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This paper presents a detailed design and modeling approach for power planes with integrated high-impedance electromagnetic surfaces (HIS). These novel power planes, which were introduced recently, have the unique ability of providing effective broadband simultaneous switching noise (SSN) mitigation. Full-wave electromagnetic simulation is used to study the impact of the geometry on the performance of these novel power planes. It is demonstrated that power planes using inductance-enhanced HIS can be designed for broadband mitigation of the SSN from the upper hundred megahertz to the gigahertz frequencies. Physics-based compact models for the unit cell of power planes with integrated HIS are developed and several of them connected in a two-dimensional array to build full models for large and multilayer power planes. The compact model offers fast analysis of power planes. As an example, we show that the full-wave simulation time of a 10×10 cm power plane with integrated HIS can be dramatically reduced from 24 to 48 h using a commercially available three-dimensional full-wave solver to less than 1 min when using the compact circuit model developed here.