An accurate model for intrinsic dielectric loss in sapphire (α-Al2O3) is presented. The proposed model is based on a theory of electromagnetic field absorption governed by multiphonon relaxation processes influenced by a finite lifetime of thermal phonons. Expressions for anisotropic sapphire dielectric loss tangent are derived utilizing sapphire dielectric function given in terms of the quasiharmonic approximation. The frequency-dependent two- and three-phonon damping constants of each fundamental transverse optical mode were determined numerically employing the accurate anharmonic coefficient computations based on sapphire lattice-dynamical data. The results of the dielectric loss tangent calculations in microwave and millimeter-wave regions are presented. The developed sapphire dielectric loss model offers excellent agreement between the experimental and calculated magnitudes of the tan δ components and also accurately reproduces their frequency and temperature dependencies.
is 82%, has been increased to 90% as the lower cut-off frequency is further lowered due to insertion of slits in the ground plane. The radiation patterns at the resonant frequencies are measured and are as shown in the Figure 6. From the figures it is observed by inserting slits in the ground plane both H-plane and E-plane radiation patterns are quite closer to omnidirectional.
CONCLUSIONSCompact L-shaped notched printed antennas with dual slits for multiband and wideband applications are studied experimentally. Here, the ground plane is kept 2 mm away from the radiating patch. Two types of ground plane effects for the proposed antennas have been studied, which are one with rectangular ground plane and the other with modified ground plane, in which dual slits are introduced in the ground plane. Using rectangular ground plane, wideband and multiband operation is achieved with an overall bandwidth of 6.84 GHz (110%). And by using modified ground plane, the overall bandwidth of this multiband antenna is further increased to 7.86 GHz (114.5%). The over all size of the antenna is quite compact, i.e., 38 ϫ 38 mm 2 .
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