Numerical Modeling of Magnetic Characteristics of Ferrite Core Taking Account of Both Eddy Current and Displacement Current.

摘要

Summary form only given. Ferrite cores are widely used in transformers and inductors, etc. for high frequency electronic devices because of high magnetic permeability and low conductivity. In the magnetic field analyses of such magnetic devices using a ferrite core, the frequency-domain analysis is often carried out using measured effective complex permeability under different frequencies. However, the harmonics caused by the magnetic nonlinearity of the ferrite core cannot be evaluated by using the frequency-domain analysis. To carry out the time-domain analysis of ferrite core taking account of the nonlinearity of the core, the modeling method of the effective complex permeability characteristics, which decreases in high frequency region due to dimensional resonance, should be established. In this paper, a simple finite element magnetic field analysis model taking account of eddy current and displacement current is proposed. The suitable conductivity and permittivity which can realize the effective complex permeability is investigated by using the catalogue data of a toroidal MnZn ferrite core. 2. Analysis Model and Method In this paper, our investigation is carried out using the data in the catalogne [2] of a toroidal MnZn ferrite core (TDK/EPCOS: T37). In [2], the real part and imaginary part of complex relative permeability with different frequency, measured using the toroidal core (outer radius: 16 mm, inner ra dius 9.6 mm, height: 6.3mm), and its conductivity cy =5 S/m are shown. The frequency characteristics of the complex permeability in the catalogne are tried to be represented by using the magnetic fi eld analysis. The ac linear steady state axisymmetric magnetic fi eld analysis taking account of eddy current and displacement current is carried out using the A method (A: magnetic vector potential) with the first order square edge finite element method and the phasor method. The fundamental equation is shown as follows: roftvrotA)=-jwca+co 2 wi where v is reluctivity and w is angular frequency. The superscript (.) denotes the complex variable. The first term in the right-hand side is the eddy current and the second term is the displacement current. The permeability 11, 0 of ferrite core is set to be 6100 by referring at 10 kHz because which is generated by hysteresis phenomena and eddy current effect, is relatively small and it can be neglected at 10 kHz. The original conductivity 0 0 is set to be 5 S/m following the catalogue [2]. The original relative permittivity e B0 is set to be 300 which is a typical value of MnZn ferrite core. The conductivity cy and relative permittivity e B are adjusted to realize the frequency characteristic of the effective complex permeability. 3. Results and Discussion First, the frequency characteristics of the complex effective permeability and calculated using the original conductivity 0 0 and relative permittivity e B0 are compared with those in catalogne data. The tendencies of the calculated permeability are similar with the catalogne data. Namely, both the real and calculated do not change in lower frequency region and they decrease in higher frequency region. Moreover, both the real and calculated increase in lower frequency region and they decrease in higher frequency region. However, the peak positions are shifted and the gradients are different with each other. Therefore, to realize the real frequency characteristics, the conductivity and relative permittivity should be changed. The frequency characteristics of the complex effective permeability and calculated using the modified conductivity cy = 4 , and permittivity e B = 400 E, 0 are compared with those in catalogne data. The calculated complex permeability has relatively large error in the low frequency region. However, the frequency characteristics of the complex permeability in catalogne data can be represented roughly overall by changing both the conductivity and permittivity. As basic investigation, only linear ac steady state magnetic field analysis of a simple model is carried out in this paper. However, the time domain analysis taking account of nonlinear magnetic characteristics for more actual model can be carried out using the suitable conductivity (i.e. σ = 4σ) and permittivity (i.e. e B = 400 e so ) obtained from the simple method proposed in this paper.