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 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.     

Full‐wave modelling of microstrip line and its sensitivities on lossy multilayer dielectric substrate and superstrate with laminated ground plane

This paper presents a new formulation useful for modelling multilayered microstrip and its geometrical sensitivities with laminated ground plane. New integral equations are formulated, in the spectral domain, using the exact dyadic Green's function of bianisotropic planar media. We have applied a dynamic two‐dimensional least‐square algorithm as an optimization procedure. Obtained results agree well with those of other approaches. Copyright © 2002 John Wiley & Sons, Ltd.     

A hybrid moment-ray-mode method for wave scattering from an aperture coupled system

Wave scattering from an aperture coupled system is studied using a new method which combines the hybrid ray-mode method and method of moments. The latter is used to formulate the coupling process and the former to provide the Green's function of a parallel plate waveguide. Following standard procedures of the method of moments, we first formulate a system equation for field distributions across the aperture. By expressing these unknown distributions in terms of appropriate basis functions and choosing appropriate weighting functions, the system equation is then reduced to a matrix equation which is solved numerically. In the system of equations, one needs to compute the Green's function of the waveguide for various arrangements of locations of source and receiver. The hybrid ray-mode formulation is best suited for this purpose because it combines rays and modes self-consistently to optimize the advantages of each. The efficiency of the ray-mode Green's function makes use of the moment method practical in waveguides, and the flexibility of the moment method permits application of the Green's function considered to arbitrarily shaped and placed apertures. Numerical implementation illustrates these aspects.     

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.     

Green's function approach for modeling of electrostatic effects in nanoscale fully depleted double‐gate silicon‐on‐insulator metal‐oxide‐semiconductor field‐effect transistors

Exact solution of two‐dimensional (2D) Poisson's equation for fully depleted double‐gate silicon‐on‐insulator metal‐oxide‐semiconductor field‐effect transistor is derived using three‐zone Green's function solution technique. Framework consists of consideration of source–drain junction curvature. 2D potential profile obtained forms the basis for estimation of threshold voltage. Temperature dependence of front surface potential distribution, back surface potential distribution and front‐gate threshold voltage are modeled using temperature sensitive parameters. Applying newly developed model, surface potential and threshold voltage sensitivities to gate oxide thickness have been comprehensively investigated. Device simulation is performed using ATLAS 2D (SILVACO, 4701 Patrick Henry Drive, Bldg. Santa Clara, CA 95054 USA) device simulator, and the results obtained are compared with the proposed 2D model. The model results are found to be in good agreement with the simulated data. Copyright © 2013 John Wiley & Sons, Ltd.     

A generalized CAD model for the full‐wave modelling of microstrip line and its regular and irregular discontinuities

In this paper we present a new theoretical model for the modelling of the microstrip line as well as two types of discontinuities: regular (open end, step, bend and T‐ and cross‐junctions) and irregular (stub and bent‐stub). The two‐dimensional exact dyadic Green function of a grounded dielectric slab has been used with the Galerkin's technique. The subdivision of the discontinuity in a network of juxtaposed unit cells, characterized by their own longitudinal and transversal current distributions, allowed the treatment of a large class of irregular discontinuities in addition to the regular discontinuities. The obtained results have been commented and compared with those of different approaches and with experimental results where a good concordance has been observed. Copyright © 2006 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.     

Network analysis of strongly coupled transverse apertures in waveguide

Methods of field and network theory are jointly applied to the problem of transverse aperture-type discontinuities in cascade under the conditions of multimodal excitation and interaction. A space Fourier transformation (modal analysis) translates the field problem into a network problem, whereby discontinuities take the significance of Hilbert-ports à la Zemanian. When a discontinuity is considered as enclosed by an ideal cavity, representing energy storage in the ‘localized’ modes, Foster's form of the reactance matrix of the discontinuity is recovered. The relationship with the variational method in computing the resonance matrix of the ‘accessible’ modes is illustrated. Green's function of cascaded apertures is obtained by finite network analysis. A few examples of thick interacting inductive irises in cascade are numerically investigated. Results show very good agreement with experiment.     

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.     

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.     

Multiscalet basis in Galerkin's method for solving three‐dimensional electromagnetic integral equations

Multiscalets in the multiwavelet family are used as the basis and testing functions in Galerkin's method. Since the multiscalets are orthogonal to their translations under the Sobolev inner product, the resulting Galerkin's method behaves like a collocation method but possesses the ability of derivative tracking for unknown functions in solving integral equations. The former makes the method simple in implementation and the latter allows to use coarse meshes in discretization. These robust features have been demonstrated in solving two‐dimensional (2D) electromagnetic (EM) problems, but have not been exploited in three‐dimensional (3D) scenarios. For 3D problems, the unknown functions in the integral equations are dependent on two coordinate variables. In order to preserve the use of coarse meshes for 3D cases, we realize the omnidirectional derivative tracking by tracking the directional derivatives along two orthogonal directions, or equivalently tracking the gradient. This process yields a nonsquare matrix equation and we use the least‐squares method (LSM) to solve it. Numerical examples show that the multiscalet‐based Galerkin's method is also robust in solving for 3D EM integral equations with a minor cost increase from LSM. Copyright © 2007 John Wiley & Sons, Ltd.     

Modelling of electrically thick cylindrical antennas

Hallen's integral equation has been used as the basis for the formulation of cylindrical antenna theories for many years. Being a Fredholm integral equation of the first kind, its solution is mathematically an ill-posed problem. The stability of the numerical methods based on this integral equation is dependent on the singularity and the non-smoothness of the kernel function. For electrically thick cylindrical antennas, the dominance of the singular part of the kernel (logarithmic) is weakened and the kernel function becomes relatively smooth. This observation implies possible deteriorations of the stability of the numerical methods based on Hallen's integral equation. This paper describes the development of an alternative formulation for the electrically thick cylindrical antennas based on the singular integral equation of the first kind with a Cauchy-type kernel which eliminates the potential instability problem. A numerical method based on this formulation of the antenna problem has been implemented and case studies show that it is very stable and efficient for the numerical modelling of electrically thick cylindrical antennas.     

Modelling of printed discontinuities on open microstrip lines by mode matching techniques

The dynamic analysis of discontinuities in printed circuits has been performed using the mode matching technique. This study concerns the open end of microstrip lines and suspended microstrip lines. The fields on either side of the discontinuity are described by means of the continuous (radiated and evanescent) and guided modes of the structure. The conditions of continuity of the electromagnetic fields are then applied in the plane of the discontinuity. By taking into account the relations of orthogonality of the modes of the same region, a system of coupled Fredholm integral equations is obtained and solved by the iterative method of Neumann's series. The study calls for the use of the continuous spectrum of microstrip lines, which can be obtained analytically only after a great amount of calculation and CPU time. Thus, the first approach consists in neglecting this continuous spectrum. This gives accurate results for the reflection coefficient but it is not sufficient for the derivation of the radiation pattern. So, two simple models for the continuous spectrum, both based on the physical behaviour of such discontinuities, are considered and discussed. © 1997 John Wiley & Sons, Ltd.     

Disordered lattice networks: general theory and simulations

In this work we develop a theory for describing random networks of resistors of the most general topology. This approach generalizes and unifies several statistical theories available in literature. We consider an n‐dimensional anisotropic random lattice where each node of the network is connected to a reference node through a given random resistor. This topology includes many structures of great interest both for theoretical and practical applications. For example, the one‐dimensional systems correspond to random ladder networks, two‐dimensional structures model films deposited on substrates and three‐dimensional lattices describe random heterogeneous materials. Moreover, the theory is able to take into account the anisotropic percolation problem for two‐ and three‐dimensional structures. The analytical results allow us to obtain the average behaviour of such networks, i.e. the electrical characterization of the corresponding physical systems. This effective medium theory is developed starting from the properties of the lattice Green's function of the network and from an ad hoc mean field procedure. An accurate analytical study of the related lattice Green's functions has been conducted obtaining many closed form results expressed in terms of elliptic integrals. All the theoretical results have been verified by means of numerical Monte‐Carlo simulations obtaining a remarkably good agreement between numerical and theoretical values. Copyright © 2005 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。     

Partial element equivalent circuit (PEEC) models for on‐chip passives and interconnects

The accurate simulation of the electromagnetic behaviour of interconnects and on‐chip inductors is becoming more and more important for chip designs. For this purpose, we investigate the use of the electric field integral equation, which can be used to construct a full‐wave electromagnetic model. To facilitate the combined analysis of the chip's circuit and the electromagnetic behaviour, the electromagnetic model can be formulated as an equivalent circuit. We have conducted some simple experiments to see the method at work and to obtain an idea of the frequencies for which retardation effects are important. Copyright © 2004 John Wiley & Sons, Ltd.