Research On Integral Equation Modeling Method Of Irregular Multiple Vias

As important structure of multilayer printed circuit board(PCB),vias can cause a series of signal integrity(SI)problems due to their discontinuity,and the coupling between vias can lead the power integrity(PI)and electromagnetic interference problems.Therefore,in order to ensure the success of the system design,accurate and effective via modeling is very important.With the development of science and technology,more and more compact via structures are designed.In these PCBs with compact vias,some of them have irregular shape,and some of them have antipads with multiple vias sharing.These complex structures present a new challenge to the via modeling.This paper mainly discusses the integral equation modeling methods for power ground plane with irregular antipads that multiple vias share(hereinafter referred to as the irregular multiple vias structure).Three kinds of modeling methods are as follows: the contour integral equation method(CIE),TE-based integral equation method(TE is short for (?) · (?) where (?) denotes a unit tangent vector),and EFIE-PMCHWT-based integral equation method,which are discussed in three parts.First,based on the equivalence principle,a new derivation method of contour integral equation is proposed,and the result of the idea is consistent with that of the existing method.After that,numerical examples are used to verify the contour integral equation method,and the advantage of the contour integral equation method is illustrated by comparing with the three-dimensional full wave method.Finally,the limitations of the contour integral equation method are studied.It is pointed out that when the working wavelength can be compared with the thickness of the power ground plane,the contour integral equation will fail and the method can not model the via structure.Therefore,the three-dimensional integral equation modeling method is introduced.Second,for the three-dimensional integral equation modeling method,TE-based integral equation method is proposed which tests both electric current and magnetic current well.Firstly,the unified integral equation of the irregular multiple vias structure is obtained by this method.After that,in order to solve the unified integral equation,the moment method and the integral equation of the perfect electrical conductor are studied respectively,which lays the foundation for the solution of the unified integral equation.However,this method can not deal with the internal resonance caused by the power ground plane and the impedance matrix generated in the modeling process has poor performance.Therefore,EFIE-PMCHWT-based integral equation method is introduced.Third,use EFIE-PMCHWT-based integral equation method to model the irregular multiple vias structure.In order to solve conveniently,the vias are approximated by metal strips.EFIE is used on the conductor surface,and PMCHWT is used on the dielectric surface.Then the EFIE-PMCHWT-based integral equation method is constructed.After that,the method is verified by the examples.In the modeling process,because the vias are approximated by metal strips,the equivalent relationship and error between the real via structure and the via structure using metal strip approximation are analyzed finally.