Figure 7.215 Return-loss characteristics for even-mode (solid line) and odd-mode (dotted line) excitation of the elliptical patch antenna ([113], copyright C 2010 IEEE).

case. This is an attribute of the MNG material with μ1 = –5.618 at 0.5 GHz, and –1 at 0.91 GHz, respectively, obtained by using the Drude dispersion relation (7.72) with the magnetic plasma frequency ωmp = 1.286 GHz and 0.707 GHz, respectively. These correspond to the excitation of both the first odd and second even modes in the spectrum. In these cases, ε1 = 2ε0 is used. At higher frequencies, resonances with broader bandwidth are observed. These correspond to standard patch resonances for even mode (at 2.67 GHz) and odd mode (at 3.65 GHz) with μ1 = μ0, as the substrate permeability turns to become positive.

Realization of artificial MNG material may be approached with a technique introduced in the previous section employed for the circular patch [112]. Properly designed MSRR or MSR may perform similar magnetic resonance within a sub-wavelength volume, consistent with the miniaturized size of an antenna. Gain varies depending on the magnetic plasma frequency. The calculated gain normalized to the case of an ideal lossless MM at the resonance frequency (0.5 GHz) is shown in Figure 7.216. In this case, mismatch loss at the feed is excluded and only the effect of MM absorption, which concerns the damping frequency ωτ is included.

7.2.5.1.1.3 Small loop loaded with CLL

Artificial materials exhibiting negative mu implemented by Capacitive-Loaded Loops (CLL) are employed for miniaturization of a loop antenna [109]. The MNG interacts with the highly inductive near field produced by a small loop to attain resonance and also obtain matching in space, even though the antenna has an electrically small size, that is, ka ≤ 0.5 (a: radius of a sphere circumscribing the maximum size of antenna). Some examples, using a semi-circular loop and a rectangular loop, are illustrated in Figure 7.217, which shows use of different types of capacitance in the CLL: (a) a spacing between a loop, (b) an inter-digital capacitor, and (c) a lumped component. Various types of antennas with different geometries and dimensions are designed, and

Figure 7.221 (a) Return loss and (b) impedance ([114], copyright C 2006 IEEE).

Output power (linear, normalized)

Figure 7.222 Radiation pattern ([114], copyright C 2006 IEEE).

An ENG MM can be implemented by using an LH TL structure [115]. A compact TL MM antenna consisting of two unit cells, each of which comprises a microstrip TL loaded with five spiral inductors, is introduced in [115]. The antenna is illustrated in Figure 7.223, in which are shown (a) 3D schematic and (b) top view photograph of the fabricated antenna. Each of two arms works independently at its own frequency and corresponding to two frequencies designed to be merged into one passband so that wideband performance can be obtained. The TL MM unit cell employs a round spiral inductor (Figure 7.224(a)), which has dimensions of d × d = 4.5 mm × 4.5 mm. The spiral element is connected to the ground through a via, to form a shunt inductance with a larger inductance, and is equivalently represented by a circuit shown in Figure 7.224(b),

Shunt inductor Lo

Via

Coaxial

feed

Figure 7.223 The proposed two-arm TL-MM antenna with compact size and enhanced bandwidth:

(a) 3D schematic and (b) top view photograph ([115], copyright C 2009 IEEE).

Figure 7.224 Spiral-inductor-loaded TL-MM unit cell: (a) geometry of the cell and (b) transmission line representation ([115], copyright C 2009 IEEE).

in which the dispersion characteristics are shown, and Z0 and θ denote the TL characteristic impedance and the electrical length per cell, respectively. The TL MM can

be considered equivalently as an ENG MM with the corresponding plasma frequency fsh

√

given by 1/(2 π L0C), where L0 is a combined inductance of the spiral and the via, and C is the intrinsic capacitance of the TL. The metallic area of the antenna (Figure 7.223) is 22.5 mm × 13.5 mm and the size of the ground plane is 50 mm × 50 mm. The return-loss (–10 dB) bandwidth is about 100 MHz from 3.23 to 3.33 GHz, as a consequence of two resonances merged into the frequency range of 3.25 to 3.30 GHz. The radiation pattern is similar to that of a short monopole. Measured directivity and gain, respectively, are 2.61 dBi and 0.79 dBi, giving an efficiency of 65.8%. Effective extension of the bandwidth achieved by using a two-resonance TL MM with a small size is recognized by the comparison with a single patch antenna having the same bandwidth, which has a larger size than the TL MM antenna.

Figure 7.225 Planar meander-line structure (an ENG equivalence) combined with a short monopole ([109], copyright C 2008 IEEE).

z

Metal thickness

Pitch length

Monopole antenna

length Helix width

y

x

Coaxial

feed

Figure 7.226 Cylindrical helix strip (an ENG equivalence) combined with a short monopole ([109], copyright C 2008 IEEE).

Other examples of ENG MM applications to small antennas are use of a planar meander line structure and a cylindrical helix combined with a small monopole as shown in Figure 7.225 and Figure 7.226 [109], respectively. These planar meander line structure and cylindrical helix strip provide inductance effectively to interact with highly capacitive fields near the electrically small monopole to obtain matching in space. The behavior is similar to that of the ENG MM.