Figure 6.25 Examples of fractal shape [31].

Figure 6.26 Examples of meander line (dipole structure) [32].

Metamaterials composed by this transmission line model will be discussed in Section 6.2.5.

6.2.2Full use of volume/space circumscribing antenna

There have been some discussions on improvement of bandwidth or maximization of gain in an antenna with a given antenna size. Balanis described in [29] that bandwidth of an antenna circumscribed by a sphere of radius r can be improved only if the antenna utilizes efficiently the available volume of the sphere, with its geometrical configuration. Also Hansen commented in [30] that improvement of bandwidth for an ESA is possible only by fully utilizing the volume in establishing a TE or TM mode or by reducing efficiency. These comments can be interpreted as that full use of a volume which circumscribes an antenna structure is the only means to improve the antenna bandwidth. In other words, even with small size, if an antenna is constructed so as to occupy a whole volume of a sphere in which the antenna is contained, the bandwidth can be improved. Increase in bandwidth with a given size of an antenna corresponds to creation of a small antenna. However, in practice, this is an idealized concept, because an antenna structure can never occupy fully the space or volume that circumscribes the antenna. The concept may be followed by filling such space or volume efficiently; that is, to use the space with the antenna geometry as much as possible. The space is not necessarily three dimensional, but perhaps two dimensional depending on an antenna structure. Fractal shape is a typical example, which fills a space efficiently with the antenna geometry as Figure 6.25 shows [31]. There are some other examples of two-dimensional antennas; meander lines (Figure 6.26) [32], Peano geometry (Figure 6.27) [33], and Hilbert curve

Figure 6.27 Examples of Peano curve geometry (the original to the higher mode) [33].

Figure 6.28 Examples of Hilbert curve geometry (the original to the higher mode) [34].

z

y

x

Figure 6.29 A four-arm helical antenna [35].

geometry (Figure 6.28) [34]. With a helical structure, a four-arm helical antenna, which is designed to occupy a volume of a sphere as much as possible as shown in Figure 6.29, is one of the three-dimensional applications [35].

6.2.3Arrangement of current distributions uniformly

A similar concept to the full use of space, but slightly different method, by which the maximum gain with a given size of an antenna is obtained, is to arrange the current distribution on an antenna element to be uniform. Chu discussed that the ideal current distribution to attain the maximum gain with a given size of an antenna is uniform [37] and the gain at this condition is π r/4λ, where r is the radius of a sphere enclosing the antenna. However, uniform distribution can never be realized by a small antenna. On a small dipole, for instance, the current distribution tends to zero toward the end of the element, taking the maximum value at the center, that is, the feed point. Usually it is assumed to be a triangular shape with the maximum at the feed point and zero at the end as Figure 6.30(a) depicts, where a uniform case is also shown (Figure 6.30(b)). One way