An extended Huygens' principle for modelling scattering from general discontinuities within hollow waveguides

The modal fields, generalized scattering matrix (GSM) theory and dyadic Green's functions relating to a general uniform hollow waveguide are briefly reviewed in a mutually consistent normalization. By means of an analysis linking these three concepts, an extended version of the mathematical expression of Huygens' principle is derived, applying to scattering from an arbitrary object within a hollow waveguide. The integral‐equation result expresses the total field in terms of the incident waveguide modal fields, the dyadic Green's functions and the tangential electromagnetic field on the surface of the object. It is shown how the extended principle may be applied in turn to perfect conductor, uniform material and inhomogeneous material objects using a quasi method of moments (MM) approach, coupled in the last case with the finite element method. The work reported, which indicates how the GSM of the object may be recovered, is entirely theoretical but displays a close similarity with established MM procedures. Copyright © 2001 John Wiley & Sons, Ltd.     

基于等效磁流法的平面近场测量技术研究

为了进一步论证等效磁流法的近场-远场变换算法在平面近场测量中的实用性与准确性,本文首先根据矩量法（MOM）建立了平面天线口径面上等效磁流的辐射电场方程,利用波导探头采集待测天线平面近场的电场分布,通过共轭梯度法求解矩阵方程,得到天线口径面上的等效磁流分布,之后由格林函数计算出天线远场方向图。最后,通过两种喇叭天线进行实验测试验证。同时将等效磁流法计算出的远场方向图以及由传统的平面波展开法计算出的远场方向图与紧缩场天线测试暗室的测量结果进行对比,结果发现本文算法反演出的远场方向图比平面波展开法在相同测试数据下反演出的远场方向图与紧缩场测量结果相比一致性更好,其中线性角锥喇叭天线的E面和H面方向图吻合度均达到,双脊喇叭天线的E面方向图吻合度达到,H面方向图吻合度达到,验证了等效磁流法算法在平面近场测量中的准确性。     

Calculation of radiated electromagnetic fields from electronic systems

The electromagnetic radiation from electronic systems is formulated in terms of an integral equation for the electric and the equivalent magnetic current density, which is numerically solved by the method of moments. The electromagnetic coupling to conducting thin wires, thin plates, and aperture fitted cabinets is taken into account by appropriate operator equations. In order to solve the integral equation of electrically large conducting structures, suitable basis functions are needed to minimize the computation time. B-spline functions of the second and third degree are used as a basis in the moment method, which lead to a decrease of the computation time. A second way to decrease the computation time is given by the possibility of determining which parts of the structure of a printed circuit board (PCB) have to be considered and which parts can be neglected. Examples show that the influence of near source conducting areas to the radiated emissions is strong. It will be shown that this influence depends on the geometrical symmetry, the shape, and the distance of the scattering body.     

Analysis of quadruple corner‐cut ridged square waveguide by hybrid mode‐matching boundary‐element method

In this paper, the square waveguide with quadruple corner‐cut ridges is analyzed using the hybrid mode‐matching boundary‐element method. Because of its symmetry, only a quarter of its cross‐section needs to be considered and it is then divided into three regions. The electromagnetic field components in two regular regions can be obtained using the mode‐matching method and the third irregular region is discretized using the boundary‐element method. The combination of two methods produces one matrix equation, from whose determinant the cutoff wavenumbers of waveguide modes can then be computed. This hybrid technique takes advantage of the mode‐matching method's high efficiency and the boundary‐element method's versatility. The convergence of this hybrid method is studied, and numerical results are compared with the conventional boundary‐element method and commercial finite‐element software package, which shows that our hybrid method can achieve the same accuracy with much less time. The influence of the cut‐corners on the cutoff wavenumbers of the dominant and higher‐order modes is then examined. A simple approximate equation is found to accurately predict the cutoff wavenumber of TE₂₀ mode. The single‐mode bandwidth of a quadruple ridged square waveguide is calculated thereafter, which shows that this corner‐cut structure can provide a broader bandwidth compared to the one without cut‐corners. Copyright © 2010 John Wiley & Sons, Ltd.     

Analysis of co‐axial transmission lines with arbitrary cross‐section

A numerical model for the determination of electromagnetic fields and characteristic impedance of co‐axial cables with arbitrary cross‐section is developed, based on dyadic Green's functions and the moment method. The advantages of the method are generality, simplicity and accuracy of its results. Besides this, the fields are represented as series over orthogonal functions, which can be useful in the solution of some problems, such as discontinuity between lines of different cross sections. A numerical application to cables of rectangular cross‐section shows the accuracy of the method. Copyright © 1999 John Wiley & Sons, Ltd.     

Comparison Between Non-Equilibrium Green's Function and Monte Carlo Simulations for Transport in a Silicon Quantum Wire Structure

We present comparisons of simulations conducted with non-equilibrium Green's functions and Monte Carlo approaches. As prototype, we consider an idealized silicon quantum wire structure, consisting of a conduction channel of rectangular cross-section, terminated by two contacts. The Monte Carlo model treats the particles as semi-classical, but distributed over up to seven subbands and with scattering model similar to the one used for the Green's functions model. Results for drift velocity under various field conditions agree very closely using the two techniques, suggesting that particle simulation may continue to be a useful physical investigation tool at the nanoscale with an appropriate introduction of the most important quantum features of the transport.     

A generalized CAD model for the full‐wave modeling of Coplanar striplines discontinuities

In this work, the coplanar stripline (CPS) and its discontinuities: open‐end, short‐end, gaps and resonator have been modeled. New integral equations for the electrical field components are formulated, in the spectral domain, using an exact dyadic Green's function, applied to the CPS structure. The use of this form of Green's function allows the consideration of the effects of the dielectric losses, the surface wave excitation and the space wave radiation on the propagation characteristics of the CPS and its discontinuities. The resulting integral equation has been solved using the two‐dimensional Galerkin's technique. The resolution of the resulting matrix equation gives the scattering parameters of the studied structures. The obtained results are commented and compared with those of other approaches and measurements. Copyright © 2011 John Wiley & Sons, Ltd.     

Efficient direct and iterative electrodynamic analysis of geometrically complex MIC and MMIC structures

Rigorous full -wave analysis techniques are presently receiving much attention in the design of MICs and, in particular, of MMICs due to increasing circuit packing densities and structural complexity. In this paper, the problems associated with such techniques and previous related work are briefly outlined in the introduction. To obtain self -consistency, the electrodynamic Green's functions and related terms are then formulated for the shielded (M)MIC problem. The final operator equation for the numerical solutions derived and the associated functions space are presented and discussed. The central portion of the paper describes a new numerical solution using a discretized Green's function database technique. The resulting linear system of equations is solved by direct inversion for geometrical complexities involving up to about 1000 unknowns; for a higher number of unknowns, an iterative solution is generated. As an alternative to the database technique developed, a variety of spectral domain iterative solutions has been written and tested as well. This includes application of the conjugate gradient method to the normal operator equation (CGN algorithm), an implicit iterative Galerkin approximation called the modified planar conjugate gradient technique (MPCG) and monotonically convergent iteration procedure being a version of the conjugate residual algorithm (CR). Supplementary to this, the extraction of (M)MIC design data from the numerical 3D solutions obtained and error considerations are presented. The paper concludes with a variety of analysis examples of medium to high geometrical complexity and with verification of some results by comparison with measurements and with numerical data from other sources. CPU times required on typical workstations (Micro VAX, HP 9000, etc.) are moderate, thus rendering the techniques presented as useful in the solution of MIC and MMIC design problems.     

Modelling of impedance‐loaded wire frequency‐selective surfaces with tunable reflection and transmission characteristics

In this paper an efficient means to control the reflection and transmission characteristics of wire‐based frequency‐selective surfaces (FSS) using linear‐lumped impedance loading is presented. We show that by varying the topology of the RLC loading circuits and the component values it is possible to control the resonance frequency of the array as well as its angular characteristics. We discuss several examples, particularly a switchable dual band bandpass filter and enhancement of FSS angle‐of‐arrival properties. The analysis is based on the self‐consistent solution of thin wire Hallen's type integral equation solved by Galerkin's method. The periodic Green's function in the kernel of integral equation has been accelerated using the Ewald transformation, which leads to a highly accurate and efficient numerical procedure. Copyright © 2008 John Wiley & Sons, Ltd.     

A Green's function‐based method for the transient analysis of plane waves obliquely incident on lossy and dispersive planar layers

This paper presents a new methodology for the transient analysis of plane waves obliquely incident on a planar lossy and dispersive layer. The proposed model is based on the Sturm–Liouville problem associated with the propagation equations. Green's function is calculated in a series form and the open‐end impedance matrix is obtained as the sum of infinite rational functions. This form permits an easy identification of poles and residues. Furthermore, the knowledge of poles leads to the development of a model order reduction technique by selecting only the dominant poles of the system. The pole–residue representation is converted into a state‐space model that can be easily interfaced with ordinary differential equation solvers. The numerical results confirm the effectiveness of the proposed modeling technique. Copyright © 2008 John Wiley & Sons, Ltd.     

Transmission parameter representation of non-uniform transmission line Green's functions

The Green's function G(x, x') of a non-uniform transmission line is formulated exactly in terms of partial transmission matrix parameters associated with different segments of the line. Exact differential expressions relate the transmission parameters to each other, and it is shown that G(x, x') can be expressed entirely in terms of a single transmission parameter B(x, x') and its derivatives. The voltage response V(x) on any doubly-terminated line with arbitrary current source density along the line is given. A new perturbation technique, based on a Volterra integral equation, is developed which determines V(x) in terms of known functions and arbitrary perturbing immittances on the line.     

ANALYSIS OF A GRID DIPOLE ARRAY PLACED INSIDE A WAVEGUIDE CAVITY WITH A RECTANGULAR COUPLING APERTURE

The circuit and coupling properties of a dipole grid array placed inside a rectangular cross-section waveguide are analysed when also a rectangular aperture is used to couple the resonator energy into a semi-infinite waveguide. A Green function approach is employed to determine the current distribution on the dipole elements by solving an integral equation and taking into account the boundary conditions on the rectangular cavity walls. Both mutual and self-impedance terms are calculated for the dipole grid array, and the effects of the rectangular coupling aperture are also examined. © 1997 by John Wiley & Sons, Ltd.     

Discrete Green's functions and hybrid modelling of thermal and particle diffusion

This paper provides details of a widely applicable technique of hybrid modelling of thermal and particle diffusion which can help to reduce computational load in explicit formulation. The undesirable effects of artificial boundaries, which are introduced when a simulation is truncated or when an expanding mesh is used, can be eliminated by the use of discrete Green's functions. The technique can also be applied to problems involving infinite or near-infinite domains or problems where a complex thermal region is embedded within a larger, more simply described domain.     

Numerical analysis of waveguide apertures radiating into lossy media

Three numerical methods are applied to the analysis of a rectangular waveguide-fed aperture radiating into a lossy media. A novel approach, the finite element method with an impedance boundary condition, and two established methods, the moment method and the mode-matching method, are presented. The methods are compared with respect to accuracy, execution time, memory requirement, and versatility. Four aperture geometries are chosen for detailed study: the full aperture of the rectangular waveguide, and three reduced apertures. The reflection coefficient of the aperture in contact with five known dielectrics is calculated in the frequency range 8·5–11·5 GHz. The theoretical results are validated by measurements performed on an HP8510 network analyser.     

A Calderón‐preconditioned single source combined field integral equation for analysis of bi‐isotropic object

In this paper, a Calderón‐preconditoned single source combined field integral equation (SSCFIE) has been developed to analyze electromagnetic scattering from bi‐isotropic objects. The field decomposition method is adopted to split the homogeneous bi‐isotropic media into two uncoupled isotropic media instead of direct calculation of complicated Green's function in bi‐isotropic material. Unlike dual source integral equation, the Calderón‐preconditioned single source electric and magnetic integral equations in the presence of bi‐isotropic media are constructed and combined to make the proposed algorithm free from dense mesh breakdown and spurious resonance. Numerical results show good performance of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical optimization of a waveguide transition using finite element beam propagation

We consider a waveguide with principal guiding direction for which the beam propagation method is applicable. A simulation method based on an FEM for Maxwell's equation with 3D Nedelec elements is developed. The power loss of the waveguide is minimized by varying a finite number of shape parameters. We validate the method by comparing our findings to some published results. Copyright © 2014 John Wiley & Sons, Ltd.     

Inhomogeneous ladder networks,part I

In this paper the theory of orthogonal polynomials is taken as the starting point for developing the theory of semi-infinite inhomogeneous ladder networks of two element kinds. It is shown that the transfer impedance of the ladder network, suitably normalized, is just the Green's function of a self-adjoint difference operator of ‘Sturm–Liouville’ type. An integral representation for this Green's function is given, and is evaluated in product form. The theory is illustrated with a number of examples based on classical orthogonal polynomials, the use of which enables all the calculations to be carried through explicitly.     

Numerical analysis of discontinuities in a rectangular waveguide loaded with isotropic or anisotropic obstacles by means of the coupled-mode method and the mode-matching method

A hybrid method obtained as a combination of the coupled-mode method (CMM) and the mode-matching method (MMM) is developed and applied in the analysis of multiple dielectric and magnetic discontinuities in rectangular waveguides. As both are moment methods, some kind of truncation has to be carried out in the computer implementation. It is shown that selection of a different number of modes in the two methods is not necessary, unless low-permittivity meida inside the waveguide are considered. As a consequence, the procedure for slecting the number of basis functions is only done in one of the methods. Numerical examples are presented showing the behaviour of the method and the proofs of convergence. Examples are included illustrating the power of this hybrid technique, especially in relation to non-reciprocal structures containing magnetized ferrites.     

Delaunay–Voronoi surface integration: a full‐wave electromagnetics discretization for electronic device simulation

A promising time domain electromagnetics numerical method for treating the highly nonlinear problem of charge transport in electronic devices called Delaunay–Voronoi surface integration is presented. This method couples the rotational electric and magnetic fields governed by Ampere's and Faraday's laws with the electrostatic potential dictated by Poisson's equation in a simultaneous solution. Discretization of the governing equations using dual meshes and the relevant boundary conditions are presented. The engineering application details specific to electronic device simulation are treated, and an example calculation is shown to compare with an analytical solution for propagation in a waveguide. Benchmark results are presented for the rotational equations, Poisson's equation, and the complete set of electromagnetic equations. Copyright © 2016 John Wiley & Sons, Ltd.