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In recent studies, high-impedance surfaces (HIS) also known as electromagnetic bandgap structures (EBG) have been successfully employed to suppress simultaneous switching noise (SSN) generated between power buses of printed circuit boards (PCB). HIS structures, when embedded in a PCB, can suppress electromagnetic wave propagation within a predictable range of frequencies. In this paper, a highly-accurate model for HIS structures embedded in PCBs is presented. This circuit is then added to a physics-based model for power buses of PCBs, creating a compact 3D model to represent the power bus together with Embedded HIS (EHIS) structures. The circuit models presented allow for accurate prediction of the center frequency and bandgap of the EHIS without a priori full-wave modeling of single or multiple cells.