Computation of TM and TE modes in waveguides based on a surfaceintegral formulation

The surface integral formulation is used for the computation of TM and TE modes propagating in dielectric loaded waveguides. This formulation makes use of the surface equivalence principle whereby the field at any point internal or external to the waveguide can be expressed in terms of equivalent surface currents. This procedure reduces the original problem into a set of integro-differential equations which is then reduced to a matrix equation using the method of moments. The solution of this matrix equation provides the propagation characteristics of the waveguide and the equivalent surface currents existing on the waveguide walls. The equivalent surface currents can be used to compute the fields at all points, both inside and outside the waveguide. The surface integral method has been used to compute the propagation characteristics of waves propagating in dielectric loaded waveguides. The computed results agree very well with analytical and published data. A method that can be used to remove spurious modes is illustrated     

A coupled mode formulation by reciprocity and a variational principle

A coupled mode formulation for parallel dielectric waveguides is presented via two methods: a reciprocity theorem and a variational principle. In the first method, a generalized reciprocity relation for two sets of field solutions(E^{(1)}, H^{(1)})and(E^{(2)}, H^{(2)})satisfying Maxwell's equation and the boundary conditions in two different mediaepsilon^{(1)}(x,y)andepsilon^{(2)}(x,y), respectively, is derived. Based on the generalized reciprocity theorem, we then formulate the coupled mode equations. The second method using a variational principle is also presented for a general waveguide system which can be lossy. The results of the variational principle can also be shown to be identical to those from the reciprocity theorem. The exact relations governing the "conventional" and the new coupling coefficients are derived. It is shown analytically that our formulation satisfies the reciprocity theorem and power conservation exactly, while the conventional theory violates the power conservation and reciprocity theorem by as much as 55 percent and the Hardy-Streifer theory by 0.033 percent, for example.     

On lateral waves in slab configurations and their relation to other wave types

The customary analysis of radiation from sources in the presence of a dielectric slab involves a plane-wave superposition wherein the boundary conditions are satisfied by a single composite reflection coefficient. The far field is then comprised of the incident and reflected waves as well as a diffracted contribution of surface and leaky waves (pole waves). An alternative formulation is discussed wherein the interface effects are accounted for one at a time and the resulting diffraction field is then shown to involve lateral waves (branch-cut waves). The two representations are compared and their respective utility is illustrated by examples. When the source and observation points are located exterior to a large dielectric gap, diffraction effects due to an accumulation of leaky waves are found to be equivalent to a single lateral wave. For source and observation points inside a lossy dielectric slab, the pole-wave formulation provides a somewhat more convenient but physically less transparent result than the one comprising lateral waves.     

An efficient approach to modeling of quasiplanar structures usingthe formulation of power conservation in spectral domain

An enhanced spectral domain approach (SDA) is developed for analysis of complex quasi-planar transmission lines. The method is based on a combination of the spectral domain formulation and power conservation theorem. The relationship between electric and magnetic fields is established inside dielectric layers by using the conventional SDA while the characteristic equation related to interface conditions is derived through the power conservation theorem. Maintaining the inherent advantages of the SDA, this technique is able to easily handle more complex quasi-planar structures. Generalized power formulation is also presented to calculate characteristic impedance. Convergence behavior is discussed considering the nature of power conservation. Various finlines with finite thickness of conductors are analyzed to demonstrate its applications     

Time-domain analytic and numeric analysis of vertical dipoles infront of a dielectric planar interface

Potentials excited by impulsive vertical electric and magnetic dipoles in a geometry of two dielectric media with a planar interface are studied both analytically and numerically. Closed-form expressions for the Hertzian potential are derived in cases when the observation point is on the axis of the dipole or when both the dipole and the observation point are located at the interface. Numerical results are given for more general observation points     

无线网络介质访问控制基于不动点的模型收敛性分析及其应用

In the Internet of things, it is of critical importance to fully utilize the potential capacity of the network with efficient medium access control (MAC) mechanisms. In this paper, we study the convergence property of the fixed point formulation of distributed coordination function (DCF), which is widely used for medium access control in wireless networks. We first find that the fixed point could be repelling, which means that it is impossible for an MAC system to converge at its fixed point. Next, we show the existence of periodic points to prove that the fixed point function will oscillate between two periodic points when the fixed point is repelling. We also find that the average of the two periodic points is a close approximation of the fixed point. Based on the findings, we propose an algorithm to compute the fixed point efficiently. Simulation results verify the accuracy and efficiency of our algorithm compared with the previous fixed point computing method.     

Finite-element time-domain algorithms for modeling linear Debye and Lorentz dielectric dispersions at low frequencies

We present what we believe to be the first algorithms that use a simple scalar-potential formulation to model linear Debye and Lorentz dielectric dispersions at low frequencies in the context of finite-element time-domain (FETD) numerical solutions of electric potential. The new algorithms, which permit treatment of multiple-pole dielectric relaxations, are based on the auxiliary differential equation method and are unconditionally stable. We validate the algorithms by comparison with the results of a previously reported method based on the Fourier transform. The new algorithms should be useful in calculating the transient response of biological materials subject to impulsive excitation. Potential applications include FETD modeling of electromyography, functional electrical stimulation, defibrillation, and effects of lightning and impulsive electric shock.     

介质覆盖导电球上缝隙天线的辐射

给出了用位函数方法推导介质覆盖导电球上缝隙天线辐射场严格解的过程.基于球Hankel函数加法定理,将基本磁流源激励的场展开为以球心为原点的球面波的叠加.利用球矢量波函数的定义及性质,提取出场的径向分量,将初级场分解为相对于径向的TE波和TM波,避免了复杂的矢量微分运算.在此基础上依据散射叠加原理,构造出各区域中场的一般表示形式,其中待定系数直接由球面分层介质中波的反射和透射规律给出.作为实际应用的例子,给出了介质覆盖导电球上均匀环缝问题的计算结果,并对结果进行了分析.     

Application of a new MPIE formulation to the analysis of adielectric resonator embedded in a multilayered medium coupled to amicrostrip circuit

A new mixed-potential integral-equation (MPIE) formulation is developed for the analysis of electromagnetic problems due to conducting or dielectric objects of arbitrary shape embedded in a planarly stratified medium. In the new MPIE formulation, the dyadic kernel of the vector potential is kept in the simple form originally developed by Sommerfeld. The scalar potential, which is related to the vector potential via the Lorenz gauge, is then represented by a double dot product of a dyadic kernel with a dyadic charge density. An extra line integral term, which is well behaved and nonsingular, will appear when the object penetrates an interface. The numerical implementation of the double dot product is found to be trivial if one takes advantage of the well-established basis functions in which the unknown current density is expressed. The new MPIE formulation is employed in conjunction with the triangular patch model to treat the problem of a dielectric resonator (DR) excited by microstrip circuit. A matched-load simulation procedure has been used to extract the network S-parameters of a DR microstrip circuit. The diameters of the Q circles have been measured to determine the coupling coefficients and the Q factors of the DR excited by a microstrip circuit. The validity of the new MPIE formulation and the numerical procedure have been verified by comparing the obtained S-parameters, with available measurement data     

Coupling mechanism of two dipoles within a conductor-backed thindielectric slab above the earth

A coupling mechanism between two dipoles within a conductor-backed thin dielectric layer above the earth, suggested as subsurface interface CW radar transmitting and receiving antennas, is calculated by a saddle-point method. When the dielectric layer is thin enough to support a cutoff mode, the electric field at the point of receiving dipole due to a transmitting point dipole may be approximated by sum of contributions of branch points of TE mode and poles of TM mode. The branch points and poles contributions are interpreted as evanescent lateral-waves and leaky-waves, respectively. Comparison of numerical results and asymptotic results shows excellent agreement     

Quasi-static finite-element analysis of a skewed microstripcrossover

In this work, we present a quasistatic analysis of a microstrip crossover on a dielectric substrate. The microstrips are located at different planes and may cross at an arbitrary angle. Capacitances and inductances are calculated from scalar potentials. For magnetostatic formulation, the boundary conditions for scalar potential are introduced by means of partitioning surfaces. The use of the adaptive finite element method provides the required flexibility with respect to the analyzed geometry, optimal discretization and good efficiency     

A common formalism for the integral formulations of the forward EEG problem

The forward electroencephalography (EEG) problem involves finding a potential V from the Poisson equation inverted Delta x (sigma inverted Delta V) f, in which f represents electrical sources in the brain, and sigma the conductivity of the head tissues. In the piecewise constant conductivity head model, this can be accomplished by the boundary element method (BEM) using a suitable integral formulation. Most previous work uses the same integral formulation, corresponding to a double-layer potential. In this paper we present a conceptual framework based on a well-known theorem (Theorem 1) that characterizes harmonic functions defined on the complement of a bounded smooth surface. This theorem says that such harmonic functions are completely defined by their values and those of their normal derivatives on this surface. It allows us to cast the previous BEM approaches in a unified setting and to develop two new approaches corresponding to different ways of exploiting the same theorem. Specifically, we first present a dual approach which involves a single-layer potential. Then, we propose a symmetric formulation, which combines single- and double-layer potentials, and which is new to the field of EEG, although it has been applied to other problems in electromagnetism. The three methods have been evaluated numerically using a spherical geometry with known analytical solution, and the symmetric formulation achieves a significantly higher accuracy than the alternative methods. Additionally, we present results with realistically shaped meshes. Beside providing a better understanding of the foundations of BEM methods, our approach appears to lead also to more efficient algorithms.     

Solution of a periodic boundary-value problem by direct application of Floquet's theorem

Laplace's equation is solved under periodic-boundary conditions, by consideration of one period, by direct use of Floquet's theorem. Successive point over-relaxation computer techniques are used. Such solutions require the use of complex mesh points, and convergence is rapid. Analytical results are compared.     

Capacitance computations in a multilayered dielectric medium usingclosed-form spatial Green's functions

An efficient method to compute the 2-D and 3-D capacitance matrices of multiconductor interconnects in a multilayered dielectric medium is presented. The method is based on an integral equation approach and assumes the quasi-static condition. It is applicable to conductors of arbitrary polygonal shape embedded in a multilayered dielectric medium with possible ground planes on the top or bottom of the dielectric layers. The computation time required to evaluate the space-domain Green's function for the multilayered medium, which involves an infinite summation, has been greatly reduced by obtaining a closed-form expression, which is derived by approximating the Green's function using a finite number of images in the spectral domain. Then the corresponding space-domain Green's functions are obtained using the proper closed-form integrations. In both 2-D and 3-D cases, the unknown surface charge density is represented by pulse basis functions, and the delta testing function (point matching) is used to solve the integral equation. The elements of the resulting matrix are computed using the closed-form formulation, avoiding any numerical integration. The presented method is compared with other published results and showed good agreement. Finally, the equivalent microstrip crossover capacitance is computed to illustrate the use of a combination of 2-D and 3-D Green's functions     

Spectral-domain analysis of E-plane waveguide tomicrostrip transitions

The spectral-domain technique and a residue calculus theorem are used to compute the input impedance of a microstrip transition to a rectangular waveguide. The transition consists of a printed circuit board inserted into a waveguide housing along the E-plane. The effects of the dielectric layer are considered in the present analysis. The behavior of the input impedance of the transition is studied with respect to the critical dimensions of the probe length and backshort location. Calculated results by the new formulation agree well with those computed using an integral equation and those measured at Ka -band frequencies     

A numerical analysis of wire antennas loaded withvaristor-composite materials

The behavior of wire antennas loaded at the driving point with varistor-composite materials is analyzed in the time domain via a numerical formulation. Varistor-composite materials are nonlinear transient arresters with a subnanosecond response time. Connecting these nonlinear elements in parallel with the feeding transmission line and adjusting the characteristic curves of varistor materials (i.e., current density and dielectric constant versus electric-field strength), the nonlinear load drains off currents of excessive potential levels. At operating voltages the material presents a higher impedance path and the arrester interference with the normal operation of the antenna under protection is minimal     

Coupled-mode formulation of multilayered and multiconductortransmission lines

A novel coupled-mode formulation for multilayered and multiconductor transmission lines is developed. In this formulation, the solutions to the original multiconductor system are approximated by a linear combination of eigenmode solutions associated with the isolated single conductor line located in an appropriate reference dielectric medium. The reciprocity theorem is used to derive the coupled-mode equations. The coupling coefficients are expressed in terms of the simple overlap integrals between the eigenmode fields and currents of the individual conductor lines. As a basic application, the dispersion characteristics of two identical coupled-microstrip lines are analyzed using the proposed coupled-mode theory. It is shown that the results are in very close agreement with those obtained by the direct Galerkin's moment method over a broad range of weak to strong coupling     

Performance degradation of dielectric radome covered antennas

Performance is evaluated by a method based on the reciprocity theorem. The asymptotic expression for the radome Green's function that allows the characterization of the radome by itself, independently of any specific antenna, is identified. The concept of the modified aperture distribution, which radiating in free space produces the same pattern as the radome-covered antenna, is introduced. It can be used for the design of the radome stratification and for the optimization of the antenna location. On the basis of the formulation of a computer code has been developed that analyzes the degradation induced by radomes with surfaces and dielectric stratifications that can be defined numerically. Theoretical predictions and experimental results are compared     

High-frequency analysis of integrated dielectric lens antennas

A high-frequency method for the three-dimensional analysis of integrated dielectric lens antennas is presented. This method consists on improving the physical optics (PO) currents on the lens surface by modifying, via suitable transition functions, the spreading factor of those rays from the source point which arrive at the lens-air interface close to the critical angle of incidence. Invoking the locality principle of the high-frequency phenomena, the method uses the rigorous canonical solution of the semi-infinite dielectric space locally tangent at the lens surface. A uniform asymptotic evaluation of this canonical solution is provided with the introduction of a new transition function for the TM case. The present formulation provides significant correction from the PO currents of an elliptical lens, with a consequent improvement of the radiation pattern prediction, testified by comparisons with results from a full-wave analysis.     

Multiobjective Optimization of Real and Coupled Antenna Array Excitations via Primal-Dual, Interior Point Filter Method From Spherical Mode Expansions

A novel method for the multiobjective optimization of arbitrary planar array excitations is presented. The optimization problem formulation, which inherently takes into account every array element pattern as well as all interelement couplings, is based on matrix-valued functions which are computed from the generalized-scattering-matrix characterization of an array and spherical mode expansions of its radiated field. It allows the maximization of the directive gain subject to a maximum sidelobe level, a maximum crosspolar level and a minimum aperture illumination efficiency, the setting of null-pointing directions and the dynamic range control. To solve the resulting non-linear optimization problem, we have developed a primal-dual interior point method specifically adapted to the presented formulation, which makes use of novel filtering techniques. Numerical examples of arrays of microstrip patches and dielectric resonator antennas covering a wide variety of requirements on these parameters are presented.