Here Z11 and Z22 are self-impedance of each antenna, Zij is the mutual impedance between two antennas, and V1, V2, I1, and I2 are voltages and currents at the input port of the antenna elements as Figure 8.73(b) shows. Since the two antennas are identical and the system is symmetrical, Z11 = Z22, and Z12 = Z21. Also V1 = V2, and I1 = I2 = I. Thus the input impedance Zin of the antenna is given by

To obtain wide bandwidth, variation of Z11 and Z12 with respect to frequency must counteract each other. This can be achieved by optimizing the geometrical parameters of the antenna that are the loop inner and outer radii Rin and Rout and the sector angle α. When Rin and Rout, respectively, are 13 and 14 mm, relatively constant Zin is obtained for 40◦ < α < 80◦. These three parameters also determine the lowest operating frequency

f , which is given by

√

f = 2c/(π − α + 2)(Rin + Rout ) εr . (8.5)

By using this, the average radius of the loop Rav = (Rin + Rout)/2 can be determined. Then optimum α and τ = (Rin – Rout) need to be determined. Through studies of some experimentally fabricated antennas, the optimum values for these parameters are found. They are α = 60◦, Rav = 13.5 mm, and τ = 0.4 mm. This τ = 0.4 mm, which is the smallest value (thinnest loop radius), is chosen, because bandwidth becomes wider as τ tends to be smaller. With these parameters, an antenna with bandwidth of 3.7 to

11.6 GHz is obtained.

8.1.3Integration of functions into antenna

An antenna, into which active devices or circuits are integrated to enhance the antenna performance or function, is referred to as AIAS (Active Integrated Antenna System) [48]. It has received considerable attention, because the technique will provide surpassing performances or functions to antennas without enlarging the dimensions. There have been quite a few papers and books which have dealt with AIAS [49–51]. The AIAS is not necessarily ESA, but most of them are FSA. However, they have useful features in possibly being manufactured with relatively small size, compact structure, and yet low cost. Representative AIASs are those with enhanced gain [52], operating band [53, 54], and functions of reconfigurable performances such as variation of tuning frequency, switching of operating bands [55, 56], or control of radiation patterns [57–59], and so forth.

IPASs (Integrated Passive Antenna Systems) also play an important role in reducing the antenna size and enhancing the antenna performances; however, because integration of slots/slits into antenna systems has been treated in other sections, it is not mentioned here.

Here in this section, three examples will be described.

8.1.3.1An oscillator-loaded microstrip antenna

Configuration of the antenna along with the dimensions is shown in Figure 8.74 [60]. The antenna is comprised of two transmission lines, one wide line as a radiator and

4.88

Drain

2.14

1.00

y 2-D

x

Gate

Figure 8.74 Geometry and dimensions of single-element antenna integrated with an oscillator along with dimensional parameters ([60], copyright C 2008 IEEE).

one narrow line to serve as a feedback loop. A transistor oscillator circuit is mounted on the wider transmission line with two source terminals connected to the central line with narrow width and the drain and gate terminals connected to the two wider lines. The length of the two radiating sections combined with the feedback loop is 3/2λg (λg: guided wavelength). Similar current and charge distributions are created by this circuit arrangement and the radiation patterns typical of a microstrip patch antenna can be obtained. The antenna pattern is etched on the microwave laminate with thickness of 0.635 mm and dielectric constant of 10.2. The transistor is an HF FET (High Frequency Field Effect Transistor) having super low-noise characteristics and gain of 8.5–9 dB over the frequency range between 6 and 12 GHz. A 1.2 pF capacitor is placed on the radiator line to serve as DC isolation between the drain and gate and at the same time provide RF feedback from the drain to gate. The transistor circuit is biased using a single 1.5 V battery between the source and drain terminals with the gate terminal remaining open.

This antenna is fabricated for testing and the performances are measured. The gain is 10 dBi at 8.5 GHz and the EIRP is 11.2 dBm. The phase noise is –87.5 dBc/Hz at 100 kHz offset, that is attributed primarily to the transmission feedback circuit in addition to low-noise characteristics of the HF FET. Figure 8.75 shows measured transmission data S21 with Vdrain = 1.2 V and Vgate = 0, and for the no-transistor case. The inset in the figure depicts radiated power.

Figure 8.78 Simulated radiation patterns along ϕ (on left) and θ (on right) for (a) configuration 1,

(b) configuration 2, and (c) configuration 3 ([59], copyright C 2009 IEEE).

radiation patterns are varied by short-circuiting or open-circuiting the center of the slot, resulting in cancelling or producing radiation. This action can be performed by using a PIN diode which switches the state of on or off to cause shortor open-circuiting the slot. Reconfiguration of the pattern is realized by selecting which slots are short-circuited. Three configurations 1, 2, and 3 are considered; each one contains two short-circuited slots on the lower sides and one on the upper side on the cube. Figure 8.78(a), (b), and (c), respectively, illustrate the simulated radiation patterns at 5.4 GHz for the configurations 1, 2, and 3, for Gϕ (gain pattern along ϕ) on the left and Gθ (gain pattern along θ ) on the right. Switching the configuration is equivalent to rotating the cube around the probe on an angle of 120◦. As can be noted in Figure 8.78 the antenna radiates in a 4π steradian range with a maximum gain toward a certain direction, and hence by switching the configuration the maximum gain direction changes. The maximum gain is evaluated as approximately 3.7 dBi. In addition to the variation in the maximum gain direction, the radiated powers, in other words Gϕ and Gθ , in a given direction are not identical