Time Domain Surface Impedance Research Articles

Time-Domain Behavior of Plasmonic Half-Spaces

The time-domain surface impedance for a plane-wave incidence on a half-space with conductive and plasmonic properties is theoretically investigated. This paper provides closed-form time-domain expressions of time-domain surface impedance values that can be readily evaluated numerically within any prescribed accuracy. Based on the surface impedance concept, time-domain responses of conductive and plasmonic half-spaces are analyzed and discussed. In this respect, changes in incident pulse shapes upon transmission and reflection against plasmonic boundaries are predicted. Numerical results for practically used metallic materials are presented.

Time domain surface impedance concept for low frequency electromagnetic problems—Part II: Application to transient skin and proximity effect problems in cylindrical conductors

A time domain boundary element formulation employing the surface impedance boundary conditions (SIBCs) is developed for the 3-dimensional transient eddy current problem of cylindrical conductors. SIBCs of different orders of approximation are implemented using the perturbation technique in the small parameter proportional to the ratio of the skin depth and characteristic size of the conductor cross-section. The formulation consists of a set of time domain surface integral equations that have identical left-hand sides and can be solved using the same program procedure. The number of equations is determined by the order of approximation of the SIBC, namely: solutions in the perfect electrical conductor (PEC) limit (lowest order) and in the so-called Rytov approximation (highest order) are given by one and four equations, respectively. It is demonstrated that each equation admits separation of variables into space and time components, a property that significantly reduces computational costs compared with traditional time domain formulations that require the integral equations to be solved at each time step. For the purpose of validation, a test problem is solved by the proposed formulation and by the ‘original’ BEM based on the time-dependent fundamental solution. Conditions of applicability are discussed and the effect of such factors as the shape of the incident current pulse and proximity effect are considered.

Time domain surface impedance concept for low frequency electromagnetic problems—Part I: Derivation of high order surface impedance boundary conditions in the time domain

The surface impedance boundary conditions (SIBCs) for the tangential component of the electric field and normal component of the magnetic field on the smooth curved surface of a homogeneous non-magnetic conductor are derived in time- and frequency-domain. Scale factors for the basic variables are introduced in such a way that, a small parameter, equal to the ratio of the penetration depth and the body's characteristic size, appears in the dimensionless Maxwell's equations for the conducting region. The perturbation method is then used to represent the SIBCs in the form of power series in this small parameter and the first four terms of the expansions are derived. The zero-order, first-order, second-order and third-order terms of the expansions are the solution of the problem in the perfect electrical conductor limit, the Leontovich approximation, the Mitzner approximation and in the high order approximation (referred to as Rytov's approximation), respectively. Therefore, the accuracy of the proposed conditions exceeds the accuracy of the SIBC for planar surfaces (Leontovich's approximation) that are usually used in the time-domain analysis, by two orders of magnitude. In Part II of this paper, the formulation of the SIBCs developed here in conjunction with a boundary element method is demonstrated and applied to the problem of transient skin and proximity effect problems in cylindrical conductors.

Application of surface impedance concept to inverse problems of reconstructing transient currents

The inverse eddy-current problem of fast transients is solved by a new boundary element formulation employing time domain surface impedance boundary conditions. The integral equation is transformed to invariant form and is solved only once for a given geometry of the problem. Numerical results are in good agreement with measured data.

FDTD Analysts of Dielectric-Loaded Longitudinally Slotted Rectangular Waveguides

A versatile electromagnetic (EM) computational algorithm, based on the Finite-Difference Time-Domain (FDTD) technique, is developed to analyze longitudinally oriented, square-ended, single slot fixtures and slot-pair configurations cut in the broad wall of a WR-975 guide operating at a frequency of 915 MHz. The finite conductivity of the wave guide walls is accountedfor by employing a time-domain Surface-Impedance Boundary Conditions (SIBC) formulation. The proposed FDTD algorithm has been validated against measurements performed on a probe-excited slot cut along the center line of the broad wall of a WR-284 guide and available experimental data for energy coupled from a longitudinal slot pair in the broad wail of a WR-340 guide. Numerical results are presented to exploit the influence of the constitutive parameters of the processed material as well as protective insulating window slabs mounted on the exterior surface of the slots. Particular attention is given to the resonant length, scattering parameters, and the electric field distribution within lossy objects placed in the near-field region over a range of slot offsets and workloads with extensive results being reportedfor the first time. It is shown that the FDTD technique can accurately predict the coupling and power absorption characteristics in loads located in the near field zone of the slotted wave guide structures and, therefore, should prove to be a powerful design tool applicable to a wide class of slotted waveguide applicators that may be difficult to analyze using other available techniques.

Approximating the surface impedance of a homogeneous lossy half-space: an example of "dialable" accuracy

We present an approximation by exponentials of the time-domain surface impedance of a lossy half space. Gauss-Chebyshev quadrature of order N-1 is employed to approximate an integral representation of the modified Bessel functions comprising the time-domain impedance kernel. An explicit error estimate is obtained in terms of the physical parameters, the computation time and the number of quadrature points N. We show that our approximation is as accurate as other approaches which do not come with such an error estimate. The paper investigates the conditions under which the derived error estimate also applies to the approximation of J.A. Roden and S.D. Gedney (see Trans. Microwave Theory Tech., vol.47, p.1954, 1999).

Theoretical and experimental characterization of the EMP-interaction with composite-metallic enclosures

A numerical procedure is developed for the prediction of the electric and magnetic field distribution inside an enclosure having aluminum and carbon-fiber reinforced composite (CFRC) walls, illuminated by a transient electromagnetic plane wave. The composite panel is simulated by an effective layer model; time-domain surface impedance boundary conditions are enforced on the external faces of the composite slab, to express the relations among the tangential electric and magnetic field components. A coupling model for the calculation of the current induced along thin wires inside the enclosure is presented. The proposed models are implemented in a three-dimensional (3-D) finite-difference time-domain (FDTD) procedure, which is applied to the analysis of the shielding performances of an aluminum box with one CFRC face, illuminated by a transient electromagnetic wave. The computed results are compared with measured data obtained by using a full scale EMP generator.

A unified time domain surface impedance concept for both linear and non-linear skin effect problems

A new time-domain boundary element technique for calculation of the magnetic field and temperature distribution in the skin layer of conductors of isotropic material with general BH-curve and /spl sigma/(T) relationship is proposed. The formulation consists of the surface integral equation for the scalar magnetic potential and the time-domain surface impedance boundary condition (SIBC) for the normal component of the magnetic field. The SIBC is obtained in the form of 1-D nonlinear diffusion equations for the magnetic field and temperature inside the conductor normal to its surface. The number of integral equations is the same for 2-D and 3-D problems. The technique requires the same computational expenses as solving the problem in the well-known perfect electrical conductor limit. Numerical examples are also considered.

Efficient implementation of the time domain surface impedance boundary conditions for the boundary element method

Efficient implementation of the time domain surface impedance boundary conditions on the surface of homogeneous lossy dielectric body for the space-time domain surface integral equations for the electric and magnetic fields is proposed. The governing equations are transformed by using the perturbation techniques in small parameters, equal to the ratio of the penetration depth and body's characteristic dimension. As a result, the terms, containing time-convolution integrals, are moved from the left-hand side to the right-hand side of the integral equations, so that the computer resources required for numerical realisation of the formulations are greatly reduced. A numerical example is included to illustrate the theory.

Time domain surface impedance boundary conditions of high order of approximation

The problem of diffusion of transient electromagnetic field into a lossy dielectric homogeneous body is solved by using the perturbations method in the small parameter p, equal to the ratio of the electromagnetic penetration depth and characteristic dimension of the body. Time and frequency domain solutions for the tangential component of the electric field and the normal component of the magnetic field on the smooth curved surface of the body (the surface impedance boundary conditions-SIBCs) are obtained with accuracy up to O(p/sup 4/) It is shown that the proposed SIBCs in the frequency domain generalize well-known Leontovich's and Mitzner's boundary conditions that provide approximation errors O(p/sup 2/) and O(p/sup 3/), respectively. A numerical example of using the high order SIBCs with the surface integral equations in time domain is considered to illustrate the method.

Surface impedance time domain reflectometry for the determination of ice depth

The analysis of the surface impedance of a horizontally stratified earth is similar to the impedance of a step‐wise discontinuous lossy transmission line. Time Domain Reflectometry (TDR) is commonly used in transmission line assessment to determine the location of faults. There are electrical conditions where TDR can be applied to a two layered subsurface to determine the time of flight of the EM wave and hence the thickness of the top layer. When the upper layer resistivity is sufficiently contrasted over a conductive second layer, then transforming surface impedance data measured across a broad band of frequencies into the time domain allows one to determine the time of flight to the subsurface boundary.If the maximum frequency, frequency step size and number of steps are optimised for the two layers a periodicity appears in the surface impedance profile. It is demonstrated through computer modelling that a layer of ice on rock or sea water gives a return time of flight equal to the separation time of peaks in the time domain surface impedance profile. The technique requires a vertically polarised transmitter which steps up to the high frequency (HF) range. For example an ice layer of 30 to 400 meters thickness requires frequencies up to 5MHz.In this paper, the basic theory for the use of TDR techniques in the interpretation of the surface impedance data is explained, and computer modelling results are presented