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A novel miniaturized simple planar electromagnetic bandgap (EBG) structure is proposed. The new structure mitigates different types of electromagnetic noise in packages. The design of the new EBG structure proposed here relies on the use of high-k dielectric material (epsivr >100), and consists of Meander lines and patches. The Meander lines serve to provide current continuity bridges between the capacitive patches. High-k dielectric material increases the capacitance of the patches substantially in comparison to commonly used material with much lower dielectric constant. Simulation results are provided to show that using the proposed EBG, it is possible to obtain a very wide stop band (~ 10 GHz) which covers the operating frequency of current processors and a wide range of the resonant frequencies of a typical package. The wideband is obtained using a unit cell of less than 2 mm.