We present the formulation of a finite-element/boundary-integral method for the analysis of three-dimensional doubly periodic structures based on arbitrary nonorthogonal lattice configurations. The method starts from a functional description of the field problem where only a single unit cell of the array is considered. This unit cell is meshed with triangular prismatic volume elements and the electric field intensity is discretized with edge-based expansion functions. On the sidewalls of the unit cell, phase boundary conditions are employed to relate the fields on opposing walls of the unit cell. On the top and/or bottom unit cell planar surfaces, the mesh is terminated using a mixed potential integral equation. The required space-domain periodic Green's function is calculated after applying the Ewald (1921) transformation to convert the slowly converging series representation into two rapidly converging series. The method is validated for simple slot and strip frequency-selective surfaces as well as microstrip dipole arrays. More complex geometries investigated are slot-coupled microstrip patches, photonic bandgap materials, and the so-called "artificial puck plate" frequency-selective surface bandpass structure.

Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation

Simulations and measurements are presented for an all-metal flared-notch array element in both single and dual-polarization configurations. The ultrawideband radiator exhibits an operational bandwidth of 12:1 for broadside scan and 8:1 bandwidth at a 45-degree scan in all planes, maintaining active VSWR<;2. The feed consists of a direct coax-to-slot-line transition that mounts directly into the base of the radiator. The all-metal flared-notches are machined from common metal stock and fed via SMA coaxial connectors. No soldering is required for any part of the design-including the feed-and assembly is simple and modular. The array parts are machined using a high-precision wire-EDM cutting technology, ensuring that measurements (in the 700 MHz-9 GHz range) are repeatable and give close agreement with theory, even through multiple assembly cycles of the modular construction system. This paper presents results for a 32-element linear array of horizontal elements and also an 8 × 8 planar array of dual-polarized elements, comparing measurements with full-wave simulations of the complete finite array structures.

Ultrawideband All-Metal Flared-Notch Array Radiator

A parameter study of dual-polarized tapered slot antenna (TSA) arrays shows the key features that affect the wide-band and widescan performance of these arrays. The overall performance can be optimized by judiciously choosing a combination of parameters. In particular, it is found that smaller circular slot cavities terminating the bilateral slotline improve the performance near the low end of the operating band, especially when scanning in the H-plane. The opening rate of the tapered slotline mainly determines the mid-band performance and it is possible to choose an opening rate to obtain balanced overall performance in the mid-band. A longer tapered slotline is shown to increase the bandwidth, especially in the lower end of the operating band. Finally, it is shown that the H-plane anomalies are affected by the array element spacing. A design example demonstrates that the results from the parameter study can be used to design a dual-polarized TSA array with about 4.5:1 bandwidth for a scan volume of not less than /spl theta/=45/spl deg/ from broadside in all planes.

Parameter study and design of wide-band widescan dual-polarized tapered slot antenna arrays

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

We present a novel frequency-selective surface (FSS) design aimed at enhancing the performance of broad-band reconfigurable antenna apertures. In particular, reconfigurable printed dipole arrays are examined in the presence of a multilayer FSS. Of particular interest is the design of FSS structures whose reflection coefficient has prespecified phase response over a broad set of frequencies. Previous FSSs primarily considered designs on the basis of the reflection coefficient amplitude and were intended for radome applications rather than substrates. Designing FSSs subject to phase requirements is seen to require some compromise in the magnitude. Broad-band requirements also present us with a need for noncommensurate FSS designs.

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Frequency-selective surfaces to enhance performance of broad-band reconfigurable arrays

We present a rigorous frequency domain variational 3-D electromagnetic formulation for the general nonself-adjoint infinite periodic array problem. The hybrid method described combines the vector finite element and Floquet boundary element techniques. It is general in the sense that it is applicable to infinite periodic arrays of the open or aperture-types. It is thus effective for modeling both the scattering and radiation performance of diverse FSS, absorber, and phased-array structures. The technique accurately handles arbitrarily complicated 3-D geometries, lossy inhomogeneous media and internal as well as external excitations. These analyses can be applied to general skewed grids under arbitrary scan and polarization conditions. >

E.W. Lucas

Papers

A 3-D hybrid finite element/boundary element method for the unified radiation and scattering analysis of general infinite periodic arrays