Investigation and Modeling Nonlinear Characteristics of High-Tc Superconducting Resonators

The high-quality resonators and pass-band filters based on high-T _c superconducting (HTS) films are of the most interest for practical applications. The industrial application of the devices is retarded by nonlinearity of the film surface impedance under microwave power of a high level. The phenomenological model of nonlinear characteristics of HTS resonators was developed and applied to different kinds of planar resonators: disk, parallel plate, and micro-strip resonator. A comparison of experimental and modeled characteristics of the resonators revealed the distinctive difference in the model parameters. Some limiting characteristics are discussed.     

Resonant measurements of surface resistance of high-Tc superconducting films: How good or bad are they?

Errors in measurements of surface resistanceR _s of HTS materials are due to discrepancy between a mathematical model describing physical phenomena and a real measurement environment, finite accuracy of measurements of theQ-factor, and finite accuracy of constants used for calculation ofR _s . In this paper we analyze errors inR _s due to uncertainties in theQ-factor, geometrical coefficients, loss tangent,R _scu, and other factors when a cylindrical copper cavity with an HTS end plate, a stripline resonator, and sapphire rod resonators are used for HTS characterization.     

Harmonic Balance Algorithms for the Nonlinear Simulation of HTS Devices

This paper describes the application of Harmonic Balance algorithms to predict nonlinear effects in planar High Temperature Superconductors (HTS) microwave circuits. The resulting algorithms are fast and efficient and can be used both for the characterization of the nonlinearities in the HTS material, and for the prediction of the behavior of an HTS circuit given the parameters of these nonlinearities (such as a dependence of the surface impedance on the current density). Most previously published nonlinear HTS models can be used, because the algorithms are not restricted to a specific model of HTS nonlinearities. Two different types of algorithms are described: (1) algorithms specific for one-dimensional resonators (transmission lines and TM₀₁₀ disk resonators) and (2) an algorithm based on the combination of Method of Moments and Harmonic Balance, applicable to 2D planar structures with few restrictions in their shape. Several cross-checks with theory and measurements are presented.     

Dielectric resonator as a possible standard for characterization of high temperature superconducting films for microwave applications

The performance of several designs of dielectric resonators used for microwave characterization of FITS films has been analyzed from the point of view of accuracy, sensitivity, and range. Designs discussed include Hakki-Coieman shielded types as well as open-ended resonators with sapphire, rutile and (ZrSn)TiO₃ dielectrics. The best dielectric resonators have proved to have an uncertainty in surface resistance measurements only twice the uncertainty in theQ-factor. high sensitivity, and ability to measure a wide range of surface resistances. Hence the dielectric resonator technique can be considered as a standard for measurements of surface resistance of HTS films for wireless and PCS communication systems applications provided that adequate measurement procedures of theQ ₀-factor are followed.     

Low Loss Sintered Dielectric Resonators with HTS Thick Films

The combination of high-Qdielectric resonators and high-temperature superconducting (HTS) films offer many advantages in the area of cellular and satellite communications. The high cost of single crystal dielectrics and HTS thin films may be unattractive in certain applications. Superconducting thick films and polycrystalline ceramic dielectrics offer a high performance, low-cost alternative to high-Qthin film/single crystal dielectric resonators. The loss of polycrystalline ceramics of A1₂O₃, Ba(Mg_1/3Ta_2/3)O₃ (BMT), and Zr_0.875 Sn_0.25Ti0.875O₄ (ZTS) has been studied. Alumina, A1_2Oin3, has been studied as a model material for dielectric loss. Theory predicts that the loss in single crystal sapphire should follow aT ₅ dependence. However, at low temperatures the loss is dominated by extrinsic losses due to crystal imperfection, residual dopant atoms, dislocations, and other lattice defects and theT ₅ dependence does not hold. In polycrystalline alumina the intrinsic loss is immediately masked by these extrinsic losses, even at room temperature, and a simpleT dependence is observed. Results on polycrystalline alumina show that Q’s well in excess of 105 at 10 GHz and 77 K can be achieved in a design made compact by the use of a HTS thick film shield.     

Experiments and Model of Intermodulation Distortion in a Rutile Resonator with Y-Ba2-Cu3-O7?δ Endplates

We have derived general equations to calculate intermodulation distortion in resonators with high temperature superconducting (HTS) films which are not restricted to a specific resonator shape and may be used whenever the fields in a resonator generate currents on the surface of one or more HTS films. These equations are applied to rutile-loaded cavities with one or two 10 × 10 mm² Y-Ba₂-Cu₃-O^7– endplates and are used to extract parameters characterizing the nonlinearities of these films from intermodulation measurements. Even though the films have similar small-signal performance, we have found large variation in the strength of their nonlinearities.     

Field Deployable Microwave Filters Made from Superconductive Thick Films

Radio frequency (RF) resonators are made by depositing thick films of YBa₂Cu₃O_7– onto three-dimensional substrates. The superconducting resonators are then coupled together to form high performance RF filters. The topologies and frequency responses of some of these devices are briefly discussed prior to beginning a more detailed discussion aimed at addressing some of the common misconceptions of high temperature superconductive (HTS) thick film devices, namely the nonlinearity and the size. The intermodulation distortion (IMD) is shown to be below the noise floor in most practical applications, and a mathematical model that uses the empirical surface impedance data to predict the behavior of the IMD is described.     

Modeling and experimental investigation of microstrip resonators and filters based on High-Temperature Superconductor films

Complex approach to the investigation of microstrip resonators and filters based on High-Temperature Superconductor (HTS) films is described, which includes modeling of the electrodynamic parameters of HTS films, designing of microstrip resonators and filters, their manufacturing, and testing. Test samples were prepared using YBCO films on 0.5-mm-thick lanthanum aluminate substrates. The resonators and filter structures were patterned using ion-beam photolithography. Experimental data were used to determine the parameters of the model of surface impedance of the YBCO film and the film thickness and permittivity. Adequacy of the model and reliability of the model parameters, which were used for the synthesis and design of a 4th-order filter, were confirmed by coincidence of the experimental and calculated characteristics.     

Thin Film Tl-Based HTS Microwave Devices

Linear microstrip resonators suffer from high peak current density inside the resonators which limit the power handling characteristics. To realise higher power filters for cellular applications it is possible to use two dimensional microstrip resonators (such as disks) to equalise the internal current distribution. We have designed and tested such microstrip resonators, fabricated from TBCCO 2212 thin films deposited by RF sputtering onto 10×10mm and 20×20mm LaAlO₃, substrates. The R_s of such films has been measured at 24 GHz using a sapphire dielectric resonator and shown to be less than 500 scaled to 10 GHz and at 80K. Q values of 3-12 GHz disk resonators have demonstrated considerable improvements when compared to both linear HTS microstrip resonators and comparable copper disk resonators. Additionally, the power handling of such resonators has been shown to be superior to that of conventional linear resonators fabricated from similar material.     

Dielectric Resonators for the Measurement of Superconductor Thin Films Surface Impedance in Magnetic Fields at High Microwave Frequencies

We present the design and realization of cylindrical dielectric resonators operating in the 40–60 GHz frequency range, designed for the measurement of the surface resistance and of the surface reactance shift in High-T _c Superconductors (HTS) thin films in a dc magnetic field. The resonators are single tone, based on the TE ₀₁₁ mode, and multiple tone, the latter allowing in principle to exploit the simultaneous determination of the surface impedance at different frequencies. As an application example, we report the temperature and field dependencies of the effective surface impedance of some cuprate superconductors thin films. The results are compared with those obtained through the use of a standard metal cavity with a similar Q-factor and operating in the same frequency range. The comparison highlights a superior stability and a higher sensitivity, resulting in an increase of about two orders of magnitude in the resolution of the surface impedance measurement. By contrast, the dissipative part of the superconducting transition (above T/T _c = 0.97) is better studied with the metal cavity. We also present measurements in the vortex state in YBaCa₂Cu₃O_7−δ and Tl₂Ba₂CaCu₂O_8+x that show significantly different physics. PACS: 74.25 Nf.     

Experiments and Model of Intermodulation Distortion in a Rutile Resonator with Y-Ba2-Cu3-O7−δ Endplates

We have derived general equations to calculate intermodulation distortion in resonators with high temperature superconducting (HTS) films which are not restricted to a specific resonator shape and may be used whenever the fields in a resonator generate currents on the surface of one or more HTS films. These equations are applied to rutile-loaded cavities with one or two 10 × 10 mm² Y-Ba₂-Cu₃-O^7?δ endplates and are used to extract parameters characterizing the nonlinearities of these films from intermodulation measurements. Even though the films have similar small-signal performance, we have found large variation in the strength of their nonlinearities.     

High-temperature superconducting microwave devices: Fundamental issues in materials, physics, and engineering

High-T _c superconductivity has generated a great deal of interest because of the challenges it presents in the fields of material science, condensed matter physics, and electrical engineering, and because of the potential applications which may result from these research efforts. Thin-film passive microwave components may become the first high-temperature superconducting (HTS) devices available for widespread use and commercialization. In this article, we review aspects of material science, physics, and engineering which directly impact high-T _c superconducting microwave devices and discuss issues which determine the performance of these devices. Methods of growing HTS thin films on large-area substrates, techniques for fabricating single-level HTS passive microwave components, and the relevant properties of high-T _c superconducting films are discussed, with a focus on thin films of the HTS material YBa₂Cu₃O_7–. Several known mechanisms for microwave loss in both the superconductor and the dielectric substrate are presented. An overview of the general classes of superconducting passive microwave devices is given, and representative microwave devices which have been recently demonstrated are described in detail. Examples of a select few HTS active microwave components are also presented. Potential microwave applications are illustrated with comparisons to current technology.     

Characteristic of the Guidance Force in the High-T c Superconducting Levitation System with Pre-Load Process

The stable levitation above permanent magnet is an important characteristic of the bulk high-T _c superconductor (HTS). When an external force pushes the bulk HTS up, down or sideways, or tries to tilt it, a restoring force can return it to its initial position. The HTS Maglev relied on this characteristic can overcome the external force from wind or pass the curve lines successfully. The change of guidance force (GF) during many times lateral movement is studied. Experiments show that GF increases during the lateral movement, no matter what kind of PMG or HTS is used, and the change of the GF slows down after 5 times lateral movement. The pre-load method can reduce the levitation force decay during lateral movement. So the influence of GF by the pre-load method is needed to be studied. It is found that the pre-load method can increase GF and reduce the change of the GF during lateral movement. The Halbach permanent magnetic guideway (PMG) can offer much more GF but the change is larger just as the levitation force decays. The GF of cylindrical bulk HTS increases more than of the rectangular bulk HTS in the pre-load case. The characteristics of the GF during the lateral movement are explained. These results are important for further HTS Maglev vehicle system designs.     

Numerical study on self-field losses of 30 m BSCCO HTS transmission cable

The self-field losses of the one phase of high-T_C superconducting (HTS) transmission cable are calculated by the electric circuit (EC) model. The one phase of HTS cable is constructed by the former of fine-strands copper rod, HTS conductor with four superconducting layers, the insulation made by polypropylene laminated paper, and HTS shielding with two superconducting layers, which was fabricated by Sumitomo Electric Industries (SEI). The length of the cable is 30 m. Each HTS layer comprises BSCCO tapes. The current-dependent resistance of HTS layers in EC model is estimated on the base of Norris expressions for ellipse. The calculated losses are compared with the experimental results measured by 4-terminal method by SEI. The calculation of alternating current (AC) losses, a summation of the self-field losses in HTS layers and the eddy-current losses in the former, is almost equal to the measurement at wide transport-current range below the lowest value of the layer critical current. This result indicates that the numerical calculation by EC model is quite reliable. The minimum AC loss is also calculated by obtaining the optimum helical-pitch lengths of HTS layers at transporting 1 kA_rms. The minimum loss is 36% lower than the loss of HTS cable designed by SEI at the transport current value. In HTS cable with the optimum helical-pitch lengths, the calculation of the layer currents are not uniform in HTS conductor but are almost uniform in HTS shielding, which is contradict to SEI’s one. It is considered that the numerical calculation by EC model is useful to obtain the optimum helical-pitch lengths in HTS cable with the minimum AC loss.     

Current controlled high Tc superconducting switch

When a current is applied above the critical current l_c of a superconductor, the material is in its normal state and has a finite resistance. Below l_c the material becomes a superconductor with zero resistance. Switching between these two states can be achieved by modulating a current through the sample. Various high T_c superconducting (HTS) line structures have been made. In the normal state these structures are ordinary resistors with resistances ranging from 10 μ to 100 kμ. The critical currents are in the range 10 μA–100 mA. Switching behaviour has been observed in a simple divider circuit using the HTS lines at 77 K. Applications of the current controlled HTS switch to digital and logic circuits are discussed.     

Excess noise in strip off-axis confocal unstable resonators

The lowest-loss mode and higher-order modes in strip off-axis confocal unstable resonators are calculated by the eigenvector method. The moduli of all pairs of the adjacent order eigenvalues exhibit crossing behavior. For the lowest- and next-lowest-loss modes, crossings occur when the equivalent Fresnel number N _eq is close to s?+?0.08 (s positive integer), and the lowest-loss mode profile calculated by the Fox–Li iteration is no longer self-reproducing, but the superposition of both eigenmodes with unfixed complex weights varies as the number of iterations. Numerical calculations of excess noise factors K in strip off-axis confocal unstable resonators are described in detail. The value of K shows an irregular resonance switching against N _eq. The hybrid model presented by van Eijkelenborg et al. is modified in this paper, and shows a good quantitative agreement with nonorthogonality theory.     

Influence of Re-magnetized HTS Bulk Samples on the Levitation Performances of a Maglev System

High-T _c superconducting (HTS) bulk samples used for a maglev system can be re-magnetized after being subjected to another applied magnetic field which may influence the levitation performance of a HTS bulk over the permanent magnetic guideway (PMG). In order to clarify the relationship between the HTS bulk’s re-magnetization and its levitation performance, a YBCO bulk was re-magnetized at different values and its levitation performance studied experimentally above a permanent guideway (PMG) system. The results show that the increase of trapped magnetic flux inside the HTS bulk is closely related to the magnitude and direction of the applied field during the re-magnetization process. Furthermore, the levitation force changes on the HTS-PMG system affected by the re-magnetized HTS bulk are discussed allowing for optimization improvements to the maglev system load capabilities.     

Dynamic Simulation of High Temperature Superconductors Above a Spinning Circular Permanent Magnetic Guideway

Before a high temperature superconducting (HTS) magnetic levitation (Maglev) vehicle system can be fully applied and operational, the study of its dynamic characteristics is necessary. With the developed HTS Maglev dynamic measurement system (SCML-03), with a circular permanent magnet guideway (PMG) of 1.5 m in diameter, the vehicle’s translational motion above a PMG can be effectively simulated with the PMG allowed to rotate freely. Levitation force measurements of a high temperature superconductor (HTSC) array of seven YBa₂Cu₃O_7−x bulks were carried out above regular (linear) and a simulated (circular) PMG. The levitation force above a linear PMG segment and a circular PMG segment in the static state is found to be in good agreement with each other. The levitation force in the dynamic state is found to slowly attenuate since the presence of a rotating circular PMG below the HTS array is found to be analogous to the application of an AC external magnetic field.     

Power-Dependent Impedance of High Temperature Superconductor Thin Films: Relation to Harmonic Generation

We present measurements of the power-dependent microwave surface impedance of YBa₂Cu₃O_7– thin films, performed using patterned coplanar waveguide (CPW) resonators at 5.87 GHz and 76 K. We compare these resonator measurements with third-harmonic generation measurements performed on CPW transmission lines of the same geometry patterned onto the same thin-film sample at the same frequency and temperature. We find that the power-dependent surface reactance X_s(P_rf) is directly related to the magnitude of the generated third-harmonic signal, indicating a common origin for both of these manifestations of nonlinearity in high temperature superconductor (HTS) devices. These results are consistent with the nonlinear response generated by a current-dependent penetration depth (J), which provides a material limitation on the linearity that can be achieved in any practical HTS microwave device.     

Re-evaluation of the intercept temperature for HTS current leads based on practical and economical considerations

An optimization analysis was performed to determine the intercept temperature that minimizes the net room-temperature refrigeration requirements for a binary-type HTS current lead. Two types of HTS material systems were investigated: (1) Bi₂Sr₂Ca₁Cu₂O_x (2212) melt-cast-processed tube and (2) Bi₂Sr₂Ca₂Cu₃O_x (2223) Ag–Au alloyed powder-in-tube tape. An example analysis was performed on a conduction-cooled HTS current lead using a cryocooler. The presence of a safety lead and a background magnetic field strongly influences the optimum intercept temperature. In addition, an analysis was performed to determine the optimal intercept temperature based on economic considerations. In the economic analysis, the optimal intercept temperature is determined by minimizing the capital investment cost of the HTS current lead and its corresponding refrigeration system. It was the economic impact that the intercept temperature has on combined system cost that provided the motivation for this analysis and may be of interest for commercial applications.