Analytical approach of permittivity and permeability of spiral-resonator shaped planar structure implemented as antenna radiator

This paper presents analytical approach of permittivity and permeability of planar structure which takes a shape of spiral-resonator (SR) implemented as an antenna radiator. The use of planar structure for instance as an antenna radiator is recently required in order to have communication devices with compact and light in weight. The approach is carried out by calculating the effective impedance of SR shaped planar structure through its equivalent circuit which consists of resistance, inductance, and capacitance. Afterwards, the effective permittivity and permeability are obtained. To verify the proposed analytical approach, the SR shaped planar structure is also characterized using 3D simulation software to gain the effective permittivity and permeability. It shows that the effective permittivity and permeability which are yielded from simulation and analytical approach have good agreement each other for positive permittivity (μ > 0) and negative permeability (μ < 0) at the frequency range above 0.8 GHz.