4. Fractal-shaped radiators

The multiband behaviour of fractal-shaped antennas was introduced by C. P. Baliarda. In that study, Sierpinski and Koch monopole antennas were initiated, and these fractal antennas have multiband performance over different frequency bands as shown in Figure 8. Such performance

is based on the repetitive nature of the fractal structures, bends and corners [12–15], and some more fractal antennas such as modified Sierpinski monopole, modified half-Sierpinski gasket and Mod-P Sierpinski fractal antennas were introduced for multiband applications in [16–18].

Fractal Array Antennas and Applications http://dx.doi.org/10.5772/intechopen.74729 19

Figure 8. Logarithmic frequency response of from Sierpinski fractal structure.

Figure 7. Basic classifications of fractal antennas.

Figure 8. Logarithmic frequency response of from Sierpinski fractal structure.

3. Fractal geometric technology in antenna engineering

18 Emerging Microwave Technologies in Industrial, Agricultural, Medical and Food Processing

Figure 6. Triangular and circular landscape of a city zone.

antennas depends on iterative functions and their recursive algorithms.

4. Fractal-shaped radiators

to their magnificent radiation characteristics and miniaturized design techniques.

The concept of fractal geometric technology to the antenna engineering was pioneered by Kim and D. L. Jaggard [11]. They introduced random fractal array antennas for less side-lobe levels. Conventional methods to the design and analysis of antennas have their base in Euclidean geometric methodology. There has been a substantial amount of current interest, however, in the option of developing antennas and array antennas that utilize fractal geometric technology in their design methodologies. Actually, designing of antennas using Euclidean geometry is based on a certain formula and analytical equations, but in this fractal geometry, designing of

Fractal antenna engineering is having two main branches of antenna design methods to fulfil the requirements of wireless-based communication systems. Figure 7 shows the two main branches of 'fractal antenna engineering'. Depending on their properties and designing parameters, both fractal-shaped radiators and fractal array antennas are again classified into various types. Both types are playing a significant role in the advanced communication systems owing

The multiband behaviour of fractal-shaped antennas was introduced by C. P. Baliarda. In that study, Sierpinski and Koch monopole antennas were initiated, and these fractal antennas have multiband performance over different frequency bands as shown in Figure 8. Such performance is based on the repetitive nature of the fractal structures, bends and corners [12–15], and some more fractal antennas such as modified Sierpinski monopole, modified half-Sierpinski gasket and Mod-P Sierpinski fractal antennas were introduced for multiband applications in [16–18].

feasible and simple design methodologies and algorithms of fractal array antennas, usage of these arrays increases quite commonly in the antenna literature from the past two to three decades. Due to these properties, fractal array antennas find applications in celestial and other

Random and deterministic fractal array antennas are the two basic types of fractal arrays based on their geometric construction. Again, deterministic fractal array antennas are also divided

This chapter focused on the design methodology of linear and planar deterministic fractal array antennas using concentric elliptical ring sub-array design methodology. In this process of design, the behaviour of fractal nature should apply to the regular concentric elliptical antenna array. This recursive process will produce self-similar concentric elliptical geometry as depicted in Figure 10. It is clear from the definition of fractal that the same shape repeats again and again; in this manner geometric structure considered here also repeats again and again. The array antennas proposed in this work can be defined as arrays of arrays, which means that the original counterpart of the array antennas repeats again and again. The general array factor of fractal nature is defined in Eq. (1), which is based on the definition of self-similar nature. The equation

P

GSA S<sup>p</sup>�<sup>1</sup>

ð Þ <sup>A</sup>:Fð Þ <sup>θ</sup>;<sup>φ</sup> � (1)

Fractal Array Antennas and Applications http://dx.doi.org/10.5772/intechopen.74729 21

jkSp�1Ψmn " # (2)

<sup>N</sup> ð Þ mn � <sup>1</sup> (4)

(3)

p¼1

P

p¼1

<sup>φ</sup>mn <sup>¼</sup> <sup>2</sup><sup>π</sup>

<sup>ψ</sup>mn <sup>¼</sup> <sup>a</sup>cosφmncos<sup>φ</sup> <sup>þ</sup> <sup>b</sup>sinφmnsin<sup>φ</sup> � �sin<sup>θ</sup> � acosφmncosφ<sup>0</sup> þ bsinφmnsinφ<sup>0</sup> � �sinθ<sup>0</sup>

where GSA and A.F stand for generating sub-array and array factors, respectively. The array factor of concentric elliptical ring sub-array geometric generator for the design of linear and

> X M

X N

Imne

n¼1

m¼1

where S is the scaling factor and two is the scaling factor of the considered sub-array; P is the iterations and four successive iterations have considered in this work, and it can be extended up to infinite iterations; M is the number of concentric rings and here only one concentric has been considered; N is the number of antenna elements and a number of antenna elements are

for the fractal array factor is the product of generating sub-array factor [37–38]:

<sup>A</sup>:Fpð Þ¼ <sup>A</sup>:Fð Þ <sup>θ</sup>; <sup>φ</sup> <sup>Y</sup>

<sup>A</sup>:FPð Þ¼ <sup>θ</sup>;<sup>φ</sup> <sup>Y</sup>

planar deterministic fractal array antennas is given in Eq. (2):

advanced communication systems.

1. Linear (1D) fractal array antennas 2. Planar (2D) fractal array antennas

3. Conformal (3D) fractal array antennas

into three types based on their geometric patterns [33–36]:

Figure 9. Miniaturized Giuseppe Peano microstrip patch antenna [32].

Like Sierpinski fractal gasket antennas, Sierpinski fractal carpet structures have also been used in the designing of antenna elements [19]. One of the serious setbacks with a small loop antenna is that the input resistance is very small, building it hard to couple power to the antenna. By using a fractal loop, the input impedance of the antenna increases. Koch Island, Minkowski and hexagonal geometry with triangular loop are the best examples for the fractal loop antennas [20–24].

Fractal geometric technology was also introduced in microstrip patch antennas instead of conventional rectangular, circular and square geometries, and this leads to improved gain of those antennas with multiband and ultrawideband behaviour [25]. The analogous insight of raising the electrical length of a radiator can be applied to a patch antenna [26]. The patch antenna can be analysed as a 'microstrip transmission line'. So, if the current will be forced to pass through the convoluted path of a fractal structure rather than a conventional Euclidean pathway, the area needed to engage the resonant transmission line will be reduced. This method has been applied to patch antennas in a range of forms [27–29]. Recently, novel patterns of fractal antennas are projected for miniaturization applications, and miniaturized Giuseppe Peano microstrip patch is shown Figure 9 [30–32].
