| In recent years,the multi-frequency,miniaturization and integration of the electronic communication system are becoming a trend with the rapid development of the corresponding technique in wireless communication field.As the structure of radio frequency integrated circuits and microwave circuit becomes more and more complex and multi-layered,cross-scale packaging and design problem is gradually highlighted.Hence,the design and efficient simulation of the interconnect structure in integrated circuit has become an important research orientation.Generally,the interconnect structure needs to work in a broadband.In low-frequency regime,the quasi-static method can be used to analyze the structure.Nevertheless,when the frequency rises to the microwave band,the electric field and magnetic field are coupled,which means the quasi-static method becomes unreliable.Therefore,the demand of the full-wave method to solve the broadband and multi-scale problem appears.Considering that the widespread application of low-frequency electromagnetic field in earthquake prediction,seabed exploration and biomedicine,a full-wave method which can cover static/quasi-static regime and microwave band has a good application prospect.Integral equation method is one of the commonly used full-wave methods for electromagnetic simulation.However,surface integral equation has low-frequency breakdown problem in static/quasi-static regime,which leads to the singularity of the coefficient matrix.It may influence the convergence performance when using an iteration method.Augmented electric field integral equation(A-EFIE)is one of the mainstream methods to solve low-frequency breakdown.This dissertation mainly solves the numerical cancellation of A-EFIE in low-frequency regime and achieve efficient simulation of electromagnetic structure.For the numerical cancellation of A-EFIE in low frequency regime,this dissertation proposes a generalized form for the augmented electric field integral equation with perturbation method to broaden the bandwidth of this method.Also,the formula corresponding to approximate solution and the expansion term of the A-EFIE matrix is derived.According to this formula,the method which can determine the expansion term of the A-EFIE matrix corresponding to the given frequency is proposed.Then,the quasi-Helmholtz projectors are combined with A-EFIE to solve numerical cancellation and ensure the efficiency of solving A-EFIE.Compared to perturbation method,this work does not need to solve A-EFIE on different frequency.The correct solution can be obtained by only one iteration.Meanwhile,this method can eliminate the singularity of A-EFIE matrix caused by charge neutrality.To improve the convergence performance when iteration solver applied,a tailored constraint preconditioner is constructed according to the new matrix.This method can solve the numerical cancellation for both plane wave scattering problem and circuit problem.The improved A-EFIE system is stable in low frequency regime.It can be applied to analyze scattering and radiation of electromagnetic objects and extract the capacitance and inductance parameters of microwave circuits.On the other hand,this dissertation investigates a fast frequency-sweep technique for the requirements of high-efficiency simulation.A model order reduction technique based on singular value decomposition is combined with A-EFIE.The reduced-order model of A-EFIE system can obtain the frequency response of microwave circuits in the given bandwidth rapidly.Because of the frequency dependence of A-EFIF matrix,the general Newton interpolation polynomial is used to expand the matrix.Moreover,an adaptive algorithm is proposed.This method achieves a good effect.It can be applied to obtain the frequency response of the wireless power transfer system,microwave circuit and antenna.Finally,the periodic Green’s function is applied with A-EFIE to analyze the periodic metasurface and frequency selective surface structure.This method can achieve the high efficiency of periodic structures.Numerical results show that this method can improved the efficiency of simulation compared to simulating the whole structure directly.Meanwhile,compared to electric field integral equation with periodic Green’s function,this method overcomes the bad convergence performance caused by refining the mesh.In consideration of the high efficiency simulation of periodic structure for A-EFIE,wideband simulation requirements of periodic structure are satisfied. |
