A novel expression for resonant length obtained by using artificial bee colony algorithm in calculating resonant frequency of C-shaped compact microstrip antennas

c TÜBİTAK Turk J Elec Eng & Comp Sci, Vol.19, No.4, 2011,  doi:10.3906/elk-1006-466 A novel expression for resonant length obtained by using artificial bee colony algorithm in calculating resonant frequency of C-shaped compact microstrip antennas Ali AKDAĞLI1,∗, Mustafa Berkan BİÇER1 , Seda ERMİŞ2 1 Department of Electrical and Electronics Engineering, Mersin University, Mersin-TURKEY e-mails: , 2 Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA e-mail: Received: 02.06.2010 Abstract This paper presents a novel and simple expression for resonant length to calculate the resonant frequency of C-shaped compact microstrip antennas operating on UHF band applications. C-shaped compact microstrip antennas with different physical dimensions and electrical parameters were simulated by means of a software package that employs the method of finite difference time domain. With the aid of the artificial bee colony algorithm, an expression for the resonant length depending on physical dimensions was constructed by using simulation data. The resonant length expression provided less than 1.6% error on average over the simulated 144 antennas. A comparison between the results obtained in this work and previous results presented in the literature is given to show the accuracy of the proposed expression. Key Words: Artificial bee colony algorithm, compact microstrip antenna, microstrip antennas, resonant frequency 1. Introduction Microstrip antennas (MAs) have evolved from an academic novelty to a commercial reality with wide variety in microwave systems because of their attractive features, such as low profile, planar configuration, low cost, conformal structure, ease in fabrication, and integration with solid-state devices [1-6]. Although MAs have proven to be a significant advance in antenna technology, they suffer from a number of serious drawbacks, including very narrow bandwidth, poor crosspolarization, and low power handling capacity. Most of the studies on patch antennas proposed in the literature have concentrated on rectangular, triangular, and circular MAs, because of their regular shapes. Principally, markets in personal communication systems (PCS), mobile ∗ Corresponding author: Department of Electrical and Electronics Engineering, Mersin University, Mersin-TURKEY 597 Turk J Elec Eng & Comp Sci, Vol.19, No.4, 2011 satellite communication (MSC), direct broadcast television (DBS), wireless local area networks (WLANs), and other miniaturized communication systems demand a small-sized antenna. The size of a regularly shaped MA operating in the UHF band is relatively large. For this reason, conventional MA configurations need to be modified at these frequencies. A compact MA (CMA) with a C-shape may be used rather than the rectangular microstrip antenna (RMA) due to its being about half the size [3,7,8]. In analysis and design of CMAs, analytical techniques, such as the transmission line model [9] or cavity model [10], may not be directly used due to their irregular shapes. Theoretical studies related to CMAs are, therefore, based on experimental or simulation results in general [3,7,8,11-15]. Nowadays, electromagnetic simulation packages, which utilize numerical techniques such as the finite difference time domain (FDTD) method [16] and method of moment [17], have been widely used. MAs can only operate effectively in the vicinity of the resonant frequency, and a significant disadvantage is that they have very narrow bandwidth, as mentioned above. Therefore, the calculation of resonant frequency is very important. The analysis of microstrip patches in points of resonant frequency is a complex problem because of the fringing fields at the edges. Several methods [3,7,8,11,14] varying in accuracy and simplicity have been presented in the literature for determining the resonant frequencies of CMAs with various shapes, including H, L, O, C, and arrows. In fact, the increasing use of MAs in electronic communication markets forces the use of simple methods for analyzing their performance. Therefore, the expression for resonant length, which can be readily used by the designer without any extensive background, has been considered in this work, and a simple expression in calculating the resonant frequency of a C-shaped CMA is proposed. The expression was extracted from simulation data, which belonged to 144 C-shaped CMAs operating in the UHF band. The XFdtd [18] software package, which uses the FDTD method, was used as an electromagnetic simulation tool. The FDTD model used in XFdtd for simulation of C-shaped CMAs was constructed to determine the resonant frequency. In the simulation, the antenna was assumed to be fed by a coaxial cable with 50 ohm near the center. The source waveform was chosen as Gaussian. The maximum cell size for the meshing process was set to 0.07 cm in a cubical region. Unknown coefficients given in the resonant length expression depending on physical dimensions were determined by the artificial bee colony (ABC) algorithm. The ABC algorithm, which simulates the intelligent foraging behavior of honeybee swarms, was recently introduced by Karaboga for numerical optimization problems [19]. Since the ABC algorithm is simple, robust, and uses few control parameters, we expect that it will gain popularity in a wide application area. The following section explains how the ABC algorithm works; further details can be found in [19-23]. 2. Artificial bee colony (ABC) algorithm Swarm intelligence has become a research interest to many scientists of related fields in recent years. The ABC algorithm [19-23] is one of the most recently defined algorithms among population-based optimization algorithms to find near-optimal solutions to difficult optimization problems by the motivation foraging behavior of honeybee swarms. In swarm intelligence, there are 2 fundamental concepts. These are self-organization and division of labor, which are necessary and sufficient properties to obtain intelligent swarm behavior, such as distributed problem-solving systems that self-organize and adapt to the given environment. In the ABC algorithm, the colony of artificial bees contains 3 groups of bees: employed bees, onlookers, and scouts. Artificial bees fly around in a multidimensional search space. The employed bees associate with specific food sources depending on their experiences. The onlooker bees choose food sources based on watching 598 AKDAĞLI, BİÇER, ERMİŞ: A novel expression for resonant length obtained..., the dance of the employed bees within the hive and adjust their positions. The scout bees search for food sources randomly. The first half of the colony consists of the employed artificial bees and the second half includes the onlookers. The employed bee whose food source has been exhausted by the bees becomes a scout. Both onlookers and scouts are also called unemployed bees. Initially, all food source positions are discovered by scout bees. Ther (...truncated)