Optimisation globale de formes d antennes diélectriques : Couplage d un algorithme génétique avec un simulateur FDTD en 2-D A.ROLLAND, R.SAULEAU, A.BORISKIN 2, M.DRISSI anthony.rolland@univ-rennes.fr IETR, UMR CNRS 664, Avenue du Général Leclerc, 3542 Rennes cedex 2 Institute of Radiophysics and Electronics NASU, Kharkov 685, Ukraine UMR 664
Motivations INSTITUT D ÉLECTRONIQUE ET DE TÉLÉCOMMUNICATIONS DE RENNES Context - EM Optimization of metallo-dielectric antennas such as : - Rod antennas - Resonators - Lens antennas What is a lens antenna? Optimization of the lens shape Primary feed Focusing dielectric system Radiation pattern Beam shaping 2
Outline I. Methodology Block diagram Basics on FDTD Basics on BIE Numerical validations II. GA optimization Lens profile representation Definition of the cost-function Optimization scheme III. Optimization results Numerical validation Optimization of the antenna directivity Optimization of amplitude-shaped radiation pattern IV. Conclusion 3
Specifications in radiation : I. Methodology: Block diagram - Radiation pattern template - Directivity - Bandwidth EM analysis: - FDTD - BIE Optimization algorithm: Genetic Algorithm (GA) Lens optimal shape 4
Nz cells INSTITUT D ÉLECTRONIQUE ET DE TÉLÉCOMMUNICATIONS DE RENNES I. Methodology: Basics on FDTD method z Numerical Solving of Maxwell s Equations in Time Domain : Yee Scheme z in Time Domain : Limitation of the computational space (Nx,Ny,Nz) Space and time discretizations ( x, y, z, t) CFL Criteria t 2 Partial Derivative Approximation : 2 nd order Finite Difference x z x H y E x Ny cells y Field update equations (E n t and H (n+½) t) Advantages Intuitive method: easy to understand run: results in a wide frequency spectrum band c x y 2 + z 2D-FDTD solver (infinite z-dimension) + 2 E z Drawbacks Memory resources (3D) Computation time (3D) H z H x E y x Nx cells (i,j,k) y y Numerical dispersion (max( )<λ g /) TM case (Ez, Hx, Hy) TE case (Hz, Ex,Ey) 5
I. Methodology: Basics on MBIE method Muller s Boundary Integral Equations (MBIE) 2-D case S y Aperture source in the emitting mode u o D 2 γ Plane wave in the receiving mode D ε ε 2 x The problem geometry Advantages No limitation on wavelength size of the scatterer No limitation on contrast between the scatterer and background media Drawbacks Complexity of analytical approach 6
I. Methodology: Numerical validations (/2) Geometry of the structure Hemielliptic lens Diameter = a = 2 λ -2.5-5 Normalized Radiation Patterns TM Case Normalized total radiation pattern FDTD MBIE TE Case FDTD MBIE ε r =2.53 λ /5 Normalized pattern (in db) -7.5 - -2.5-5 -7.5-2 -22.5 Current Line Source : TM case: J z -25 3 6 9 2 5 8 2 24 27 3 33 36 Angle (in degrees) TE case: M z 7
I. Methodology: Numerical validations (2/2) Directivity Directivity 5.5 5 4.5 4 3.5 3 2.5 2.5.5 9.5 9 8.5 8 7.5 7 6.5 TM Case Comparison of directivity.8.9..2.3.4.5.6.7.8.9 Normalized Frequency (a/λ ) Normalized frequency (a/λ ) FDTD MBIE Directivity Directivity 3 2.5 2.5.5 9.5 9 8.5 8 7.5 TE Case Comparison of directivity 7 FDTD 6.5 MBIE.8.9..2.3.4.5.6.7.8.9 Normalized Frequency (a/λ ) Normalized frequency (a/λ ) 8
II. GA optimization: Lens profile representation Parameterization : Discrete number of points polar angle (θ i ) fixed module (r i ) to be optimized Curve representation : Interpolation of the points cubic splines Parameter (r i ) encoding : Differential encoding : r 2 r 2 r θ r (absolute encoding) r i = r i- + r i, i=2 N r i θ i Binary encoding : Parameter (i) = Gene (i) encoded on Ni bits r i Parameter (i-) = Gene (i-) encoded on N i- bits Parameter (i+) = Gene (i+) encoded on N i+ bits An antenna geometry = A chromosome Origin Point (,) Reference Point (r, θ ) Profile Points (r i, θ i ) 9
Fitness = i INSTITUT D ÉLECTRONIQUE ET DE TÉLÉCOMMUNICATIONS DE RENNES - Far-field radiation pattern II. GA optimization: Definition of the cost-function db Penalization area Superior template A A 2 A i Fitness = i A i 36 Inferior template Example of antenna radiation pattern θ 2- Directivity of the structure
Set of user-parameters (specifications, constraints, etc.) II. GA optimization: Optimization scheme Multi-processor analysis (GA+FDTD) Mutations Fitness Evaluations : EM Solver: MBIE / FDTD Optimization Algorithm : Genetic Algorithm Elitism Mating Goodness of the fitness? Not Good enough / No Convergence of the alg. Pairing Good enough / Convergence of the alg. Solution of the optimization
Validation (TE case) III. Optimization results: - Numerical validation (/3) Elementary FDTD simulation: 3s f = 4 GHz ε r = 2.53 Aim : Far field radiation pattern Configuration of the optimization 2
AG Parameters: Population: 25chromosomes NBits/Chromosome: 5bits Proba crossing = 9% Rate mutation = 5% III. Optimization results: - Numerical validation (2/3) Optimization time : 2h 3
Optimization results III. Optimization results: - Numerical validation (3/3) λ g /5 Optimized radiation pattern Optimized profile 4
Directivity Dire ctivity 5.5 5 4.5 4 3.5 3 2.5 2.5.5 9.5 9 8.5 8 7.5 7 6.5 III. Optimization results: 2- Directivity optimization (/4) TM Case Comparis on of directivity Directivity at f : 8.62.8.9..2.3.4.5.6.7.8.9 Normalized Frequency (a/λ ) Normalized frequency (a/λ ) FDTD MBIE Reminders: ε r =2.53 Diam=2a=2λ Optimization of the directivity at f for the TM case 5
Configuration of the Optimization III. Optimization results: 2- Directivity optimization (2/4).5.5 Origin Point Changeable Nodes Fixed Nodes Mirror Nodes Freedom of Nodes Optimization area J z line source GA Parameters for GA+FDTD: -.5 λ /2 - -.5-2 -.5 - -.5.5 Population: 3 chromosomes NBits/Chromosome: 59 bits Proba crossing = 9% Rate mutation = 5% 6
Optimization Results III. Optimization results: 2- Directivity Optimization (3/4) D Hemielliptic = 8.62 GA+MBIE D optimized =.3 GA+FDTD D optimized = 2.29 Normalized pattern (in db) -2.5-5 -7.5 - -2.5-5 -7.5-2 Hemielliptic lens Optimized lens - FDTD Optimized lens - MBIE Normalized Radiation Pattern Normalized total radiation pattern -22.5-25 3 6 9 2 5 8 2 24 27 3 33 36 Angle (in degrees) 7
Optimized profile MBIE III. Optimization results: 2- Directivity Optimization (4/4).5 FDTD Mod(Ez) - TMz Mode.9.5 -.5 -.8.7.6.5.4.3.2 -.5 -.5 - -.5.5. - Optimization under mechanical constraints (fabrication tolerances, radii of curvature, etc.) 8
Normalized Magnitude (db) INSTITUT D ÉLECTRONIQUE ET DE TÉLÉCOMMUNICATIONS DE RENNES Flat-top pattern -2.5-5 -7.5 - -2.5-5 -7.5-2 -22.5-25 -27.5 Radiation Pattern Templates III. Optimization results: 3- Amplitude-shaped radiation pattern (/4) RADIATION P ATTERN db Min Reference Pattern Max Reference P attern -3-9 -6-3 3 6 9 φ (deg) Specifications: Aperture: minimum: 8 maximum: Maximum ripples: db 8 2 db Side lobes rejection < -2dB GA Parameters: Population: 24 chromosomes NBits/Chromosome: 43 bits Proba crossing = 9% Rate mutation = 5% 9
-2.5-5 -7.5 Results (TM case) Optimized Radiation Pattern RADIATION PATTERN III. Optimization results: 3- Amplitude-shaped radiation pattern (2/4) λ <Height<4.5λ λ <Radius<3λ Optimized Profile Normalized Magnitude (db) - -2.5-5 -7.5-2 -22.5 Min Reference Pattern Max Reference Pattern Optimized Pattern -25-27.5-3 -9-6 -3 3 6 9 φ (deg) 2
Analogy 2D 3D III. Optimization results: 3- Amplitude-shaped radiation pattern (3/4) 2D Shape Optimization: GA+FDTD 3D Shape Optimization: GA+GO/PO [] λ =.7mm Justification of a 2D approach [] G. Godi, R. Sauleau and D. Thouroude, Performance of Reduced Size Substrate Lens Antennas for Millimeter-Wave Communications, IEEE Trans. Antennas Propagat., vol. 53, n 4, pp. 278-286, Apr. 25. 2
III. Optimization results: 3- Amplitude-shaped radiation pattern (4/4) Increase of the lens dimensions 3λ <Height<5λ 3λ <Radius<5λ -2.5-5 Optimized Radiation Pattern RADIATION PATTERN Optimized Profile Normalized Magnitude (db) -7.5 - -2.5-5 -7.5-2 -22.5-25 -27.5 Min Reference Pattern Max Reference Pattern Optimized Pattern -3-9 -6-3 3 6 9 φ (deg) 22
IV. Conclusion Conclusions Numerical validation of our optimization tool (GA+FDTD) One frequency point and low permittivity structures Optimization of the directivity of a lens antenna Optimization of amplitude-shaped radiation pattern Perspectives Wide band optimization (FDTD) Configurations with improved performance High-k structures Multi-layer structures Optimization under constraints 23
Optimisation globale de formes d antennes diélectriques : Couplage d un algorithme génétique avec un simulateur FDTD en 2-D A.ROLLAND, R.SAULEAU, A.BORISKIN 2, M.DRISSI anthony.rolland@univ-rennes.fr IETR, UMR CNRS 664, Avenue du Général Leclerc, 3542 Rennes cedex 2 Institute of Radiophysics and Electronics NASU, Kharkov 685, Ukraine UMR 664 24
ANNEXES 25
Near field maps Comparisons 2D-FDTD vs 2D-MBIE (2/3) MBIE.5 FDTD Mod(Ez) - TMz Mode - TM Case.5 -.5 - -.5.5 Mod(Hz) - TEz Mode -.5 - -.5.5 - TE Case.5 -.5 - -.5 -.5 - -.5.5 26
Similitude 2D 3D Sectorial Radiation Pattern Optimization (3/4) 2D Shape Optimization: GA+FDTD 3D Shape Optimization: GA+GO/PO [] λ =.7mm [] G. Godi, R. Sauleau and D. Thouroude, Performance of Reduced Size Substrate Lens Antennas for Millimeter- Wave Communications, IEEE Trans. Antennas Propagat., vol. 53, n 4, pp. 278-286, Apr. 25. 27
Validation of the Solvers Comparisons 2D-FDTD vs 2D-MBIE Radiation Patterns a = 3 λ ε r =2.53 Current Line Source : TM case : J z TE case : M z Near-field map (TM Case) Near-field map (TE Case) 28