Figure 7.134 Measured gain of the 2-inch square spiral antenna with a resistive taper and a single resistor termination ([53], copyright C 2005 IEEE).

This implies 36% size reduction or lowering of the operation frequency for the same size aperture without additional effort to improve impedance matching.

7.2.2.1.4.6.4 Spiral antenna loaded with inductance

Spiral arms are modified to increase their effective length by loading inductance on the arms. Inductive loading on the spiral wire arms can be formed with either planar meandering with rectangular or zigzag, or 3D coiling of the spiral line. Figure 7.136 illustrates a spiral element replaced with (a) planar meander line, and (b) loop-like winding (rectangular or conical) [58]. Gain of the 6-inch spiral antennas is evaluated to compare dependence of the spiral structures such as planar meandering spiral, volumetric spiral, and simple (straight wired) spiral as Figure 7.137 illustrates.

7.2.2.2 Three-dimensional (3D) structure

To improve antenna performance in a small antenna, efficient use of a volume, within which an antenna is contained, is considered. When an antenna takes a three-dimensional (3D) structure, the utmost 3D structure for this purpose is a sphere, and use of the periphery of the sphere is ideal. So far some attempts at placing helical elements on the periphery of a sphere have been made for efficient use of the periphery of a sphere so as to obtain the lower Q compared with other types of antenna having an electrically small size [31].

Other types of structures than spheres are possible to realize small antennas having lower Q in comparison with 2D structures of the same size, if the volume is within the reasonable dimensions for practical use. Typical antennas having such 3D structures are Koch tree, cylindrical helix, cube, and so forth.

Figure 7.135 (a) Cross section of tapered dielectric superstrate placed on the slot spiral and photos, and (b) variation of measured total circularly polarized gain for the 2-inch square spiral antenna depending on various dielectrics ([53], copyright C 2005 IEEE).

Thickness

Figure 7.136 Inductive loading of the 6-inch diameter spiral antennas: (a) with planar meandering and (b) with volumetric coiling ([58], copyright C 2006 IEEE).

Figure 7.137 Gain comparison between three types of spiral antennas; ordinary wire spiral, planar meandering, and volumetric coiling ([58], copyright C 2006 IEEE).

Koch dipole

Quasi-fractal tree dipole

3D Quasifractal tree dipole

Figure 7.138 Three types of fractals: Koch dipole, quasi-fractal tree dipole and 3D quasi-fractal tree dipole ([44], copyright C 2002 IEEE).

7.2.2.2.1 Koch trees

Modeling dipoles with Koch Fractal structures are shown in Figure 7.138, where ordinary Koch dipole, quasi-fractal tree dipole, and 3D fractal tree dipole are depicted [44]. In the fractal tree, the top third of every branch is split into two sections and the 3D version has the top third of each branch split into four segments that are each one-third in length. The 3D fractal here implies only that the structure is not contained in a plane.

As one way for evaluating the performance, Q of the antenna for each type is compared. Figure 7.139 provides Q of (a) Koch dipole, (b) quasi-fractal tree dipole, and (c) 3D

(a)50

45

40 K0 Q

35 K1 Q

30 K2 Q

Figure 7.139 Comparison of Q between (a) Koch dipole, (b) fractal tree, and (c) 3D fractal tree ([44], copyright C 2002 IEEE).

quasi-fractal tree dipole, respectively. The 3D fractal tree shows the lowest Q, and the lowest resonance frequency as shown in Figure 7.140 [45], meaning that this type uses the given space most efficiently.

7.2.2.2.2 3D spiral antenna

A very small spiral antenna to be used for bio-medical telemetry has been developed, and the design and realization of the antenna is introduced [65]. Antenna design started from a planar meander line structure, then its folded structure, and finally progressed to 3D spiral structure as shown in Figure 7.141. Geometry and dimensions of the optimized design of the antenna are shown in Figure 7.142. Reflection factor |S11|