...(7) Inset feed locations (y f- -mm) = W/2...(8)

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1 Volume 119 No , ISSN: (on-line version) url: ijpam.eu Patch-Surface Optimization & Design using Genetic Algorithm Yash Vedi,S. Siddhartha, M. Susila,Mitali Gulati, SRM Institute of Science and Technology, Kattankulathur, Chennai, India Abstract:In order to conceptualize unique antennae designs which are otherwise unattainable by conventional approaches, this paper proposes a new method of using Genetic Algorithm to optimize Antenna design. The antennae proposed thereby have 50Ω feed line impedance and operate in a frequency range of 2GHz to 9GHz. The patch surface is divided into a total of 625 cells. The cells are arranged in an array of 25x25, each of which may or may not be radiating for that given antenna. The arrangement of the cells is optimized by using a genetic algorithm which calculates the antenna parameters such as the dimensions of the patch and reflection coefficient. The experimental values were produced to get agreeable results. Keywords:Design Automation;Genetic Algorithm(GA); Patch Antenna; Parallel Computing;Ultra-Wide Band(UWB) 1.Introduction While designing an antenna, extensive and detailed research is needed to identify the kind of environment in which the antenna would operate, the frequency of operation, the amount of power to be delivered, impedance matching, SAR and other parameters. These parameters are important while designing an antenna as they have an influence over antenna performance and complexity. This is followed by using an appropriate software tool to simulate the antenna for the evaluation of antenna performance. Based on this evaluation, the antenna structure is further optimized to get the desired results[1,4,5]. The proposed design process aims at using genetic algorithm for optimizing the surface of a patch antenna. The patch surface is treated as an arrangement of individual cells which may or may not be radiating. The arrangement of cells forms the patch surface. Since there are virtually infinite possible arrangements of cells which can be explored before any reasonably performing patch surface is obtained, a genetic algorithm can explore the design space intuitively and accelerate the overall process. The process begins by calculating the dimensions of the antenna using pre-defined formulae. Followed by computer simulation and design analysis. It is important to mention here that it is entirely possible that the antenna achieved in the end doesn t perform as well as its simulated model. Considering the case of a planar patch antenna, ithasbeen observedthat the size of the effectiveportionofthepatchsurfacethat contributesto effectiveradiation islessascompared tothe size ofentire patch surface-ascalculated usingtheformulae. This implies it is possible to reduce antenna size while at the same time keep the performance at acceptable levels [2,13].Furthermore, ithasbeenobservedthat thedesigncomplexity of such antennaeincreases astherangeofoperational frequencyisincreased,limitingtheirapplicability inuwb frequencyrange[3,7,11].thismeansthat,whileitispossibletoattain smallerandmoreintelligentsurfacedesigns,theyarefarmore complex to realize. There areinnumerabledesignchoicesonecanconsiderbeforedecidingonanoptimalsurface[9,10,12].thispaperex plores onesuchantennadesign. 1.1 Patch design and related parameters Patch antenna or Microstrip patch antenna is one of the most commonly used antenna. It has a wide range of applicability. Most of the modern communication systems such as mobile communication requires a 12593

2 small and low-cost antenna which can be fabricated easily and in bulk. Microstrip patch antenna fits that profile. For satellite communication a circular or square shaped patch may be used. Other applications include GPS tracking devices, manufacturing, logistics, healthcare, remote sensing etc. Microstrip antennae may also be used as Rectennae[14,15]. To design a patch antenna, we have to know the following [14] a) Size of the substrate b) Substrate thickness c) Operational Frequency d) Input impedance Using these, we can find the dimensions of the antenna using the following formulae: - For designing the ground plane, substrate and the patch surface: Resonant frequency(f r )= C 2W r Effective dielectric constant (ε 0 ) =...(1) Effective length (L eff ) (mm) = Length of patch (L-mm) = εr εr C 2f r ε h1 W (2)...(3) ( W h h 1 ) L eff 2h 0.412(ε ) 1 (ε )( W + 0.8) h 1 Length of ground plane (L g- -mm) = 6h+ L...(5) Width of ground plane (W g -mm) = 6h + W...(6) Inset feed locations (x f- -mm) = 2 ε0...(7) Inset feed locations (y f- -mm) = W/2...(8) L...(4) For designing the microstrip feed line: The input impedance(z o ) is usually 50 ohm

3 The width of the micrsoft feed line (W f )Z o = 60 ε 0 ln [ 8h w 0 + w 0 4h ] 1.2Genetic Algorithm = εreff Wo h, 120π ln Wo h for Wo <=1...(9A) h for Wo >1...(9B) h Different from most of the traditional optimization methods, the genetic algorithm tries to replicate the natural process of evolution[6,8]. Every organism in the present world is a direct product of evolutionary process that guided its ancestors ever since the inception of living creatures. Biologically, organisms can be made of single or multiple cells. Each cell has a specific function, which it derives from the genetic information stored in the nucleus called genes. Genes store a sequence of purines and pyrimidines which dictate the formation of different parts of the cells and ultimately the complete organism. Genes are stored in the form of chromosomes. These chromosomes are passed from parent organism to its progeny. It stands to reason that fitter individuals are favoured by nature and they are allowed to leave progeny and there by ensure the survival of their species. The genetic algorithm makes use of the design space as genetic space[1]. Chromosomes define the different parameters of an antenna. Effectively establishing a basis for simulation. Furthermore, fitness of each individual -in this case antenna-can be calculated by a function called fitness function. After finding the fitness of each individual in the population, parents are selected and next generation of individuals are created. The genetic algorithm requiresthe followingparameters i. Population size - total number of individuals per generation ii. Fitness function - evaluation function used to calculate the fitness of an individual iii. Selection function - method by which parents are selected from the generation iv. Crossover function - method using which the crossover of chromosomes is performed v. Crossover probability - defines how much of parent genetic material is inherited by the offspring vi. Mutation function - defines how the genetic material is mutated vii. Mutation rate - defines the number of mutation introduced over time Figure 1-Chromosome and DNA [1] 12595

4 2.Proposed work In order to obtain optimal surface design, the patch surface is divided into 625 cells by using a grid of 25x25. This brings the size of each cell as1.189x0.9 sq. mm. This surface is initialized using a random binary matrix as seen in Figure 2. Figure 2 Random Binary Matrix for initial population Every position with Boolean one is placed as a radiating surface on the substrate. The feed, substrate and partial ground plane is kept consistent for every antenna of a particular generation. Feed, patch surface and the ground plane are initialized as perfect electrical conductor(pec) material. The substrate is made of FR-4. The excitation signal is gaussian with a frequency of 5.5GHz. Figure 3 Showing 5 Antennae from 1st generation By using a simulation tool, each individual of the population is simulated and evaluated for its fitness.the fitness is evaluated based on the cost function given below: Cost= N i=1 s 11 i f i N...(10) 12596

5 Where s 11 i is the magnitudeofthereflection coefficient, f i is Figure 4 Back view showing ground plane the sample frequency in UWB band and N is the number of samples taken for the given frequency range. This is followed by ranking and roulette selection of parents.before crossover the binary matrix is converted to a linear binary array. The crossover method used is Uniform Binary Crossover. In order to favour the evolution of better performing antennae, only 50% of the parents are allowed to create progeny. This also means that there are 25 pairs of parents available for crossover. Each parent pair performs crossover twice, creating 4 individuals for the next generation.thus, restoring the generation size back to 100. The total number of generations is 48. The crossover probability is 100%. And mutation probability is 10%. This process is repeated until 48 generations of antennae have been evaluated. A good indicator to check the convergence of the genetic algorithm is to lookat the change in fitness level each generation. 2.1 Antenna Designs and Simulation Graphs Figure 5 Optimized antennae as seen in generation 48 Given below are some of the simulation results from generation 1 and generation 48. These graphs show how the surface design is different between these two generations and how the antenna performance has been affected. Figure 6 Design of Antenna 83 and its Reflection Coefficient - Generation

6 Figure 7 Design of Antenna 9 and its Reflection Coefficient - Generation 1 In figure 6 and figure 7, it is clear to observe that the antennae fail to perform. For the entire UWB the reflection coefficient is almost 0 and not even close to the -10dB line. Only certain high order harmonics show abrupt changes in performance. Figure 8 Design of Antenna 17 and its Reflection Coefficient - Generation

7 Figure 9 Design of Antenna 18 and its Reflection Coefficient - Generation 48 The antenna surfaces as seen in figures 8 and 9, still appear to have a highly irregular shape. However, the reflection coefficient is well over the -10dB mark for most of the UWB frequency range. 2.2 Results A clear understanding can be derived by comparing the average fitness levels of individuals in generation 1 vs the fitness in generation 48. Figure 10 Fitness Generation

8 Figure 11 Fitness Generation 48 In generation 1 the average fitness of individuals is about while the average fitness of individuals in generation 48 is It stands to reason that while most antennae structure appear to be irregularly shaped, the change in the average fitness of the individuals from generation 1 to generation 48 is indicative of an optimized patch surface. The genetic algorithm has successfully created a population of antennae which have high performance over the ultra-wide band frequency range. 3. Conclusion TheaforementionedantennadesignhasbeenoptimizedbytheGeneticAlgorithm scodeusingavisualbasicscript writerandthevbacodecompletelyautomatingthesimulation toolrenderingandcalculationsubroutinethussimplifyingthe process. Post o ptimi zation, theresultsobtainedbythealgorithmi.e.thereflectioncoefficientstimulationversus thefrequencyrangehasshowngoodmatchingin Ultra-WideBand presence andhighlightthepotentialofthegeneticalgorithm in speeding updesign processwithlittledownside intermsof performancein simulations References [1]Shibaji C, anduddipan M.,2010. Microstrip Patch antenna optimization using Genetic Algortihms. International Conference on Computer & Communication Technology. [2] Mohammed L., Abdelouahab El Hamichi, M. Boussouis, Naima A and Taj-eddinElhamadi, Genetic algorithm optimization for microstrip patch antenna miniaturization. Progress in Electromagnetics Research Letters (Vol. 60, pp ) [3] B. Fette, Cognitive Radio Technology, Academic press edition, Elsevier Icn. [4] J.M. Johnson and YahyaRahmat-samii, Genetic algorithm optimization and its applications to antenna design. Antennas and Propagation Society International Symposium, AP-S Digest (pp ) 12600

9 [5] G.S.Hornby and AL Globus,2004. Automated antenna design with evolutionary algorithm. Antennas and Propagation Society International Symposium. IEEE 3, [6] J. M. J. W. Jayasinghe and D. N. U, Design of dual band patch antennas for cellular communications by genetic algorithm optimization. International Journal of Engineering and Technology. (pp ) [7] JeevaniJayasinghe, J. Anguera, D. Uduwawala, September Genetic Algorithm Optimization of a High-Directivity Microstrip Patch Antenna Having a Rectangular Profile. Radio Engineering (Vol. 22, No.3, pp ) [8] NikolayTelzhensky and Yehuda Leviatan, August Novel Method of UWB Antenna Optimization for Specified Input Signal Forms by Means of Genetic Algorithm. IEEE transactions on antenna and propagation (Vol. 54, No.8, pp ) [9] S. Santarelli, Tian-Li Yu, David E. G., E. Altshuler, T.O Donnell,H. Southhall and R. Mailloux, Military antenna design using simple and competent genetic algorithms. Mathematical and Computer Modelling, Elsevier (pp ) [10]Stylianos C., Panagiotou, Stelios C. A. Thomopoulos and C.N. Capsalis, Genetic algorithms in Antennas and Smart Antennas Design Overview: Two Novel Antenna Systems for Triband GNSS Applications and a Circular Switched Parasitic Array for WiMax Applications Developments with the Use of Genetic Algorithms. International Journal of Antennas and Propagation Hindave Publishing Corporation (Vol 2014, Artl. Id ) [11]Werner W., G. Adamiuk and C.Strum, Basic Properties and Design Principles of UWB Antennas. Proceedings of the IEEE (Vol.97, No. 2, pp ) [12]GZ. Altman, R. Mittra and A. Boag, Oct New designs of ultra-wide-bandcommunication antennas using a genetic algorithm, IEEE Transactionson Antennas and Propagation (vol. 45, no. 10, pp ) [13]F. Guichi and M. Challal, February Ultra-Wideband Microstrip Patch AntennaDesign using a Modified Partial Ground Plane IEEE - 7th Seminaron Detection Systems: Architectures and Technologies (DAT 2017,20-22, Algiers, Algeria). [14] C.A. Balanis, Antenna Theory: Analysis and Design.WileyPublications. [15] Indrasen Singh and V.S.Tripathi Microstrip Patch Antenna and its Applications: A Survey. IJCTA(Vol 2, No.5 pp ) 12601

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