Antenna Design: Simulation and Methods

Radiation Group Signals, Systems and Radiocommunications Department

Universidad Politécnica de Madrid

Álvaro Noval Sánchez de Tocae-mail: anoval@gr.ssr.upm.esJavier García-Gasco Trujillo

e-mail: jtrujillo@gr.ssr.upm.es

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• 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?

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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

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• 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

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• 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

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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

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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

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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

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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®

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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

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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