The reliability of electromagnetic relay (EMR) which contains a permanent magnet (PM) can be improved by a robust design method. In this parameter design process, the calculation of electromagnetic system is very important. In analytical calculation, PM is often equivalent to a lumped parameter model of one magnetic resistance and one magnetic potential, but significant error is often caused; in order to increase the accuracy, a distributed parameter calculation model (DPM) of PM bar is established; solution procedure as well as verification condition of this model is given; by a case study of the single PM bar, magnetic field lines division method is adopted to build the DPM, the starting point and section magnetic flux of each segment are solved, a comparison is made with finite element method (FEM) and measured data; the accuracy of this magnetic field line based distributed parameter model (MFDPM) in PM bar is verified; this model is applied to the electromagnetic system of a certain type EMR, electromagnetic system calculation model is established based on MFDPM, and the static force is calculated under different rotation angles; compared with traditional lumped parameter model and FEM, it proves to be of acceptable calculation accuracy and high calculation speed which fit the requirement of robust design.

A semi-analytical method for a planar periodic array formed by a finite number of magnetized ferrite circular cylinders is presented using a model of layered cylindrical structures. The method uses the T-matrix approach and the extraction of the reflection and transmission matrices based on the cylindrical harmonic mode expansion. Based on the proposed method, plane wave scattering by the finite number of magnetized ferrite circular cylinders is numerically studied from the viewpoint of realization the electronic switching and electronic scanning effects by varying the applied magnetic field.

Evaluation of addition coefficients introduced by the addition theorems for vector spherical harmonics is one of the most intractable problems in electromagnetic scattering by multi-sphere systems. The derivation of the analytical expressions for the addition coefficients is lengthy and complex while the computation of the addition coefficients is annoyingly time-consuming even with the reasonably fast computers available nowadays. This paper presents an efficient algorithm for calculating addition coefficients which is based on the recursive relations of scalar addition coefficients. Numerical results from the formulation derived in this paper agree with those of previous published results but the algorithm proposed here reduces the computational time considerably. This paper also discusses the strengths and limitations of other formulations and numerical techniques found in the literature.