Figure 7.145 Variation of S11 depending on insulator thickness and 3D radiation pattern in free space [65].

Figure 7.146 Prototype antenna [65].

insulator and 3D radiation pattern for h = 1.5 mm (PEEK is the product name of the glue insulator [66]). The final structure is shown in Figure 7.146 and simulated and measured |S11| are depicted in Figure 7.147.

7.2.2.2.3 Spherical helix

Wheeler stated [67] that the fundamental limitation on the bandwidth and the practical efficiency of a small antenna are related to the radiation power factor, which is defined as the ratio of the radiated power to the reactive power. It can be increased by utilizing as much as possible of the volume of a sphere whose diameter is equal to the maximum dimension of the antenna, when the antenna is restricted in its maximum dimension, but not in its volume. The spherical helix is considered as the most appropriate candidate

Figure 7.147 Variation of S11 depending on the thickness of glue layer [65].

for realizing such an antenna, as it can be constituted to occupy substantially nearly the whole volume of a sphere by wiring along the perimeter of the imaginary sphere having the radius a corresponding to the maximum size of the antenna.

The radiation properties of several spherical helices have so far been studied [68–78]. The major antenna parameters are number of helical turns, number of helical arms, and the shape. Among the research work, Best did extensive study and demonstrated radiation properties of electrically small spherical helices [71, 72] and compared with that of a normal mode and cylindrical helix [73, 74]. In other papers, different types of antennas such as spherical wire [75] and spherical magnetic dipole antennas have been introduced [76–78].

7.2.2.2.3.1 Folded semi-spherical monopole antennas

Radiation properties such as resonance frequency, radiation resistance, Q and efficiency, of spherical helix monopole and dipole antennas are investigated with respect to the number of turns and number of arms [71]. The antenna model has a wire diameter of 2.6 mm and the maximum spherical radius (and height) is about 6 cm. Geometry of the antennas such as one-turn non-folded, one-turn two-arm, and one-turn fourarm folded spherical helices, respectively are illustrated in Figure 7.148(a), (b), and

(c). With increase in number of arms, resonance frequency becomes higher, radiation resistance tends to be higher, Q becomes lower, and radiation efficiency increases. They are observed in Table 7.15; (a) with two arms and (b) four arms. There is a difference in the height; in the four-arm antenna it is reduced to 5.77 cm from 5.89 cm in the other antennas. Figure 7.149 shows variation of Q with respect to frequency and ka. Note the significance of the four-arm folded spherical helix, which shows the radiation resistance Ra of about 43 , suitable for matching to 50feed line, and the radiation efficiency of over 95%, and Q, which is the most notable result, being within 1.5 times

Table 7.15 Antenna performances of folded spherical helix at resonance: (a) two-arm and (b) four-arm antenna. ([71], copyright C 2004 IEEE)

Figure 7.148 One-turn spherical helix (a) non-folded, (b) two-arm folded, and (c) four-arm folded ([71], copyright C 2004 IEEE).

Frequency (MHz)

ka

Figure 7.149 Comparison of Q of folded and non-folded spherical helix antennas ([71], copyrightC 2004 IEEE).