Electrically small oblate spheroidal and spherical antennas in confocal shells with negative permittivity represent perspective antenna design to combine moderately small size, wide bandwidth, high e±ciency and power of radiation. However, optimization of the antennas performance parameters imposes contradictory restrictions on permittivity of the shells, electrical size of the antennas, shape of the antennas and shells. Simulation results based on method of eigen-functions have shown that the antennas can be tuned on resonance for small magnitudes of negative permittivity of the shells and antiresonance for higher magnitudes. Optimal combination of power and efficiency of radiation of the antenna and the quality factor is obtained in an intermediate range of negative permittivity by combining merits of resonance and antiresonance of the antenna. Antiresonant range of the oblate spheroidal antenna emerges for lower permittivity magnitudes as compared with the spherical antenna. As a result, the optimal size of the shell of oblate spheroidal antenna is comparatively small. However, more gradual emerging of antiresonant properties of the spherical antenna makes spherical design more suitable for higher level of inherent absorption of the shell medium with negative permittivity.
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