Antenna Design: Simulation and Methods Radiation Group Signals, Systems and Radiocommunications Department Universidad Politécnica de Madrid Álvaro Noval Sánchez de Toca e-mail: anoval@gr.ssr.upm.es Javier García-Gasco Trujillo e-mail: jtrujillo@gr.ssr.upm.es What solves a numerical method? In any mathematical or physical problem: Differential equations with boundary conditions. Integral-Differential Equations. In electromagnetic problems: Maxwell Equations or equations derived from those Static systems: capacitors or resistances... Transmission line parameters. Magnetic fields in Engines. Analysis of linear antennas (HF) in a real environment. Analysis of microwave antennas (patch antennas, slot antennas ) Analysis of microwave circuits: microstrip, stripline, Analysis of Waveguides Electromagnetic Compatibility (EMC) Radar Cross Section (RCS) of complex structures. Near to far field transformation in antenna measurements. Source reconstruction in antenna measurement (inverse problem). 2
Electromagnetic problems classification Source E Electric and Geometrical description of the antenna G Transfer Functioni: Field propagator (Maxwell Equations) F(G) Currents and fields S Problem Known Unknown Example Analysis E, F(G), G S Radiated field by an antenna Simple Synthesis S, F(G), G E Excitations for an array antenna to get a radiation pattern Complex Synthesis E, S F(G), F Antenna geometry that produces a radiation pattern with a feeding structure. 3 Electromagnetic problems classification According to the field propagator: - Integral operator: Green function in free space or other conditions. - Diferential operator: Maxwell equations in differential form - Modal expansion: Maxwell Equations solutions in a specific coordinate system and the corresponding modal expansion. - High frequency approximation: Geometry optics, PO, PTD or UTD approximations. According to the application: - Radiation: Calculation of the sources that produces the electromagnetic fields. - Propagation: Calculation of the fields far from the sources. - Scattering: Calculation of the effect of some obstacles. 4
Electromagnetic problems classification According to the class of problem: - Solution domain: Time or frequency - Space of the solution: Spatial or Spectral - Dimension: 1D, 2D, 3D - Electrical properties: dielectric, conductor (perfect or lossy), anisotropy, homogeneous, lineal... - Geometry: revolution, linear, plane, curve, arbitrary,... 5 Computational models Steps in the development of a computational model: 1. Conceptualization: analysis of the physical phenomena and the elemental mathematical description. 2. Formulation: formal and complete mathematical representation. 3. Numerical algorithm programming: algorithm description using numerical techniques. 4. Execution: quantitative results solution. 5. Validation: numerical and physical determination of the valid range. 6
Computational models Desired properties of a numerical method: 1. Accuracy: quantitative measure of the results and the modeled reality after the geometrical and numerical approximations. 2. Efficiency: computational cost of the algorithm (time and memory). 3. Utility: applicability of the computational model to the problem, easiness of use, graphical presentation 7 Computational models Approximations or errors in the computational model: 1. Conceptualization step: - High frequency methods: GO, GTD, PO. PTD - Full Wave Methods: Integral equation methods or differential equations methods. 2. Formulation step: - Surface impedance: ratio between tangential components E and H. - Linear source approximation: reduction of volumetric integrals to linear (or surfaces). 3. Programming step: 4. Execution step: - Meshing: source domain division in sub-domains or representation of sources as a finite number of polynomials. - Numerical integration or differentiation. - Deviation of the results to the physical solution. - Convergence of the solution. 8
Selection of Computational models Selection of the model: differential versus integral equation: FIELD PROPAGATOR BOUNDARY CONDITIONS SAMPLING(spatial, time, excitations) DIFFERENTIAL EQUATION MODEL Differential Maxwell Equation Field sampling in D directions. Field value in boundaries. Large and disperse linear system. INTEGRAL EQUATION MODEL Green Function GF implies the radiation in (D-1) directions. Field values in the boundaries of the materials. Reduced but dense linear system. EXECUTION TIME Lower Higher 9 Selection of Computational models TIME DOMAIN FREQUENCY DOMAIN DIFERENTIAL INTEGRAL DIFERENTIAL INTEGRAL Lossydispersive medium Inhomogeneous, non-linear, time variant medium Closed surface Open surface Linear source Volume Symmetries Radiation Complex Structure
EXAMPLE: CST MICROWAVE STUDIO Antenna Simulation Different antenna types require different solver technologies. Antenna array simulation Small arrays Feed networks Large arrays Active element pattern Installed performance EXAMPLE: CST MICROWAVE STUDIO Different antenna types require different solver technologies.
EXAMPLE: CST MICROWAVE STUDIO General purpose solver 3D-volume Transient Frequency Domain large problems broadband arbitrary time signals narrow band / single frequency small problems periodic structures with Floquet port modes Special solver 3D-volume: closed resonant structures Eigenmode FD Resonant strongly resonant structures, narrow band cavities strongly resonant, non radiating structures Special solver 3D-surface: large open metallic structures Integral Equation Asymptotic Solver large structures dominated by metal EXAMPLE: CST MICROWAVE STUDIO Transient Solver: PBA meshing Broadband Linear memory GPU acceleration
EXAMPLE: CST MICROWAVE STUDIO Frequency Solver: Single frequency Electrically Small Tetrahedral mesh Multiple ports 8 balun fed dipoles EXAMPLE: CST MICROWAVE STUDIO Integral Equation Solver: Surface mesh (Iterative) MOM MLFMM method
EXAMPLE: CST MICROWAVE STUDIO Simulation of Antenna Arrays: Small arrays Large arrays www.navsys.com/products/hagr.htm www.macomtech.com/markets/aerospacedefense EXAMPLE: CST MICROWAVE STUDIO Simulating one element and multiplying by the array factor is inaccurate since the radiation pattern is different for each element.
EXAMPLE: CST MICROWAVE STUDIO Small Arrays: 1 2 1 2 6 6 3 3 5 5 4 4 EXAMPLE: CST MICROWAVE STUDIO Simultaneous excitation one simulation, one combined far field. Combine results multiple simulations, any combination of far fields.
EJEMPLO: CST MICROWAVE STUDIO Simulation of the feeding network: Full simulation Circuit simulation: CST DS EJEMPLO: CST MICROWAVE STUDIO Large arrays: 1. Simulate full array. 2. Simulate unit cell.
EJEMPLO: CST MICROWAVE STUDIO Large arrays: approximation of infinite arrays Most elements have the same pattern. Edge elements have less influence. Edge elements Interior elements EXAMPLE: CST MICROWAVE STUDIO Large arrays: approximation of infinite arrays Single element multiplied by array factor good approximation of large finite array behaviour. Array Factor
EXAMPLE: CST MICROWAVE STUDIO Large array: simulation of the far field: Array Factor Main lobe steered to 0 Main lobe steered to 30 Main lobe steered to 45 25 x 25 Array Factor EXAMPLE: CST MICROWAVE STUDIO Large array: simulation of the far field: Finite array results infinite array results 5 5 15 15 25 25 infinite
EXAMPLE: CST MICROWAVE STUDIO Installed performance: Both small and large arrays, when implemented, are rarely decoupled from the surroundings (radomes, other antennas, etc.). Simulating installed performance is usually easier than measuring it, so long as you have enough memory. Large computational resources combined with specials software implementations or specialized solution techniques are required. EXAMPLE: CST MICROWAVE STUDIO Installed performance: Main lobe gain is reduced but the sidelobes are improved (when phi = 0).
Antenna Database Examples Principal design Printed Antennas Aperture Antennas Linear Antennas Fed Antennas Coaxial Transitions 29 Rectangular Inset-Feed Partch
Circular Pin-Fed Linear Polarised Parch Circular Edge-Fed Patch With Sectoral Slot Also called: Pac-Man Antenna
Self-Complementary Archimedes Spiral Square Truncated Pin-Fed Circulary Polarised
Bow-Tie Antenna U-Slot Dual-Band Planar Patch
Siniuos 4-Arm Antenna Conical Helix Antenna
Cylindrical Dipole Yagi Dipole Array
Vivaldi Antenna Circular Horn Antenna
Rectangular Horn Antenna Splash Plate Reflector
Offset-Fed Cassegrain Antenna