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Antenna Design: Simulation and Methods
Radiation Group Signals, Systems and Radiocommunications Department
Universidad Politécnica de Madrid
Álvaro Noval Sánchez de Tocae-mail: [email protected] García-Gasco Trujillo
e-mail: [email protected]
2
• Differential equations with boundary conditions.
• Integral-Differential Equations.
In any mathematical or physical problem:
Maxwell Equations or equations derived from those
In electromagnetic problems:
• 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).
What solves a numerical
method?
3
Source E
Transfer Functioni:
Field propagator
(Maxwell Equations)
F(G)
Electric and Geometrical
description of the antenna 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.
Electromagnetic problems
classification
4
• 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.
Electromagnetic problems
classification
5
• 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, ...
Electromagnetic problems
classification
6
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.
Steps in the development of a computational model:
Computational models
7
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 …
Computational models
8
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:
- Meshing: source domain division in sub-domains or representation of sources as a finite number
of polynomials.
- Numerical integration or differentiation.
4. Execution step:
- Deviation of the results to the physical solution.
- Convergence of the solution.
Approximations or errors in the computational model:
Computational models
9
Selection of the model: differential versus integral equation:
DIFFERENTIAL
EQUATION MODEL
INTEGRAL EQUATION
MODEL
FIELD PROPAGATOR Differential Maxwell
Equation
Green Function
BOUNDARY CONDITIONS Field sampling in D
directions. Field value in
boundaries.
GF implies the radiation
in (D-1) directions.
Field values in the
boundaries of the
materials.
SAMPLING(spatial, time,
excitations)
Large and disperse linear
system.
Reduced but dense
linear system.
EXECUTION TIME Lower Higher
Selection of Computational
models
TIME DOMAIN FREQUENCY DOMAIN
DIFERENTIAL INTEGRAL DIFERENTIAL INTEGRAL
Lossy dispersive
medium� �
Inhomogeneous,
non-linear, time
variant medium�
Closed surface � �
Open surface � �
Linear source � �
Volume � �
Symmetries � �
Radiation � �
Complex Structure � �
Selection of Computational
models
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
• Different antenna types require different solver
technologies.
EXAMPLE: CST MICROWAVE STUDIO®
General purpose solver 3D-volume
Transient
� large problems
� broadband
� arbitrary time signals
Frequency
Domain
� narrow band / single frequency
� small problems
� periodic structures with Floquet port modes
Special solver 3D-volume: closed resonant structures
Eigenmode� strongly resonant structures, narrow band
� cavities
FD Resonant � 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.macomtech.com/Markets/AerospaceDefensewww.navsys.com/Products/hagr.htm
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®
1
1
2
2
33
44
5
5
66
Small Arrays:
EXAMPLE: CST MICROWAVE STUDIO®
• Simultaneous excitation– onesimulation,
– onecombined far field.
• Combine results– multiplesimulations,
– any combinationof far fields.
EXAMPLE: CST MICROWAVE STUDIO®
EJEMPLO: CST MICROWAVE STUDIO®
� Full simulation � Circuit simulation: CST DS
Simulation of the feeding network:
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
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:
Main lobe steered to 45°Main lobe steered to 30°Main lobe steered to 0°
25 x 25
Array Factor
Array Factor
EXAMPLE: CST MICROWAVE STUDIO®
5×5
15×15
25×25
infinite
� Finite array results � infinite array results
Large array: simulation of the far field:
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).
EXAMPLE: CST MICROWAVE STUDIO®
Antenna Database Examples
29
Principal design
• Printed Antennas
• Aperture Antennas
• Linear Antennas
Fed Antennas
• Coaxial
• Transitions
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