This paper presents simple correct models of high-temperature superconductor (HTS) film parameters at microwave frequencies. The models are based on the enhanced two-fluid model of a superconductor. The quasi-particle scattering and peculiarities of the normal conductivity of the HTS at microwaves, including residual resistance of a material, are taken into account. The difference between the known Gorter and Casimir two-fluid model of low-temperature superconductor and the enhanced two-fluid model of HTS is proven. A simple quasi-static model of current distribution across the microstrip line and coplanar waveguide is used for a simulation of a contribution of the superconductor transport processes into impedance per unit length of the transmission lines considered. The models developed were applied to a simulation of microstrip line and coplanar waveguide resonators. Good agreement of simulated results and measurements in a wide temperature range has been demonstrated. The model presented can be considered as a starting point for the formation of the computer-aided design (CAD) package of HTS microwave components.

Empirical model of the microwave properties of high-temperature superconductors

Cette Note est consacree a l'analyse spectrale d'un operateur non borne associe a un probleme de transmission bidimensionnel non coercif. Nous montrons par une methode d'equations integrales que si l'interface est reguliere, cet operateur est auto-adjoint a resolvante compacte. Si l'interface presente un coin, une etude des singularites par transformee de Mellin permet d'obtenir une condition necessaire et suffisante, portant sur le contraste entre les deux milieux, pour que l'operateur soit auto-adjoint. S'il ne l'est pas, nous donnons une caracterisation de ses extensions auto-adjointes.

Analyse spectrale et singularités d'un problème de transmission non coercif

A posteriori error estimates for a finite element approximation of transmission problems with sign changing coefficients

We consider the time-harmonic Maxwell equations, involving wave transmission between media with opposite sign dielectric and/or magnetic coefficients. We prove that, in the case of sign-shifting dielectric coefficients, the space of electric fields is compactly embedded in L 2. We build a three-field variational formulation equivalent to Maxwell system for sign-shifting magnetic coefficients and show that, under some suitable conditions, the formulation fits into the coercive plus compact framework. © 2008 World Scientific Publishing Company.

A new compactness result for electromagnetic waves. application to the transmission problem between dielectrics and metamaterials

The compact meander-shape configuration of planar resonators is suggested for applications in narrowband filters with quasi-elliptic characteristic. The quasi-elliptic frequency response with two transmission zeroes at the edges of the passband is provided by the specific symmetry of the coupled resonators and is controlled by an appropriate choice of the resonator dimensions and the couplings between the resonators. The 12-pole quasi-elliptic filter with 0.5% fractional bandwidth at 1.775 GHz has been designed using meander-line microstrip resonators and manufactured on a double-sided YBCO film on a LaAlO/sub 3/ substrate. The filter exhibited the in-band insertion loss less than 0.5 dB at T=60 K, the return loss of 20 dB, the out-of-band rejection better than 75 dB, and 40 dB/MHz slope of the characteristic.

Narrowband Y-Ba-Cu-O filter with quasi-elliptic characteristic

In this paper a macroscopic phenomenological model for the microwave properties of superconductors is presented. The model is based on the idea that there are two kinds of current carriers, and instead of the first London's equation a new equation is derived. This model can be applied to both low- and high-temperature superconductors. Using this model, an expression for the microwave surface resistance is derived and the surface resistance versus frequency is calculated. The results show that the relation between resistance and frequency is not R/sub 3//spl sim//spl omega//sup 2/ as indicated by both BCS theory and London model, but R/sub s//spl sim//spl omega//sup a/, where a is between 1 and 2 (e.g. a=1.35) for thin film high-T/sub c/ superconductors YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta//. The temperature dependence of R/sub s/ is simulated using the given model. These relations and the values of the surface resistance agree well with experimental results. A residual resistance may be interpreted from this model. >

Jian-Guo Ma

Papers

Modeling the microwave properties of superconductors