z

(a)

(c)

Figure 7.227 CRLH (microstrip) materials of (a) 1D, (b) 2D, and (c) 3D structure ([116], copyright C 2008 IEEE).

7.2.5.2Applications of DNG (Double Negative Materials)

The representative DNG MM is the CRLH TL MM (Composite Right/Left Handed Transmission-Line Metamaterial), which exhibits various significant functionalities and/or performances predicated on the notable dispersion properties and fundamental RH/LH duality, thus has drawn much attention of engineers for applying it to practical antennas [116]. The typical CRLH antennas are leaky wave (LW) antennas and resonant antennas. The LW antennas can provide full-space dynamic scanning capability, with various types of beams and actively shaped beams. The resonant antennas offer various performances such as multiband operation, and high efficiency and high directivity with zeroth-order mode constitutions. In addition, they have distinct features in implementation of CRLH antennas in planar, small, and compact dimensions that are an urgent requirement for various recently emerged small wireless systems.

Figure 7.227 illustrates three implemented structures: (a) 1D, (b) 2D, and (c) 3D, respectively, of periodic CRLH materials. The unit cell of the 1D structure, which is extendable to 2D or 3D structure, consists of a series resonant tank with a capacitor CL (inter-digital capacitor) and an inductor LR (parasitic), and a shunt anti-resonant tank with a capacitor CR (parasitic) and an inductor LL (a stub), which is depicted in the inset in Figure 7.227(a). The equivalent circuit of the unit cell is shown in Figure 7.228(a). The series tank components CL and LR are related to the metamaterial (MM) permeability

Figure 7.229 Performance of CRLH LW antenna: (a) typical dispersion characteristics and

(b) scanning performance ([103(b)], copyright C 2004 IEEE, [116], copyright C 2008 IEEE).

which are characterized by the pole at ω = 0 and one zero at the plasma frequency (ωse, ωsh). These parameters may take values of positive, negative or smaller than unity. In case of both being zero/negative (balanced transmission frequency ω0), the refraction index is zero/negative.

7.2.5.2.1 Leaky wave antenna [116]

The CRLH MM exhibits unique dispersion characteristics that contain a radiation (or fast wave) region where |β| < k0 = ω/c (k0: free space propagation constant, and c: velocity of light), i.e, the phase velocity vp > c, in addition to a guided (or slow wave) region (β > k0) as shown in Figure 7.229(a). In the figure, these regions are categorized into four; I: LH guided, II: LH radiation, III: RH radiation, and IV: RH guided regions. An antenna constituted with an LW structure, on which a travelling wave travels faster than the speed of light (vp > c), is referred to as a LW antenna. The radiation angle θ of the main beam of this antenna, defined from the normal direction, is given by

In a conventional LW antenna, β is positive and not dispersive, which implies the RH structure, where the radiation occurs in the direction θ > 0, meaning only forward direction. In addition, broadside radiation (θ = 0) is impossible, because it requires β = 0, that requires vg (group velocity; ∂β(ω)/∂ω) = 0. This means that the guided structure is associated with a standing wave, whereas a travelling wave is necessary for the LW radiation. On the contrary, as a CRLH TL MM exhibits dispersion characteristics, where β(ω) varies from the region β < –k0 to the region β > +k0, the CRLH structure performs backfire-to-endfire frequency scanning. This can be understood by (7.77), where θ (β =

–k0) = –90◦ (backfire radiation) and θ (β = –k0) = +90◦ (endfire radiation). In addition, if the CRLH structure has balanced resonances, transition of the transmission from the

234Design and practice of small antennas I

LH regions to the RH regions with travelling wave (vg = 0) is continuous at β = 0, providing unique broadside radiation that cannot be achieved by the conventional LW antenna. Figure 7.229(b) illustrates typical scanning operation of this type of antenna.

7.2.5.2.1.1 Beam forming

By varying circuit parameters LR, CR, LL, and CL, in the CRLH TL structure, electronic scanning can be achieved. The easiest method is to use varactors for capacitors. When an antenna is of 1D structure, scanning is only in one plane. In this case, the beam can be highly directive in the y–z plane, whereas it is broad in the perpendicular direction (y–z plane in Figure 7.229(b)). This is a fan beam.

A 1D CRLH structure can be extended to a 2D structure. The 2D CRLH structure, when excited in its center, can support a circular wave. When the wave exists in the CRLH dispersion regions II and III in Figure 7.229(a), it radiates in an LW manner and produces a conical beam.

When a maximum radiation in a unique direction is required, as usually necessary for point-to-point communications, a pencil-beam antenna is desired. The CRLH TL MM is useful for producing such pencil-beam scanning antennas [117, 118]. The antennas introduced in [117, 118] consist of arrays of LW elements using a combination of frequency tuning and phase-shift tuning to achieve pencil-beam scanning. By using 2D CRLH TL structures, pencil beams can be produced economically and flexibly compared to use of conventional phased arrays, which require complicated, lossy, burdensome matters in design, and 2D dispersive feeding networks.

7.2.5.2.1.2 Active beam scanning

Integration of active circuits along a CRLH TL structure is suitable to manipulate the magnitude of the signal along it as well as its phase, and active beam scanning is easily realized. The beam width of an LW antenna constituted of TL structure is controlled by its leakage factor, αlw (ω), which is the real part of the propagation constant γ (ω) = αlw (ω) + jβ(ω). With passive structure, the leakage factor is fixed, and hence the effective aperture and the directivity cannot be increased, without otherwise extending the length of the LW structure. Meanwhile, since an active CRLH LW antenna, in which active circuitry is integrated, may have an unlimited effective aperture, it can provide an arbitrarily high directivity with single and simple TL excitation. Incorporation of amplifiers as repeaters into a CRLH LW antenna was reported in [119].

7.2.5.2.2 Resonant antennas 7.2.5.2.2.1 Multiband antennas

By reactively terminating a CRLH TL structure open to free space, by a short or an open circuit, a resonant CRLH antenna having effective wavelength and frequency response that are attributes of a CRLH MM property is obtained. The resonant modes of a CRLH structure of length l are given by l = nλg/2, with n = 0, ± 1, ±2, . . . ±∞. The n can be either positive (RH band) or negative (LH band) and even zero (at transition). Each positive (n > 0) resonance mode (at frequencies ω+n) has a twin negative (n < 0) resonance mode (at frequencies ω–n), and a zeroth-order (n = 0) mode exists at the transition frequency ω0 as was shown in Figure 7.207. A CRLH TL structure consisting

η= 56%, G = 3.14 dB, (no sidelobe)

η= 72%, G = 5.88 dB, (no sidelobe)

η= 71%, G = 9 dB, SLL = –14 dB

Figure 7.230 Three CRLH zeroth-order microstrip resonant antennas of different sizes operating at 2.44 GHz with; (a) η = 56%, G = 3.14 dB, (b) η = 72%, G = 5.88 dB, and (c) η = 71%, G = 9 dB, and SLL (sidelobe level) = −14 dB. ([116], copyright C 2008 IEEE).

of N unit cells has a finite number of 2N (2N – 1 in the balanced case) resonances, corresponding to βn p = βn (l/N) = nπ /N. Figure 7.207 shows such a discrete spectrum of a CRLH resonator.

By utilizing the positive and negative resonance pairs of a CRLH structure, a dualband resonant antenna is obtained. The antenna is back fed by a coaxial line at the off-center location for 50 matching at one frequency. In principle, all of the (2N – 1) resonances may be excited and matched to the source with proper excitation. Since the modes of each pair have the same guided wavelength and field distributions, input impedance of each mode has a similar value. By this means an efficient dual-mode operation can be achieved by a single resonator.

In principle, with higher-order CRLH TL structure, operation in multibands such as tri-band, quad-band, or even higher number of bands, is possible.

An example of this type of antenna is a square patch antenna, in which LH structures are partially filled [116].

7.2.5.2.2.2 Zeroth-order antennas

Unique application of a CRLH TL structure to antennas is of a zeroth-order mode, by which zeroth-order CRLH resonance (l/λg = 0, n = 0) is attained. Examples are shown in Figure 7.230, where three different-size microstrip antennas are illustrated [116]. The unit cell of the antenna uses an inter-digital capacitor and a stub inductor shorted at the end with a via as was shown in Figure 7.227(a). The size of a resonant CRLH antenna may be flexibly designed to attain required effective aperture and directivity, as the operating frequency is independent of the size, but is determined by LC unit-cell elements (Figure 7.228(a)). This feature can be used for designing either electrically small or larger antennas. In this type of resonant CRLH LW antenna, directivity can be enhanced by increasing the length of antenna at a given frequency. Gains and efficiencies, respectively, for each antenna of the three shown in Figure 7.230, are 3.14 dB and 56% for the smallest antenna, 5.88 dB and 72% for the middle-size antenna, and 9 dB and 71% for the longest antenna, respectively, all at 2.44 GHz.