Analysis of Nonlinearities in Superconducting Microstrip Straight Bends; FDTD Method in Comparison with Nonlinear Circuit Modeling

This paper presents the prediction of nonlinearities in the superconducting microstrip straight bends in microwave frequencies based on two different methods; FDTD simulation as a numerical approach, and nonlinear circuit modeling as an analytical method. In the FDTD method, the superconducting microstrip structures are simulated with London’s equations. In the simulation, the penetration depth and normal conducting coefficient are considered as functions of current density of superconductor. To simulate the thin strip of superconductor, a non-uniform mesh has been used. For the nonlinear circuit modeling, we use distributed RLGC parameters for superconducting microstrip transmission lines. These parameters are considered as functions of the current distribution. This yields an equivalent nonlinear circuit model for bends. The final equivalent nonlinear circuit is analyzed using the harmonic balance (HB) method. Different straight bend structures have been considered and the two methods’ results are compared.     

Monolithic HTS microwave phase shifter and other devices

We describe a monolithic high-temperature superconductor (HTS) phase shifter based on the distributed Josephson inductance (DJI) design integrated monolithically into a 10-GHz microstrip line. This microwave circuit incorporates >1000 HTS rf SQUIDS. Recent data demonstrate the performance of this broadband HTS circuit. We observed phase shifts greater than 150° in resonant structures, and 20° in broadband circuits. The nonlinear inductance of the superconducting transmission line can be used for other novel applications, including parametric amplification. A comparison of the DJI circuit to a series array of Josephson elements (used for pulse sharpening) will contrast these two new and exciting nonlinear transmission line circuits.     

Observation of X-band SQUID signals in a High-T c superconducting film device

A microwave superconducting magnetometer is described in which a microstrip resonator is coupled to a two-hole high-T _c thin-film SQUID device. Both the microstrip circuit and the thin-film SQUID were fabricated by photolithography techniques. The YBCO thin film was deposited on single-crystal substrate of yttria-stabilized zirconia [YSZ(100)] by an ion beam sputtering technique producing a superconducting transition measured at a critical temperature ofT _c =92 K to within ΔT ～ 3 K. Non linear oscillatory behavior was observed in the microstrip resonator when inductively coupled to the SQUID. This nonlinear behavior yielded a microwave device in which the reflected microwave power varied with applied DC magnetic flux.     

Observation of X-band SQUID signals in a High-Tc superconducting film device

A microwave superconducting magnetometer is described in which a microstrip resonator is coupled to a two-hole high-T _c thin-film SQUID device. Both the microstrip circuit and the thin-film SQUID were fabricated by photolithography techniques. The YBCO thin film was deposited on single-crystal substrate of yttria-stabilized zirconia [YSZ(100)] by an ion beam sputtering technique producing a superconducting transition measured at a critical temperature ofT _c =92 K to within T 3 K. Non linear oscillatory behavior was observed in the microstrip resonator when inductively coupled to the SQUID. This nonlinear behavior yielded a microwave device in which the reflected microwave power varied with applied DC magnetic flux.     

Tunable Wave Propagation in Superconducting Microstrip Line Based on Ferroelectric Thin Films

The microwave propagation characteristics in superconducting microstrip line supported by ferroelectric layer are theoretically investigated. The control of propagation constant and attenuation coefficient of the waveguide with biasing electric field is analyzed using the spectral domain method. The dependence of propagation characteristics on thickness of ferroelectric thin film as well as operating frequency for different applied electric fields is studied. The variation of propagation constant with temperature is also investigated. This method of analysis can be easily implemented in the design of tunable microwave devices.     

YBa2Cu3Ox Josephson junctions on a bicrystal sapphire substrate for devices in the millimeter and submillimeter wavelength ranges

High-temperature superconducting Josephson junctions on bicrystal sapphire substrates were fabricated and investigated experimentally. The critical parameters of the junctions satisfy the constraints for the design of devices in the millimeter and submillimeter wavelength ranges. The results of dynamic measurements show that in these junctions the superconducting current exhibits a sinusoidal dependence on the phase difference of the superconducting wave functions of the electrodes, and a simple resistive model is used to analyze their microwave properties. At the same time, the temperature dependence of the critical current of the junctions differs appreciably from that typical of tunnel junctions with s-superconductors and may be explained as d-type pairing of the superconducting electrodes and an SNS junction. Pis’ma Zh. Tekh. Fiz. 25, 1–8 (April 12, 1999)     

Numerical Model of the Microwave Properties of Superconducting Resonators and Transmission Lines

We propose a model for microwave power transmission in superconducting lines and resonators. The correct current density incorporating the critical current density is used. A numerical self-consistent method is suggested to calculate different transport quantities, such as the surface resistance and the quality factor as function of both temperature and magnetic field. The effect of the strength of pinning on the transport properties is studied, as well. Some of these results are compared with experiment.     

Modeling, simulation, and measurement of nonlinearities in superconducting transmission lines and resonators

A simple phenomenological model of a nonlinear microwave transmission line is suggested. The dissipation of a traveling wave in the line is derived as a function of the microwave power. The phenomenological parameter of nonlinearity is introduced and found from experimental data. Nonlinear phenomena in a half-wavelength resonator, based on a superconducting microstrip line, are studied. The response in the form of output fundamental frequency, third harmonic, and intermodulation signals is found. Simulations based on the model are in good agreement with experimental data. Some problems of YBCO film production technology are discussed in connection with the high-power handling.     

Influence of the Substrate Layer on the Lightning Current Performance of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−δ</Subscript> Tapes

In a power grid, the superconducting power devices might also experience lightning impulse current except for the common over-currents. However, the study of the performance of YBCO tapes suffering a lightning current is scarcely reported. This paper mainly focuses on the influence of the substrate layer on the thermal stability of YBCO tapes suffering a lightning current. A numerical model which took into account both the thermal and the electromagnetic aspects was proposed. The validity of this model was verified by experiment. Based on this model, the influence of the dimension and material type of thesubstrate layer on the thermal stability were investigated in detail. The simulated results showed that the substrate layer could affect the temperature distribution on different layers, and stainless steel substrate layer is a more desired choice for decreasing the maximum temperature. Moreover, a theoretical explanation based on a simplified equivalent circuit was also used to study the influence of the substrate layer.     

Modeling the Microwave Impedance of High-Tc Long Josephson Junctions

A circuit model is presented for Josephson junctions (JJs) that solves the nonlinear long-junction equation, driven by a nonuniform current distribution. This extended resistively shunted junction (ERSJ) model consists of a parallel array of ideal resistively shunted JJs coupled by inductors. The junction array is connected to an array of current sources that simulate the time- and space-dependent current distribution in a stripline. The rf-current dependent complex impedance of a long JJ calculated using this model agrees with measured data on a YBCO grain-boundary JJ and provides an explanation of the measured steps in the resistance resulting from the creation, annihilation, and motion of Josephson vortices under the influence of rf currents. This model contributes to a better understanding of the power-handling characteristics of high-T _c microwave devices, in which the power losses are believed to result from JJ effects associated with imperfections in the films. The model also predicts second-harmonic generation with a highly nonlinear and nonmonotonic power dependence. Details of the dynamics of Josephson vortices are presented and discussed.     

Microstrip coupling techniques applied to thin-film Josephson junctions at microwave frequencies

Three different schemes for coupling to low impedance Josephson devices have been investigated. They all employ superconducting thin-film microstrip circuit techniques. The schemes are: (i) a quarterwave stepped impedance transformer, (ii) a microstrip resonator, (iii) an adjustable impedance transformer in inverted microstrip. Using single microbridges to probe the performance we found that the most primising scheme in terms of coupling efficiency and useful bandwidth was the adjustable inverted microstrip transformer.     

Modeling the Microwave Impedance of High-Tc Long Josephson Junctions

A circuit model is presented for Josephson junctions (JJs) that solves the nonlinear long-junction equation, driven by a nonuniform current distribution. This extended resistively shunted junction (ERSJ) model consists of a parallel array of ideal resistively shunted JJs coupled by inductors. The junction array is connected to an array of current sources that simulate the time- and space-dependent current distribution in a stripline. The rf-current dependent complex impedance of a long JJ calculated using this model agrees with measured data on a YBCO grain-boundary JJ and provides an explanation of the measured steps in the resistance resulting from the creation, annihilation, and motion of Josephson vortices under the influence of rf currents. This model contributes to a better understanding of the power-handling characteristics of high-T _c microwave devices, in which the power losses are believed to result from JJ effects associated with imperfections in the films. The model also predicts second-harmonic generation with a highly nonlinear and nonmonotonic power dependence. Details of the dynamics of Josephson vortices are presented and discussed.     

Thickness-Dependent Current Density and Flux Distribution in Thin Current-Carrying Superconducting Films Exposed to a Magnetic Field

With the rapid development of high-temperature superconductors, it is of great significance to get the precise current density and flux distribution within thin high-temperature superconducting films subjected to a transport current and an applied magnetic field. The transport current distribution and flux density in thin high-temperature superconducting films are calculated by a numerical method based on the Kim model and exponential model in this paper. The influences of transport current, applied magnetic field, width, and thickness of a superconducting film on the current distribution are discussed. The results reveal that the thickness has a significant effect on the critical current density of superconducting films.     

Noncontacting low-cost instrument for film thickness measurement

A low-cost, noncontacting, nondestructive technique is presented for measuring the thickness of thin liquid or solid films and coatings in real time by utilizing the resonance properties of microstrip structures. A new measurement system in which all the microwave components are internal to the instrument, thereby eliminating the need for microwave test equipment, is described. Only a low-voltage DC source, such as a battery, is required to power the unit; the output is also a DC voltage or current. Using a linear model, sample coefficients of determination, r², greater than 0.98 have been obtained for film thickness measurements of water, enamel paint, and silicon rubber up to 0.8-1.5- and 2-mm thick, respectively. Copper sheet metal up to 0.9-mm thick has been measured with an r² greater than 0.99. The measurement range can be extended or improved even further if nonlinear circuit behavior is accounted for     

Simulation of Microwave Losses of Superconductive Microstrip Line Resonators and Filters Using Commercial Software

The microwave losses of double-sided superconducting YBa₂Cu₃O_{7 – x} thin films is presented. The films were grown on both sides of LaAlO₃ substrates. The microstrip resonators and the filters were patterned and etched using the technique of photolithography. The performance of high frequency microstrip resonator was studied for a resonance frequency of 5 GHz and for a temperature range of 17–100 K. The power dependence of the quality factor measured and the shift in the resonant peak with respect to temperature are also reported. We performed simulations using two phenomenological models. These models were confirmed by our experimental results. Several commercial software were used in our simulations, with appropriate modifications. We were able to reproduce our experimental results using the models mentioned above. The physical parameters used in the model were chosen from among those reported and accepted in literature. In order to validate these models we designed a band-pass filter. Theoretical simulation was performed on a two-pole filter using the models mentioned above. Then two real filters have been prepared using the technique of photolithography. Experimental measurements have been performed on these filters. Comparison between the experimental and simulation results are presented. The goal of this paper is to demonstrate that it is possible to use commercial software to design planar microwave devices by performing only few appropriate modifications.     

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.     

Vortex Matter in Active and Passive Superconducting Devices

In this contribution it is demonstrated (i) that active as well as passive superconducting devices can be used as very sensitive tools for detecting motion and penetration of vortices in superconducting material and (ii) that the analysis of the distribution of vortices in the device can be used for optimization of these devices for application. The potential for applications of superconducting devices strongly depends upon the reduction of dissipative processes due to vortex motion. Whereas vortex motion in active devices leads among others to increased low-frequency noise and, thus, reduces the sensitivity of e.g. SQUIDS, vortices in microwave devices reduce the quality factor and, finally, the power handling capability. For both types of devices vortex penetration at extremely low magnetic induction can be observed and the position of penetrating vortices can be deduced by adequate analysis of the recorded magnetic flux or power handling property for SQUIDS or resonator, respectively. The effect of vortex penetration and trapping of flux-for instance by strategically positioned antidots-upon the performance of the device will be demonstrated and, finally, methods to reduce or avoid the negative impact of vortices in these devices are sketched.     

基于增量谐波平衡法的含索铰可折展桁架非线性动力学特性

为了揭示含索铰可折展桁架的非线性动力学行为,建立了考虑铰链间隙、刚度和阻尼及索非线性特性的可折展桁架纯弯曲动力学模型。对非线性动力学方程进行一次泰勒展开和参量的多次谐波描述,实现了非线性动力学方程到代数方程的转化,通过迭代进行非线性动力学系统的响应计算。并利用龙格库塔方法对非线性系统进行数值分析,与增量谐波平衡(IHB)法进行对比,验证了IHB法计算的正确性。以激振频率为变化参数,对悬臂支撑的含索铰桁架结构进行解的稳定性分析,得到铰链间隙、铰链刚度、激振力和索对结构响应稳定性的影响。基于IHB法可快速准确的进行多自由度可折展结构动力学求解,为研究大型折展桁架的动力学行为奠定了基础。     

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.