Analytical model for tilted coils in eddy-current nondestructive inspection

The electromagnetic field and impedance of a cylindrical eddy-current probe coil are calculated analytically for arbitrary coil orientation above a conductive half-space. The remarkably simple closed-form expressions are provided as a function of coil tilt angle. The effect of tilt on the impedance change produced by a long crack is also investigated by combining the analytical model with an existing thin-skin theory for surface crack inspections. Results for both cracked and uncracked conductors are expected to be useful for evaluation of movement-generated noise in eddy-current inspections.     

Modeling the passive microwave devices based on planar multilayer anisotropic structures with high-temperature superconductors

The electrodynamic properties of an arbitrary multilayer medium, including anisotropic layers and conductors of an arbitrary shape on one of the interfaces, are studied. The conductors represent thin layers of a high-temperature superconductor (HTSC). A system of integral equations for the electric field is solved in the spatial domain. The electrodynamic problem was solved by numerical methods to determine the surface current density by applying the Galerkin procedure and by solving the main matrix equation relative to coefficients of the current density expansion in a basis set of finite functions. The losses in HTSC layers are taken into account by using the concept of the equivalent surface impedance and the Leontovich boundary conditions. The anisotropy is taken into account in determining the Green dyad for a structure with an arbitrary number of anisotropic or isotropic layers. Correctness of the proposed model is confirmed by the results of calculations of the surface current density distribution.     

Microwave measurements on the heavy fermion superconductors UPt3 and UBe13

The complex microwave impedance at 11.5 GHz was measured in the superconducting state of two well characterized heavy fermion single crystals, UPt ₃ and UBe ₁₃ . This microwave photon energy is about 30% and 20% of the zero-temperature energy gap, respectively, and is higher than previous measurements. The results for UBe ₁₃ seem to be well described by the Mattis-Bardeen theory in the dirty-limit for a conventional superconductor. However, the behavior in UPt ₃ deviates from this conventional theory even when paramagnetic impurity scattering effects are taken into account.     

A General Waveguide Circuit Theory

This work generalizes and extends the classical circuit theory of electromagnetic waveguides. Unlike the conventional theory, the present formulation applies to all waveguides composed of linear, isotropic material, even those involving lossy conductors and hybrid mode fields, in a fully rigorous way. Special attention is given to distinguishing the traveling waves, constructed with respect to a well-defined characteristic impedance, from a set of pseudo-waves, defined with respect to an arbitrary reference impedance. Matrices characterizing a linear circuit are defined, and relationships among them, some newly discovered, are derived. New ramifications of reciprocity are developed. Measurement of various network parameters is given extensive treatment.     

Electromagnetic behavior of superconductors in a microwave field

Our research on the surface impedance of superconductors in microwave, millimeter, and submillimeter wave frequency ranges has revealed the nature of the interaction between microwave and superconductors. The complete solution to the Mattis-Bardeen (MB) quadruple [Phys. Rev. 111, 412 (1958)] and the analytical simplification of the MB formula to a double integral have been given. The theoretical calculations for metallic superconductors (Al and Sn) are in excellent agreement with the typical experimental data [Biondi and Garfunkel,Phys. Rev. 116, 853 (1959); S. Sridhar,J. Appl. Phys. 65, 159 (1988)]. Whereas for oxide superconductors a new microscopic model has been suggested because of its distinctive electromagnetic behavior compared to that of conventional superconductors, we think that the nonlinear effect caused by the strong anisotropy in superconductivity is one of the reasons why oxide superconductors give an unusual response.     

Tunneling into 1D and Quasi-1D Conductors and Luttinger-Liquid Behavior

The paper addresses the problem whether and how it is possible to detect the Luttinger-liquid behavior from the IV curves for tunneling to 1D or quasi-1D conductors. The power-law non-ohmic IV curve, which is usually considered as a manifestation of the Luttinger-liquid behavior, can be also deduced from the theory of the Coulomb blockaded junction between 3D conductors affected by the environment effect. In both approaches the power-law exponents are determined by the ratio of the impedance of an effective electric circuit to the quantum resistance. Though two approaches predict different power-law exponents (because of a different choice of effective circuits), the difference becomes negligible for a large number of conductance channels.     

Compositional effects on microstructure evolution and microwave properties of silver–palladium based thick film microstrips

Recent improvements in materials and processing technologies have dramatically increased the frequency range where ceramic thick film circuits can be utilized. Coupled with inherent advantages of thick film technology viz. low manufacturing cost, multilayering capability and relative insensitivity to substrate surface characteristics, such improvements have resulted in circuits that are penetrating the domain which was previously reserved to thin film technology. In view of newer developments in modern electronics, there is still ample scope for the development of new materials and processes especially in thick film technology. In thick films, conductors play a major role and silver–palladium is one of the important conductor materials in microelectronic circuits. Efforts are made in this work towards the development of suitable silver–palladium thick film conductors from the standpoint of microwave applications. The properties such as surface microstructure, sheet resistance, adhesion and microwave performance of the indigenously developed silver–palladium paste compositions is reported here. Highly porous surface structure, low adhesion and low characteristic impedance of thick film microstrip are observed for pastes with high palladium concentration.     

Circuit-Coupled ${bf t}_{0}hbox {-}phi$ Formulation With Surface Impedance Condition

A finite-element formulation based on the use of magnetic scalar potential is proposed. It allows to describe circuit-coupled electromagnetic formulation using magnetic scalar potential in presence of multiply connected solid conductors (with holes), treated by surface impedance condition. This formulation offers powerful solutions at a low cost. An example of application is given.     

Superconductivity and phase stability of Nb3Ge

A method is described for calculating the surface impedance of thin superconducting films using the theory of Mattis and Bardeen of the surface impedance of superconductors. An approximate extension of the theory to the case where the superconducting order parameter inside the film varies slowly in space is presented. Calculations using the theory are compared with experimental measurements of the surface impedance at 3 GHz of thin tin films on bulk lead substrates. Agreement between theory and experiment is good.     

Subdomain Perturbation Finite-Element Method for Skin and Proximity Effects

Skin and proximity effects are calculated in both active and passive conductors via a subproblem finite-element method based on a perturbation technique. A reference limit problem considering either perfectly electric or magnetic conductors is first solved. It gives the source for eddy-current perturbation subproblems in each conductor with its actual conductivity or permeability and its own mesh. These subproblems accurately determine the current density distributions and ensuing losses in conductors of any shape in both frequency and time domains, overcoming the limitations of the impedance boundary condition technique.     

Compositional effects on microstructure evolution and microwave properties of silver–palladium based thick film microstrips

Recent improvements in materials and processing technologies have dramatically increased the frequency range where ceramic thick film circuits can be utilized. Coupled with inherent advantages of thick film technology viz. low manufacturing cost, multilayering capability and relative insensitivity to substrate surface characteristics, such improvements have resulted in circuits that are penetrating the domain which was previously reserved to thin film technology. In view of newer developments in modern electronics, there is still ample scope for the development of new materials and processes especially in thick film technology. In thick films, conductors play a major role and silver–palladium is one of the important conductor materials in microelectronic circuits. Efforts are made in this work towards the development of suitable silver–palladium thick film conductors from the standpoint of microwave applications. The properties such as surface microstructure, sheet resistance, adhesion and microwave performance of the indigenously developed silver–palladium paste compositions is reported here. Highly porous surface structure, low adhesion and low characteristic impedance of thick film microstrip are observed for pastes with high palladium concentration.     

Analysis of diffracted fields with the extended theory of the boundary diffraction wave for impedance surfaces

Uniform diffracted fields from impedance surfaces are investigated by the extended theory of boundary diffraction wave (ETBDW). The new vector potential of the ETBDW is constructed by considering the pseudoimpedance boundary condition. The method is applied to the diffraction problem from an impedance half-plane. It is shown that the total fields from an impedance half-plane reduce to the case of a perfectly electric or magnetic conducting and opaque half-plane for special values of surface impedance. The total and diffracted fields are compared numerically with the exact solution for the impedance half-plane and modified theory of physical optics (MTPO) solution for an impedance wedge. The numerical results show that the field expressions are in very good agreement with the exact and MTPO solutions.     

The Realization of High-Frequency Impedance Standards Using Air-Spaced Coaxial Lines

Impedances of devices with coaxial inlets, having small reflection coefficients relative to a given characteristic resistance, can be determined accurately (± 0.1 per cent) by comparison with the nominally calculable characteristic impedance of a quarter-wavelength, air-spaced coaxial line in which the inner conductor is supported by the inner conductors of the apparatus connected at each end. In carrying out such comparisons, errors may be introduced by the presence of small series impedances at the connections between the rigid coaxial lines. Such connections cannot be eliminated because they must be made and broken during the process of making comparisons. Errors may also arise from the distributed resistance and the "internal" reactance of the line conductors, as well as from departure of the lines from uniformity in diameter. This paper describes experimental techniques for measuring these residuals and discusses their effects. The design requirements of suitable air-spaced coaxial lines as standards are stated, together with a brief mention of techniques for making comparisons with the standards.     

Development of an Impedance Matching Program for Balancing the Current Distribution in a Tri-axial HTS Power Cable

The tri-axial high temperature superconducting (HTS) power cable design has several advantages when compared with other HTS power cables. However, this design has an imbalance in the three phase currents, as the phase conductors of the tri-axial HTS power cable have different radii. The radii of the phase conductors impact the value of inductance and capacitance for the cable, and the values are determined by the winding pitch length and the winding direction. Thus, the current imbalance can be minimized through the adjustment of the winding pitch length, the radius of each layer, and the winding direction. It takes a lot of time to manually calculate an impedance and to find a matched impedance. So the impedance of the tri-axial HTS power cable, according to its shape, was analyzed and the impedance matching program (IMP) was developed using LabVIEW (Laboratory Virtual Instrument Engineering Workbench) to solve this problem. IMP finds the matching impedance automatically by calculating the impedance according to the tri-axial HTS cable dimension. Consequently, this could save a lot of time, and so this program will be applied to the design of the tri-axial HTS power cable effectively.     

Approximate model of eddy-current probe impedance for surface-breaking flaws

A theoretical model is derived for the prediction of eddy-current probe impedance changes caused by three-dimensional, surface-breaking flaws. Magnetic scalar potential theory and the surface impedance approximation are used to calculate fields on the flaw surface for arbitrary probe position and flaw geometry. Impedance changes are determined by a first-order perturbation calculation, with skin depth being the perturbation parameter. The end result is a relatively simple, three-dimensional model for simulating an eddy-current inspection. Numerical results for rectangular slots include maps of the impedance signals obtained in raster scan patterns and studies of skin-depth effects as a function of probe size, lift-off, and flaw dimensions.     

Scattering of a line source by a cylindrical parabolic impedance surface

The scattering of the radiated fields of a line source by a cylindrical parabolic reflector, which has impedance boundary conditions on its surface, is obtained by using the surface integrals of the modified theory of physical optics. The reflected geometrical optics and edge diffracted fields are evaluated by using the asymptotic methods. The scattered fields are plotted numerically for various parameters such as surface impedance and angles of the edges.     

A finite element method for analysing skin effect in conductors with unknown values of surface boundary conditions

This paper presents a method of analysing the distribution of a two-dimensional electromagnetic field in a conducting medium of known cross-section carrying sinusoidal current and of unknown numerical values of boundary conditions on conductors surfaces. The method combines the finite element and separation of variables methods. An example is given of application of the method to calculation of impedance and electrodynamic forces of two thick, full and round conductors carrying oppositely directed sinusoidal currents. On the basis of numerical computation, graphs of resistance, reactance and electrodynamic forces are plotted.     

Reconstructing electrical conductivity profiles from variable-frequency eddy current measurements

A method for reconstructing radially varying conductivity profiles in cylindrical conductors is described. Solenoidal driving and sensing coils surround the cylindrical sample and an AC magnetic field applied by the driving solenoid induces axisymmetric eddy currents in the sample. It is shown how a radially varying conductivity profile can be recovered from measurements of the complex impedance recorded as a function of frequency, where impedance here is defined as the ratio of the induced electromotive force (EMF) in the sensing coil to the current in the driving coil. An iterative nonlinear least-squares algorithm is employed to reconstruct the profiles. Demonstrations of the reconstruction method are presented based on both simulated and experimentally recorded impedance data.     

利用迭加法计算阶梯圆板辐射阻抗

辐射阻抗是描述声学振动系统的一个重要物理量。对阶梯圆板的辐射阻抗而言，运用传统理论计算时，由于辐射面不在同一几何面，积分上下限很难选取而无法计算。从辐射声功率角度，基于叠加原理，提出了计算阶梯板辐射阻抗的算法——迭加法，并计算了带有一个阶梯的阶梯板辐射阻抗。     

The near-IR surface impedance of thin metallic films with unlike surfaces

A simple formula is proposed for the near-IR surface impedance of thin metallic films with unlike surfaces. It is derived from a previous N-dimensional model based on the Reuter and Sondheimer anomalous skin effect theory. The relative precision on the surface resistance thus calculated is found to be a few times 0.1% at wavelengths smaller than or about 2 μm.Anisotropy may easily be introduced into the electron relaxation time to treat the polycrystalline case or (and) into the Fuchs electron-surface scattering parameters.