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In this paper, we propose a novel field-circuit method for the signal and power integrities simulation of power distribution networks. The electromagnetic field inside the power distribution network is expressed in the modal field distribution. The modal field is then decomposed into the parallel plate mode and transmission mode, which are related to the power-ground planes and signal traces respectively. Integral equations are created for these two modes. During the discritization of the integral equations, network ports are defined between the power-ground planes and signal traces. In this way, their equivalent networks are extracted through the moments method solution of the integral equations. Finally, the two equivalent networks are combined to provide the whole circuit model of the power distribution network. This circuit model can be used for the signal and power integrities analysis. Through numerical examples, the accuracy and efficiency of the proposed method is verified.