Air Gap Tuning Effect on the Resonant Frequency and Half-power Bandwidth of Superconducting Microstrip Patch

Abstract

An accurate analysis of an air gap tuned high Tc superconducting microstrip an- tenna is presented. To include the efiect of the superconductivity of the microstrip patch in the Full wave analysis of the tunable rectangular microstrip patch, a surface complex impedance is considered. This impedance is determined by using London's equation and the model of Gorter and Casimir. Numerical results obtained are found to be in excellent agreement with the the- oretical and experimental data available in the literature. Finally, numerical results for the air gap tuning efiect on the operating frequency and bandwidth of the high Tc superconducting microstrip antenna are also presented. Rectangular microstrip patches can flnd an application in microwave integrated circuits as planar resonators for oscillators and fllters. Also, rectangular microstrip patches can be used as resonant antennas fed by means of either coaxial probes, or microstrip lines. Since the bandwidth of mi- crostrip patch resonators and antennas around their operating resonant frequencies is known to be very narrow, it is important to develop accurate algorithms for the computation of those res- onant frequencies. The resonant frequency value of the rectangular microstrip patch depends on the structural parameters, and it is evident that if the resonant frequency is to be changed, a new microstrip antenna is needed. In order to achieve tunable resonant frequency characteristics, an adjustable air gap layer can be inserted between the ground plane and the substrate, resulting in a two-layer structure (1,2). Apart from tunable microstrip patches, in the last few years, there has been a growing interest in the use of superconducting materials in microwave integrated circuits, which is due to their main characteristics, such as: very small losses, which means low-attenuation and low-noise, very small dispersion up to frequencies of several tens of GHz, smaller devices due to the lower losses, which leads to larger integration density and reduction in the time of propagation of the signals in the circuits (3). In this paper, a rigorous Full-wave analysis of an air gap tuned high Tc superconducting mi- crostrip antenna is presented. To the best of our knowledge, this structure has not been analyzed previously. Only results for the case of perfectly conducting patch have been reported in the open literature (1,2). In Section 2, the authors provide details of the application of the Galerkin's method in the Fourier transform domain to the analysis of high Tc superconducting microstrip antennas with air gaps. In Section 3, the validity of the solution is tested by comparing the computed results with theoretical and experimental data available in the literature. Numerical results for the air gap tuning efiect on the operating frequency and half power bandwidth of the high Tc superconduct- ing microstrip patch antenna are also presented. Finally, concluding remarks are summarized in Section 4. 2. OUTLINE OF THE NUMERICAL PROCEDURE The high Tc superconducting microstrip patch antenna considered in this work is shown in Figure 1. It was obtained by depositing a superconducting patch of thickness e on a dielectric layer. The dielectric layer of thickness d2 is characterized by the free-space permeability 0 and the permittivity 0, r (0 is the free-space permittivity and the relative permittivity r can be complex to account for dielectric loss). An adjustable air gap layer of thickness d1 is inserted between the substrate and the perfectly conducting ground plane. Following the conventional spectral domain approach, the Fourier transform domain relationship between the surface electric fleld at z = d1 +d2 and surface