IEEE Power Electronics Magazine - March 2020 - 45

advantages and disadvantages, and the translation
between them.
In addition, we introduced a necessary-and-sufficient
circuit model with characterization advantages over the
extended cantilever model. In a three-winding structure,
the complete set of parameters can be obtained with only
one-port impedance and two-port voltage ratio measurements, which can reliably be obtained to very high frequencies (compared to three of six parameters in the extended
cantilever model). In a four-winding structure, the proposed
model can find seven of 10 parameters in this way (compared to four of 10 for the extended cantilever model). This
model may therefore be useful for a wide range of manywinding magnetic structures, with a high ceiling on appropriate frequencies.

DC-DC converter for efficient wide load range operation," IEEE Trans.
Power Electron., vol. 33, no. 12, pp. 10,428-10,448, Dec. 2018. doi: 10.1109/
TPEL.2018.2801306.
[7] M. Chen, K. K. Afridi, S. Chakraborty, and D. J. Perreault, "Multitrack
power conversion architecture," IEEE Trans. Power Electron., vol. 32, no. 1,
pp. 325-340, Jan. 2017. doi: 10.1109/TPEL.2016.2526973.
[8] S. J. Gunter, K. K. Afridi, D. M. Otten, R. A. Abramson and D. J. Perreault, "Impedance control network resonant step-down DC-DC converter
-architecture," in Proc. 2015 IEEE Energy Conversion Congr. Exposition
(ECCE), Montreal, QC, pp. 539-547. doi: 10.1109/ECCE.2015.7309736.
[9] L.F. Casey, A.F. Goldberg, and M.F. Schlecht, "Issues regarding the capacitance of 1-10 MHz transformers," in Proc. 1988 IEEE Applied Power Electronics Conf., pp. 352-359. doi: 10.1109/APEC.1988.10583.
[10] W. G. Hurley, E. Gath, and J. G. Breslin, "Optimizing the AC resistance
of multilayer transformer windings with arbitrary current waveforms,"
IEEE Trans. Power Electron., vol. 15, no. 2, pp. 369-376, Mar. 2000. doi:

About the Authors
Alex J. Hanson (ajhanson@utexas.edu) received his B.E.
degree from Dartmouth College, Hanover, New Hampshire,
in 2014 and his S.M. and Ph.D. degrees from the Massachusetts Institute of Technology, Cambridge, in 2016 and 2019,
respectively. He received the William M. Portnoy First Place
Prize Paper Award. In 2019, he joined the University of
Texas at Austin as an assistant professor. His research interests include high-frequency circuits and magnetics for energy conversion. He is a Member of the IEEE.
David J. Perreault (djperrea@mit.edu) received his
B.S. degree from Boston University, Massachusetts, and his
S.M. and Ph.D. degrees from the Massachusetts Institute of
Technology, Cambridge. He received the Richard M. Bass
Outstanding Young Power Electronics Engineer Award, the
R. David Middlebrook Achievement Award, the Office of
Naval Research Young Investigator Award, and the Society
of Automotive Engineers Ralph R. Teetor Educational
Award. He is coauthor of 12 IEEE prize papers. His research
interests include design, manufacturing, and control techniques for power electronic systems and components and
their use in a wide range of applications.

10.1109/63.838110.
[11] M. Chen, M. Araghchini, K. K. Afridi, J. H. Lang, and D. J. Perreault, "A
systematic approach to modeling impedances and current distribution in
planar magnetics," IEEE Trans. Power Electron., vol. 31, no. 1, pp. 560-580,
Jan. 2016. doi: 10.1109/TPEL.2015.2411618.
[12] K. Venkatachalam, C. R. Sullivan, T. Abdallah, and H. Tacca, "Accurate
prediction of ferrite core loss with nonsinusoidal waveforms using only
Steinmetz parameters," in Proc. 2002 IEEE Workshop on Computers in
Power Electronics, pp. 36-41. doi: 10.1109/CIPE.2002.1196712.
[13] C. Desoer and E. Kuh, Basic Circuit Theory, 1st ed. New York: McGrawHill, 1966.
[14] T. C. Neugebauer, J. W. Phinney, and D. J. Perreault, "Filters and components with inductance cancellation," IEEE Trans. Ind. Appl., vol. 40, no. 2,
pp. 483-490, Mar./Apr. 2004. doi: 10.1109/TIA.2004.824487.
[15] A. E. Kennelly, "The Equivalence of triangles and three-pointed stars
in conducting networks," Elec. World Eng., vol. 34, no. 12, pp. 413-414,
1899.
[16] D. Maksimovic, private communication, Mar. 2019.
[17] E. C. Cherry, "The duality between interlinked electric and magnetic circuits and the formation of transformer equivalent circuits," Proc. Phys. Soc.,
B, vol. 62, no. 2, pp. 101-111, 1949. doi: 10.1088/0370-1301/62/2/303.
[18] J. G. Hayes, N. O'Donovan, and M. G. Egan, "The extended T model
of the multiwinding transformer," in Proc. 2004 IEEE 35th Annu. Power

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IEEE Power Electronics Magazine - March 2020

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