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A novel miniaturized planar electromagnetic bandgap (EBG) structure is proposed for microprocessor packages. The design of the proposed EBG structure consisting of meander lines and patches are based on the use of high-k dielectric material with epsiv r ges 100. High-k dielectric material increases the effective capacitance of the EBG cell in comparison to commonly used materials with much lower dielectric constant. Simulation results are provided to show that using the proposed EBGs with periodicities less than 2 mm; it is possible to obtain a very wide stop-band (~10 GHz) in addition to more than 10 times in unit cell size reduction. This wide bandgap can cover the operating frequency of current processors and a wide range of the resonant frequencies of a typical package.