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This paper investigates the behavior of heterogeneous dielectric substrates synthesized by adding micro-sized inclusions to a host medium. This paper compares different analytical formulations for small spherical inclusions in infinite media and assesses their suitability to be applied to different geometries. The effective permittivity of the mixture has been shown to be dependent on the properties of the host and inclusions' materials as well as the size and spacing of the spheres. Electromagnetic (EM) simulations using a plane wave excitation have also been carried out investigating thin (finite) layers of both spherical and cubical inclusions. A rectification algorithm was employed to correctly obtain the effective permittivity from the scattering parameters. The analytical results of the infinite medium showed good agreement with the EM simulations of our samples of finite thickness. Finally, a patch antenna with a heterogeneous substrate has been designed to show that the method can be applied to a finite geometry which is finite in three dimensions.