Topology Optimization of Metallic Antennas

We introduce an approach to carry out layout optimization of metallic antenna parts. An optimization technique first developed for the optimization of load-bearing elastic structures is adapted for the purpose of metallic antenna design. The local conductivity values in a given region are used as design variables and are iteratively updated by a gradient-based optimization algorithm. Given a set of time-domain signals from exterior sources, the design objective is here to maximize the energy received by the antenna and transmitted to a coaxial cable. The optimization proceeds through a sequence of coarsely-defined lossy designs with successively increasing details and less losses as the iterations proceed. The objective function gradient is derived based on the FDTD discretization of Maxwell's equations and is expressed in terms of field solutions of the original antenna problem and an adjoint field problem. The same FDTD code, but with different wave sources, is used for both the original antenna problem and the adjoint problem. For any number of design variables, the gradient is evaluated on the basis of only two FDTD simulations, one for the original antenna problem and another for the adjoint field problem. We demonstrate the capability of the method by optimizing the radiating patch of both UWB monopole and microstrip antennas. The UWB monopole is designed to radiate over a wide frequency band 1-10 GHz, while the microstrip patch is designed for single and dual frequency band operation. In these examples, there are more than 20,000 design variables, and the algorithm typically converges in less than 150 iterations. The optimization results show a promising use of the proposed approach as a general method for conceptual design of near-resonance metallic antennas.

[1]  E. M. Freeman,et al.  A method of computing the sensitivity of electromagnetic quantities to changes in materials and sources , 1994 .

[2]  Ole Sigmund,et al.  Topology Optimization of Sub-Wavelength Antennas , 2011, IEEE Transactions on Antennas and Propagation.

[3]  Waymond R. Scott,et al.  Accurate computation of the radiation from simple antennas using the finite-difference time-domain method , 1989 .

[4]  R. Mittra,et al.  Analysis of frequency selective surfaces using the finite difference time domain (FDTD) method , 2002, IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313).

[5]  Young Sik Kim,et al.  An Equivalent Feed Model for the FDTD Analysis of Antennas Driven Through a Ground Plane by Coaxial Lines , 2009 .

[6]  A.A. Kishk,et al.  Invasive Weed Optimization and its Features in Electromagnetics , 2010, IEEE Transactions on Antennas and Propagation.

[7]  Wei Li,et al.  Level-set based topology optimization for electromagnetic dipole antenna design , 2010, J. Comput. Phys..

[8]  W. Gautschi.  Numerical analysis: an introduction , 1997 .

[9]  E. Hassan,et al.  Topology optimization of UWB monopole antennas , 2013, 2013 7th European Conference on Antennas and Propagation (EuCAP).

[10]  Dimitris Psychoudakis,et al.  Topology design optimization of dielectric substrates for bandwidth improvement of a patch antenna , 2003 .

[11]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[12]  J. Basterrechea,et al.  Comparison of Different Heuristic Optimization Methods for Near-Field Antenna Measurements , 2007, IEEE Transactions on Antennas and Propagation.

[13]  G. Allaire,et al.  A level-set method for shape optimization , 2002 .

[14]  David A. Lowther,et al.  Automated design of magnetic devices by optimizing material distribution , 1996 .

[15]  Ole Sigmund,et al.  Topology optimization for nano‐photonics , 2011 .

[16]  M. Bakr,et al.  Sensitivity analysis with the FDTD method on structured grids , 2004, IEEE Transactions on Microwave Theory and Techniques.

[17]  Young-Seek Chung,et al.  Optimal design method for microwave device using time domain method and design sensitivity analysis. II. FDTD case , 2001 .

[18]  You Chung Chung,et al.  Broadband and Multiband Antenna Design Using the Genetic Algorithm to Create Amorphous Shapes Using Ellipses , 2006, IEEE Transactions on Antennas and Propagation.

[19]  Sailing He,et al.  An optimization approach to multi-dimensional time-domain electromagnetic inverse problems , 1998 .

[20]  Eddie Wadbro,et al.  Megapixel Topology Optimization on a Graphics Processing Unit , 2009, SIAM Rev..

[21]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[22]  E. Jordan,et al.  Electromagnetic Waves and Radiating Systems , 1951 .

[23]  A. Bondeson,et al.  Shape optimization for radar cross sections by a gradient method , 2004 .

[24]  B. Strand,et al.  Solving inverse electromagnetic problems using FDTD and gradient‐based minimization , 2006 .

[25]  Krister Svanberg,et al.  A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations , 2002, SIAM J. Optim..

[26]  Tsuyoshi Nomura,et al.  Structural topology optimization for the design of broadband dielectric resonator antennas using the finite difference time domain technique , 2007 .

[27]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[28]  Ole Sigmund,et al.  On the usefulness of non-gradient approaches in topology optimization , 2011 .

[29]  T. Rylander,et al.  Shape optimization of the total scattering cross section for cylindrical scatterers , 2009 .

[30]  James G. Maloney,et al.  A simple FDTD model for transient excitation of antennas by transmission lines , 1994 .

[31]  S. Gedney.  An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices , 1996 .

[32]  Y. Rahmat-Samii,et al.  Parallel particle swarm optimization and finite- difference time-domain (PSO/FDTD) algorithm for multiband and wide-band patch antenna designs , 2005, IEEE Transactions on Antennas and Propagation.

[33]  M. Sadiku.  Numerical Techniques in Electromagnetics , 2000 .

[34]  Byungje Lee,et al.  Optimal Shape Design of Dielectric Micro Lens Using FDTD and Topology Optimization , 2009 .

[35]  S. Nordebo,et al.  Optimal Antenna Currents for Q, Superdirectivity, and Radiation Patterns Using Convex Optimization , 2013, IEEE Transactions on Antennas and Propagation.

[36]  Constantine A. Balanis,et al.  Modern Antenna Handbook , 2012 .

[37]  Young-Sik Kim,et al.  An Equivalent Feed Model for the FDTD Analysis of Antennas Driven Through a Ground Plane by Coaxial Lines , 2009, IEEE Transactions on Antennas and Propagation.

[38]  Andreas Griewank,et al.  Advantages of Binomial Checkpointing for Memory-reduced Adjoint Calculations , 2004 .