Method Of Moments Of Low-frequency Applications In Microwave Integrated Circuits And Electromagnetic Scattering

Applying numerical value algorithm to solve the problem of electromagnetic field by use of computer has gotten extensive application since the 1960's. Among the possible numerical methods applied to the analysis of this type of structures, the spatial-domain method of moment (MoM) in the mixed-potential integral-equation (MPIE) formulation is considered as one of the most powerful models for comprehensive treatment of various complex planar structures such as monolithic microwave integrated circuits (MMIC) and microstrip antennas.This thesis Firstly introduces the fundamentals of MoM and an accurate method exacting the network parameters of microwave integrated circuit called "Four-points technique". Secondly, the traditional MoM has numerical instability (the so-called low frequency breakdown) that occurs when frequency is low enough. At very low frequencies, the contribution from the vector potential to the impedance matrix is much smaller than the contribution from the scalar potential. Due to the finite machine precision, the contribution from the vector potential will be lost during the numerical process when ωâ†' 0. This makes the impedance matrix nearly singular and difficult to invert. To solve this problem, we introduce the Loop/Tree basis function which can separate the contribution from the vector potential and the scalar potential in the impedance matrix. We represent the unknown currents in terms of its solenoidal and irrotational components and use Loop/Tree basis function as the expansion function, respectively. The number of unknowns is equal to the conventional MoM's. Then we obtain the matrix equation by use of Galerkin's method and solve it by iterative solvers.