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Based on a pair of linear frequency modulation waveforms with opposite slopes, the mathematical model of the influence of intermediate frequency deviation (IFD) and sampling frequency deviation (SFD) on simultaneous polarisation measurement is derived. An IFD and SFD joint estimation and calibration method is proposed in this article. Simulation and real data results show that the radar frequency stability can change the position and phase of the polarisation scattering matrix (PSM) measurement. The approach proposed in this article can regulate the peak deviation effectively, compensate the phase error and accurately acquire the four elements of PSM.

In this paper, we model multiple vias with irregular antipad in arbitrarily shaped 3-D integrated circuit and packaging system based on generalized Foldy-Lax equations method, boundary integral equation method, and generalized T matrix. We first obtain the impedance matrix for finite cavity, which includes the reflection features of the cavity boundaries. Then, the scattered field from a single via and a generalized T matrix, including the wall effects, are derived. The Foldy-Lax multiple scattering equations are generalized to include the wall effects using impedance matrix and the generalized T matrix. To obtain the incident field for the case of vias in the arbitrarily shaped antipad, we calculate the exciting and scattering field coefficients based on the transformation that converts surface integration of magnetic surface currents in antipad into 1-D line integration of surface charges on the vias and ground plane. The coupling among vertical vias are solved by applying Foldy-Lax multiple scattering equations. The scattering matrix of coupling among vias is calculated to make corresponding signal/power integrity analysis. Numerical results for the method are in a good agreement with a commercial full-wave numerical tool up to 50 GHz.

A uniform and closed-form spatial Green's function for finite dielectric structures is derived by using a combination of the characteristic Green's function (CGF) and rational function fitting method (RFFM). Employing the concept of quasi leaky waves, CGF-RFFM represents both of the discrete and continuous spectrum contributions efficiently by using the modified VECTFIT algorithm. The method is examined for 2-D truncated dielectric slab while it can be implemented for 3-D structure straightforwardly. An error of less than 0.2% is achieved compared with the direct numerical integration of the spectral integral. The derived Green's function is exact for separable structures while it is approximate for nonseparable structures like truncated dielectric substrates where the corner regions are replaced with fictitious materials. To obtain more accurate results, mode conversions due to the surface waves (SWs) incident on the end-facet are considered by employing the scattering matrix in the formulation for structures supporting several guided modes. The main advantage of this method lies in its speed as well as accuracy. Excellent agreements with the rigorous method of moments (MoM) are shown in several examples.

A technique is described to measure the generalized scattering matrix (GSM) of a waveguide device whose ports are multimodal. The device-under-test is placed in between suitable converters, thereby transforming multimodal ports into monomodal ports. The needed data are then measured using a standard vector network analyzer. A dedicated algorithm is finally used to recover the multimode GSM of the device. The experimental validation is reported in this paper for rectangular and square waveguides showing excellent agreement between theory and measured results.

An efficient approach is presented to compute the eigensolutions of closed and open radiating periodically loaded waveguides by modal series expansion. The eigensolutions of the homogeneous background waveguides serve as basis functions for the fields in the periodic boundaries. The corresponding scattering matrix of an isolated periodic unit cell is determined by commercial software solvers. The scattering matrix is transformed into the transfer matrix, which can be used to formulate an eigenproblem. Open field problems are converted into a closed equivalence while the characteristics of the original open configurations are preserved, even for radiating (leaky) waveguiding structures. Consequently, the original continuous spectrum of modes is represented by a discrete and proper set of modes. An eigenproblem must still be solved but it is considerably reduced in size and complexity for configurations where relatively few expansion modes are sufficient.

A full-wave antenna modeling method by means of elementary sources described in terms of colocalized infinitesimal dipoles is presented in this paper. The procedure provides a generalized scattering matrix (GSM) in terms of equivalent infinitesimal dipoles from the GSM of the antenna by using rotation and translation of spherical modes. The number of equivalent infinitesimal dipoles and their positions are optimized by using a genetic algorithm. The application to the full-wave analysis of arrays is also presented, providing very accurate results even when the minimum spheres of the antennas in the array environment overlap considerably, which cannot be solved by the direct coupling of generalized scattering matrices in terms of spherical waves. Some examples of antenna modeling and their application to the analysis of arrays of antennas on a metallic plane will be shown.

We present a variation of the electric-field volume integral equation (VIE) for inhomogeneous media that is tailored for microwave S-parameter measurements. The kernel of the standard VIE is a dyadic Green's function that can relate fields in the object domain to observed scattered fields outside the object domain. Here, we derive a kernel we call a vector Green's function that gives, instead of observed fields, observed S-parameter measurements that would be obtained in a bistatic antenna setup. This formulation directly links the object properties to microwave measurements in a way that is useful to many microwave applications. This derivation uses an antenna model based on the source-scattering matrix formulation. We show how this vector Green's function can be obtained from simulation and validate this model with several experiments.

Arrays of volumetric antennas whose minimum spheres overlap are efficiently analyzed by means of translational addition theorems for spherical modes in this letter. For this purpose, an improved model of the isolated antenna in terms of elementary sources of infinitesimal dipoles is used. The model provides a generalized scattering matrix (GSM) in terms of infinitesimal dipoles that allows synthesizing the whole behavior of the isolated antenna and enables its precise application to array environments by using translational addition theorems. The search region for the optimization procedure that finds the positions of the elementary sources to model the isolated antenna has been extended to the volume occupied by the antenna, so that the model becomes very precise. As a consequence, even when the minimum spheres of the array elements are strongly overlapped, it provides accurate results since the equivalent models will never overlap. Additionally, the optimization procedure is carried out only once for a wide band. The proposed approach has been validated by means of two different radiating elements such as monopoles and dielectric resonator antennas (DRAs), with good agreements obtained in comparison to the full-wave results simulated by commercial software.

S-matrix reconstruction transforms are based on two stages of matrix transformation to remove the mismatch-induced errors. Over the years, these transforms are widely used in measurements of multiport devices using a two-port vector network analyzer, especially for noncoaxial applications because high-quality matched loads are hardly accessible. In this paper, analytical error analysis of the S-matrix reconstruction transforms is performed to develop the accuracy criterion that is explicitly expressed in matrix form in terms of the S-matrix of the multiport device and the reflection coefficient matrix of the auxiliary terminations. The analytical insights in this paper can pave the way for using strongly reflecting auxiliary terminations. For noncoaxial measurements, strongly reflecting termination, such as a short-circuited or an open-circuited transmission line is more repeatable, reliable, and economical than terminations with loss like resistors. Consequently, the use of strongly reflecting auxiliary terminations is speculated to ease noncoaxial multiport measurements.

An analytical method to synthesize shaped-beam patterns with planar arrays, based on the handling of spherical waves, is proposed. Translational Addition Theorems will be used here for two different purposes: (1) relating the spherical modes produced by each element in the array to calculate the mutual coupling effects, and (2) expressing the field radiated by each element in terms of spherical modes corresponding to the whole array, to carry out a spherical-wave synthesis procedure based on the orthogonal properties of spherical modes. This field synthesis method is based on the fact that any antenna radiated field can be expressed as a discrete series of weighted spherical vector wave functions and it only requires the a priori knowledge of the Generalized Scattering Matrix of each array element considered as isolated from the rest of the array elements.

The combination of the generalized transverse resonance technique, a field-matching method, and the generalized scattering matrix (GSM) concept is proposed in this paper as an efficient, versatile, and accurate method for the analysis of laterally open periodic waveguides. The proposed method accounts for both open and periodic boundary conditions without any approximation. Its only drawback is its restriction to the analysis of structures that can be segmented in the Cartesian coordinate system. How ever, a staircase approach has been successfully applied to over come this basic limitation. The segmentation of the waveguides, the field expansions for TMp,qz Bloch modes in each partition, and a modification of the well-known GSM cascading procedure for the analysis of a particular type of structure are detailed. In order to demonstrate the capabilities of the proposed approach, four structures, similar to the substrate integrated waveguide, have been analyzed, built, and measured. These examples include single-row square-post and circular-post waveguides, and displaced-row and multiple-row square-post waveguides. The computations and measurements confirm the efficiency, accuracy, and great versatility of this method.

A different and useful approach is presented for detecting new events in a scene, such as the presence or absence of landmines or perhaps the movement of people, vehicles, or structures. The approach rests on the radar examination of an area several times, once, before there are targets present, and the other (or others) after. The change detection algorithm notices if there are any changes after the first view. In the present approach the prospective target is represented, not in terms of three complex elements of a scattering matrix, but in terms of phenomenologically-based Huynen parameters. Each element of the Huynen parameter set conveys a different type of physical and geometrical attribute about the scatterers, thus the potential for significant false-alarm mitigation is increased. We provide results of the application of this approach on fully polarimetric signatures of simulated pairs of buried cylindrical targets. These results indicate the following. 1) Huynen parameters are more effective for change detection than the scattering matrix elements because of their ability to generate higher unambiguous autocorrelation peaks and fewer dominating cross-correlation curves. 2) A large number of symmetries are observed in the plots of the Huynen parameters for both one and two buried cylinders. These symmetries may eventually lead to further classification insights. 3) By using standard Prony methods, relevant resonance frequencies are extracted from the parameter plots, from which the height of either one of the cylinders is estimated. 4) The diameter of either cylinder can also be obtained by a simple procedure based on ray-tracing and time delays. Numerical calculations substantiate all the above assertions.

A new hybrid mode matching and method of moments formulation based only on electric currents is presented in this paper. The use of only one equivalent current allows the introduction of a new set of unknowns. The chosen new unknowns are the weights related to the scattered modes that emerge from the ports to the waveguides that feed the problem. Applying this new formulation, the matrices that must be inverted are smaller and the generalized scattering matrix can be obtained directly from the solution of the resulting system of equations, so that no additional projection is needed to obtain the scattering parameters, as happens with traditional approaches with two equivalent currents. As a result, certain efficiency improvement is obtained, as can be seen when this technique is applied to the solution of H plane problems in rectangular waveguide

Even in light of all the multiport vector network analyzers (VNAs) that appear to be on the market at present, the measurement of noncoaxial multiport devices remains a critical challenge due to the lack of a multiport counterpart of the two-port thru-reflect-line (TRL) calibration. Accordingly, based on the concept of virtual auxiliary termination and the two-port TRL calibration technique, a scattering matrix reconstruction procedure is developed for the use of a two-port VNA to characterize noncoaxial multiport devices up to the intrinsic ports located at the ends of the planar transmission lines such as microstrips, coplanar waveguides, and substrate integrated waveguides (SIWs). The four-port scattering matrix of a 60-GHz SIW 0-dB coupler for experimental validation is reconstructed. The final results are in agreement with not only the simulation results, but also the fully corrected TRL results.

By characterizing the condition number as an indicator of accuracy, an error analysis is performed to determine how different auxiliary terminations affect the accuracy of the scattering matrix renormalization transform. Such an error analysis plays an essential role in enhancing the accuracy and widening the applicability of the port renormalization method for measuring multiport devices with a two-port vector network analyzer.

The formulation of the generalized scattering matrix (GSM) of a finite array is revised to take into account the feeding network effects in the calculation of the external mutual coupling. It allows the analysis of finite arrays of externally coupled elements whose radiated field can be described by means of spherical waves on a ground plane, such as apertures, monopoles, cavity-backed patch antennas, or dielectric resonator antennas (DRAs), including rigorously the mismatching and internal coupling effects because of the feeding network.

This letter presents a flexible method to compensate the interelement mutual coupling (MC) effects that may degrade the field pattern of an array of real and coupled antennas. A closed-expression for a mutual coupling compensation matrix (MCCM) is derived. The MCCM is used to compensate the presence of the real individual elements' patterns and the interelement MC effects for any excitations obtained with an isotropic-based pattern synthesis method. The MCCM is calculated from the generalized scattering matrix (GSM) of an antenna array and the spherical mode expansion (SME) of its radiated field. For a given array, this MCCM has to be calculated only once since it only depends on the radiating and scattering characteristics of the antenna elements as well as on their location in the array. Conditions regarding null field pattern directions can also be reinforced in the MCCM. To compute the GSM of the array and the SME of the radiated field, a validated full-wave hybrid and modular methodology is used. Numerical results of synthesized patterns where the MC effects have been compensated are presented for arrays made up of dielectric resonator antennas.

We propose a generalized T -matrix definition that facilitates the conversion between the S-parameter and T-parameter for multiport networks based on the well understood and mathematically simple two-port relations. This approach generalizes all multiport networks into two cases: balanced and unbalanced. Balanced networks have the same number of entrance and exit ports and are symmetric to the two-port network. Unbalanced networks generate a nonsquare T -matrix and do not have the same number of entrance and exit ports. Through careful selection of the T -matrix, this method extends two-port symmetry to multiport networks and provides an engineering implementable relationship between the S-parameter and T-parameter for multiport networks. This symmetry extension allows a practical means to cascade and de-embed such networks.

Most of the existing methods for the analysis of meanderline polarizer assume that the embedded metallic grids are infinitely thin. A modal procedure is presented here for treating meanderline grids with finite thicknesses. The space between the metallic grids in a unit cell is considered as a meanderline waveguide with a stepped cross-section and length given by the grid thickness. The modes of this guide are obtained using the transverse resonance technique. A generalized scattering matrix characterization of the grid is obtained by field matching of the modes of the meanderline guide and the free space Floquet guide. The accuracy of this approach is verified by the very good agreement obtained between predicted and measured transmission phases of polarizer grids.

This paper proposes a generalization of the Huynen theory to bistatic radar configurations for which the scattering matrices can no longer be assumed symmetrical. A set of parameters characterizing the physical mechanisms is extracted from the disoriented bistatic Kennaugh matrix. The distribution of amplitude between the parameters of the disoriented Kennaugh matrix is studied.

Some new results are presented on the properties of generalized scattering matrix representations for metallic waveguides with axially periodic dielectric loadings. A unified framework is given for describing the frequency dependence and for identifying the emergence of propagating, nonpropagating, and complex Floquet modes in single mode, as well as multimode, regions. Two new conservation relations are formulated for the generalized scattering matrix of the unit cell in lossless periodic structures. One of these relations provides a convenient means for checking the correctness of the values of calculated matrix elements, while the other relation yields accurate estimates for the stopband-passband transition frequencies located within single Floquet-mode regions.

This paper introduces a general multigrid-subgridding formulation aimed at improving the efficiency of the transmission line matrix method. The rigorous algebraic procedure, based on Hilbert space formulation, leads to the definition of a general boundary scattering matrix, which interfaces 3-D regions of uniform computational mesh with different spatial resolution, thus allowing the modeling of objects of very disparate geometrical or electrical scale, e.g., such occurring in nanodevices. Computational acceleration and accuracy are measured by comparing the run time of simulations performed with subgridding to the run time of simulations without any subgridding.

Almost all methods for measuring the scattering matrix of an n-port device with the use of a two-port vector network analyzer (VNA) require one to terminate the other n - 2 ports in the fully characterized auxiliary terminations and prefer auxiliary terminations with small or moderate reflection coefficients. In this paper, a technique is presented to measure the auxiliary terminations indirectly. It not only eases the measurement of auxiliary terminations, but also makes the concept of virtual auxiliary termination realizable. In practice, examples of virtual auxiliary terminations can be the inherent connectors or bonding pads of the test device. Also studied is the remedy for the numerical pitfall possibly coexisting with the use of strongly reflecting auxiliary terminations such as virtual auxiliary terminations. The scattering matrix of a four-port circulator is then acquired accordingly from measurements using a two-port VNA and virtual auxiliary terminations.

This paper derives, in the exact framework of multiple scattering theory for point targets, a noniterative analytical formula for the nonlinear inversion of the target scattering strengths from the scattering or response matrix that can be applied after the target positions have been estimated in a previous step via, e.g., time-reversal multiple signal classification or another approach. The new formula provides a noniterative analytical alternative to the iterative numerical solution approach for the same problem presented in a recent paper [A. J. Devaney, E. A. Marengo, and F. K. Gruber, "Time-reversal-based imaging and inverse scattering of multiply scattering point targets," J. Acoust. Soc. Am. 118, 3129-3138 (2005)]. The two methods (noniterative versus iterative) are comparatively investigated with two numerical examples.

The properties of conservative symmetric polarimetric scatterer scattering matrices are examined. It is shown that the unambiguous rotation angle for "conservative" symmetric polarimetric scatterers is the interval (-pi/4,+pi/4] as compared with (-pi/2,+pi/2] for nonconservative symmetric scatterers. Errors relating to the Cameron decomposition, which are recently introduced into the literature, are discussed. It is demonstrated that these errors arise from a faulty symmetric scatterer scattering matrix distance measure. This, in turn, leads to an improper mapping of the symmetric scatterer unit disk to a hemisphere. The correct mapping of the symmetric scatterer unit disk to the symmetric scatterer unit sphere is described

In this paper, a generalized deembedding technique is presented. It provides a multimodal characterization for microwave devices fed with planar guiding structures of arbitrary configurations. Instead of the conventional scattering matrix, the proposed technique leads to the multimodal scattering matrix. This matrix describes all possible kinds of mutual coupling between the different modes present on the feeding ports. In order to achieve this task, the feeding planar guiding structures are analyzed a priori using a full-wave two-dimensional solver. The generalizability of the proposed deembedding technique is demonstrated by characterizing a couple of coplanar-waveguide-based discontinuities. The results show that the proposed technique provides a rigorous and a detailed characterization.

An accurate method for analyzing two-dimensional electromagnetic scattering from periodic arrays of metallic cylinders with arbitrary cross section is proposed. A simple formula to calculate the scattered fields is presented using the generalized scattering matrix combined with the modal method. Numerical examples show that the convergence of the solutions is very fast and the accuracy is very high.

Digital waveguides are generalized to the multivariable case with the goal of maximizing generality while retaining robust numerical properties and simplicity of realization. Multivariable complex power is defined, and conditions for "medium passivity" are presented. Multivariable complex wave impedances, such as those deriving from multivariable lossy waveguides, are used to construct scattering junctions which yield frequency dependent scattering coefficients which can be implemented in practice using digital filters. The general form for the scattering matrix at a junction of multivariable waveguides is derived. An efficient class of loss-modeling filters is derived, including a rule for checking validity of the small-loss assumption. An example application in musical acoustics is given.

A method is presented for full-wave modeling of vertical vias in multilayered circuits. The analysis of the interior problem is based upon the cylindrical wave expansion of the magnetic field Green's function. The multiple interaction among vertical vias is modeled by the Foldy-Lax scattering formula. Multilayered effects are included by using cascaded network of the single-layer components. The exterior problem of the via and the transmission line is analyzed using the method of moments approach. The exterior and interior problems are combined into a system of equations to facilitate the solution of a large number of vias. Using this approach, the scattering matrix of problems of several thousand vias can be calculated with moderate CPU and memory requirement. Numerical results have been obtained for different via configurations and for a large range of frequency. Also illustrated are results for common and differential mode in differential signaling with surrounding idle and shorting vias.

The theory of scattering in junction by posts consisting of a segment of conducting cylinder is developed using a combination of a modified iterative scattering procedure and an orthogonal expansion method. The multimode scattering matrix of the junction is obtained. The change of the post's configuration, as well as a simple rotation of the post, makes it possible to vary the electrical characteristic. The validity and accuracy of the method is verified by comparing the numerical results with those given in literature, received from finite-difference time-domain (FDTD) simulation and our own measurements. The proposed procedure is efficient and faster than alternative numerical solutions such as the FDTD method used for comparison.

A full-wave methodology for a broadband analysis of isolated cavity-backed and probe-fed arbitrarily shaped microstrip patch antennas is combined with an analytical method based on the properties of rotation and translation of spherical modes for obtaining an efficient scattering matrix description of the mutual coupling in a two-element array. The proposed procedure is validated and results are given for identical circular cavity-backed patch antennas.

We provide a comprehensive study of two- and three-dimensional discontinuities in chirowaveguides. The multimode coupled-mode method is an effective numerical approach to analyze this problem. After obtaining the coupled-mode equations, we diagonalize the coupling matrix to obtain a multimode scattering matrix rather than the usual two-mode approximation. We calculate the scattering properties of coaxial waveguides partially filled with lossy chiral media. Excellent agreement is observed between our results and those obtained by the mode-matching method. We also compare our results in the achiral case for dielectric material partially filled rectangular waveguide with experimental data and results obtained by the mode-matching method. Excellent agreement is again found. Based on our analysis, numerical and analytical results are displayed to provide physical insight into the problem. First, we discuss the effects of the chirality admittance on scattering properties and find that the sensitivity of the scattering parameters to chirality admittance increases as the chirality admittance increases. Second, we find the dielectric constant has a great influence on the scattering parameters. Third, we find the relative influence of height and width of chiral obstacles in rectangular waveguides.

A new and efficient hybrid mode-matching method is presented for the analysis of arbitrarily shaped inductive obstacles and/or discontinuities in a rectangular waveguide. The irregular region with obstacles and/or discontinuities is characterized using a full-wave hybrid spectral/numerical open-space technique expanding the fields in cylindrical wave functions. Next, a full-wave mode-matching procedure is used to match the cylindrical wave functions to guided modes in all ports and a generalized scattering matrix for the structure is finally obtained. The obstacles can be metallic or dielectric with complex permittivities and arbitrary geometries. The structure presents an arbitrary number of ports, each one with different orientation and dimensions. The accuracy of the method is validated comparing with results for several complex problems found in the literature. CPU times are also included to show the efficiency of the new method.

The guiding influence of some of Stanley Mandelstam's key contributions to the development of theoretical high energy physics is discussed, from the motivation for the study of the analytic properties of the scattering matrix through to dual resonance models and their evolution into string theory., Comment: a contribution to Memorial Volume for Stanley Mandelstam, ed. N. Berkovits et al., (World Scientific, Singapore, 2017)

Based on the Buttiker dephasing model, we propose an analytical scattering matrix approach to the long-range electron transfer phenomena. The present efficient scheme smoothly interpolates between the superexchange and the sequential hopping mechanisms. Various properties such as the drastic dephasing-assisted enhancement and turnover behaviors are demonstrated in good agreement with those obtained via the dynamical reduced density-matrix methods. These properties are further elucidated as results of the interplay among the dephasing strength, the tunneling parameter, and the bridge length of the electron transfer system.

Exact and approximate formalisms describing the interactions of acoustic plane waves with an elastic isotropic plate immersed between two different fluids (asymmetrically fluid-loaded plate) are presented. This constitutes an extension of the Fiorito, Madigosky, and Uberall (FMU) [R. Fiorito et al., J. Acoust. Soc. Am. 66, 181 (1979)] theory, refined later by Freedman [A. Freedman, J. Sound Vib. 82, 181 (1982); ibid. 82, 197 (1982)]. The method, based upon the multichannel resonant scattering theory derived from quantum physics [A. Bohm, Quantum Mechanics, Foundations, and Applications (Springer, New York, 1993)], consists of two parts. First, a 2×2 scattering S-matrix in which the diagonal elements are the two reflection coefficients and the off-diagonal elements are the two transmission coefficients, is built. Second, in order to compare our results with the FMU theory, resonant approximations are given for these coefficients, assuming light fluids when compared to the plate. The approximated coefficients show that the resonance widths are the sum of two independent partial widths, each of them being related to one fluid and to the plate physical properties. Of importance in this extension is the fact that the eigenvalues of the matrix, which reveal all the resonant features of the immersed plate, allow the separation between antisymmetrical and symmetrical modes, contrary to the reflection and transmission coefficients. The eigenvalues also allow the analysis of resonances despite the overlapping phenomenon. For the computations, the exact coefficients and eigenvalues, rather than their approximate forms, are used. This allows us to check the validity of the exact part of the theory under any fluid loading and not especially for light fluid loading.

In a co- or cross-polarized channel, the polarization states of the transmitting and receiving antennas are the same or orthogonal, and the corresponding target nulls (i.e., the co-pol nulls or x-pol nulls) are defined as the polarization states of the transmitting antenna such that the received power equals zero. However, no systematic studies have been carried out to solve the problem of the corresponding target nulls if the polarization states of the transmitting and receiving antennas are independent. In this paper, the target null theory is extended to the case of two independent polarization states. For two arbitrary independent symmetric scattering matrices, it is proved that there exists only one pair of polarization states such that both of the received powers equal zero. This polarization states' pair is called the co-null of the two targets, which can easily be obtained by solving an eigenvalue problem. Based on this concept and algebraic theory, the concept of the co-null space is introduced for the symmetric scattering matrix case, and many important results are presented, e.g., the relations between the co-null and the co-pol/x-pol nulls, the properties of the co-null space, and the relation between the co-null and target decomposition. Finally, the co-null for the asymmetric scattering matrix case is studied. The concepts of the mono-co-null space and the bi-co-null space are introduced, and the relations between both spaces are presented.

Kern's plane-wave scattering-matrix formulation is extended to treat the case of two interfaces plus a scatterer imbedded in the second region. This formulation can treat different shapes for the scatterer and only requires two different evaluations depending upon the location of the observer: 1) in the near field, a two-dimensional (2-D) fast Fourier transform (FFT) (one-dimensional (1-D) FFT is treated by an analytical integration), and 2) in the far-field an asymptotic evaluation of the integral. These two regimes are in contrast to the Sommerfeld integral approximations where different approximations are required for various parameter ranges (quasistatic, saddle-point evaluation for the radiation field, saddle point evaluation for the surface field when the saddle point is near a pole, and the lateral wave field evaluated using a uniform asymptotic evaluation for the integrals).

In this paper, we reconsider the question of the definition of the generalized scattering matrix (GSM) of a lossless device, and show the conditions that the GSM must satisfy in order to correctly represent a lossless device, independently of the method used for its calculation. Moreover, starting from circuit theory, possible choices are considered, and among them the one is examined that seems to be the most meaningful when dealing with modes below cutoff. When the circuit is lossless, in fact, the resulting GSM is unitary, even when modes below cutoff are taken as accessible. This property provides an immediate check of the correctness of the computational implementation of actual problems. Finally, a practical example of the usefulness of the conditions provided is shown.

The rates of change of the scattering matrix of a microwave device with respect to geometric or material parameters are of interest to designers, and useful in automatic optimization. They are most efficiently calculated by the adjoint variable method, but this usually entails the additional cost of funding the adjoint solutions. In the finite-element formulation presented here, no new solutions are needed beyond those required to calculate the complete scattering matrix. Explicit expressions are given for the calculation of the required matrix for a tetrahedral edge element. Results are presented for three rectangular waveguide problems: a uniform length terminated in a short-circuit; an H-plane miter bend; and a two-step waveguide impedance transformer.

This paper introduces a new TLM (transmission line modeling method) three-dimensional cell model, based on a "/spl pi/-type" transmission-line. Using this new design, the main equations of this cell are demonstrated, as well as its scattering matrix for a time domain modeling. This new model is applied to the wave propagation analysis into resonators, and the results are compared to analytical results and to the results of other methods.

In this paper, we present a multidomain and multi-method coupling scheme called FACTOPO, based on generalized scattering matrix computations on three-dimensional (3-D) subdomains. The global target /spl Omega/ is split in N/sub V/ subdomains (V/sub i/)(i=1, N/sub V/), separated by N/sub I/ fictitious surfaces (/spl Gamma//sub j/)(j=1,N/sub I/). We use a modal representation of the tangent fields on the interfaces. In each domain, the generalized scattering matrix S/sub i/ is computed with different methods such as the 3-D finite-element method (FEM) or the electric field integral equation (EFIE). This coupling scheme leads to an important reduction in computational resources, especially for cavities with one dimension much larger than the other two. The advantages of this formulation for parametric studies is illustrated by two cases: computing the RCS of an air-intake terminated with a flat PEC or a fan (CHANNEL) and of an antenna structure coupled to an electronic feed with a varying parameter (DENEB). Numerical as well as experimental results are presented.

In this paper, a method-of-moments integral-equation formulation of a generalized scattering matrix (GSM) is presented for the full-wave analysis of interactive planar electric and magnetic discontinuities in waveguide. This was developed to efficiently handle a variety of waveguide-based strip-to-slot transitions, especially on thin substrates. This single matrix formulation replaces the problematic procedure of cascading individual GSM's of an electric (strip) layer, a thin substrate, and a magnetic (slot) layer.

H- and E-plane waveguide structures having arbitrarily polygonal boundaries and piecewise homogeneous fillings are considered in this paper. A modified version of the generalized scattering matrix (S-matrix) method is applied to their analysis. More specifically, the segmentation of the whole unit is carried out. A homogeneously filled multiangular region, supplied with flanged apertures, is taken as a key building block. The scattering matrix of the block consists of amplitudes of elliptic waves propagating from the apertures in the corresponding half-spaces. Evaluation of the S-matrix is based on the domain product technique (DPT). Numerical examples demonstrating the efficiency, flexibility, and reliability of the approach are also presented.

In this paper the plane-wave scattering matrices for a range-dependent seabed and upper free surface are computed using the Rayleigh hypothesis at the surfaces. These matrices can then be used to compute the pressure field within a waveguide bounded by these surfaces; they can also be easily combined with the scattering matrix characterizing an object. Computational examples are given for range-dependent acousto-elastic waveguides and the fields compared with those computed by other methods. An example with a steel cylinder in the waveguide is also shown.

An integral-equation-based procedure is developed for determining the scattering parameters of a multiport Rotman lens device. The device is intended for use at millimeter-wave frequencies and incorporates rectangular waveguide feeds. The integral equation model takes higher order modes in the feed apertures into account and incorporates mutual coupling between neighboring ports. A prototype lens was designed using the integral equation model and fabricated. The lens S-parameters were measured and modified with an ideal -40 dB (n=3) Taylor weighting function. The resulting beam sidelobe level is better than -30 dB.

The method of moments (MoM) in conjunction with the generalized scattering matrix (GSM) approach is proposed to analyze transverse multilayered structures in a metal waveguide. The formulation incorporates ports as an integral part of the GSM formulation, thus, the resulting model can be integrated with circuit analysis. The proposed technique permits the modeling of interactive discontinuities due to the consideration of a large number of modes in the cascade. The GSM-MoM method can be successfully applied to the investigation of a variety of shielded multilayered structures, iris coupled filters, determining the input impedance of probe excited waveguides, and of waveguide-based spatial power combiners.

A full-wave method to analyze probe-fed infinite phased arrays of arbitrarily shaped microstrip patches residing in a cavity is proposed. The method is based on a combination of the mode matching and finite-element methods (MM-FEM) and provides a rigorous characterization of the coaxial feed. The radiated field to the half space is expressed as a Floquet's harmonic expansion reducing the analysis to a single elementary cell of the periodic antenna. The unit cell is analyzed as an open-ended succession of homogeneous waveguides of diverse cross sections. Each transition between waveguides is solved by a hybrid MM-FEM procedure to obtain its generalized scattering matrix (GSM). Finally, the GSM of the structure, which characterizes the array, is obtained from the individual GSMs by a cascading process. The method is also extended to the analysis of conventional probe-fed microstrip arrays by using the waveguide simulator model. Several prototypes, implemented and measured in a waveguide simulator, have been analyzed to prove the validity and efficiency of the proposed method.

We examine the scattering from cylindrically periodic engine-like structures using integral-equation methods. The periodic scatterer is enclosed in a cylindrical waveguide, and the primary goal of this paper is to show that this type of geometry affords substantial computational reductions by exploiting the periodicity of the blade structure and characteristics of the modal scattering matrix of the engine-like termination. Also, as a result of the periodic waveguide termination, a limited number of modes are excited by a given incoming mode, and this is exploited for a further reduction of the storage requirements of the modal scattering matrix.

Application of Newmann's principle, well known in crystallography, to electromagnetic N-ports is demonstrated. Using this approach, it is possible to find those symmetrical structures which can be considered as candidates for implementation of the electromagnetic functions including the nonreciprocal ones. Starting from the ideal scattering matrix, a systematic procedure is suggested to find the symmetry of this matrix and the corresponding symmetry of the geometrical structure and dc magnetic field. Two examples from the field of ferrite devices are given in order to illustrate the method.