Proceedings of iWAT2008, Chiba, Japan

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Printed Metamaterials:Antennas Emulating Anisotropic Media

#John L. Volakis and Kubilay SertelElectroScience Laboratory, Electrical and Computer Engineering Dept.

The Ohio State University1320 Kinnear Rd, Columbus, OH 43212, USA, volakis1 u.edu

1. IntroductionOver the past 3 years, we studied a new class of substrates that supported modes allowing forantenna miniaturization and increased antenna gain. It was first demonstrated that anisotropicmultilayered substrates (consisting of only a few periods) [1] can indeed support focused fieldsthat could in turn be harnessed for high gain antennas (see Figures 1 and 2). This initial effort ledto a good understanding of the field focusing leading to the realization of the frozen mode withinthe anisotropic medium[2,3]. Fabrication and realization of the periodic anisotropic layers(anisotropy is realized by rotating consecutive layers composed of alternating ceramic bars oftitanium and alumina, see Fig. 2) verified the mode existence and their potential for high gainantennas [4]. Of course, the fabrication of these periodic anisotropic layers is cumbersome andexpensive. So, we pursued an approach to realize the frozen modes using low cost printed circuittechnology. This led tothe discovery of a Radiation patterns of an embedded dipole - finite DBE crystalcoupled transmission a .) t e F -P

line to emulate the i -l _anisotropy [5] in ---volumetric media (see g EFig. 2b). Thus, there-was impetus to design 95 10.1and realize printed Frequency (GHz)circuits for miniature Figure 1. Gain increase as the frequency of operation coincides withhigh gain antennas[6]. the Degenerate Bandedge(DBE) and Fabry Perot resonances.The presentation willbegin with a review of our recentDegenerate Bandedge (DBE) antenna,followed by variations of these (in plane orin volume) to realize multimode and

m

wideband configurations. Ferrite and IT,La eW2 2Layei¶smultilayer substrates will be also examined (a)to realize the Magnetic Photonic Crystal Uncolft||ed-A1 nco|led||Al(MPC) modes to further improve bandwidthand multifunctionality. Of particular interest I lllloupe-in this regard is the use of thin magneticlayers which can still realize the MPC mode G _lwithout stringent requirements on low loss. (b)2. Microstrip DBE (MS-DBE) Fig. 2. (a) Volumetric degenarate bandgap (DBE)Antenna crystals composed of misaligned anisotropic layers;

The MS-DBE antenna iS based on (b) Emulating the DBE crystal on a microstripthe emulation of DBE dispersion in bulk substrate using coupled and uncoupled transmissionperiodic media using coupled microstrip line pairstransmission lines. The developed antenna[6], exploits the degenerate bandedge (DBE) mode fields originally observed in volumetric media

978-:1-42=1-lL523-3/O8/$25 .00 @t 2008 IEEE 5 9

(see Fig. 2). This allows for a straightforward and low cost approach to realize small antennas thattake advantage of new design parameters. Indeed, the fabricated DBE antenna, shown in Fig. 3, isamong the very bestmetamaterial antennas in therecent literature. It is only )ko/9x so/9 in size and its gain x

bandwidth product is near the theoptimum Chu limits ofminiaturization. The prototypedesign employs alumina Fig. 3. Printed DBE antenna on a 2" x 2", 500mil thick alumina; footprint size is

(E1r=9.6, tan &-0O.0003) 2XO/9 xXO/ X2/16 at 1.48GHz; measured 300 bandwidth and 4.5dB realized gain.substrate and is depicted inFig. 4 and consists of two cascaded unit cells in circular form. Thus, fields circulating within thestructure see an infinite medium. The number of unit cells (2 in this case) are therefore kept to aminimum, implying a physically small antenna. The prototype was designed to resonate at 1.43GHz (around the DBE frequency) and was fed by a coaxial line at the uncoupled section. Theresulting structure (less that a tenth of the free-space wavelength) has a reasonable bandwidth of3.5% (-1OdB) with a 4dB gain (see Fig. 5). At the meeting, we will present array configurationsof the MS-DBE elements with a goal to really nearly 100% (or even larger) aperture efficiencies.We will also discuss the printing of these on flexible polymer substrates using novel techniquesbased on metalized carbon nanotubes used to increase the surface area and significantly improveadhesion to the polymer.

Unit Cell 1 ) 0.87 inch (2.21 cm)a) ~c

50 Q _Coaxial Cabl(Capacitiv~elyCoupled) 0 __ |0.88 inch

Unit Cell 2 ( cm)b) 2.5X

Substrate: Alumina, £=9.6 tan- 0.00031.5 ~~~~~~~~~~~~2inch x 2inch -(5.08 cm x 5.08 cm)

(Same with Ground Plane)

4>T'he.antennahasdimensionso6f -

0 Tr/4 ir/2 3ir/4 it 5ir/4 3ir/2 7ir/4 2/x/Bloch Wavenumber (K)

Fig. 4: The DBE antenna concept: (a) 2 DBE unit cells wrapped around to form the antenna resonator, (b) Dispersiondiagram of the DBE unit cell, (c) Coaxial fed antenna structure.

SI1I (dB) 3.5% Bandwidth 4 dB Gain at 1.43 GHz y

-1.0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,17,0

20.0 --- F3 (Z : _ev.0 1.2 1.3 1.41.01.6

(a) (b)

Fig. 5: DBE antenna performance: (a) Return loss matched to 50Q at 1.43 GHz (b) Gain pattern at 1.43 GHz.

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3. Multi-arm Coupled TRLs for Improved BandwidthIn addition to their simplicity, there are other advantages when using the coupled

transmission lines (CTRLs) instead of bulk media to realize anisotropy. Mostimportantly, the CTRLS allow for Propagation Band Structure Flatter igher Qlgain (sloW velocity)

much greater flexibility and Inflection point -) high Q, greateradditional degrees of freedom in mibidd6athing aBdielectricitefce-zero

a-- ~acceleratioh)design. Specifically, bulk s d 0t 7rk-feunypoieitsnanesubstrates can supports up to 4th M size)

d: standard DBE/resonanceorder degeneracy (as harnessed by the W., Realization:prototype in Fig. 2) due to theadditional design degrees of freedomafforded by the additionaltransmission lines. As we add more Propagation Constant(K/TRLs to the unit cell configuration Ordinary S ow

(see Figure 6 and 7) it is possible toarbitrarily increase mode degeneracy. Engineered Crystals to Controlm diagram .,d

Further, the inclusion of lumped loads(capacitors and inductors) can realize Fig. 6. New concepts and k-w diagrams to be pursued and realized as partadditional design flexibility to realize of the proposed research.

novel k-co diagrams. Fig. 6 shows theband diagrams for multi-arm coupled TRL unit cell which can be tuned to succession to increasethe frequency bandwidth of a small volumetric antenna. As depicted in Fig. 7, we can achieve upto 6th order degeneracy, allowing for even more dramatic mode behavior (Fig. 7b). Since thesesimple 3-coupled TRL structures are non-magnetic, they allow for reciprocal stationary inflectionpoint (SIP) behavior as shown in Fig. 7d. This eliminates the need for (lossy) ferromagneticmaterials in realizing the frozen modes.

Nevertheless, magnetic substrate offer even greater potential for increasing bandwidth.As an example, lets us consider the unit cell in Fig. 9 printed on a 60 mil-thick ferrite substratemade from a commercially available garnet (Trans-Tech G-810, having 4_Ms = 800 G and _r =

14.6). The internal bias field is 68.5 kA/m (860 Oe) and extracted the k-co diagram, assuming nolosses (since an infinitely periodic structure must be used to construct the k-co diagram, losses arenot included in the analysis). As noted, the length of the unit cell is d = 560 mils, implying ko/10at the SIP frequency of 2.02 GHz. The resulting dispersion diagram is shown in Fig. 5b for threedifferent values of s1, the separation distance between the printed lines in the uncoupled regions.As seen, the k-co relation can be tuned by adjusting si, among other parameters, to achieve theSIP within the diagram. As observed, it is indeed possible to realize very slow group velocities(i.e., dcw/dk= 0 for s, = 129 mils), and for s, = 147 mils, the dispersion around the SIP frequencyimplies negative group velocity since dwo/dk < 0

Multiple TRL DBE structure

On Dielectric Substrate

Port 1 Port 2

Port 3 Port 4 i 4VI order DBEPort 5 1 | | 8 l 0 Irt 6 1 ~~~~2Xld order RBE|Uncoupled /|\3 ormore ll|sections coupled sections Wavenumber

(a) (b)

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Double Band Edge i Double Band Edge

2nd orderRBE 2nd order R1BE

Wavenumber Wavenumber

(c) (d)Fig. 7. (a) Three coupled TRLs to allow for higher order degeneracy in the dispersion diagram, (b) 6th order degenerateband edge, (c) double and triple band edges, (d) reciprocal stationary inflection points realizing frozen modes.

2. 15t' ' [2" -'| C|,-,IdsA > () SIP _-_vv, __ 9 ~~~~~~~~2.05p

(E) V1 *_ L /

(Es) V2 EcLold < 0 S 18 il

0.7 0&.87 0.9 tm1. 17 1.2w 1.3Nornxilized Bloch Wa enumiber

(a) (b)Fig. 8. (a) Microstrip model ofDBE and MPC structures using a single substrate, showing dimensions and port numbers.DBE model uses a dielectric substrate; MVPC model uses a ferrite substrate biased in the indicated direction (normal to theplane of the printed lines). l1 = 170 mil, 12 = 220 mil, w1 = 60 mil, w2 = 30 mil, w3 = 40 mil, s2 = 10 mil. (b) Dispersiondiagram of the transmission line structure printed on a ferrite substrate. For the separation s, = 138 mils (solid line), anSlIP (dwl/dk =d2wl/dk2 =0) appears at 2.02 GHz. Other separations result in non-stationary (dwl/dk 6= 0) inflection points.

References[1] G. Mumcu, K. Sertel, and J. L. Volakis, "Miniature antennas and arrays embedded withinmagnetic photonic crystals," IEEE Antennas and Wireless Propagation Letters, vol. 5, no. 1,pp. 168-171, Dec. 2006.

[2] A. Figotin and I. Vitebsky, "Gigantic transmission band-edge resonance in periodic stacks ofanisotropic layers," Physical Review F, vol. 72-036619, pp. 1-12, Sept. 2005.

[3] G. Mumcu, K. Sertel, J. L. Volakis, I. Vitebskiy, and A. Figotin, "RF propagation in finitethickness unidirectional magnetic photonic crystals," IEEE Transactions on Antennas andPropagation, vol. 53, no. 12, pp. 4026-4034, Dec. 2005.

[4] S. Yarga, G. Mumcu, K. Sertel, and J. L. Volakis, "Degenerate band edge crystals andperiodic assemblies for antenna applications," in 2006 IEEE International Workshop onAntenna Technology Small Antennas and Novel Metamaterials,, Mar. 2006, pp. 408-411.

[5] C. Locker, K. Sertel, and J. L. Volakis, "Emulation of propagation in layered anisotropicmedia with equivalent coupled microstrip lines," IEEE Microwave and Wireless ComponentsLetters, vol. 16, no. 12, pp. 642-644, Dec. 2006.

[6] G. Mumcu, K. Sertel, and J.L. Volakis, "Miniature Antenna Design via Printed Coupled Linesemulating Degenerate Band Edge Crystals," submitted to IEEE Trans. Antennas Propagat.

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