856 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 4, JULY 2006 Frequency-Dependent Resistance in Litz-Wire Planar Windings for Domestic Induction Heating Appliances Jesús Acero, Member, IEEE, Rafael Alonso, José M. Burdío, Member, IEEE, Luis A. Barragán, and Diego Puyal Abstract—In this paper, the frequency-dependent resistance in Litz-wire planar windings for domestic induction heating appli- ances is analyzed. For these inductors, in which the size is not an es- sential constraint, an analytical model is developed based on the su- perposition of different loss effects in the wire. Eddy current losses, including conduction losses and proximity-effect losses, both in- ternal and external, were considered and modeled. The magnetic field necessary to evaluate the external proximity losses is as well analytically calculated considering the complete winding and load properties. To verify this model and its limitations, several induc- tors with different wires and numbers of turns were constructed and results with both non-loaded and loaded inductors are com- pared with theoretical predictions. Index Terms—Frequency-dependent resistance, home appli- ances, induction heating, Litz wire, resistance measurements. I. INTRODUCTION D OMESTIC induction cookers consist of an induction system situated below a metallic pan. The induction system is supplied by a medium-frequency power source, pro- ducing an alternating magnetic field. According to Faraday’s law the alternating magnetic field induces eddy currents in the metal pan and, additionally in ferromagnetic materials, produces magnetic hysteresis. Both phenomena heat up the pan. The induction system (see Fig. 1), which comprises the inductor itself and the pot, works like a transformer [1]: the winding is the primary and the pot is the secondary. Usually the power source is a resonant inverter operated between 20–60 kHz. A cooking surface consisting of a vitroceramic glass is placed between the winding and the pot. In commercial arrangements ferrite bars are placed under the winding mainly to shield the electronics situated below the induction system. However, in this paper, for simplicity, such ferrite bars are not included, considering that they do not affect the methodology proposed here. Traditionally the inductor was wound with solid wires, prin- cipally due to cost reasons. Fortunately in traditional arrange- ments, a considerable efficiency is achieved with such wires due to the relatively low operating frequencies (about 20–30 kHz). Manuscript received April 22, 2005; revised September 9, 2005. This work was supported in part by the Spanish MEC under Project TEC 2004-02545, by DGA and Bosch and Siemens Home Appliances Group. Recommended by Associate Editor J. A. Ferreira. J. Acero, J. M. Burdío, L. A. Barragán, and D. Puyal are with the Depar- tamento Ingeniería Electrónica y Comunicaciones, Universidad de Zaragoza, Zaragoza 50018, Spain (e-mail: jacero@unizar.es). R. Alonso is with the Departamento Física Aplicada, Universidad de Zaragoza, Zaragoza 50009, Spain. Digital Object Identifier 10.1109/TPEL.2006.876894 Fig. 1. Basic induction system structure. Pot, cooking surface, and winding. In these systems, an appreciable efficiency is reached with ferro- magnetic pans. However, nowadays, in order to achieve a better design and a global optimization of the efficiency, Litz-wire in- ductors are used in the same way that Litz wire is used in mag- netic components for switching mode power supplies (SMPS). In addition, some users require the capability to heat non fer- romagnetic pots and, consequently, the market of the all-metal appliances (those that can work with pots made of any metal) is increasing. The simplest way to increase the induction heating is to increase the frequency of excitation currents [2], however it is well know that this also increases the ac losses in the windings and, as a result, the induction heating efficiency is not increased appreciably over a critical frequency [2]. Some all-metal appa- ratus have been patented [3] in which mainly two strategies are used: first, higher operating frequencies are used and second, inductors are wound with Litz wire. The ac losses in Litz wire used in components for SMPS have been analyzed in different ways: — using the finite element analysis (FEA) [4]–[6], applied principally to high frequency transformers; — using analytical models [7]–[10]. In such devices, the losses depend on the magnetic field applied to conductors. The magnetic field has been calculated using an analytical one-dimensional (1-D) approximation according to Ampère’s circuital law [8], [11], [12], [14]; but normally two-dimensional (2-D) effects are significant and in these cases finite-element or other numerical field-calculation methods are used [4]–[6], even a computationally-efficient method has been proposed [16] in order to reduce the high computational cost inherent to the calculation of the eddy currents in conductors. The objective of the present work is to develop a frequency- dependent model to evaluate the losses in planar windings for induction heating appliances. Taking advantage of cylindrical symmetry, an analytical model for loss calculations in Litz-wire 0885-8993/$20.00 © 2006 IEEE