Modeling Of Moment Method Based On VSIE For Planar Multilayer Structure And Its Frequency Sweep

In the electromagnetic engineering problems,there are many planar structures,such as patch antennas,microstrip antennas,PCB plates,and frequency selective surfaces,which are of great value for studying the electromagnetic characteristics of such problems.With the development of computational electromagnetics and computer technology,the method of moments(Mo M)is widely used for full-wave simulation of such planar multi-layer structures due to its high accuracy and versatility.Compared to the surface integral equation(SIE),the volume integral equation(VIE)can deal with a planar structure with edges and corners without additional process to achieve high accuracy.Since there is a boundary condition where the electric field vanished in the dielectric-conductor interface,the basis function used to expand the electric flux density vector in the dielectric also needs to satisfy this condition.For the most commonly used SWG basis functions,it is difficult to accurately simulate the electric flux density vector in the dielectric because it does not satisfy the boundary conditions well.At the same time,for the frequency sweep in a wide frequency band,an impedance matrix calculation is needed at each frequency point to generate a complex high-order dense matrix,which makes the calculation process very time-consuming.It is also worthwhile to increase the efficiency of frequency sweep without sacrificing its accuracy.For the accurate and effective method of Mo M modeling in the model of planar multi-layer structure,this paper mainly focus the following work:1.In order to satisfy the boundary condition that the tangential electric field vanishes at the interface of the dielectric-conductor,we developed a basis function suitable for the planar structure.The basis function consists of tangential and normal components to expand the electric flux density.The tangential basis function can effectively satisfy the boundary condition where the tangential electric field is zero and simulate the change of the electric flux density near the interface of dielectric-conductor.And the basis function is relatively simple in meshing,and the number of unknowns is relatively smaller than that of the SWG basis functions.In the thin dielectric plate case,the accurate modeling can work well.2.For the singularity of VSIE,when the source basis functions are tangent basis functions and normal basis functions,the items with singularities are extracted.The volume integral is converted to a numerical line integral of the height and the surface integral of the triangular in analytical form.The integral on the rectangular element is divided into the sum of the integrals on the two triangular elements.The integrals in all regions are converted into the integral forms on triangular patches.The addition and subtraction singularities are used to divide the integrals into two items with singularity and no singularity.The part without singularity can be obtained by numerical integral,while the part with singularity is of analytical expression in the existing literature.3.For attaining the fast frequency response of the electromagnetic parameters in the broadband,the dominant phase factor in the impedance matrix element of the VSIE is extracted first,and the remained term of impedance matrix element from the RWG basis function is multiplied by the frequency f to eliminate drastic changes.Inter/Extrapolation Method based on the zero point of Chebyshev is used to obtain the interpolation matrix at the operating frequency,this can effectively reduce the matrix-filling time and significantly improve the efficiency of calculating electromagnetic characteristics over a wide frequency band.