Antenna Miniaturization, Directivity, and Bandwidth Improvement

Antenna miniaturization is a desirable property in antenna engineering. Reduction in antenna dimensions helps accommodate small mobile devices, such as smartphones and portable transceivers. A way to miniaturize the antenna is to lower its resonance frequency [29]. Typically, the resonance frequency occurs when ftp = K = ±p in the dispersion diagram, and where the group velocity vanishes. For the RBE that occurs in second-order dispersion diagrams, reasonable bandwidth and miniaturization can be achieved. Lower resonances, viz. greater miniaturization, can be achieved using fourth-order dispersion engineering, but the bandwidth will be smaller. That is, DBE modes achieve maximally flat fourth-order dispersion [20] but lead to a more narrowband behavior.

Although the DBE, DbBE, and MPC modes can be exploited to slow down wave, in practice, there is a need to have several periods of the CTL. This requirement implies large structures (at least five periods next to each other) to create the mode, defeating the goal of miniaturization. A way to realize periodicity and overcome the need to stack unit cells next to each other is to adapt circular periodicity. Such an arrangement of unit cells is depicted in Fig. 3.15a and is key to exploiting dispersion engineering for antenna miniaturization. The dispersion diagrams to the left also depict how the dispersion diagrams can be modified to achieve resonance reduction and, therefore, miniaturization.

As already noted, DBE mode formation can be attributed to anisotropy in the dielectric layers, and a challenge is how to realize such an anisotropy in practice. Losses must also be considered since slowly propagating DBE modes are known to experience greater losses per unit cell. To realize DBE modes in practice, a naturally available material, referred to as 'rutile' was chosen due to its very low loss and large permittivity (cxx = 165, ?yy = ?zz = 85, tand = 1 x 10-4 at X-band) [11], both important for small antennas. To create the DBE crystals, a periodic arrangement of printed metal strips was printed on the dielectric layers, as depicted in Fig. 3.16. These strips were printed on two of the three dielectric layers forming the unit cell. But the strip directions on each printing surface are rotated. This leads to polarization rotation of the propagating modes through the unit cell, implying an effective anisotropy [3,

30-32]. Also the dimensions of the strips can be varied to change the effective permittivity tensor of the overall medium, polarization rotation, and propagation properties. The arrangement and unit cell profile are depicted in Fig. 3.16. Similar arrangement can be done on different substrates to realize the DBE mode. Specifically, instead of “rutile,” a thick Rogers RO4350 substrate was used to form the DBE crystal. A dipole antenna was then placed on the maximum field position of the crystal to enhance radiation. This enhancement was experimentally demonstrated, and the DBE resonance was verified, leading to a directivity as high as 18 dB [3].

Demonstration of circular periodicity to realize the DBE, DbBE, and MPC modes for antenna miniaturization

Figure 3.15 Demonstration of circular periodicity to realize the DBE, DbBE, and MPC modes for antenna miniaturization. (a) Unit cell arrangement, viz. flipping of the unit cell, to achieve circular periodicity. (b) Dispersion diagram associated with the unit cell forming the loop; resonances of this circularly periodic structure (two unit cells) are marked by dots, and occur at вр = K = ±p. (c) Bending of the K-ш diagram to shift resonances to lower frequencies with the magnified view of the dispersion diagram around the band edge to the rightmost. Reprinted with permission from Ref. 23, Copyright 2009, IEEE.

Using the concept of rotated layer strips or rotated dielectric bars, a DBE resonator antenna was designed and experimentally demonstrated by Yarga et al. [33]. The antenna was a dielectric resonator antenna (DRA) type using a multilayered cavity. The layers were formed of BaTiO3 and Al2O3 bars in an effort to create anisotropy in the unit cell. It was observed that the dielectric resonator modes TE101 and TM011 led to the formation of DBE modes. It was observed that DRA resonance was shifted to lower frequencies due to the maximally flat DBE mode (see Fig. 3.17). We remark that the misalignment angle between the bars forming the layers added more degree of freedom, leading to the creation of the DBE mode.

(a) DBE unit cell configurations. (b) Dispersion diagram of unit

Figure 3.16 (a) DBE unit cell configurations. (b) Dispersion diagram of unit

cell. Reprinted with permission from Ref. 3, Copyright 2008, IEEE.

Having an understanding of the DBE mode and its practical realization, as in Figs. 3.16 and 3.17, Mumcu et al. [23] proceeded to use the coupled dual transmission line to realize the DBE mode. Specifically, Fig. 3.18 shows the correspondence between the actual three-layer unit cell and the CTL coupling to realize anisotropy. Explicitly, the shown CTL unit cell includes three sections. Two of these are uncoupled transmission lines, and the middle sections refer to a coupled CTL having a coupling capacitance CM. The propagation mechanism in the three-section unit cell is rather straightforward. Each of the transmission lines can be thought of as carrying one of the polarization components of the electric field propagating within the DBE crystal. In fact, the non-identical transmission lines of Fig. 3.18a are associated with the propagation constants in Eqs. (3.19) and Fig. 3.8b. Concurrently, the different line lengths provide a phase delay between the two polarizations to emulate diagonal anisotropy. Similarly, even-odd mode impedances and propagation constants on the coupled lines can be used to emulate a general anisotropic medium (i.e., non-diagonal anisotropy tensor). Further, by cascading the uncoupled and coupled transmission line sections, as in Fig. 3.18a, an equivalent printed circuit is realized, which emulates the volumetric DBE crystal [34].

(a) DBE-DRA dispersion diagram and the realized DBE-DRA

Figure 3.17 (a) DBE-DRA dispersion diagram and the realized DBE-DRA

antenna: (b) top view; (c) side view; (d) bottom and top view showing the slot coupled microstrip line feed; (e) simulated and measured gain pattern in principle cuts. Reprinted with permission from Ref. 33, Copyright 2009, IEEE.

As can be realized, the tunable capacitance between the CTLs can play a key role in controlling the dispersion diagram, as in Fig. 3.18c. Specifically by referring to our earlier analysis, the coupling capacitance controls the value of the coupling coefficients K1, K2, K3 in Eqs. (3.19). This approach was actually used to design the double loop antenna supporting the DBE mode in Ref. [37]. To realize CM, the transmission lines were bent toward the center to keep the footprint as small as possible while concurrently modifying the property of the coupling coefficients K1, K2, K3 (see Fig. 3.19). For additional control in creating the dispersion diagram, lumped loads were used to further modify the individual transmission line parameters. By doing so, the DBE mode was achieved with ease.

(a) Concept of emulating an anisotropic medium using cascaded

Figure 3.18 (a) Concept of emulating an anisotropic medium using cascaded

coupled and uncoupled transmission lines, (b) lumped circuit model of the partially coupled lines, (c) dispersion diagrams obtained by changing the coupling capacitance CM for transmission lines with L1 = L2 = L3 = 1n H, C1 = 10 pF, C2 = C3. Reprinted with permission from Ref. 23, 34, and 36, Copyright 2009, 2010, and 2009, IEEE, respectively.

(a) Capacitively loaded double loop (CDL) antenna layout

Figure 3.19 (a) Capacitively loaded double loop (CDL) antenna layout

printed on a 2" x 2", 125 mil thick Duroid substrate (er = 2.2, tan 6 = 0.0009). This antenna is 1" x 1" in size and exhibits improved gain of 3.9 dB with 51% efficiency at 2.26 GHz. (b) Fabricated double loop antenna on a 250 mil thick 1.5" x 1.5" Rogers TMM 10i (er = 9.8, tan 6 = 0.002) substrate. An additional 0.4 pF capacitor is connected between the coaxial probe and the outer microstrip line to improve Sn < -10 dB. (c) Comparison of simulated and measured return loss. (d) 4.34 dB x-pol gain is measured at 2.65 GHz on the y-z plane. Antenna footprint is Л0/9.8 x Л0/9.8 x Л0/19.7 at 2.4 GHz. Reprinted with permission from Ref. 37, Copyright 2011, IEEE.

But the DBE antennas resulting from the concept in Fig. 3.18 do not have significant bandwidth since the DBE resonances are maximally flat near the band edge. Thus, a modification on the dispersion diagram was considered by using magnetic substrates to create an MPC mode. In this case, the ferrite substrate was only placed below the coupled middle section of the three-section transmission line unit cell. This led to unequal coupling coefficients (K1 n K2) as discussed in the previous section (Fig. 3.9). Consequently, it provided the means for creating anisotropy. The ferrite blocks/substrates were made of CVG (from TCI Ceramics, 4nMs = 1000 G, AH = 6 Oe, ?r = 15, tan S = 0.00014) [12] and were inserted as in Fig. 3.20. The ferrite biasing was also controlled to improve bandwidth by introducing an SIP in the dispersion diagram, viz. a third-order dispersion curve. A bias field of 1000 G was applied normal to the ground plane to saturate the magnetic inserts. This antenna achieved 3.1 dB realized gain with 8.1% bandwidth at 1.51 GHz. The radiation efficiency of the antenna was 73% due to losses associated with non-uniformly biased ferrite sections. Nevertheless, the antenna had a remarkably small footprint ofA0/9.8 x A0/10.4 on a A0/16 thick substrate, making it near optimal in terms of gain-bandwidth product with respect to the Chu-Harrington limit.

(a) MPC unit cell with design parameters (in mils)

Figure 3.20 (a) MPC unit cell with design parameters (in mils): w1 = w2 = w3 = 100, w4 = 20, w5 = 80, w6 = 120, s1 = 50, s2 = 70, s3 = 10, l1 = 50, l2 = 60, l3

= 100, lf = 500. (b) Corresponding third-order dispersion diagram of the unit cell. (c) Fabricated MPC antenna on composite substrate. Calcium vanadium garnet (CVG, 4nMs = 1000 G, AH = 6 Oe, er = 15, tan 5 = 0.00014) sections are inserted into the low contrast Duroid substrate (er = 2.2, tan 5 = 0.0009). The bottom view of the antenna with magnets is shown on the bottom right inset. (d) Comparison of simulated and measured gains. (e) Miniature MPC antenna performance. The substrate is formed by inserting CVG sections into the high- contrast Rogers RT/Duroid 6010 laminate (er = 10.2, tan 5 = 0.0023). Reprinted with permission from Ref. 39, Copyright 2011, IEEE.

We can conclude that the DBE modes can lead to miniaturization and high directivity, but lack wideband characteristics. On the contrary, MPC modes can have moderate miniaturization with significant bandwidth enhancement. A comparison of the DBE and MPC mode antennas along with typical microstrip patch antennas is provided in Fig. 3.21.

Comparison of the MPC, DBE, and patch antenna performance on a 2"x2" in size and 500 mil thick grounded substrate. Reprinted with permission from Ref. 38, Copyright 2010, Elsevier

Figure 3.21 Comparison of the MPC, DBE, and patch antenna performance on a 2"x2" in size and 500 mil thick grounded substrate. Reprinted with permission from Ref. 38, Copyright 2010, Elsevier.

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