The design of integrated systems requires the knowledge of the values of the effective permittivity of the substrate. Designing antenna using computer-aided design tools is a long process that necessitates doing iterative steps to find the correct dimensions that meet specific requirements at a certain operating frequency. The objective of this work is to propose an analytic model to reduce the time required for the design. By using electromagnetic simulation, the effect of the relative permittivity and the height of the substrate on the final effective permittivity have been studied. An analytic model that helps the designer in estimating the value of the effective permittivity has been proposed.