Chapter 5 OPTIMIZATION OF BOW TIE ANTENNA USING GENETIC ALGORITHM

Transcription

1 Chapter 5 OPTIMIZATION OF BOW TIE ANTENNA USING GENETIC ALGORITHM 5.1 Introduction This chapter focuses on the use of an optimization technique known as genetic algorithm to optimize the dimensions of a special type of antenna i.e. bow-tie antenna to improve the performance compared to simple microstrip patch antenna. Design of bow-tie antenna has been previously reported in few papers such as [Bretones et al 2006], and [Abri, 2012]. In this chapter, an optimization technique using geneti algorithm (GA) is proposed to optimize important antenna parameters. [Haupt, 1994] have implemented GA to optimize thinned array of antenna whereas in another paper, [Saxena et al. 2011] have applied GA for optimization of different design parameters of magnetically biased microstrip antenna with circular patch. In this chapter, GA is implemented to optimize the design parameters of bow tie antenna. The two design parameters that are optimized are length and width of the patch Genetic Algorithm GA is a of the most popular optimization techniques which is yet another artificial technique influenced by human biological system. This is an optimization technique which is inspired by natural selection and is the backbone of genetics. GA is a search method which can be used to handle the common characteristics of electromagnetism much better than any other optimization techniques. The fundamental block of genetic algorithm is gene which consists of binary encoding of various parameters. An array of genes is known as chromosomes. GA generally initiate with a population of randomly selected solutions. Each solution has a set of properties 68

2 which can be altered or mutated for a best solution. Generally these solutions are represented in binary as strings of zeros and ones. The process of evolution undergoes numerous iterations with the population known as generation. The objective function or the cost function of each and every individual in the given population is evaluated in each iteration to calculate the fitness function. The individuals with more fitness value are selected from the population and the genome of each individual is mutated to form a next generation. The newly generated solution is then used in the next iteration of the algorithm and the process continues till the maximum number of generations has reached or the desired fitness value has been achieved. Basically there are two requirements for applying GA: a. An exact genetic representation of the solution. b. A fitness function to evaluate the solution domain. Each solution of a given population is represented in form of array of bits. These arrays are generally of fixed length so that crossover becomes simple and easy. Crossover can be made possible between chromosomes of variable length but the entire process becomes very much complicated. Various advanced technique like genetic, evolutionary and gene expression programming utilizes tree like, graph form representation of chromosomes of variable length. After proper genetic representation and fitness functions are defined, a GA initializes a population of solutions and then improves it through repetitive application of the mutation, crossover, inversion and selection process. Initialization: The size of the population generally contains many solutions depending on the nature of the problem. The initial population is set randomly giving a scope of wide range of possible solution. This is known as initialization. Selection: In this process, a proportion of the existing population is selected depending on the better fitness function to breed a new generation. 69

3 Genetic operators: There are two types of genetic operators i.e. crossover and mutation which leads to generation of new population for the next generation. For generation of a new solution to be produced, a pair of parent solution is selected from the previously selected pool of solutions. Crossover is a process in which data from parent solution are swapped to produce new child solution. Mutation is a process of changing one or more gene values in chromosomes from its previous state. Mutation takes place by one or more crossover techniques as discussed in [Eiben, 1994], crossover can be of the following types: One point crossover: One point crossover means there is a common point on both parents string of chromosome beyond which the data in either parent string will be swapped resulting to children solution. Two point crossover: In this type two points are selected on the parent strings. All the data between the two points are swapped giving rise to two child solutions. Cut and Slice: In this case, the two parent strings will be cut at two different points and then the slices will be swapped to give rise to two child solutions of different length. Uniform and Half Uniform crossover: Uniform crossover is a technique in which the parent chromosomes are mixed in the fixed ratio. In this technique, parent chromosomes contribute according to a ratio rather than in segments. In uniform crossover each bit in the string are compared between two parents and then swapped with a fixed probability. In half uniform crossover, exactly half of the non-matching bits are swapped. Termination: The generations will continue until a termination condition has been reached. Common conditions based on which the process gets terminated are: i) A minima criteria has been satisfied by the solution ii) Desired number of generations reached 70

4 iii) Desired computational time has been over iv) Most optimized value of the fitness function is reached such that more iteration does not bring any more changes Bow Tie Antenna A bow tie antenna as shown in Fig. 5.1 is a type of antenna which is made of two conical conductive radiating surfaces connected at one point. It can be defined as two dimensions bi-conic dipole antenna. These antennas have wide bandwidth and are used for UHF reception of television. Fig. 5.1 Bow tie antenna The radiation pattern given by bow tie antenna is almost omni-directional in pattern and the gain generally ranges between dbi. The bandwidth is also wide and better than dipole antenna. A bow tie antenna is an example of miniaturized antenna. Present day wireless communication demands antenna of compact structure but designing them keeping the lower spectrum of microwave frequency covered is really challenging task. One of the probable solutions was given by the French mathematician in [Mandelbrott, 1975] who had put forward the concept of fractal. By implementing the concept of fractal, the size of the antenna can be miniaturised and can also achieve multi-band characteristics. The two main characteristics of fractal which provides compactness and multi-band applications are self similarity and space filling. Besides these advantages, fractal antennas also provide wide 71

5 bandwidth. The concept of fractal has been implemented in bow tie antenna and therefore it proves to be a compact antenna with multiband applications. Bow tie antenna is designed on a rectangular patch antenna. It consists of biconical radiating surface of copper metal mounted over a larger sheet of metal known as ground plane. These two structures are separated from each other using dielectric material i.e. FR4 sheets. The performance of antenna is based on few fundamental properties which affect the gain and efficiency of the antenna. Moreover, in this case, to analyze the performance of bow-tie antenna the properties like gain, directivity, resonant frequency, efficiency and area are analyzed and compared with a patch microstrip antenna with same dimensions. 5.2 Methodology In this chapter GA is implemented to optimize two parameters of bow tie antenna i.e. length and width of bow tie such that the various properties of antenna i.e. directivity, gain and bandwidth can be improved while keeping the other parameters i.e. dimensions of the groundplane and feedgap as constant. The feed which is on the same side of substrate is kept constant as 3 x 1.6 mm. The substrate has the thickness of 1.6 mm and relative permittivity of 4.4 and tan of The dimensions of the ground plane is taken as 13.6 mm x mm. Using the optimized values of length and width, a bow tie antenna is designed on IE3D software. Another simple rectangular microstrip patch antenna is designed using the same length and width. The results obtained from the IE3D software in case of bow tie antenna and microstrip patch antenna are then compared to validate the performance of proposed GA optimization technique. The codes for length and width of the bow-tie antenna is developed using MATLAB software. 72

6 The various steps followed are as stated below: Step 1: A proper fitness function is selected. Fitness function considered is the resonating frequency. Length and width of the bow tie antenna are to be optimized such that resonant frequency should be 12 GHz. Resonant frequency are related to length and width as shown in equations 5.1 to 5.5. Moreover the values of length and width should not be zero and bounded by boundary limits. Step 2: MATLAB codes are written for length and width of the bow-tie antenna. Step 3: Using GA tool (genetic algorithm tool), the optimized values for the desired antenna design parameters have been obtained. Following mathematical equations were used to find out the length and width of the bow-tie antenna Width of the antenna can be calculated by W= c 2f (εr+1)/2 The effective dielectric constant is given by ξ eff = ξr ξr h w (5.1) (5.2) For TM10 mode, length of patch must be less than λ/2. This difference in length is given by L=0.412h (ξeff+0.3)(w h ) (ξeff 0.258)( W h +0.8) (5.3) The effective length of the antenna is given by L eff = c 2 ξeff The length of the bow-tie antenna can be calculated by L=L eff - 2 L (5.4) (5.5) 73

7 5.3 Results and Discussion Optimized values of the antenna design parameters are obtained using the genetic algorithm. The values of length and width obtained using GA are shown in Table 5.1, which when developed resonates at 12 GHz. The other parameters i.e. dimensions of the groundplane and feedgap as constant. The substrate is FR4 sheet having thickness of 1.6 mm, permittivity of 4.4 and tan Table 5.1 Antenna design parameters using Genetic Algorithm method Sl. Antenna design parameters Values using genetic No. algorithm method 1 Length mm 2 Width mm The convergence plot of the fitness function is shown in Fig Fig. 5.2 Convergence Plot Rectangular Microstrip Antenna A simple microstrip patch antenna with a rectangular patch as radiating element having length as mm and width of mm is simulated on IE3D software using the dimensions as given by the genetic algorithm as shown in Fig The feed which is on the same side of substrate is kept 74

8 constant as 3 x 1.6 mm. The substrate has the thickness of 1.6 mm and relative permittivity of 4.4 and tan δ of The dimensions of the ground plane is taken as 13.6 mm x mm Fig. 5.3 A Rectangular Microstrip antenna The 3-D radiation pattern of the microstrip square patch antenna is given in Fig Fig D radiation pattern of the Microstrip antenna. The s-parameter graph of the simulated rectangular microstrip antenna given in Fig. 5.5 shows a resonant frequency of GHz. 75

9 Return Loss (db) Frequency (GHz) Fig. 5.5 S 11 parameter curve for the Microstrip antenna Fig 5.5 shows the s-parameter curve which shows the resonant frequency of the microstrip antenna is GHz. The directivity and the gain are shown in Fig. 5.6 and Fig. 5.7 which is found to be dbi and dbi. Efficiency is calculated as given below: g % (5.6) d Where is efficiency of the antenna, g denotes gain and d denotes directivity. 76

10 Gain (dbi) Directivity (dbi) Frequency (GHz) Fig. 5.6 Directivity vs. Frequency curve for the Microstrip antenna Frequency (GHz) Fig. 5.7 Gain vs. Frequency curve for the Microstrip antenna 77

11 5.3.2 Simple Bow-Tie Antenna The same microstrip antenna designed with the optimized dimensions as provided by genetic algorithm is now fragmented to obtain a bow tie antenna as shown in Fig The feed which is on the same side of substrate is kept constant as 3 x 1.6 mm. The substrate has the thickness of 1.6 mm and relative permittivity of 4.4 and tan δ of The dimensions of the ground plane is taken as 13.6 mm x mm. The various antenna characteristics are also measured from the simulated results so that a comparison can be done. The 3-D radiation pattern is shown in Fig Fig. 5.8 Simulation of a simple bow-tie antenna Fig D radiation pattern for the bow-tie antenna. 78

12 Directivity in dbi Return Loss (db) Frequency (GHz) Fig S-parameter curve for the bow-tie antenna. Fig shows the s parameter graph for the bow-tie antenna where the resonant frequency is GHz. Fig the directivity of the bow-tie antenna at 12 GHz is found to be dbi and gain is found to be dbi as seen in Fig Frequency (GHz) Fig Directivity for the bow-tie antenna 79

13 Gain (dbi) Fig Gain vs. Frequency curve for the bow-tie antenna. Efficiency is calculated as given below: Frequency (GHz) d g % Where is efficiency of the antenna, g denotes gain and d denotes directivity Table 5.2 gives the comparison between both the antennas in terms of antenna output parameters which are optimized using GA to resonate at 12 GHz. Table 5.2 Comparison between square patch and simple bow-tie antenna Sl. No. Antenna parameters Square patch antenna Simple bow-tie antenna 1 Resonant Freq GHz GHz 2 Directivity Gain Efficiency 71.76% 80.98% 5. Radiating area Length x 2XArea of Breadth=120.2mm 2 Triangle=2xBase x height =60.1 mm 2 The antenna was designed to resonate at 12 GHz. When antenna is designed using the optimized value given by GA, it is found that the designed microstrip 80

14 rectangular antenna resonate at GHz. The error percentage for this case calculated according to equation 4.2 is 7%. Designed bow tie antenna which is a compact or miniaturized version of the same, resonates at GHz. The error percentage which is calculated by equation no. 4.2 is found to be 2.66%. Table 5.2 shows that bow-tie antenna is not only better compared to rectangular microstrip antenna in terms of resonating frequency but it is also better in terms of directivity, gain, efficiency and size. 5.4 Conclusion It can be concluded from this chapter that bow tie antenna provides better performance compared to ordinary microstrip antenna after proper optimization done by GA. Moreover bow-tie antenna is a miniaturized form of square patch antenna which is compact in size due to 50% less effective area and therefore can be easily integrated into different types of communication system. In the previous chapter, various techniques based on ANN were implemented to design different conventional antenna structures. In this chapter, an optimization technique i.e. GA has been successfully implemented to optimize conventional square microstrip as well as unconventional bow-tie antenna. After successful implementation of ANN and GA, a hybrid method known as ANFIS which is a combination of learning as well as optimization techniques, has been attempted in next chapter to design conventional as well as unconventional antenna structures. 81