cube was reduced, more wire segments were required. Altshuler used GA to optimize the S-RWA with a minimum Q and maximum bandwidth. In [96], an antenna consisting of a set of wires connected in series and with impedance loads is investigated. The shape of the antenna, the location of the loads, and their impedance are optimized using a GA. The resultant antenna mounted over a ground plane radiates elliptically polarized waves in almost near hemispherical coverage. It has a VSWR less than about 4.5 over the 50 to 1 frequency band ranging from 300 to 15 000 MHz.

It is well known that antenna miniaturization impacts antenna efficiency as well as bandwidth. Therefore multi-objective optimization should be performed to design small antennas with improved efficiency. An optimal set of designs using Pareto GA approach is implemented for designing electrically small wire antennas taking into consideration both bandwidth and efficiency [97]. For the antenna configuration, multi-segment wire structure is employed. The resulting GA designs followed the trend of the fundamental limit, but were about a factor of two below the limit. To further improve the performance of the GA-designed antennas, other design freedoms such as variable characteristic impedance, multi-arm wires, and multiple wire radii could be considered.

6.6.2Particle swarm optimization

As a novel evolutionary algorithm proposed in the mid 1990s [98, 99], particle swarm optimization (PSO) has been introduced into the EM community [100, 101], and its applications have received enormous attention in recent years. Unlike GAs, the swarm intelligence in nature is modeled by fundamental Newtonian mechanics in PSO for optimization purposes. This corporative scheme manifests in PSO the concise formulation, the ease in implementation, and many distinct features in different types of optimizations. PSO is based on the principle that each solution can be represented as a particle (agent) in a swarm. PSO has been widely used in antenna optimal design in recent years, such as antenna arrays [102–104], and wideband printed antennas [105–107].

Figure 6.57 shows the working procedure of the PSO algorithm using a simple flow chart. The detailed description of PSO can be found in [101, 102], where, as an example, a microstrip array and a corrugated horn have been optimized.

PSO has also been applied to small antenna design in recent years, but the design procedure is not much different from GA. For example, the hybrid real-binary PSO algorithm is used to design a dual-band handset patch antenna operating at 1.8 GHz and 2.4 GHz [108]. The unique hybrid representation of candidate antenna designs using real and binary variables enables the optimized benefit from the advantages of both continuous and discrete optimization techniques. With the fitness function evaluated by an MoM-based full-wave simulator, the design is accomplished in quite a limited space with a dimension of 0.23λg × 0.13λg at 1.8 GHz (λg is a wavelength).

6.6.3Topology optimization

A full three-dimensional (3D) antenna design methodology is presented using concurrent shape, size, metallization as well as dielectric and magnetic material volume optimization

Randomly initialize particles’ positions and velocities

For each particle

Out of bounds?

Update Pbest

gbest,x,y

Term. crit. satisfied?

End

Figure 6.57 Flow chart depicting the PSO algorithm.

by Volakis et al. [109, 110]. It is reasonable to expect that designs resulting from the optimal selection of materials, metallization, and matching circuits would lead to novel configurations with much higher performance as compared to simpler approaches employing a subset of these parameters. Nevertheless, volumetric optimization would provide for greater design flexibility.

In the early works [109, 110], optimum topology/material design of dielectric substrates was applied to a patch antenna and obtained remarkable improvement in the bandwidth. The topology algorithm has generally been used to optimize size/shape of objective and it provides a possibility of volumetric design [111]. In applying it to RF design, the optimization scheme will bring the best geometrical and topological configuration from its volumetric variation, along with consideration of geometry and physical dimensions as well as material composite. It performs iteration of evaluation to reach the optimum (maximum) value initially set to obtain the objective shape/configuration. It was demonstrated that the volumetric material design led to significant improvement of