The parasitic effects in stranded, twisted, and Litz wire windings operating at high frequencies are studied. The skin and proximity effects that cause the winding parasitic resistance of an inductor t o increase with the operating frequency are considered. An expression for the ac resistance as a function of the operating frequency i s given. The measured and calculated values of the inductor ac resistance and quality factor are plotted versus frequency and compared. The theoretical results were in good agreement with those experimentally measured.

The paper reviews several expressions for high-frequency winding resistance of inductors proposed by several authors and compares the theoretical predictions calculated from these expressions with experimental results. It identifies the expressions that yield the most accurate prediction of the winding high-frequency resistance. The comparison shows that the method proposed by Dowell accurately predicts the ac resistance if the winding contains less than three layers. The methods proposed by several other authors accurately predict the high-frequency resistance only in certain frequency ranges. In addition, these expressions yield inaccurate results for the inductor quality factor. One expression, however, accurately predicts both the high-frequency winding resistance and the quality factor of inductors over a wide frequency range from the dc to the first resonant frequency. The paper concludes with a simple and accurate circuit model describing the frequency behavior of inductors.

Abstract-This paper presents the design, analytical estimation of power losses, and experimental measurement of choke inductors for switched-mode power inverters. The described approach is applicable to a wide variety of circuits such as Class-E inverters and converters. The expressions required to design the magnetic core in the choke inductor using the area-product ( A p ) method are given. The equations for the dc resistance, ac resistance at high frequencies, and dc and ac power losses are provided for the solid round winding wire. To validate the presented approach, an example class-E zero-voltage switching power inverter with practical specifications is considered. A core with air gap is selected to avoid core saturation in the choke inductor, which conducts dc current and a small ac current. The gapped core power loss density and power loss are estimated using Steinmetz empirical equation. It is shown that the winding power loss due to the dc current is dominant for the given design. A comparison between the area-product A p method and the preexisting core geometry coefficient K g method is presented. The measured magnitude of the inductor impedance has shown that the designed choke is useful up to ten times the switching frequency.

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