Electromagnetic Modeling Of Grid Power Distribution Network

Grid power distribution network(PDN)is a very significant part in the electronic packaging,which is used to apply a stable and clear power to active circuits.Howerever,with the increase in the working frequency and the decrease in the working voltage,the parasitic parameters of the grid PDN would lead to the voltage drop.The voltage drop will couse electromagnetic fields between the power network and ground network in electronic system,which will lead to unwanted electromagnetic coupling and radition.With the lower supplied voltage,a large transient current flowing along the PDN will lead to the simultaneous switching noise(SSN),which produces problems of signal integrity(SI),power integrity(PI)and electromagnetic compatibility(EMC).Therefore,the estimation and calculation of the parasitic parameters of the grid PDN is very necessary.From the viewpoint of electromagnetic field,this dissertation mainly focuses on the electromagnetic modeling of the grid PDN,in order to simply the calculation and analysis of grid PDN parasitic parameters.The main work of this dissertation includes following three aspects.Firstly,this dissertation has proposed a closed-form solution for the impedance calculation of grid power distribution network.Through the comparison of the equivalent circuit of the unit cell between the grid PDN and plane PDN,the complex 3D grid PDN is equivalent to a simple 2D plane PDN with the same size.The parasitic parameter of this equivalent plane PDN can be calculated by the closed-form method.In order to further increase the accuracy of the proposed method,a modified modal function is proposed.And the original double series summation formula is reduced to a single series summation formula to accelerate the calculation.The results of 3D full-wave simulation and measurement are compared with the results of the proposed method to veritfy the closed-from method.The proposed closed-form method can further used to analyze the grid PDN modal voltage and current distributions,which can provide guidance for the distribution of decoupling capacitors in engineering application.Secondly,basing on the above method,this dissertation has proposed an efficient method calculate the impedance of grid power distribution networks with irregular shapes.Based on the analysis of the equivalent circuits of grid unit cell and plane unit cell,the irregular shaped grid PDN is simplified to a plane PDN with the same shape.Then,the equivalent plane PDN is efficiently calculated by the finite element method(FEM)due to its simplified structure.The proposed method promotes the effeiciency of calculation of the grid PDN with irregular shapes.Thirdly,parasitic inductance is one of the important parameters to estimate the quality of grid PDN.This dissertation has proposed a closed-form solution to calculate the inductance of the grid PDN..The proposed method also can be expanded to the case that the grid PDN has load impedances.In comparing with the numerical methods,the proposed method can give a more easy-to-understanding explanation of the new anti-resonant frequency produced by the load impedance.