Current distribution in superconducting thin-film strips

A closed-form expression is presented for the current distribution in an isolated strip made from a superconducting thin film with thickness less than a few penetration depths. This equation gives a good approximation within certain limits for the resistance and inductance per unit length of superconducting striplines and microstrip lines. Both the ac resistance of an isolated superconducting strip and the resistance per unit length of a superconducting stripline calculated using this closed-form expression agree well with the numerical results generated by the modified Weeks' method. The possibility of using this expression along with the integral equation method to develop an efficient full-wave method for analyzing superconducting planar transmission lines is discussed     

Current distribution, resistance, and inductance forsuperconducting strip transmission lines

A method for the calculation of the current distribution, resistance, and inductance matrices for a system of coupled superconducting transmission lines having finite rectangular cross-section is presented. These calculations allow accurate characterization of both high-T_c and low-T _c superconducting strip transmission lines. For a single stripline geometry with finite ground planes, the current distribution, resistance, inductance, and kinetic inductance are calculated as functions of the penetration depth for various film thicknesses. These calculations are then used to determine the penetration depth for Nb, NbN, and YBa₂Cu₃O_7-x superconducting thin films from the measured temperature dependence of the resonant frequency of a stripline resonator. The calculations are also used to convert measured temperature dependence of the quality factor to the intrinsic surface resistance as a function of temperature for an Nb stripline resonator     

Design equations for a 2-branch stripline directional coupler/impedance transformer

Design equations are presented for a 2-branch stripline directional coupler/impedance transformer, based on an exact theory. With this design, the two separate processes of impedance matching and power splitting are combined into one device, which conserves `real estate? in a stripline or microstrip application.     

Modeling the nonlinearity of superconducting strip transmissionlines

The use of the Ginzburg-Landau (GL) theory to predict the nonlinear behavior in a superconducting stripline resonator as a function of input current is reported. A method for calculating the nonlinear inductance and the fractional change in the resonant frequency (Δf/f) of a stripline resonator is presented. By solving the GL equations inside the superconducting strip, the spatial variation of the number density of superconducting electrons and, hence, the spatial variation of the magnetic penetration depth are obtained for different values of input current. First, an infinite parallel plate transmission line is considered where the one-dimensional GL equations are solved. The two-dimensional case of a stripline is then considered. Nonlinear inductances are calculated as functions of input current for different superconducting striplines. Comparisons of the calculated Δf/f with measurements for YBa₂Cu₃O_7-x stripline resonators show excellent agreement     

Impedance of a transverse slot in the ground plane of an offset stripline

A generalized formulation for the determination of the impedance of a transverse slot in the ground plane of an offset stripline is presented. The results of the analysis are used to compute the variation of slot impedance with strip offset and also with change in position of one of the ground planes. Comparison of the theoretical results with experimental data is presented.     

Full-wave characterization of high-Tcsuperconducting transmission lines

A full-wave numerical analysis is applied to accurately characterize superconducting transmission lines embedded in a layered dielectric medium. A volume integral equation formulation is developed by using a spectral domain dyadic Green's function for stratified media. Galerkin's method with rooftop basis functions for the electric field distribution inside the superconductor is then employed to solve the complex propagation constant. The thickness of the superconducting film is arbitrary in this analysis, and the formulation rigorously accounts for the anisotropy of the superconducting film. The propagation characteristics of a superconducting microstrip transmission line with a thin dielectric buffer layer are investigated. A superconducting stripline configuration with an air gap is also studied     

Excitation of Waveguide by Stripline- and Microstrip-Line-Fed Slots

This paper presents investigations on coupling between stripline/microstrip line and a rectangular waveguide coupled through a slot in the ground plane which is fixed in the cross-sectional plane of the waveguide. A closed-form expression for the impedance loading on stripline/microstrip line is evaluated from knowledge of the complex power flowing down the rectangular waveguide supporting the dominant mode and discontinuity in the modal voltage in stripline/microstrip line. The reactance cancellation is obtained by terminating the stripline/microstrip tine exciting the slot in a short-circuited stub. The structure under this condition forms a transition between stripline/microstrip line and a waveguide. The design curves on slot length versus frequency are presented for different values of dielectric constants. The variation of coupling as a function of frequency and also the location of the slot is evaluated. Numerical results for slot coupling useful for the design of waveguide simulators are also presented.     

Double semiconductor substrate in overlay shielded superconducting microstrip lines

The Transverse Transmission Line (TTL) is used in the theory of the overlay shielded microstrip lines considering the superconductor strip on two semiconductor regions. The superconductor effect is included with the boundary condition of the surface impedance, that is related to the complex conductivity of the material, calculated from the advanced two-fluid model. Applying the moment method the complex propagation constant of the structure, including the phase constant and the attenuation constant, is obtained. Results are presented for the complex propagation constant, versus the frequency and the temperature, of this overlay superconducting microstrip lines.     

Stacked superconductor structure for microwave transmission

Propagation characteristics of microwaves along a stacked superconductor microstrip structure are investigated. The suitability of such a structure for practical applications is discussed. A rigorous integral equation formulation has been used for the analysis of such structure. The effect of thickness of superconducting strip on propagation characteristics has been studied. Results presented show that the slow wave propagation and low dispersive coupling are possible in a realistic stacked multi-dielectric and superconducting layers microstrip line package.     

Analysis of Asymmetric Stripline by Conformal Mapping

This paper presents analysis of asymmetric stripline using a conformal mapping technique. The expression obtained for the characteristic impedance shows its functional dependence on the dimensions of the stripline. Equations for equipotential and flux lines and an expression for field distribution in the stripline are derived. Plots of impedance variation with strip width and strip displacement are presented.     

An integral equation method for the evaluation of conductor anddielectric losses in high-frequency interconnects

An integral equation method is developed to solve for the complex propagation constant in multilayer planar structures with an arbitrary number of strip conductors on different levels. Both dielectric losses in the substrate layers and conductor losses in the strips and ground plane are considered. The Green's function included in the integral equation is derived by using a generalized impedance boundary formulation. The microstrip ohmic losses are evaluated by using an equivalent frequency-dependent impedance surface which is derived by solving for the fields inside the conductors. This impedance surface replaces the conducting strips and takes into account the thickness and skin effect of the strips at high frequencies. The effects of various parameters such as frequency, thickness of the lines, and substrate surface roughness on the complex propagation constant are investigated. Results are presented for single strips, coupled lines, and two-level interconnects. Good agreement with data available in the literature is shown     

Spectral-Domain Analysis of Single and Coupled Cylindrical Striplines (Short Papers)

A spectral-domain technique for finding the characteristic impedances of a single cylindrical stripline and a coupled pair of cylindrical striplines is presented. Assuming a charge distribution on the strip, the variational expression for the line capacitance for single cylindrical strip-Iine is derived. Good agreement with published results is obtained. The cylindrical coupled strip and microstrip lines are also analyzed and a comparison with their planar counterparts is made.     

Simple formulas for microstrip lines

A modification to earlier work is presented which allows for finite strip thickness in the calculation of microstrip impedance and line wavelength. It shows a considerable improvement in accuracy and scope over some earlier work which included strip thickness, but remains simple in form. Expressions are presented which allow calculation of Z and ?g for any microstrip geometry and relative permittivity.     

椭圆锥带线微带线同轴线的研究

本文首次提出了三种新型传输线－椭圆锥带线，微带线和同轴线，假设传播的是ＴＥＭ或准ＴＥＭ模式，通过坐标变换使球锥坐标系问题简化为二维问题，这样就可利用已知的同轴线和微带线的解而获得上面三种传输一的特性阻抗精确表达式，并给出数值计算结果。     

Full-wave spectral-domain computation of material, radiation, andguided wave losses in infinite multilayered printed transmission lines

A unified solution for full-wave computation of losses in a general multilayered planar transmission line is presented. It includes material losses (dielectric and conductor losses), losses due to radiation leakage, and losses caused by leakage of power to source-free characteristic modes (surface-wave or waveguide modes, for example) of the multilayered geometry. A spectral-domain moment method is used with the Galerkin testing procedure. Significant modification of the conventional spectral-domain analysis of planar transmission lines is necessary in enforcing proper boundary conditions in the Galerkin testing procedure and, more importantly, in accounting for poles and branch cuts in the complex Fourier transform domain in order to rigorously account for the different loss mechanisms discussed. Results for a few representative geometries, namely, strip and/or material loss in a microstrip line and a slotline, surface parallel plate mode leakage loss in a conductor-backed slotline and a two-layer stripline, and radiation loss in a single and a coupled stripline at the interface between two infinite mediums, are presented to demonstrate these various loss effects     

高温超导微带天线的谐振特性研究

传输线模型是分析微带天线的一种最简单的方法,但其未将导体的特性参数考虑到天线的分析中去,针对这一缺点,为研究超导体的表面阻抗对高温超导微带天线输入阻抗和谐振频率的影响,把导体特性对天线的影响看作一种微扰来处理,对传统的传输线模型进行了修正,并通过与谱域矩量法相比较,验证了修正后方法的有效性.进而利用修正后的方法计算分析了高温超导矩形微带贴片天线的输入阻抗和谐振频率,给出了关于高温超导微带天线输入阻抗和谐振频率的若干结论.     

Wide-Band Operation of Microstrip Circulators

Octave bandwidth operation of Y-junction stripline and microstrip circulators is predicted using Bosma's Green's function analysis. The width of the coupling transmission lines is found to be a significant design parameter. Theoretical and experimental results are presented which show that wide lines and a smaller than usual disk radius can be used to obtain wide-band operation. A microstrip circulator is reported which operates from 7-15 GHz. Also presented are an analysis of the input impedance and an approximate equivalent circuit for the Y-junction circulator which shows the relationship between Bosma's equivalent circuit and that of Fay and Comstock.     

A Potential Theory Method for Covered Microstrip (Short Papers)

Matrix methods are used to analyze the properties of covered microstrip. The Green's function is calculated by a potential theory method assuming the TEM mode of propagation. Computed impedance values of covered microstrip agree closely with other experimental and theoretical data. The technique is a general one and can be used to treat multiple-layer and covered microstrip.     

Adjustable microstrip transformer for use with Josephson devices in mm-wave ICs

A simple remotely adjustable cryogenic impedance transformer employing superconducting inverted microstrip circuits is described. The scheme is particularly suitable for efficiently coupling low impedance (0.1?5 ?) thin-film devices (e.g. Josephson junctions) in planar microwave integrated circuits to waveguide or other superconducting and semiconducting devices at millimetre wavelengths. Preliminary results obtained at 8 mm are presented.     

High-Tc superconducting microwave phase shifter

The relation between the surface impedance Z_S(=R_S?jX_S) of superconductors and DC current I has been derived to determine the propagation constant of a superconducting microstrip line, and the relation between the phase delay ? of the superconducting microstrip line and DC current I is also presented. On the basis of these analytical results, a microwave phase shifter has been made by using YBCO superconducting thin film. In this paper, we describe the design principle of phase shifter, its fabrication, and present the experimental results. These measured values agree well with the theoretical curves.