Measurement of electromagnetic parameters and FDTD modeling of ferrite cores

Abstract

The paper describes a methodology for an efficient design of novel products based on magneto-dielectric (ferrite) materials with desirable frequency responses that satisfy EMC and SI requirements. The methodology starts from estimating complex permittivity and permeability of these materials. This requires measurement techniques, approximation resultant frequency characteristics for permittivity and permeability using a curve-fitting procedure, and development of a full-wave numerical simulation tool that could deal with frequencydispersive materials. An example of a ferrite material measurement, constitutive parameters extraction using a genetic algorithm, and corresponding FDTD modeling over the frequency range from 10 to 500 MHz is provided.

A lumped-element circuit model of ferrite chokes

“…Measured frequency characteristics of µ and ε of ferrite chokes can be curve-fitted using (1) with an accuracy that depends on the number of terms. Typically, five terms are considered sufficient for material frequency dependencies of ferrites [9,10]. Curve-fitting using genetic algorithms works well [11], though any accurate curve-fitting technique may be applied.…”

“…Evaluated inductance as a function of frequency: (a) in present work; (b) using Fujiwara's equation[10].Once the resonance frequency and the inductance, ( ) res L f , is known, one can calculate the corresponding capacitance value by using the well-known relation…”

Behavioral Modeling of Complex Magnetic Permeability With High-Order Debye Model and Equivalent Circuits

“…The resulting effective permeability spectra are the quantity of interest in view of circuit simulation of networks in which such a core is arranged as an inductance or a transformer. Unlike measurement of the intrinsic permeability spectra, which requires the use of specific test fixtures as well as availability of suitable material specimens [14], the frequency response of the effective permeability spectra μr (ω) = µ (ω)−jµ (ω) of a magnetic core can be extracted by wounding a wire around the core, and by measuring the resulting input impedance. Once spurious effects introduced by the measurement setup (e.g., effects due to the input connector) have been excluded from the measurement data [18], the resulting impedance Ẑin is written as [7], [18]…”

Systematic Analysis and Engineering of Absorbing Materials Containing Magnetic Inclusions for EMC Applications

“…This curve-fitting procedure can be applied both to experimentally obtained (for example, using 7/3 mm coaxial airline technique and a vector network analyzer) and to modeled through mixing rules and of composites [8] (11) and (12) Such representation of frequency dependencies of dielectric and magnetic properties as sums of Debye-like terms is convenient for using them in the FDTD simulations. Previously, a curve-fitting technique based on the genetic algorithm (GA) optimization was used for extracting parameters of the Debye terms from experimentally available data [7], [8]. The GA flowchart is shown Fig.…”

“…An advantage of time-domain numerical techniques is the possibility of having broadband responses. To effectively model magneto-dielectric materials in time domain, it is important to represent frequency characteristics of both complex permittivity and permeability of these materials as analytical rational-fractional functions that would satisfy Kramers-Krönig causality relations (KKR) [6], for example, sums of the Debye terms with the poles of the first order [7]. If a material exhibits narrowband resonances, then Lorentzian terms with poles of the second order should be used [8].…”