Scattering from a periodic array of resistive strips

The problem of scattering from a resistive strip grating is formulated in the spectral domain. Results of numerical calculations of the reflection coefficient are presented for perfectly conducting strips and strips with resistivities up to750Omega/square.     

Backscattering from resistive strips

Strips made of a resistive sheet material have lower backscattering cross sections than the corresponding perfectly conducting strips, and this is true in particular when the illumination is edge-on with the electric vector parallel to the edge. Attention is focused on this case. Using the moment method applied to an appropriate integral equation, data are obtained for the surface field and backscattered far field of a resistive strip for a variety of strip widthswand uniform resistancesR. The front- and rear-edge contributions to the far field are then extracted. It is shown that for strips whose width is greater than about a half-wavelength the former is the same as for a half-plane having the same resistance, whereas the latter is proportional to the square of the current at that point on the half-plane corresponding to the rear edge of the strip. The implications of these results on the selection of a strip resistance for low backscattering are discussed.     

Electromagnetic scattering from electrically large coated flat and curved strips: Entire domain Galerkin formulation

Efficient numerical solutions are presented for electromagnetic scattering for classes of electrically large, coated, perfectly conducting strips which are flat or curved. The formulation is based on the solution of a coupled system of electric- and magnetic-field integral equations using the method of moments (MM). Entire domain Galerkin representations for the currents are used on the surface of the coating and at the coating-conductor interface. The resulting symmetric matrix equation is well conditioned and admits rapid, accurate solutions. Numerical results are presented for various coating thicknesses, strip widths, and curvatures for the transverse electric (TE) and transverse magnetic (TM) cases. The convergence of the Galerkin solution is examined as a function of these parameters. The effect of the edge approximation on the choice of expansion functions is discussed. The numerical results are compared with experimental measurements.     

Multiple microstrip lines on a multilayered cylindrical dielectricsubstrate on perfectly conducting wedge

The quasi-TEM characteristics of a class of cylindrical microstrip lines are rigorously determined. The class of microstrip lines considered consists of multiple infinitesimally thin strips on a multilayered dielectric substrate on a perfectly conducting wedge. Expressions for the potential distribution inside and outside the dielectric substrate, charge distribution on the strips, and capacitance matrix of the microstrip lines are derived. The problems of a microstrip line on a cylindrically capped wedge and on a cylindrical dielectric substrate on perfectly conducting core are also considered as special cases. Sample numerical results based on the derived expressions are given and discussed     

Scattering of E-polarized waves from conducting strips inthe presence of a magnetically uniaxial half-space-a singular integralequation approach

A method based on the theory of singular integral equations (SIE) is presented for treating analytically scattering by perfectly conducting infinitely long strips in the presence of a magnetically uniaxial half-space. A uniform plane wave, polarized parallel to the strip axis, is incident from the isotropic region. As a prerequisite to this approach, the E-mode scalar Green's function of the structure is developed. Use of the reciprocity theorem then leads to a SIE for the current density induced on the scatterer's surface. The solution of the SIE is carried out in the case of a strip parallel or perpendicular to the interface, either located above or embedded in the anisotropic space. Numerical results for the induced current density and for the scattered far field in a variety of cases are presented in graphical form     

A uniform GTD solution for the far-field scattering by polygonal cylinders and strips

The results of our recent asymptotic treatment of the double diffraction by a pair of parallel perfectly conducting wedges are applied to polygonal cylinders and strips. The combination of the appropriate nonuniform expression for the doubly diffracted ray field with the nonuniform geometrical theory of diffraction (GTD) expressions for the singly diffracted fields yields a uniform, closed-form solution for the far scattered field valid throughout the overlapping transition regions. The advantage over the existing uniform GTD solution for a polygonal cylinder consists in the extension from strictly grazing to nearly grazing incidence. For a strip, the present solution improves upon the accuracy of the previous uniform high-frequency solutions.     

The near-zone field characteristics of an E-polarization plane wavepenetrating through cylindrical multiple apertures (non) coated withlossy and lossless media

The direct integral equation is formulated for describing the current on the multiple perfectly conducting strips in cylindrical geometries for an E-polarization plane wave of normal incidence. By using the Galerkin's method, the surface currents on the conducting strips are expanded in the form of a series of Chebyshev polynomials of the first kind, while the unknown expanding coefficients are solved by a set of matrix equations of finite order with a fast convergence rate and a high accuracy. Furthermore, numerical results are presented to demonstrate the variation of the penetrated near-zone field in the presence of one, two, three, four and six cylindrical apertures, and the hybrid effects of both aperture number and aperture angular widths on the penetrated fields are investigated in detail     

The Impedance and Scattering Properties of a Perfectly Conducting Strip Above a Plane Surface-Wave System (Short Papers)

The impedance and scattering properties of a perfectly conducting strip above a dielectric-coated conducting plane is investigated both theoretically and experimentally. An integral equation for the induced current is presented and solved numerically using a point-matching technique. The values of the reflection and transmission coefficients are calculated from the computed current distributions. The results of the computations are compared to the measured values and the agreement is quite good. In addition the impedance and fractions of power reflected, radiated, and transmitted are computed and displayed graphically.     

Spectral theory of EM wave scattering by periodic strips

A new method is proposed for analyzing electromagnetic (EM) wave scattering and waveguiding by a planar periodic system of thin and perfectly conducting strips. The method exploits some known properties of Fourier series with coefficients expressed by Legendre polynomials. The method can be used to solve problems associated with EM wave propagation and polarization having an arbitrary angle with respect to strips in arbitrary anisotropic media, multiperiodic systems of strips, and layered systems of skewed periodic strips. In the paper the method is presented by an example, namely the scattering of EM waves from a grating consisting of perfectly conducting strips in vacuum. Numerical calculations show that the method converges much faster than do alternative methods     

Time-domain version of the physical theory of diffraction

A time-domain version of the equivalent edge current (EEC) formulation of the physical theory of diffraction is derived. The time-domain EECs (TD-EECs) apply to the far-field analysis of diffraction by edges of perfectly conducting three dimensional (3-D) structures with planar faces illuminated by a time-domain plane wave. By adding the field predicted by the TD-EECs to the time-domain physical optics (TD-PO) field, a significant improvement is obtained compared to what can be achieved by using TD-PO alone. The TD-EECs are expressed as the integral of the time-domain fringe wave current (the exact current minus the TD-PO current) on the canonical wedge along truncated incremental strips. Closed-form expressions for the TD-EECs are obtained in the half-plane case by analytically carrying out the integration along the truncated incremental strip directly in the time domain. In the general wedge case, closed-form expressions for the TD-EECs are obtained by transforming the corresponding frequency-domain EECs to the time-domain. The TD-EECs are tested numerically on the triangular cylinder and the results are compared with those obtained using the method of moments in combination with the inverse fast Fourier transform     

Excitation of an untilted narrow-wall slot in a rectangularwaveguide by using etched strips on a dielectric plate

We propose a novel excitation technique of an untilted slot in the narrow wall of a rectangular waveguide. The excitation is realized by inserting into the slot a dielectric plate on which there are etched conducting strips. The strip excitation can control the coupling more easily and accurately than a conventional excitation using tilted wires. We analyze the coupling to the slot by using the dyadic Green's function for the waveguide with the dielectric plate, derived by Seki's (1984) virtual cavity method. A double resonance due to the strip and the slot results in large coupling as well as small variation of the phase of the transmitted wave, both over a wide frequency band. Some results are verified by measurements. The coupling can be tuned by varying the distance between the slot and the strip     

TM and TE Diffraction by a Perfectly Conducting Half-Plane in Presence of a Perfectly Conducting Strip: Solution by Exponentially Converging Nystrom and Galerkin Methods

We study TM and TE diffraction by a perfectly conducting half-plane in presence of a perfectly conducting flat strip of finite width and infinite length; the edges of the strip are parallel to the edge of the half-plane. The relevant integral equations with unknowns the induced current densities on the strip are solved by a Nystrom and a Galerkin method that fully account for the singular nature of the kernels and the singularities of the solution at the edges. The proposed algorithms are highly accurate, and appear to converge exponentially as shown by detailed numerical examples and case studies. The Nystrom method is the most efficient of the two methods because of its simple formulation, fast computer implementation, and much less effort in computing the matrix elements. When the strip is coplanar to the half-plane, an additional formulation method in terms of equivalent surface magnetic currents is possible in the framework of the field equivalence principles. This alternative method is applied in order to validate the algorithms and test their accuracy.     

Exterior moment method analysis of conducting scatterers by using the interior Green's function

A new method using a Green's function in the interior region of a conducting scatterer is proposed to obtain a mutual admittance matrix in an exterior moment method analysis. A numerical example of a two-dimensional magnetic strip source located on an exterior surface of a perfectly conducting rectangular cylinder shows the validity of the method.<>     

Transient scattering by resistive cylinders

The two-dimensional scattering of an electromagnetic pulse normally incident on a collection of infinitely long cylinders of arbitrary shape is considered. ForE-polarization an electric field integral equation is derived that is applicable to solid cylinders and/or thin sheets, resistive and/or perfectly conducting. The contribution of the self-cell at later times is carefully analyzed. The expression obtained represents a generalization of previously known results. For an incident Gaussian pulse, numerical results are presented for surface currents and far-fields, for perfectly conducting and resistive circular cylinders and strips. A fast Fourier transform (FFT) algorithm is implemented to obtain the backscattering radar cross section, which is in good agreement with results obtained from either exact continuous wave (CW) solutions or the method of moments.     

Electromagnetic scattering from extended wires and two- and three-dimensional surfaces

Efficient numerical solutions for the electromagnetic scattering for classes of electrically large one-, two-, and three-dimensional perfectly conducting scatterers are presented. The formulation is based on solution of the electric field integral equation (EFIE) using the method of moments (MM). An entire domain Galerkin representation is used for wires and two-dimensional surfaces and a combination of entire and subdomain representations is applied to surfaces in three dimensions. The analysis is extendable to corrugated surfaces formed from sections of surfaces of translation or rotation. Numerical results are presented for wires, infinite strips, and finite strips (or plates). The behavior of the solutions with the number of terms in the entire domain expansion is examined. The reconstruction of the traveling-wave contribution to the scattering cross section using various approximations is discussed, and representative examples are given.     

Current induced on a conducting strip which resides on the planar interface between two semi-infinite half-spaces

An analysis is described for determining the current induced by a known excitation on a conducting strip which resides on the planar interface between two semi-infinite homogeneous half-spaces of different electromagnetic properties. The perfectly conducting flat strip is of infinite extent and the excitation is transverse magnetic to the strip axis. An integral equation for the induced current is formulated and it is shown that its kernel which is in general a Sommerfeld-type integral can be expressed in closed form when the permeabilities of the two media are the same. Under this practical condition the integral equation is solved numerically and data are presented for cases of interest. For the electrically narrow strip, the integral equation is approximated and this approximate equation is solved analytically.     

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     

Diffraction of plane waves by a strip in an unbounded gyrotropic orbiisotropic space: oblique incidence

Diffraction of plane waves obliquely incident on a perfectly conducting strip of infinite length, which is embedded in an unbounded gyrotropic or biisotropic space, is studied. To this end, a system of two singular integral-integrodifferential equations of the first kind is derived following two different methods. This system is efficiently discretized independently using two recently developed direct singular integral equation techniques. Analytical expressions are presented for the far- and near-scattered fields, along with typical numerical results     

EM scattering by an array of perfectly conducting strips by a physical optics approximation

The scattering of electromagnetic waves by planar arrays of perfectly conducting strips is analyzed by a simple method based on physical optics. The induced current as determined by physical optics is used in simple hand computation to obtain the amplitudes of various propagating space harmonics. Results are compared against some exact results available in the literature to show the accuracy of the proposed approximate method.     

Reply to 'Comment on 'Comparison of excess 1/f noise spectra in trimmed and untrimmed thick film resistors'

An iterative surface current density replacement technique is used to formulate the electromagnetic scattering from any perfectly conducting body defined as the intersection of two bodies for which expressions for the scattering are known. The application of the iterative surface current density replacement technique to the truncated wedge results in a secondary edge diffraction coefficient which is accurate for closely spaced edges, and is identical to the secondary diffraction coefficient of the geometrical theory of diffraction when the edges are separated by a distance which is large compared with the wavelength of the field. Results are presented which show the accuracy of this secondary edge diffraction coefficient when applied to the perfectly conducting truncated wedge and narrow strip.