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An electrically small antenna based on a dielectric resonator antenna (DRA) is investigated. Two well-known simulation techniques, the finite element method and the finite integration technique have been applied to study a low volume high permittivity DRA. It is demonstrated that the design of a compact size and wide frequency coverage DRA for 2.4-2.5-GHz ISM frequency band is possible by proper selection of the resonator shape in combination with appropriate resonant modes. Numerical results for one particular antenna design are reported.