IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 48, NO. 2, APRIL 1999 663 An Automated Measurement System for Core Loss Characterization Adalberto J. Batista, Jo˜ ao Carlos S. Fagundes, and Philippe Viarouge Abstract— This paper describes an automated measurement system for core loss characterization. This system can accomplish these aims, within speciﬁed magnetic induction and frequency ranges, and at different temperatures, with high accuracy, due to the techniques used in the acquisition and computation of the waveforms involved in loss calculation. The core loss characteri- zation, obtained by ﬁtting the core loss density (per unit volume) versus frequency and magnetic induction, permits the use of an equation, which is a very useful tool for the design optimization of high frequency magnetic components, such as transformers and inductors for switched mode power supplies. Index Terms— Automated measurement systems, core losses, design optimization, inductors, transformers. I. INTRODUCTION T HE design of compact and efﬁcient magnetic compo- nents used in high frequency power conversion, such as transformers and inductors for switched mode power supplies, has been hindered by the lack and unreliability of loss data for magnetic materials, in particular ferrites. Several attempts [1]–[5] have been made to establish a reliable method suitable for core loss measurement at high frequencies. In such mea- surements, the major challenge is to minimize amplitude and phase errors introduced by parasitic effects in the circuit, by time delays in the coaxial cables and oscilloscope, and by the digitizing process. As a large amount of data is usually to be gathered, it is highly desirable that the measurement method used be automated in addition to being accurate and reliable. The purpose of this paper is to present an improved and automated measurement system for core loss characterization, under sine wave or square wave voltage excitation. This system can accomplish these aims, within speciﬁed magnetic induction and frequency ranges, and at different temperatures, with high accuracy, due to the techniques used in the ac- quisition and computation of the waveforms involved in loss calculation. II. MEASUREMENT SYSTEM Fig. 1 presents a block diagram of the measurement system in the case of sine wave excitation. In this case, a power Manuscript received July 2, 1998. A. J. Batista, Escola de Engenharia El´ etrica, Universidade Federal de Goi´ as, 74605-220 Goiˆ ania, Brazil (e-mail: batista@eee.ufg.br). J. C. S. Fagundes is with the Instituto de Eletrˆ onica de Potˆ encia, Uni- versidade Federal de S. Catarina, 88040-970 Florian´ opolis, Brasil (e-mail: fagundes@inep.ufsc.br). P. Viarouge is with the Department de G´ enie Electrique, Universit´ e Laval, Qu´ ebec, P.Q., Canada G1K 7P4 (e-mail: viarouge@gel.ulaval.ca). Publisher Item Identiﬁer S 0018-9456(99)02919-8. ampliﬁer, whose bandwidth is 10 kHz to 250 MHz and maximum output power is 35 W, is used. As explained later, an adequate static converter replaces the power ampliﬁer for square wave excitation. In this diagram a toroidal core of the material under test (CUT) is wound as an N : N transformer with the winding turns equally distributed on its periphery in a temperature- controlled environment. The magnetic induction in the core is inferred from a voltage measurement at the open circuit secondary winding, so that the effect of the voltage drop, due to the leakage inductance and winding resistance, is avoided. In fact, a voltage divider is used in the secondary circuit, i.e., a resistor in parallel with a capacitor is introduced in this circuit to form a voltage divider with the respective input impedance of the oscilloscope. The probe so constituted is compensated in frequency as an ordinary probe at the test temperature. The primary current is determined from a voltage measurement at the terminals of a current-sensing resistor (CSR), from which the magnetic ﬁeld in the core is computed. For comparison purposes, a current probe can also be used for sensing the primary current. The core loss is obtained by computing the mean of the product between primary current and secondary voltage referred to the primary, over an integer number of acquired cycles. For such data to be truly descriptive of the material, i.e., independent of the size and shape of the core, the eddy current loss must be excluded, either by using cores suitably dimensioned to make this loss negligible or by calculating its magnitude and subtracting it from the measured loss. In practice, most measurements have been made on a small toroid, typically 15/25 mm in inner/outer diameter and 5 mm in height. It is to be expected that in such a core the eddy current loss density is negligible and the magnetic induction in its cross section area is more uniform [3]. A speciﬁc software, based on the virtual instrument con- cept [6], was developed to perform acquisition, analysis, and presentation of the measurement data; instruments and measurement process control; and output data computation and presentation. The computer communicates with the in- struments through a GPIB interface. A. Mathematical Analysis The goal of the mathematical analysis is to relate the digitized voltage waveforms to the primary current and to the secondary voltage referred to the primary, and hence to the magnetic ﬁeld and to the magnetic induction in the core, respectively. This section describes the expressions used to calculate all these variables, and to model the core loss density; 0018–9456/99$10.00  1999 IEEE