Preface. Acknowledgments. Chapter 1: Introduction. 1.1 Numerical Simulation of Antennas. 1.2 Finite Element Analysis vs. Other Numerical Methods. 1.3 Frequency- vs. Time-Domain Simulations. 1.4 Brief Review of Past Work. 1.5 Overview of This Book. References. Chapter 2: Finite Element Formulation. 2.1 Finite Element Formulation in the Frequency Domain. 2.2 Finite Element Formulation in the Time Domain. 2.3 Modeling of Complex Materials. 2.3.1 Modeling of Electrically and Magnetically Lossy Materials. 2.3.2 Modeling of Electrically Dispersive Materials. 2.3.3 Modeling of Magnetically Dispersive Materials. 2.3.4 Modeling of Doubly Dispersive Lossy Materials. 2.4 Solution of the Finite Element Equations. 2.5 Higher-Order and Curvilinear Finite Elements. 2.6 Summary. References. Chapter 3: Finite Element Mesh Truncation. 3.1 Absorbing Boundary Conditions. 3.1.1 First-Order Absorbing Boundary Condition. 3.1.2 Second-Order Absorbing Boundary Condition. 3.2 Perfectly Matched Layers. 3.2.1 PML in Terms of Stretched Coordinates. 3.2.2 PML as an Anisotropic Material Absorber. 3.2.3 PML for Truncating Computational Domain. 3.2.4 Finite Element Implementation of PML. 3.2.5 ABC-Backed, Complementary, CFS, and Second-Order PMLs. 3.3 Boundary Integral Equations. 3.3.1 Frequency-Domain Formulations. 3.3.2 Time-Domain Formulations. 3.3.3 Treatment of Infinite Ground Plane. 3.4 Summary. References. Chapter 4: Hybrid FETD-FDTD Technique. 4.1 The FDTD Method. 4.2 PML Implementation in FDTD. 4.2.1 FDTD Stretched-Coordinate PML. 4.2.2 FDTD Anisotropic PML. 4.3 Near-to-Far-Field Transformation in FDTD. 4.4 Alternative FETD Formulation. 4.5 Equivalence between FETD and FDTD. 4.6 Stable FETD-FDTD Interface. 4.6.1 Initial Approaches. 4.6.2 Stable Formulation. 4.7 Building Hybrid Meshes. 4.8 Wave-Equation Stablization. 4.9 Validation Examples. 4.10 Summary. References. Chapter 5: Antenna Source Modeling and Parameter Calculation. 5.1 Antenna Feed Modeling. 5.1.1 Current Probe. 5.1.2 Voltage Gap Generator. 5.1.3 Waveguide Feed Model. 5.2 Plane-Wave Excitation. 5.2.1 Total-Field Formulation. 5.2.2 Scattered-Field Formulation. 5.2.3 Total- and Scattered-Field Decomposition Approach . 5.3 Far-Field Pattern Computation. 5.4 Near-Field Visualization. 5.5 Summary. References. Chapter 6: Modeling of Complex Structures. 6.1 Thin Material Layers and Sheets. 6.1.1 Impedance Boundary Conditions. 6.1.2 Shell Element Formulation. 6.2 Thin Wires and Slots. 6.2.1 Thin Wires. 6.2.2 Thin Slots. 6.3 Lumped Circuit Elements. 6.3.1 Coupled First-Order Equations. 6.3.2 Wave Equation. 6.3.3 Example. 6.4 Distributed Feed Network. 6.5 System-Level Coupling Example. 6.5.1 Internal Dispersive Material Calibration. 6.5.2 External Illumination and Aperture Coupling. 6.6 Summary. References. Chapter 7: Antenna Simulation Examples. 7.1 Narrowband Antennas. 7.1.1 Coaxial-fed Monopole Antenna. 7.1.2 Monopole Antennas on a Plate. 7.1.3 Patch Antennas on a Plate. 7.1.4 Conformal Patch Antenna Array. 7.2 Broadband Antennas. 7.2.1 Ridged Horn Antenna. 7.2.2 Sinuous Antenna. 7.2.3 Logarithmic Spiral Antenna. 7.2.4 Inverted Conical Spiral Antenna. 7.2.5 Antipodal Vivaldi Antenna. 7.2.6 Vlasov Antenna. 7.3 Antenna RCS Simulations. 7.3.1 Microstrip Patch Antenna. 7.3.2 Standard Gain Horn Antenna. 7.4 Summary. References. Chapter 8: Axisymmetric Antenna Modeling. 8.1 Method of Analysis. 8.1.1 Finite Element Formulation. 8.1.2 Mesh Truncation Using Perfectly Matched Layers. 8.1.3 Mesh Truncation Using Boundary Integral Equations. 8.2 Application Examples. 8.2.1 Luneburg Lens. 8.2.2 Corrugated Horn. 8.2.3 Current Loop Inside a Radome. 8.3 Summary. References. Chapter 9: Infinite Phased Array Modeling. 9.1 Frequency-Domain Modeling. 9.1.1 Periodic Boundary Conditions. 9.1.2 Mesh Truncation Techniques. 9.1.3 Extension to Skew Arrays. 9.1.4 Extension to Scattering Analysis. 9.1.5 Application Examples. 9.2 Time-Domain Modeling. 9.2.1 Transformed Field Variable. 9.2.2 Mesh Truncation Techniques. 9.2.3 General Material Modeling. 9.2.4 Application Examples. 9.3 Approximation to Finite Arrays. 9.4 Summary. References. Chapter 10: Finite Phased Array Modeling. 10.1 Frequency-Domain Modeling. 10.1.1 The FETI-DPEM1 Formulation. 10.1.2 The FETI-DPEM2 Formulation. 10.1.3 Nonconforming Domain Decomposition. 10.1.4 Application Examples. 10.2 Time-Domain Modeling. 10.2.1 The Dual-Field Domain Decomposition Method. 10.2.2 Domain Decomposition for Iterative Solutions. 10.2.3 Application Examples. 10.3 Summary. References. Chapter 11: Antenna-Platform Interaction Modeling. 11.1 Coupled Analysis. 11.1.1 FETI-DPEM with Domain Decomposition. 11.1.2 Hybrid FETD-FDTD with Domain Decomposition. 11.1.3 Hybrid FE-BI Method with FMM Acceleration. 11.2 Decoupled Analysis. 11.2.1 Near-Field Calculation. 11.2.2 Far-Field Evaluation by Numerical Methods. 11.2.3 Far-Field Evaluation by Asymptotic Techniques. 11.2.4 Direct and Iterative Improvements. 11.3 Summary. References. Chapter 12: Numerical and Practical Considerations. 12.1 Choice of Simulation Technologies. 12.2 Frequency- vs. Time-Domain Simulation Tools. 12.3 Fast Frequency Sweep. 12.4 Numerical Convergence. 12.5 Domain Decomposition and Parallel Computing. 12.6 Verification and Validation of Predictions. 12.7 Summary. References. Index.

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Finite Element Analysis of Antennas and Arrays

A finite-element method (FEM) is developed for the analysis of complex axisymmetric radiating structures. The method is based on the electric field formulation with the transverse field expanded in terms of edge-based vector basis functions and the azimuth component expanded using nodal-based scalar basis functions. This mixed representation of the electric field eliminates spurious solutions and permits an easy treatment of boundary conditions on conducting surfaces as well as across material interfaces. The FEM mesh is truncated using a previously developed cylindrical perfectly matched layer (PML). The method has been successfully applied to three radiating structures: a corrugated horn antenna, a spherical Luneburg lens, and a half Maxwell fish eye. Numerical results are presented to show the validity, accuracy, and efficiency of the method.

Finite-element analysis of complex axisymmetric radiating structures

In this three-part sequence of papers, we outline an architecture for systematically dealing in an efficient and rigorous manner with electromagnetic field representations and computations in complex structures The approach is based on the topological partitioning of the complex structure into several subdomains joined together by interfaces In analogy with network theory, individual subdomains are characterized via subdomain relations, obtained either analytically or numerically, and described in a unified format by using a generalized network formulation; the various subdomains are linked together via connection relations provided by the complex structure topology Together these two relations yield the Tableau equations which combine all of the necessary information The suggested framework accommodates the use of different analytic/numerical methods (hybridization), the choice of problem-matched alternative Green's function representations, as well as different types of field representations In the present paper, we focus on the general architecture, various options and their implications, in Part II [1] we furnish formal expressions for the subdomain relationships via alternative Green's functions representations; and in part III [2], we discuss the connection network properties Copyright © 2002 John Wiley & Sons, Ltd

Electromagnetic field representations and computations in complex structures I: complexity architecture and generalized network formulation

Sound propagation in an acoustic waveguide is examined using a hybrid numerical technique. Here, the waveguide is assumed to be infinite in length with an arbitrary but uniform cross section. Placed centrally within the guide is a short component section with an irregular nonuniform shape. The hybrid method utilizes a wave based modal solution for a uniform section of the guide and, using either a mode matching or point collocation approach, matches this to a standard finite element based solution for the component section. Thus, one needs only to generate a transverse finite element mesh in uniform sections of the waveguide and this significantly reduces the number of degrees of freedom required. Moreover, utilizing a wave based solution removes the need to numerically enforce a nonreflecting boundary condition at infinity using a necessarily finite mesh, which is often encountered in studies that use only the standard finite element method. Accordingly, the component transmission loss may readily be computed and predictions are presented here for three examples: an expansion chamber, a converging-diverging duct, and a circular cylinder. Good agreement with analytic models is observed, and transmission loss predictions are also presented for multimode incident and transmitted sound fields.

/pdf/modeling-sound-propagation-in-acoustic-waveguides-using-a-42yqe3hsho.pdf

Modeling sound propagation in acoustic waveguides using a hybrid numerical method.

A compact horn with low cross polarization component less than -35 dB over 5% frequency bandwidth has been obtained by optimizing the taper configuration. To reduce the gain loss caused by spherical wavefront in a short length horn with a large flare angle, a serpentine-shaped taper successfully generates five higher-order modes. Such a taper configuration is represented by varying lengths of various uniform waveguides in stepwise approximation, while keeping the dimension of each step discontinuity constant. As a result, the computational time for obtaining the proposed horn is greatly reduced because scattering matrices of the step discontinuities are pre-calculated before the optimization. The verification of its high performance has been performed numerically and experimentally.

Compact low-cross-polarization horn antennas with serpentine-shaped taper

A new method for finding radiation patterns and the reflection coefficients associated with an axisymmetric waveguide fed horn is presented. The approach is based on a hybrid finite element method (FEM) wherein the electromagnetic fields in the FEM region are coupled to the fields outside by two surface integral equations. Because of the local nature of the FEM, this formalism allows for the presence of inhomogeneities to be included in the problem domain. The matrix equation which results from the application of this method is shown to be complex-symmetric. Comparisons of calculated and measured data for two different horns show good agreement.

A hybrid finite-element method for axisymmetric waveguide-fed horns

The scattered fields from axisymmetric problems containing anisotropic media are found by a hybrid finite element method. In particular a symmetric formulation for bodies of revolution that incorporates a finite element formulation for axially magnetized ferrite materials is presented. The method is applied to a ferrite cylinder with quartz matching layers. A Gaussian beam input is used to predict the Faraday rotation through the ferrite cylinder and display it visually. >

https://ieeexplore.ieee.org/iel4/75/8538/00372808.pdf

Scattering from ferrite bodies of revolution using a hybrid approach

Transmitters of the JPL/NASA Deep Space Network (DSN) typically operate at power levels in excess of 100 kW. This causes heat dissipation and loss problems even in the conventional DSN transmit frequencies of the S and X bands. These problems are compounded by operation in continuous mode, rather than in pulsed operation where the average power is low. In an effort to avoid the heat dissipation, waveguide loss, and arcing problems aggravated by high average power, the DSN has helped pioneer the development of beam waveguide antennas. These beam waveguide antennas use quasi-optical techniques to confine the fields, eliminating waveguide usage and their associated losses. The development of quasi-optical, non-reciprocal devices is natural to the beam waveguide environment. The present paper discusses the use of a ferrite circulator in this context.

Scattering from the quasi-optical ferrite circulator using a coupled integral equation/FEM solution

The finite element method (FEM) is used in conjunction with the method of moments (MoM) and the mode matching technique (MM) to calculate reflection coefficients and radiation patterns for axisymmetric waveguide fed horns. The coupling of FEM to the MoM, on one hand, and the coupling of the FEM to the MM, on the other, are performed by using boundary integrals. One advantage of this approach is that it allows for the presence of inhomogeneous materials to be included in the modelling domain as this poses no special problems for the FEM. In this respect, this method differs from the work of Berthon and Bills [1989] who use only the MoM with a single waveguide mode serving as the excitation. After describing the basic theory, the method is applied to a horn antenna on the Cassini spacecraft. The two dimensional modelling domain for this horn clearly shows where the FEM/MoM and the FEM/MM boundary surfaces are located. Comparisons of measured and calculated far field radiation patterns and reflection coefficients are then shown. It is noted that this method generates a sparse, diagonally dominant, complex-symmetric system matrix which may be solved with standard library routines. Moreover, this FEM formulation has been shown to be free of spurious solutions.

G.C. Chinn

Papers

A hybrid finite-element method for axisymmetric waveguide-fed horns

Scattering from ferrite bodies of revolution using a hybrid approach

Scattering from the quasi-optical ferrite circulator using a coupled integral equation/FEM solution

Radiation from axisymmetric waveguide fed horns