frequency plasma source," Applied Physics Letters, 66 (17) 24 April 1995, pp. 21802182
[58] P. Murgatroyd and N. Walker, "Frequencydependent inductance and resistance of foil conductor loops," Proceedings of the IEE, vol. 124, no. 5, May 1977, pp. 493496
[59] O. Oshiro, H. Tsujimoto, and K. Shirae, "A Novel Miniature Planar Inductor," IEEE Transactions on Magnetics, vol. MAG23, no. 5, September 1987, pp. 37593761
[60] M. Perry, "Multiple Layer Series Connected Winding Design for Minimum Losses," IEEE Transactions on Power Apparatus and Systems, vol. PAS98, no. 1, Jan./Feb. 1979, pp. 116123
[61] M. Quirke, J. Barrett, and M. Hayes, "Planar Magnetic Component Technology  A Review," IEEE Transactions on Components, Hybrids, and Manufacturing Technology, vol. 15, no. 5, October 1992, pp. 884892
[62] R. Reeves, "Aircored foilwound inductors," Proceedings of the IEE, vol. 125, no. 5, May 1978, pp. 460464
[63] K. Sakakibara, "Analysis of the Characteristics of Planar Power Magnetics for HighFrequency DC/DC Converters," Electronics and Communications in Japan, part 2, vol. 77, no. 2, 1994, pp. 105113
[64] N. Saleh, "Variable Microelectronic Inductors," IEEE Transactions on Components, Hybrids, and Manufacturing Technology, vol. CHMT1, no. 1, March 1978, pp. 118124. Inductance of flat spiral.
[65] I. Sasada, T. Yamaguchi, and K. Harada, "Methods for loss reduction in planar inductors," Proceedings of the 23rd Annual Power Electronics Specialists Conference, (PESC '92), vol. 2, 1992, pp. 14091415
[66] T. Sato, M. Hasegawa, T. Mizoguchi and M. Sahashi, "Study of High Power Planar Inductor," IEEE Transactions on Magnetics, vol. 27, no. 6, November 1991, pp. 52775279
[67] D. Schieber, "Operation of Eddy Current Probe Coil," Journal of the Franklin Institute, vol. 310, 1980, pp. 271280
[68] K. Shirakawa, "MicroInductors and Transformers," IEEE Translation Journal on Magnetics in Japan, vol. 9, no. 3, May/June 1994, pp. 116124
[69] R. Soohoo, "Magnetic Thin Film Inductors for Integrated Circuit Applications," IEEE Transactions on Magnetics, vol. MAG15, no. 6, November 1979, pp. 18031805. Inductance of spiral coils.
[70] T. Takahashi, "Numerical Analysis of Eddy Current Problems Involving Z Gradient Coils in Superconducting MRI Magnets," IEEE Transactions on Magnetics, vol. 26, no. 2, March 1990, pp. 893896
[71] H. Tsujimoto and I. O, "High Frequency Transmission Characteristic of Coplanar Film Transformer Fabricated on Flexible Polyamide Film," IEEE Transactions on Magnetics, vol. 31, no. 6, November 1995 pp. 42324234
[72] S. Yamada, M. Katou, M. Iwahara, and F. Dawson, "Eddy Current Testing Probe Composed of Planar Coils," IEEE Transactions on Magnetics, vol. 31, no. 6, November 1995, pp. 31853187
[73] K. Yamaguchi, E. Surawara, O. Nakajima, H. Matsuki, and K. Murakami, "Load Characteristics of a Spiral Coil Type Thin Film Microtransformer," IEEE Transactions on Magnetics, vol. 29, no. 6, November 1993, pp. 32073209
1.6. Spiral Coils  Impedance Calculations
[74] C. Aitchinson, R. Davies, I. Higgins, S. Longley, B. Newton, J. Wells, and J. Williams, "LumpedCircuit Elements at Microwave Frequencies," IEEE Transactions on Microwave Theory and Techniques, vol. MTT19, no. 12, December 1971, pp. 928937
[75] P. Barnwell, "ThickFilm Inductors at VHF," Electronic Components, June 1970, pp. 681684
[76] P. Barnwell, "Thick film inductors and their use in tuned circuits at VHF," Electronic Components, July 9 1971, pp. 749758
[77] P. Barnwell and C. Tucker, "The Radio Frequency Properties of Thick Film Components," Conference on Hybrid Microelectronics (1973, University of Kent), pp. 175190
[78] M. Caulton, S. Knight, and D. Daly, "Hybrid Integrated LumpedElement Microwave Amplifiers," IEEE Transactions on Electron Devices, vol. ED15, July 1968, pp. 459466
[79] R. Chaddock, "The Application of Lumped Element Techniques to High Frequency Hybrid Integrated Circuits," Conference on Hybrid Microelectronics (1973, University of Kent), pp. 209220
[80] J. Corkhill and D. Mullins, "The properties of thick film inductors," Electronic Components, vol. 10, no. 5, 1969, pp. 593
[81] D. Daly, S. Knight, M. Caulton, and R. Ekholdt, "Lumped Elements in Microwave Integrated Circuits," IEEE Transactions on Microwave Theory and Techniques, vol. MTT15, no. 12, December 1967, pp. 713721
[82] H. Dill, "Designing Inductors for ThinFilm Applications?" Electronic Design, Feb. 17, 1964, pp. 5259
[83] H. Greenhouse, "Design of Planar Rectangular Microelectronic Inductors," IEEE Transactions on Parts, Hybrids, and Packaging, vol. PHP10, no. 2, June 1974, pp. 101109
[84] P. Holmes and J. Corkhill, "Thickfilm integrated circuits  part 1," Electronic Components, vol. 10, no. 10, 1969, pp. 1171
[85] P. Holmes and J. Corkhill, "Thickfilm integrated circuits  part 2," Electronic Components, vol. 10, no. 11, 1969
[86] K. Kawabe, H.. Koyama, and K. Shirae, "Planar Inductor," IEEE Transactions on Magnetics, vol. MAG20, no. 5, September 1984, pp. 18041806
[87] H. Katoh, "A LumpElement Approach to Microwave Integrated Circuits," Electronics and Communications in Japan, vol. 56B, no. 6, 1973, pp. 4753
[88] B. Mathews, "Flat WorkCoil Design," AIEE Transactions, part II, November 1957, pp. 249256
[89] H. Miller, "Inductance Formula for a SingleLayer Circular Coil," Proceedings of the IEEE, vol. 75, no. 2, February 1987, pp. 256257
[90] A. Olivei, "Optimized Miniature ThinFilm Planar Inductors, Compatible With Integrated Circuits," IEEE Transactions on Parts, Materials and Packaging, vol. PMP5, no. 2, June 1969, pp. 7188
[91] R. Remke and G. Burdick, "Spiral Inductors for Hybrid and Microwave Applications," IEEE 1974 Electronic Components Conference, pp. 152161
[92] R. Rodriguez, J. Dishman, F. Dickens, and E. Whelan, "Modeling of TwoDimensional Spiral Inductors," IEEE Transactions on Components, Hybrids, and Manufacturing Technology, vol. CHMT3, no. 4, December 1980, pp. 535541. Inductance and A.C. resistance of flat spirals
[93] N. Saleh and A. Qureshi, "Permalloy ThinFilm Inductors," Electronics Letters, vol. 6, no. 26, December 31, 1970, pp. 850852
[94] D. Schieber, "On the inductance of printed spiral coils," Archiv fur Elektrotechnik, 68 (1985) pp. 155159. Analytical result for circular spiral coil.
[95] D. Schieber, Electromagnetic Induction Phenomena, pub. by SpringerVerlag, Berlin, 1986 (QC638.S35)
[96] I. Wolff and H. Kapusta, "Modeling of Circular Spiral Inductors for MMICs," Proceedings of the 1987 IEEE International Microwave Symposium, vol. 1, pp. 123159
[97] P. Barnwell and T. Jackson, "Low Profile High Frequency Power Supplies Using Thick Film Planar Transformers," Proceedings of the 5th European Conference on Power Electronics and Applications, vol. 3, 1993, pp. 9397 (TK7881.15.E97)
[98] A. Cornwell, "The Characterization of High Frequency Planar Thickfilm Transformers," Microelectronics International, no. 36, 1995, pp. 2526
[99] A. Goldberg, J. Kassakian, and M. Schlecht, "FiniteElement Analysis of Copper Loss in 110MHz Transformers," IEEE Transactions on Power Electronics, vol. 4, no. 2, April 1989 pp. 263273
[100] A. F. Goldberg, J. G. Kassakian, and M. F. Schlecht, "Issues Related to 110 MHz Transformer Design," Proceedings of the 18th IEEE Power Electronics Specialists Conference  PESC 1987.
[101] A. Goldberg and M. Schlecht, "The Relationship Between Size and Power Dissipation in a 110 MHz Transformer," Proceedings of the Power Electronics Specialists Conference, 1989, pp. 359368
[102] I. Marinova, Y. Midorikawa, S. Hayano, and Y. Saito, "Thin Film Transformer and Its Analysis by Integral Equation Method," IEEE Transactions on Magnetics, vol. 31, no. 4, July 1995, pp. 24322437
[103] W. Mo. et. al., "Study of Planar Inductors," IEEE IECON '94, pp. 102107
[104] E. Snelling, Soft Ferrites, Iliffe Books, London, 1969
[105] E. Snelling and A. Giles, Ferrites for Inductors and Transformers, Research Studies Press Ltd., John Wiley, 1983
Marc T. Thompson, Ph.D.
Engineering Consultant
Adjunct Associate Professor of Electrical Engineering
25 Commonwealth Road, Watertown MA 02472
Phone: (617) 9231392
Email: marctt@aol.com
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