Integrating magnetics for on-chip power: A perspective

IEEE Transactions on Power Electronics

Volumn 28, Issue 9, 2013, Pages 4342-4353

  Sullivan, Charles R ^a   Harburg, Daniel V ^a   Qiu, Jizheng ^a   Levey, Christopher G ^a   Yao, Di ^a  

^a DARTMOUTH COLLEGE   (United States)

Author keywords

air gaps; Air core magnetics; electromagnetics; high frequency dc dc converter; inductors; integrated power converter; magnetic films; proximity effect; soft magnetic materials; thin film inductors; transformers; very high frequency (VHF)

Indexed keywords

AIR-CORE; AIR-GAPS; ELECTROMAGNETICS; HIGH FREQUENCY HF; INTEGRATED POWER; PROXIMITY EFFECTS; VERY-HIGH-FREQUENCY (VHF);

DC-DC CONVERTERS; ELECTRIC INDUCTORS; ELECTRIC TRANSFORMERS; MAGNETIC FILMS; POWER TRANSFORMERS; SOFT MAGNETIC MATERIALS; THIN FILMS;

HIGH FREQUENCY TRANSFORMERS;

EID: 84874641803     PISSN: 08858993     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPEL.2013.2240465     Document Type: Article

References (105)

1. C. R. Sullivan, "Integrating magnetics for on-chip power: Challenges and opportunities," in Proc. IEEE Custom Integr. Circuits Conf., Sep. 2009, pp. 291-298.
2. C. O'Mathuna, N.Wang, S. Kulkarni, and S. Roy, "Review of integrated magnetics for power supply on chip (PwrSoC)," IEEE Trans. Power Electron., vol. 27, no. 11, pp. 4799-4816, Nov. 2012.
3. R. W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, 2nd ed. Boston, MA, USA: Kluwer, 2001.
4. D. J. Perreault, J. Hu, J. Rivas, Y. Han, O. Leitermann, R. C. N. Pilawa-Podgurski, A. Sagneri, and C. R. Sullivan, "Opportunities and challenges in very high frequency power conversion," in Proc. IEEE Appl. Power Electron. Conf. Expo., Feb. 2009, pp. 1-14.
5. J. M. Rivas, Y. Han, O. Leitermann, A. D. Sagneri, and D. J. Perreault, "A high-frequency resonant inverter topology with low voltage stress," IEEE Trans. Power Electron., vol. 23, no. 4, pp. 1759-1771, Jul. 2008.
6. J. S. Glaser and J. M. Rivas, "A 500 W push-pull dc-dc power converter with a 30 MHz switching frequency," in Proc. IEEE Appl. Power Electron. Conf. Expo., Feb. 2010, pp. 654-661.
7. R. C. N. Pilawa-Podgurski, A. Sagneri, J. M. Rivas, D. I. Anderson, and D. J. Perreault, "Very-high-frequency resonant boost converters," IEEE Trans. Power Electron., vol. 24, no. 6, pp. 1654-1665, Jun. 2009.
8. T. M. Andersen, S. K. Christensen, A. Knott, andM. A. E. Andersen, "A VHF class E dc-dc converter with self-oscillating gate driver," in Proc. IEEE Appl. Power Electron. Conf., Mar. 2011, pp. 885-891.
9. J. M. Rivas, O. Leitermann, Y. Han, and D. J. Perreault, "A very high frequency dc-dc converter based on a class phi-2 resonant inverter," IEEE Trans. Power Electron., vol. 26, no. 10, pp. 2980-2992, Jun. 2011.
10. G. Schrom, P. Hazucha, J. Hahn, D. S. Gardner, B. A. Bloechel, G. Dermer, S. G. Narendra, and T. D. V. Karnik, "A 480-MHz, multiphase interleaved buck dc-dc converter with hysteretic control," in Proc. IEEE 35th Annu. Power Electron. Spec. Conf., Jun. 2004, vol. 6, pp. 4702-4707.
11. G. Schrom, P. Hazucha, H. Jae-Hong, V. Kursun, D. Gardner, S. Narendra, T. Karnik, and V. De, "Feasibility of monolithic and 3Dstacked dc-dc converters for microprocessors in 90 nm technology generation," in Proc. Symp. VLSI Circuits, 2004, pp. 256-257.
12. C. R. Sullivan, D. Yao, G. Gamache, A. Latham, and J. Qiu, "Passive component technologies for advanced power conversion enabled by wide-band-gap power devices," ECS Trans., vol. 41, no. 8, pp. 315-330, 2011.
13. Y. Han, G. Cheung, A. Li, C. R. Sullivan, andD. J. Perreault, "Evaluation of magnetic materials for very high frequency power applications," in Proc. IEEE Power Electron. Spec. Conf., Jun. 2008, pp. 4270-4276.
14. C. R. Sullivan, "Optimal choice for number of strands in a litz-wire transformer winding," IEEE Trans. Power Electron., vol. 14, no. 2, pp. 283-291, Mar. 1999.
15. C. R. Sullivan, "Cost-constrained selection of strand wire and number in a litz-wire transformer winding," IEEE Trans. Power Electron., vol. 16, no. 2, pp. 281-288, Mar. 2001.
16. M. E. Dale and C. R. Sullivan, "Comparison of power loss in single-layer andmulti-layer windings with physical constraints or strong harmonics," in Proc. IEEE Int. Symp. Ind. Electron., Jul. 2006, pp. 1467-1473.
17. J. D. Pollock, W. Lundquist, and C. R. Sullivan, "The design of barrelwound foil windings with multiple layers interchanged to balance layer currents," in Proc. IEEE Appl. Power Electron. Conf., Mar. 2011, pp. 168-173.
18. M. Nigam and C. R. Sullivan, "Multi-layer folded high-frequency toroidal inductor windings," in Proc. IEEE Appl. Power Electron. Conf., Feb. 2008, pp. 682-688.
19. M. D. Seeman and S. R. Sanders, "Analysis and optimization of switched-capacitor dc-dc converters," IEEE Trans. Power Electron., vol. 23, no. 2, pp. 841-851, Mar. 2008.
20. M. S. Makowski and D. Maksimovic, "Performance limits of switched capacitor dc-dc converters," in Proc. IEEE Power Electron. Spec. Conf., Jun. 1995, vol. 2, pp. 1215-1221.
21. P. M. Lin and L. O. Chua, "Topological generation and analysis of voltage multiplier circuits," IEEE Trans. Circuits Syst., vol. 24, no. 10, pp. 517-530, Oct. 1977.
22. H.-P. Le, S. R. Sanders, and E. Alon, "Design techniques for fully integrated switched-capacitor dc-dc converters," IEEE J. Solid-State Circuits, vol. 46, no. 9, pp. 2120-2131, Sep. 2011.
23. J. T. Stauth, M. D. Seeman, and K. Kesarwani, "A high-voltage CMOS IC and embedded system for distributed photovoltaic energy optimization with over 99% effective conversion efficiency and insertion loss below 0.1%," in Proc. IEEE Int. Solid-State Circuits Conf., Feb. 2012, pp. 100-102.
24. J. T. Stauth, M. D. Seeman, and K. Kesarwani, "Resonant switchedcapacitor converters for sub-module distributed photovoltaic powermanagement," IEEE Trans. Power Electron., vol. 28, no. 3, pp. 1189-1198, Mar. 2012.
25. R. C. N. Pilawa-Podgurski, D. M. Giuliano, andD. J. Perreault, "Merged two-stage power converter architecture with soft charging switchedcapacitor energy transfer," in Proc. IEEE Power Electon. Spec. Conf., Jun. 2008, pp. 4008-4015.
26. R. C. N. Pilawa-Podgurski and D. J. Perreault, "Merged two-stage power converter with soft charging switched-capacitor stage in 180 nm CMOS," IEEE J. Solid-State Circuits, vol. 47, no. 7, pp. 1-11, Jul. 2012.
27. J. M. Rivas, D. Jackson, O. Leitermann, A. D. Sagneri, Y. Han, and D. J. Perreault, "Design considerations for very high frequency dc-dc converters," in Proc. IEEE 37th Power Electron. Spec. Conf., Jun. 2006, pp. 1-11.
28. T. Suetsugu andM. K. Kazimierczuk, "Integrated class DE synchronized dc-dc converter for on-chip power supplies," in Proc. IEEE 37th Power Electron. Spec. Conf., Jun. 2006, pp. 1-5.
29. C. O'Mathuna, "Power supply on chip-Has the ship come in?" presented at the IEEE Appl. Power Electron. Conf. Expo. Plenary Present., 2009. Available: http://www.apec-conf.org/images/PDF/2009/Plenary/06-cian-omathuna.pdf
30. R. Meere, N. Wang, T. O'Donnell, S. Kulkarni, S. Roy, and S. C. O'Mathuna, "Magnetic-core and air-core inductors on silicon: A performance comparison up to 100 MHz," IEEE Trans. Magn., vol. 47, no. 10, pp. 4429-4432, Oct. 2011.
31. J. C. Maxwell, A Treatise on Electricity and Magnerism, 3rd ed. London, U.K.: Oxford Univ. Press, vol. 2, 1892.
32. B. Brooks, "Design of standards of inductance and the proposed use of model reactors in the design of air-core and iron-core reactors," J. Res. Natl. Bur. Stand. I, pp. 289-328, 1931.
33. P. N. Murgatroyd, "The brooks inductor: A study of optimal solenoid cross-sections," IEE Proc. B: Electr. Power Appl., vol. 133, no. 5, pp. 309-314, Nov. 1986.
34. A. van den Bossche and V. Valchev, Inductors and Transformers for Power Electronics. New York, USA: Taylor & Francis, 2005.
35. E. C. Snelling, Soft Ferrites, Properties and Applications, 2nd ed. ed. London, U.K.: Butterworths, 1988.
36. C. P. Yue and S. S. Wong, "On-chip spiral inductors with patterned ground shields for Si-based RF ICs," IEEE J. Solid-State Circuits, vol. 33, no. 5, pp. 743-752, May 1998.
37. J. N. Burghartz, "Progress in RF inductors on silicon-understanding substrate losses," in Proc. IEEE Int. Electron. Dev. Meeting, Dec. 1998, pp. 523-526.
38. P. N. Murgatroyd, "The optimal form for coreless inductors," IEEE Trans. Magn., vol. 25, no. 3, pp. 2670-2677, May 1989.
39. M. E. Dale and C. R. Sullivan, "General comparison of power loss in single-layer and multi-layer windings," in Proc. Power Electron. Spec. Conf., Jun. 2004, vol. 2, pp. 853-860.
40. M. E. Dale and C. R. Sullivan, "Comparison of loss in single-layer and multi-layer windings with a dc current component," in Proc. IEEE Annu. Meeting Conf. Ind. Appl., Oct. 2006, vol. 4, pp. 1870-1875.
41. S. Wang, M. A. de Rooij, W. G. Odendaal, J. D. van Wyk, and D. Boroyevich, "Reduction of high-frequency conduction losses using a planar litz structure," IEEE Trans. Power Electron., vol. 20, no. 2, pp. 261-267, Mar. 2005.
42. J. S. Glaser and M. A. de Rooij, "A novel folded litz ribbon cable for magnetic components," in Proc. IEEE Power Electron. Spec. Conf., Jun. 2007, pp. 1-8.
43. C. R. Sullivan, S. Prabhakaran,W. Li, and S. Lu, "Design and fabrication of low-loss toroidal air-core inductors," in Proc. IEEE Power Electron. Spec. Conf., Jun. 2007, pp. 1754-1759.
44. S. Orlandi, B. Allongue, G. Blanchot, S. Buso, F. Faccio, C. Fuentes, M. Kayal, S. Michelis, and G. Spiazzi, "Optimization of shielded PCB air-core toroids for high-efficiency dc-dc converters," IEEE Trans. Power Electron., vol. 26, no. 7, pp. 1837-1846, Jul. 2011.
45. X. Yu, M. Kim, F. Herrault, C.-H. Ji, J. Kim, and M. Allen, "Siliconembedded 3D toroidal air-core inductor with through-wafer interconnect for on-chip Integration," in Proc. IEEE 25th Int. Conf. Micro Electron. Mech. Syst., Feb. 2012, pp. 325-328.
46. M. Araghchini, J. H. Lang, X. Yu, M. S. Kim, F. Herrault, M. G. Allen, J. Qiu, and C. R. Sullivan, "Modeling and measured verification of stored energy and loss in MEMS toroidal inductors," in Proc. IEEE Energ. Convers. Conf. Exhib., Sep. 2012, pp. 3293-3300.
47. X. Fang, R.Wu, L. Peng, and J. K. O. Sin, "Anewembedded inductor for ZVS dc-dc converter applications," in Proc. Int. Symp. Power Semicond. Dev. ICs, Jun. 2012, pp. 53-56.
48. W. R.Wu and J. K. O. Sin, "A novel silicon-embedded coreless inductor for high frequency power management applications," IEEE Electron. Dev. Lett., vol. 32, no. 1, pp. 60-62, Jan. 2011.
49. Ferrites and Accessories: SIFERRIT Materials, EPCOS AG, Munich, Germany, 2006.
50. Soft Ferrites and Accessories, Data Handbook, Ferroxcube, Eindhoven, The Netherlands, 2009.
51. D. Yao and C. R. Sullivan, "Effect of capacitance on eddy-current loss in multi-layer magnetic films for MHz magnetic components," in Proc. IEEE Energ. Convers. Congr. Expo., Sep. 2009, pp. 1025-1031.
52. M. Xy, T. M. Liakopoulos, C. H. Ahn, S. H. Han, and H. J. Kim, "A microfabricated transformer for high frequency power or signal conversion," IEEE Trans. Magn., vol. 34, no. 4, pp. 1369-1371, Jul. 1998.
53. S.Kelly,C.Collins, M. Duffy, F. M. F. Rhen, and S. Roy, "Corematerials for high frequency VRM inductors," in Proc. Power Electron. Spec. Conf., 2007, pp. 1767-1772.
54. T. O'Donnell, N. Wang, R. Meere, F. Rhen, S. Roy, D. O'Sullivan, and C. O'Mathuna, "Microfabricated inductors for 20 MHz dc-dc converters," in Proc. IEEE Appl. Power Electron. Conf., Feb. 2008, pp. 689-693.
55. S. C. O'Mathuna, T. O'Donnell, N. Wang, and K. Rinne, "Magnetics on silicon: An enabling technology for power supply on chip," IEEE Trans. Power Electron., vol. 20, no. 3, pp. 585-592, May 2005.
56. J.-W. Park and M. G. Allen, "Ultralow-profile micromachined power inductors with highly laminated ni/fe cores: Application to low-megahertz dc-dc converters," IEEE Trans. Magn., vol. 39, no. 5, pp. 3184-3186, Sep. 2003.
57. F. Herrault, W. P. Galle, R. H. Shafer, and M. G. Allen, "Electroplatingbased approaches for volumetric nanomanufacturing," in Proc. Tech. Dig. Technol. Future Micro-Nano Manufact., Aug. 2011, pp. 1-4.
58. P. Dhagat, S. Prabhakaran, and C. R. Sullivan, "Comparison of magnetic materials for v-groove inductors in optimized high-frequency dc-dc converters," IEEE Trans. Magn., vol. 40, no. 4, pp. 2008-2010, Jul. 2004.
59. S. Ohnuma, H. Fujimori, S. Furukawa, S.Mitani, and T.Masumoto, "Co-(N, O)-based granular thin films and their soft magnetic properties," J. Alloys Compounds, vol. 222, pp. 167-172, 1995.
60. H. Fujimori, "Structure and 100 MHz soft magnetic properties in multilayers and granular thin films," Scripta Metallurg. Materialia, vol. 33, no. 10-11, pp. 1625-1636, 1995.
61. Y. Hayakawa and A. Makino, "Soft magnetic properties of Fe-M-O (M = Hf, Zr, Y, Ce) films with high electrical resistivity," Nanostruct. Mater., vol. 6, pp. 989-992, 1995.
62. S. Ohnuma, H. Fujimori, S. Mitani, and T. Masumoto, "High-frequency magnetic properties in metal-nonmetal granular films," J. Appl. Phys., vol. 79, no. 8, pp. 5130-5135, Apr. 1996.
63. S. Ohnuma, H. J. Lee, N. Kobayashi, H. Fujimori, and T. Masumoto, "Co-Zr-O nano-granular thin films with improved high frequency soft magnetic properties," IEEE Trans. Magn., vol. 37, no. 4, pp. 3759-3761, Jul. 2001.
64. Y. Sun, W.-D. Li, P. Dhagat, and C. R. Sullivan, "Perpendicular anisotropy in Co-Zr-O granular films," J. Appl. Phys., vol. 97, no. 10, pp. 10N301-1-10N301-3, 2005.
65. W. Li, Y. Sun, and C. R. Sullivan, "High-frequency resistivity of soft magnetic granular films," IEEE Trans. Magn., vol. 41, no. 10, pp. 3283-3285, Oct. 2005.
66. D. Yao, C. G. Levey, R. Tian, and C. R. Sullivan, "Microfabricated V-groove power inductors using multilayer Co-Zr-O thin films for very-high-frequency dc-dc converters," IEEE Trans. Power Electron., doi:10.1109/TPEL.2012.2233760, 2013, to be published in this issue.
67. D. Yao and C. R. Sullivan, "Calculation of eddy-current loss in multilayer magnetic films considering displacement current," J. Appl. Phys., vol. 105, no. 7, pp. 07A335-1-07A335-3, 2009.
68. H. Mukadam, C. R. Sullivan, and S. Prabhakaran, "A high-field highfrequency permeance meter for thin-filmmaterials," in Proc. IEEE Power Electron. Spec. Conf., Jun. 2008, pp. 4044-4050.
69. J. Qiu and C. R. Sullivan, "Design and fabrication of VHF tapped power inductors using nanogranular magnetic films," IEEE Trans. Power Electron., vol. 27, no. 12, pp. 4965-4975, Dec. 2012.
70. Y. Sun, C. R. Sullivan, W. Li, D. P. Kopp, F. Johnson, and S. T. Taylor, "Soft magnetic properties of obliquely deposited Co-Zr-O films," IEEE Trans. Magn., vol. 43, no. 12, pp. 4060-4063, Dec. 2007.
71. C. R. Sullivan and S. R. Sanders, "Design of microfabricated transformers and inductors for high-frequency power conversion," IEEE Trans. Power Electron., vol. 11, no. 2, pp. 228-238, Mar. 1996.
72. C. R. Sullivan and S. R. Sanders, "Measured performance of a highpower-density microfabricated transformer in a dc-dc converter," in Proc. IEEE Power Electron. Spec. Conf., Jun. 1996, pp. 287-294.
73. C. R. Sullivan, "Microfabrication of magnetic components for high frequency power conversion," Ph.D. dissertation, Dept. Electr. Eng. Comput. Sci., Univ. of California, Berkeley, CA, USA 1996.
74. P. R. Morrow, C.-M. Park, H. W. Koertzen, and J. T. DiBene, "Design and fabrication of on-chip coupled inductors integrated with magnetic material for voltage regulators," IEEE Trans. Magn., vol. 47, no. 6, pp. 1678-1686, Jun. 2011.
75. D. V. Harburg, X. Yu, F. Herrault, C. G. Levey, M. G. Allen, and C. R. Sullivan, "Micro-fabricated thin-film inductors for on-chip power conversion," in Proc. Int. Conf. Integr. Power Electron. Syst., Mar. 2012, pp. 1-6.
76. M. Wang, J. Li, K. D. T. Ngo, and H. Xie. (2011). "Silicon molding techniques for integrated power MEMS inductors," Sens. Actuat. A Phys., [Online]. 166(1), pp. 157-163,Available: http://www.sciencedirect.com/science/ article/pii/S0924424710005108
77. J. M. Wright, D. W. Lee, A. Mohan, A. Papou, P. Smeys, and S. X. Wang, "Analysis of integrated solenoid inductor with closed magnetic core," IEEE Trans. Magn., vol. 46, no. 6, pp. 2387-2390, Jun. 2010.
78. D. W. Lee, K.-P. Hwang, and S. X. Wang, "Fabrication and analysis of high-performance integrated solenoid inductor with magnetic core," IEEE Trans. Magn., vol. 44, no. 11, pp. 4089-4095, Nov. 2008.
79. B. Orlando, R. Hida, R. Cuchet, M. Audoin, B. Viala, D. Pellissier-Tanon, X. Gagnard, and P. Ancey, "Low-resistance integrated toroidal inductor for power management," IEEE Trans. Magn., vol. 42, no. 10, pp. 3374-3376, Oct. 2006.
80. N. Sturcken, R. Davies, C. Cheng, W. Bailey, and K. Shepard, "Design of coupled power inductors with crossed anisotropy magnetic core for integrated power conversion," in Proc. IEEE Appl. Power Electron. Conf. Expo., Feb. 2012, pp. 417-423.
81. J. Qiu and C. R. Sullivan, "Radial-anisotropy nanogranular thin-film magnetic material for toroidal inductors," in Proc. IEEE Appl. Power Electron. Conf. Expo., Feb. 2012, pp. 491-497.
82. J. Qiu and C. R. Sullivan, "Radial-anisotropy thin-film magnetic material for high-power-density toroidal inductors," in Proc. Int. Conf. Integr. Power Electron. Syst., Mar. 2012, pp. 1-6.
83. L. Daniel, C. R. Sullivan, and S. R. Sanders, "Design of microfabricated inductors," IEEE Trans. Power Electron., vol. 14, no. 4, pp. 709-723, Jul. 1999.
84. J. Hu and C. Sullivan, "AC resistance of planar power inductors and the quasidistributed gap technique," IEEE Trans. Power Electron., vol. 16, no. 4, pp. 558-567, Jul. 2001.
85. N. H. Kutkut, D. W. Novotny, D. M. Divan, and E. Yeow, "Analysis of winding losses in high frequency foil wound inductors," in Proc. IEEE Ind. Appl. Soc. Annu. Meeting, Oct. 1995, pp. 859-867.
86. W. M. Chew and P. D. Evans, "High frequency inductor design concepts," in Proc. 22nd Annu. Power Electron. Spec. Conf., Jun. 1991, pp. 673-678.
87. D. V. Harburg, J. Qiu, and C. R. Sullivan, "An improved ac loss model for the optimization of planar-coil inductors," in Proc. IEEE Workshop Contr. Model. Power Electron., Jun. 2012, pp. 1-7.
88. J. Biela and J. W. Kolar, "Electromagnetic integration of high power resonant circuits comprising high leakage inductance transformers," in Proc. IEEE Power Electron. Spec. Conf., Jun. 2004, vol. 6, pp. 4537-4545.
89. M. Meinhardt, M. Duffy, T. O'Donnell, S. O'Reilly, J. Flannery, and C. O'Mathuna, "New method for integration of resonant inductor and transformer-design, realisation, measurements," in Proc. IEEE Appl. Power Electron. Conf. Expo., Mar. 1999, vol. 2, pp. 1168-1174.
90. L. Laguna, R. Prieto, O. Garcia, R. Gutierrez, and J. A. Cobos, "Generalized methodology for the analysis and design of multiphase converters with integrated magnetics," in Proc. IEEE Power Electron. Spec. Conf., Jun. 2008, pp. 2678-2684.
91. R. Prieto, R. Asensi, J. A. Cobos, and J. Uceda, "A full procedure to model integrated magnetics based on FEA," in Proc. IEEE Appl. Power Electron. Conf., 2004, vol. 2, pp. 952-957.
92. Y. Lu, K. W. E. Cheng, S. L. Ho, J. F. Pan, K. F. Kwok, and X. D. Xue, "A transformer with adjustable leakage inductance," in Proc. IEEE Conf. Electromagn. Field Comput., 2006, Paper PA8-8, p. 77.
93. M. Pavlovsky, S. W. H. de Haan, and J. A. Ferraira, "Winding losses in high-current, high-frequency transformer foil windings with leakage layer," in Proc. IEEE Power Electron. Spec. Conf., Jun. 2006, pp. 1-7.
94. J. Pleite, V. Valdivia, P. Zumel, and C. Gonzalez, "Transformer and series inductance integration for harmonic filtering in PWM inverters based in a simple design procedure," in Proc. IEEE Int. Symp. Ind. Electron., Jun. 2007, pp. 1201-1206.
95. J. Sun, K. F. Webb, and V. Mehrotra, "Integrated magnetics for currentdoubler rectifiers," IEEE Trans. Power Electron., vol. 19, no. 3, pp. 582-590, May 2004.
96. L. Yan and B. Lehman, "A capacitor modeling method for integrated magnetic components in dc/dc converters," IEEE Trans. Power Electron., vol. 20, no. 5, pp. 987-996, Sep. 2005.
97. J. T. Strydom, "Electromagnetic design of integrated resonatortransformers," Ph.D. dissertation, Dept. Elect. Electron. Eng., Rand Afrikaans Univ., Auckland Park, South Africa, 2001.
98. M. C. Smit, J. A. Ferreira, and J. D. Van Wyk, "Application of transmission line principles to high frequency power converters," in Proc. IEEE Power Electron. Spec. Conf., Jun. 1992, pp. 1423-1430.
99. P. Artillan, M. Brunet, D. Bourrier, J.-P. Laur, N. Mauran, L. Bary, M. Dilhan, B. Estibals, C. Alonso, and J.-L. Sanchez, "Integrated LC filter on silicon for dc-dc converter applications," IEEE Trans. Power Electron., vol. 26, no. 8, pp. 2319-2325, Aug. 2011.
100. S. Prabhakaran, C. R. Sullivan, T. O'Donnell, M. Brunet, and S. Roy, "Microfabricated coupled inductors for dc-dc converters for microprocessor power delivery," in Proc. IEEE Power Electron. Spec. Conf., Jun. 2004, vol. 6, pp. 4467-4472.
101. J. Wibben and R. Harjani, "A high-efficiency dc-dc converter using 2 nH integrated inductors," IEEE J. Solid-State Circuits, vol. 43, no. 4, pp. 844-854, Apr. 2008.
102. J. T. DiBene, P. R. Morrow, C.-M. Park, H. W. Koertzen, P. Zou, F. Thenus, X. Li, S. W. Montgomery, E. Stanford, R. Fite, and P. Fischer, "A 400 A fully integrated silicon voltage regulator with in-die magnetically coupled embedded inductors," in Proc. IEEE Appl. Power Electron. Conf. Expo. Special Present., Feb. 2010.
103. P.-L. Wong, P. Xu, P. Yang, and F. C. Lee, "Performance improvements of interleaving VRMs with coupling inductors," IEEE Trans. Power Electron., vol. 16, no. 4, pp. 499-507, Jul. 2001.
104. J. Li, C. R. Sullivan, and A. Schultz, "Coupled-inductor design optimization for fast-response low-voltage dc-dc converters," in Proc. IEEE 17th Annu. Appl. Power Electron. Conf. Expo., 2002, vol. 2, pp. 817-823.
105. J. Li, A. Stratakos, and A.Schultz, C. R. Sullivan, "Using coupled inductors to enhance transient performance ofmulti-phase buck converters," in Proc. IEEE 19th Annu. Appl. Power Electron. Conf. Expo., 2004, vol. 2, pp. 1289-1293.