Practical wireless systems sometimes require a very small antenna to fit to the very small electronic unit. Antenna designers thus should attempt to realize an antenna having the practically obtainable performances for the required size, although there could be still some difficulty in achieving it.

It should not be neglected to have impedance matching conditions in any antenna systems in addition to the above conditions. Matching is the inevitable condition, as being understood commonly in ordinary antenna systems; however, in small antennas, especially with physically small size, proper matching will become difficult and final results may be left without perfect matching status. Nevertheless, the lower frequency resonance should be satisfied either within the antenna structure or by network at the antenna load terminal. The matching is significant particularly in PSA, and the matching technique needs skill and experience. The latest advances are an application of NF (NonFoster) circuits to the matching circuit, and matching in space by using metamaterial, which can compensate the reactive component in near field so that resonance in space is attained.

6.6Optimization techniques

Generally, antenna miniaturization is at the expense of efficiency, bandwidth, and gain. As previously noted, small antenna design is a compromise between performance and the dimension as well as manufacturability, materials, and the operating environment. Experience and intuition are essential in the antenna design process as well. However as a certain level of design complexity is reached, design optimization tools become extremely valuable if not a necessity. In this section, some optimization methods adopted for antenna design are discussed. Specifically, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Topology Optimization, and Volumetric Material Optimization schemes are considered for antenna design improvement.

6.6.1Genetic algorithm

Genetic Algorithms (GAs) are search methods based on the principles and concepts of natural selection and evolution. These optimization methods consider a set of trial solutions (in parallel), based on a parametric variation of a set of coded geometric and material features. GA employs already known concepts, such as chromosomes, genes, alleles, mating, and mutation, to the coding and best design selection. Figure 6.53 outlines the GA optimization process. More details can be found in papers and books covering the application of GA in electromagnetics [69–73]. The most studied application of GAs in electromagnetics is antenna design. Specifically, GAs have been applied in reducing side lobes [74, 75], aperture amplitude or phase tapering [76, 77], and for adaptive array optimization [78, 79]. Several uses of GA in single element designs have also been reported [80–82] in uses of circuit elements for antenna loading. GAs have also been used to optimize the performances of standard antennas such as reflectors [83], and Yagis [84]. As is the case with all optimization algorithms, a search for an optimal

Begin

Generate initial population

Evaluate fitness of population

Selection

Crossover

(mating)

Evaluate fitness of population

Converge?

End

Figure 6.53 Flow chart of GA.

solution is carried out subject to pre-specified performance criteria (such as bandwidth, gain, return loss, etc.). Figure 6.53 displays a typical flow chart of the GA optimization process.

Antenna optimizations via GA have been demonstrated. The examples are a miniaturization of a microstrip patch antenna [85], and design of a biocompatible antenna for the 402–405 MHz band [86], where the metal patch is divided into numbers of rectangular cells, and some of them are removed to provide reduction in the patch resonance frequency. Prior to these applications, similar approaches have already been introduced in [87], in which improvement of the quality factor (Q) of a resonator is achieved, and another [88] had shown use of GA to obtain wideband patch antennas.

Figure 6.54 Generic microstrip patch antenna.

In the GA based optimization design procedure, the variables are the number of metal cells and their location, while all the other antenna parameters remain constant. The initial common rectangular microstrip patch as an example is divided into N × M equal rectangular cells. The coding is straightforward as a “1” represents a cell with metal and a “0” represents a cell with no metal. All the cells are allowed to be metallic or nonmetallic except the cell where the coaxial probe is connected, which necessarily must be metallic. Each chromosome is, therefore, coded as a string of N × M bits (genes). The initial population is generated randomly. For each cycle of the optimization procedure a start frequency, stop frequency, and number of frequency points are chosen. At each frequency point and for each individual the input reflection coefficient is obtained. If the return loss is less than or equal to 10 dB the cost function is set to zero. If it is greater than 10 dB, the resonance frequency of the individual is set as the frequency where the input reflection coefficient is minimum. The cost function is then calculated as the difference between the resonance frequencies, the higher the cost function the higher the fitness of the individual. A new generation is obtained from the previous one using tournament selection with elitism, single-point crossover, and mutation. The cycle continues until the predefined number of generations limit is reached. Since there is no information about an “absolute” or “unique” solution, a new cycle can be started. In this case, a new start frequency and stop frequency are defined to guarantee the optimization procedure efficiency.

In an example introduction in [85], a patch having dimensions of 32.94 mm in both the width w and the length L, is printed on the substrate with a thickness of 62 mils, a relative dielectric constant of 2.20, and a loss tangent of 0.0007. The conventional parameters have been chosen to provide a resonance frequency around 3 GHz in GA optimization, in which N × M = 9 and populations of ten individuals are used. For the optimized patch shown in Figure 6.54, a resonance frequency of 1.738 GHz has been obtained compared with 3 GHz of the conventional patch.

The space-filling curves are chosen to design small antennas because they utilize the space more efficiently to improve the antenna performance with a given small size. Some representative antenna geometries and structures using space-filling curves like meander,

Figure 6.55 Scheme for non-uniform MLA with indication of parameters to be optimized only half antenna is visible.

spiral/helix, and fractals are described later in Section 7.1 in conjunction with design of small antennas. However, the resonant frequency and the antenna performances do not depend only on the total wire length of space-filling curves, but also on their geometrical configuration. Thus the GAs are introduced to design these kinds of small antenna to obtain better performance while maintaining miniaturization.

Meandering structure is widely used in small antennas for wireless applications. However, for a fixed height, an ordinary meander line antenna (MLA) does not exhibit the optimum gain [89], especially when the conductor losses due to lengthening the meandered line cannot be neglected. It has already been shown that the inherent geometry of the meander line will affect the resonant frequency and the performance, such as Q, input impedance, and gain. Thus a GA-based MLA is designed to obtain better gain while taking into account the wire conductivity [90]. An MLA can be described by only three parameters: height, width, and number of turns. Whereas in the GA design, more parameters will be considered as shown in Figure 6.55: the number of turns N, the length of the horizontal (wn1 and wn2) and vertical (hn1 and hn2) segments of the nth turn, and the length of the central segments (w00 and h00). The above optimization process, involving a trade-off between miniaturization with self-resonance (long wire length) and minimization of loss (short wire length), requires all the vertical and horizontal segments to be independently designed and can be efficiently handled by the GA approach. For each pth antenna of the GA population at the kth generation, the following fitness function is then evaluated:

where Hp, Gp, Xp are the pth antenna height, maximum gain, and input reactance, respectively. Parameters have been chosen as: r1 + r2 + r3 = 10, G0 = 1.63 (maximum gain of half-wavelength perfect conductor dipole), X0 = 1 . The fitness function converges to fp = 10 as antenna gain equals G0, the height equals Hmax and the antenna is at resonance.

To investigate the GA optimization to enhance MLA gain, several trials of designs have been performed for different maximum sizes (Hmax × Wmax) ranging from 3 × 3 cm2

Hmax (cm)

Fig 6.56 Copper-wire GA-optimized MLA antennas for different maximum available areas (dashed shapes).

to 6 × 6 cm2. The antenna elements are made of copper. As depicted in Figure 6.56, the GA-optimization remains effective over the uniform MLA as the maximum available area decreases. For sizes as small as 4 × 4 cm2, an N = 2 antenna has been considered to obtain self-resonance. As the available space increases, the antenna tuning requires shorter horizontal segments, mainly localized at the wire’s ends to minimize losses.

GA techniques have also been applied to the design of pre-fractal antenna elements. For example a GA-engineered second-order Koch-like dual antenna, having a compact size and low voltage standing wave ratio (VSWR) is presented in [91]. Later Pantoja et al. extended the work to seek an optimum set of solutions in terms of resonance frequency, bandwidth, efficiency, and the design, using a multi-objective GA of wire pre-fractal Koch-like antennas [92]. Moreover, the GA code is employed to search for nonfractal structures, namely zigzag and meander type antennas. It is shown that for a given overall wire length and antenna size, GAs find Euclidean geometry designs that perform better than do their pre-fractal counterparts.

Altshuler used GA to optimize wire antennas filling the volumetric space. In [93] various wire antennas were designed. One of them consists of seven wires, with the locations and lengths determined by the GA alone, that radiates waves for GPS/IRIDIUM applications [94]. Also two Yagis were designed for different goals, one is for a broad frequency band and low sidelobes, and the other is for high gain at a single frequency. All of these antennas have unusual shapes compared to conventional ones. In [95] a SelfResonant Wire Antenna (S-RWA) was designed. First, Altshuler chose a target frequency and then constrained the algorithm to create a configuration of linear wire segments, connected in series within the volume of a cube, such that the resulting antenna was self-resonant. As a consequence of cancellation of the inductance and capacitance of the wire configuration at the target frequency, Altshuler found that as the size of the