PIERS ONLINE, VOL. 5, NO. 4, 2009 346 Study of High T c Superconducting Microstrip Antenna T. Fortaki 1 , M. Amir 1 , S. Benkouda 1 , and A. Benghalia 2 1 Electronics Department, University of Batna, Algeria 2 Electronics Department, University of Constantine, Algeria Abstract— Resonant characteristics of microstrip antennas with superconducting ﬁlms is pre- sented. The analysis is based on a full electromagnetic wave model with London’s equations and the two-ﬂuid model. It is shown that the full-wave analysis presented here gives numerical results which are in excellent agreement with the measured data available in the literature. Re- sults showing the eﬀect of the temperature on the resonant frequency and half-power bandwidth of superconducting microstrip antenna are given. Variations of the resonant frequency with the high T c superconducting ﬁlm thickness are also presented. 1. INTRODUCTION Superconducting passive microwave devices such as antennas, ﬁlters, transmission lines, and phase shifters have shown signiﬁcant superiority over corresponding devices fabricated with normal con- ductors such as gold, silver, or copper due to the advantages of superconductors [1]. Advantages of using high T c superconducting materials at high frequencies include [2]: 1) very small losses, which means reduction of attenuation and noise level; 2) very small dispersion up to frequencies of several tens of GHz; 3) smaller devises due to the lower losses, which leads to larger integration density; and 4) the propagation time can be greatly reduced because of the smaller size and the shorter interconnects. In the literature, the studies concerning the resonance characteristics of microstrip antennas using perfectly conducting patches are abundant. However, few works have been done for the case of microstrip antennas using superconducting patches. The determination of the resonant frequencies of superconducting microstrip patch antennas was initially carried out by means of the magnetic wall cavity model [3]. Later on, these resonant frequencies were obtained by using the rigorous full-wave analysis [4]. To validate the theoretical analysis, the authors in [4] have compared their numerical results with the experimental data of Richard et al. [3]. This comparison has not been done in a convenient way for two reasons: the variation of the permittivity of the lanthanum aluminate substrate with the variation of the temperature, as indicated by the experiment of Richard etal. [3], has not been take into account by Silva etal. [4] and the eﬀect of varying the temperature on the resonant frequency is insigniﬁcant. In this paper, we present a theoretical and numerical analysis of the resonant frequencies of high T c superconducting rectangular microstrip antennas which yields excellent agreement with the mea- sured data of Richard et al. [3]. To include the eﬀect of the superconductivity of the microstrip patch in the full-wave analysis, a surface complex impedance is considered. This impedance is de- termined by using London’s equation and the two-ﬂuid model of Gorter and Casimir [2]. Numerical results for the eﬀect of the temperature on the resonant frequency and half-power bandwidth of superconducting microstrip antenna are given. Finally, the inﬂuence of the thickness of the high T c superconducting ﬁlm on the resonant frequency is also presented. 2. THEORY The problem to be solved is illustrated in Figure 1. We have a rectangular superconducting patch of thickness e printed on a dielectric layer. The dielectric layer of thickness d is characterized by the free-space permeability μ 0 and the permittivity ε 0 ε r (ε 0 is the free-space permittivity and the relative permittivity ε r can be complex to account for dielectric loss). The superconducting patch is characterized by a critical temperature T c , a zero-temperature penetration depth λ 0 , and a normal state conductivity σ n . Following a mathematical reasoning similar to that shown in [5, Equations (2)–(14)] for obtaining a relation among the surface electric ﬁeld at the plane of the superconducting patch and the surface current on the patch in the spectral domain given by  ˜ E x ˜ E y  =  Q xx Q xy Q yx Q yy  ·  ˜ J x ˜ J y  (1)