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 .
This paper develops the novel method of sapphire loaded cavity microwave oscillator frequency stabilization that uses dual-mode sapphire "whispering gallery" resonator (SWGR) oscillator operation and differs from similar approaches by using the output microwave frequency division to form a control signal [l, 21. In this paper the frequency control is based on two orthogonal "whispering gallery" (WG) modes where the main WGE-mode has twice as much resonant frequency than the auxiliary WGH-mode.A block diagram of the SWGR-based dual-mode oscillator'having the 1 :2 frequency divider into a microwave section of the temperature control loop (Fig. 1) incorporates a "usual" microwave SWGR-based oscillator with combined frequency stabilization [3] and an additional temperature control. A microwave section of the last network comprises the directional coupler DC1, the 1 :2 frequency divider, the microwave amplifier (MA) working at a half frequency and the SWGR WGH-mode input. A reflected signal selected with the 3-dB hybrid (3-dB-DC) goes to the phase detector (PD) via the low noise microwave amplifier (LNA). The other PD input is excited by the directional coupler DC2. The mentioned elements constitute together a highly effective interferometric frequency discriminator (FD) sensitive to temperature fluctuations [4]. FD output is filtered and amplified (LFF + LFA) after what the formed control .signal comes to the thermal actuators [i]. The completed temperature control system SWGR-based lnicnmne . ,Figure 1 -Block diagrat of the microwave SWGR-based dual-mode oscillator having the I :2 frequency divider into a microwave section of the temperature control loop. -' This work is sponsored by Russian Ministry on Education under a grant #209.04.01.020. 0-7803-7948-9/03/$17.00 92003 IEEE '
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