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One- and two-dimensional microwave devices based on left -handed metamaterials

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U n iv e r s it y o f C a l if o r n ia
Los Angeles
O n e- a n d T w o -D im e n sio n a l M icrow ave D e v ic e s
B a se d o n L eft-H a n d ed M e ta m a te r ia ls
A dissertation subm itted in partial satisfaction
of th e requirem ents for th e degree
D octor of Philosophy in Electrical Engineering
by
A n th on y Lai
2007
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UMI Number: 3302551
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© Copyright by
A nthony Lai
2007
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T he dissertation of A nthony Lai is approved.
IVoy C arter
Harold Eeuerm an
Y uanxun E th an Wang
T atsuo Itoh, C om m ittee Chair
U niversity of California, Los Angeles
2007
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To M y Parents
iii
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T able of C o ntents
1 L eft-H anded M e t a m a te r ia ls ....................................................................
1
1.1 I n tr o d u c tio n ....................................................................................................
1
1.1.1
Backward W a v e s .............................................................................
2
1.1.2
Negative Refractive I n d e x ............................................................
3
1.1.3
Frequency D is p e rs io n ......................................................................
4
1.2 Realization: R esonant A p p ro a c h ..............................................................
5
1.3 R ealization: Transm ission Line A p p ro a c h ...............................................
6
1.3.1
Com posite R ight/L eft-H anded Transm ission L i n e ...............
1.3.1.1
9
Physical R e a l iz a tio n .....................................................
14
2 Infinite W avelen gth D e v ic e s ....................................................................
17
2.1
I n tr o d u c tio n ....................................................................................................
17
2.2
Infinite W avelength Theory
17
2.2.1
2.3
.....................................................................
Zeroth O rder R e s o n a n c e ..........................................
18
N -Port Series D iv id e r..................................................................................
21
2.3.1
CRLH U nit-Cell
............................................................................
22
2.3.2
4-Port Series D i v i d e r .....................................................................
25
2.3.3
6-Port Series D iv id e r .....................................................................
28
2.3.4
A p p lic a tio n s ......................................................................................
31
2.3.4.1
Sparse A ntenna A rray F e e d .......................................
31
2.3.4.2
Power C o m b in in g ...........................................................
33
iv
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2.4
3
Infinite W avelength Resonant A n t e n n a ...............................................
36
2.4.1
M onopolar R a d ia tio n .....................................................................
36
2.4.2
Proposed A ntenna D e s i g n ...........................................................
38
2.4.3
Two Unit-Cell A ntenna R e a liz a tio n ..........................................
41
2.4.4
Effects of Increasing th e N um ber of U n it- C e lls .....................
45
2.4.5
R adiation P a tte rn D iv e r s it y .......................................................
47
D u al-M od e C R LH M e ta m a te r ia l..........................................
49
3.1
I n tr o d u c tio n ..................................................................................................
49
3.2
D ual-M ode Concept
..................................................................................
49
3.3
M ode Selective U n it- C e ll...........................................................................
53
3.3.1
Physical Realization
.....................................................................
56
3.3.2
Num erical and Experim ental R e s u l t s ......................................
58
3.4
D ual-M ode Wave-Steering D em onstration
........................................
61
Dual-M ode Wave Focusing D e m o n s tr a tio n ............................
67
T w o-D im en sion al C R LH L e a k y -S te e r in g ..........................................
69
4.1
I n tr o d u c tio n ..................................................................................................
69
4.2
O rthogonal Feeding T h e o r y ....................................................................
70
4.2.1
Num erical S im u latio n .....................................................................
75
4.3
Beam -Scanning A p p lic a tio n ....................................................................
78
4.4
Two-Dimensional CRLH Leaky-Wave A n te n n a ..................................
80
4.4.1
U nit-Cell Analysis
........................................................................
80
4.4.2
A ntenna R e a l iz a tio n .....................................................................
83
3.4.1
4
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4.4.3
Num erical Results
.........................................................................
85
4.4.4
Experim ental R e s u lts ......................................................................
89
4.4.5
Polarization D iv ersity ......................................................................
94
C o n c lu s io n .......................................................................................................
95
R e fe r e n c e s ..............................................................................................................
98
5
vi
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L is t o f F i g u r e s
1.1
e - /j, diagram [1]............................................................................................
1.2
Effective m edium LH m aterial sim ulation [2] in Ansoft HFSS. R ect­
2
angular waveguide w ith middle section filled w ith LH m aterial
(er—- l, n r= -1); backward wave can be observed by observing phase
front for different phases..............................................................................
1.3
3
Ansoft HFSS sim ulation of negative refraction using effective medium.
(a)
F lat lens model consisting of a RH m aterial interfaced w ith a
LH m aterial; cylindrical wave source excited in RH m aterial, (b)
M agnitude plot of electric field showing focusing in LH m aterial. .
1.4
4
SR R -based LH m etam aterial; m etal wire provides negative e and
SR R provides negative /i. (a) Unit-cell, (b) Two-dim ensional SRRbased LH m etam aterial................................................................................
1.5
Equivalent circuit model, (a) Homogeneous PR H TL. (b) Homo­
geneous PLH T L ............................................................................................
1.6
7
D ispersion diagram s for th e TLs of Fig. 1.5. (a) PR H TL [3]. (b)
PLH TL [3]...........................................................................
1.7
6
8
D istributed realization of unit-cells shown in Fig. 1.5 [4], (a) RH
m icrostrip TL. (b) LH m icrostrip TL consisting of periodic cascade
of Sievenpiper m ushroom unit-cells..........................................................
9
1.8
Equivalent circuit model of homogeneous CRLH T L .........................
10
1.9
D ispersion diagram for the homogeneous CRLH TL (unbalanced).
11
1.10 LC model of CRLH unit-cell......................................................................
14
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1.11 Physical realization of LC CRLH unit-cell shown in Fig. 1.10.
(a) Lum ped com ponents based on surface m ount technology, (b)
D istributed im plem entation on m icrostrip technology; series ca­
pacitance from interdigital capacitor and shunt inductance from
shorted stub, (c) D istributed im plem entation on m icrostrip tech­
nology using Sievenpiper mushroom stru c tu re......................................
16
2.1 CRLH resonator, (a) CRLH resonator consisting of N unit-cells.
(b) D ispersion diagram of CRLH resonator showing resonance modes;
ujse and u)sh can be reversed........................................................................
2.2 Infinite wavelength resonance boundary conditions,
(a) Short-
circuit boundary condition w ith equivalent circuit,
(b) Open-
circuit boundary condition w ith equivalent circuit..............................
2.3
19
20
Infinite wavelength IV-port series divider, element spacing (d\ , d2, (h • ■•■)
and physical length (L) is a r b itr a r y ........................................................
2.4 CRLH TL unit-cell,
22
(a) Unit-cell details; w idth of fingers are
0.3 mm, w idth of stub is 1.0 mm, and gaps are all 0.2 mm. (b)
Dispersion diagram of unit-cell obtained from extracted circuit pa­
ram eters............................................................................................................
23
2.5 CRLH TL resonator, (a) 8 unit-cell realization of CRLH resonator.
(b) E-field plots of CRLH TL at different resonant modes (c) Nu­
m erical versus experim ental resonance peaks........................................
24
2.6 Layout of 4-port series divider....................................................................
25
2.7 Sim ulation and experim ental results for th e 4-port divider of Fig. 2.6.
(a) M agnitude response, (b) Phase response.......................................
27
2.8 Layout of 6-port series divider....................................................................
28
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2.9
E xperim ental results for the 6-port divider of Fig. 2.8 (a) M agni­
tu d e response, (b) Phase response............................................................
30
2.10 Quasi-Yagi antenna, (a) Top-view of fabricated antenna, (b) Ex­
perim ental retu rn loss...................................................................................
2.11 Sparse an ten n a array,
32
(a) Top view; spacing between 2 and 3:
0.184A, spacing between 3 and 4: 0.184A, spacing between 4 and
5: 0.276A, spacing between 5 and 6: 0.184 A, where /= 2 .3 8 GHz.
(b) Theoretical and experim ental radiation p a tte rn s..........................
2.12 F abricated power combiners (a) Combiner A.
(b)Com biner B. . .
33
34
2.13 E xperim ental o u tp u t power spectrum w ith m utual frequency lock­
ing of com biner A ..................
35
2.14 E xperim ental o u tp u t power spectrum w ith external injection lock­
ing. (a) Combiner A. (b) Combiner B .....................................................
35
2.15 M icrostrip patch antennas w ith dimensions p x p m m 2; resonant
length along y-direction. (a) Conventional supporting half-wavelength,
(b) CRLH supporting infinite wavelength.............................................
37
2.16 Infinite wavelength antenna composed of A unit-cells. (a) Model of
proposed design, (b) Dispersion diagram of CRLH unit-cell used
to realize an ten n as.........................................................................................
39
2.17 CRLH anten n a input impedance, (a) Real p a rt (R ). (b) Im aginary
p a rt ( X ) ............................................................................................................
40
2.18 N um erical and experim ental retu rn loss of th e two unit-cell antenna. 42
2.19 Electric-held distribution underneath two unit-cell CRLH antenna
obtained via Ansoft HFSS. (a) Half-wavelength, n = - 1 mode, (b)
Infinite wavelength, n = 0 m ode..................................................................
ix
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42
2.20 Two unit-cell CRLH antenna radiation p attern s, (a) P h i= 0 ° (x-z
plane), (b) Phi= 90° (y-z plane), (c) T heta= 90° (x-y plane), (d)
Experim ental cross-polarizations norm alized to co-polarizations. .
44
2.21 Four unit-cell CRLH antenna radiation patterns, (a) P hi= 0° (x-z
plane), (b) Phi=90° (y-z plane).................................................................
46
2.22 Six unit-cell CRLH antenna radiation patterns, (a) P h i= 0 ° (x-z
plane), (b) Phi= 90° (y-z plane).................................................................
46
2.23 E xperim ental radiation p attern s of dual-m ode antenna, (a) n = 0
m ode showing m onopolar radiation, (b) n = - 1 mode showing patchlike p a tte rn .......................................................................................................
3.1
47
CRLH prism w ith incident wave; 45° angle, (a) Incident wave w ith
/ a ; CRLH has refractive index of +1. (b) Incident wave w ith /# ;
CRLH has refractive index of -1................................................................
51
3.2
D ual-m ode m etam aterial wave-steering concept....................................
52
3.3
Proposed dispersion characteristics for dual-m ode CRLH m etam a­
te ria l...................................................................................................................
52
3.4
M ode selective unit-cell concept.................................................................
53
3.5
Modified CRLH unit-cell for even-/odd-m ode excitation; LH series
capacitance exists for bo th excitation m odes.........................................
3.6
54
Modified CRLH unit-cell w ith parallel coupled series capacitance.
(a) C ircuit model applicable to even-/odd-m ode excitation,
(b)
O dd-m ode excitation equivalent circuit, (c) Even-m ode excitation
equivalent circuit............................................................................................
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55
3.7
A perture coupled m icrostrip lines, (a) Physical m odel consisting
of two substrates sharing common ground plane w ith apertu re slot.
(b)
Equivalent circuit model; aperture slot modeled as ideal tran s­
form er.................................................................................................................
3.8
57
M odel of realized dual-m ode CRLH unit-cell, (a) Perspective view;
era=£ra—2.33, da=df,=0.784 mm. (b) D etailed view; /i= 1 5 mm,
/2=19.34 mm, 73=9.4 mm,
6 mm, ^ = 2 4 mm, 76—10.66 mm,
d—20 mm, uq=u;4=2.33 mm, W2—0-3 mm, ^3 = 0 .5 m m ....................
3.9
58
Equivalent half-circuit model of even- and odd-m ode excited m eta­
m aterial of Fig. 3.8........................................................................................
59
3.10 N um erical dispersion diagram for unit-cell of Fig. 3.8.......................
59
3.11 N um erical in sertio n /retu rn loss of five unit-cell TL for even-/oddmode ex citation..............................................................................................
60
3.12 E xperim ental dispersion diagram for unit-cell of Fig. 3.8.................
61
3.13 Wave steering simulation, (a) Numerical sim ulation space setup.
(b) RH cell, (c) Dual-mode cell...............................................................
64
3.14 E xcitation setup on boundary A for wave steering dem onstration.
65
3.15 Voltage phase distribution for wave-steering dem onstration,
(a)
Even-m ode excitation, (b) Odd-m ode excitation.................................
66
3.16 D ual-m ode flat lens sim ulation setu p ......................................................
67
3.17 Voltage phase distribution for flat lens dem onstration, (a) Even­
m ode excitation, (b) O dd-m ode excitation............................................
68
4.1
O rthogonal feeding m ethod concept........................................................
71
4.2
TE M incident waves on a homogeneous, isotropic structure.
72
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...
4.3
P lo t of (4.7) and (4.8); shaded region represents all possible az­
im uth angles versus power ratios as determ ined by (4.6)..................
4.4
74
A nsoft HFSS sim ulation setup for orthogonal feeding dem onstra­
tion using P PW G ; waveports applied to four sides for sym m etric
b oundary conditions......................................................................................
4.5
75
Poynting vector plot for different power ratios (Py:Px); (3=23 rad /m .
(a) Py:Px= 0:l. (b) Py:Px=0.2:l. (c) Py:Px =QA:l. (d) Py:Px=0.6:l.
(e) Py:Px= 0.8:1. (f) Py :Px= 1:1..................................................................
4.6
76
P lo t of net average Poynting vector azim uth angle versus power
ratio for different propagation constants of the P P W G shown in
Fig. 4.4..............................................................................................................
4.7
Single edge feeding of a two-dimensional leaky-wave stru ctu re for
two-dim ensional scanning............................................................................
4.8
78
Illustration of orthogonally fed, two-dimensional CRLH leaky-wave
an ten n a operating in th e forward fast-wave region..............................
4.9
77
79
2-D CRLH unit-cell, (a) Im plem ented 2-D CRLH unit-cell w ith
p —5.2 mm, u/i=1.0 mm, W2=w^—0.2 mm, and via diam eter, d=0.24
m m on Rogers R T /D uroid 6010 (h = 1.27 mm, ey=10.2). (b) Equiv­
alent circuit m odel.........................................................................................
81
4.10 Brillouin zone for plotting 2-D dispersion diagram; T — X — M — T
represents th e irreducible Brillouin zone................................................
81
4.11 N um erical 2-D dispersion diagram s for unit-cell of Fig. 4.9(b) using
several num erical m ethods...........................................................................
82
4.12 P hoto g rap h of realized orthogonally fed, two-dim ensional CRLH
leaky-wave an ten n a........................................................................................
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84
4.13 N um erical 2-D far-field plots for /= 3 .2 GHz (backward scan, 8=40°), /= 4 .0 GHz (broadside, 0=0°), and f = 5.1 GHz (forward scan,
0= + 4 5 °); Py:Px= 0:1......................................................................................
85
4.14 Far-Held radiation plots for different power ratios (Py\Px)\ f —3.20 GHz
w ith (3=72.5 ra d /m and 0= -40°. (a) Py:Px—0:1, ip=0°. (b) Py:Px= 0.2:1,
9? = 1 8 °.
(c) P y:Px= 0 .4 :l, ^= 28°.
Py:Px= 0.8:1, ^= 4 0 °.
<p—50°.
(d) Py:Px= 0.6:1, <p=34°.
(f) P y:Ps = l : l , <^=45°.
(h) P„:PX=1:0.6, <p=56°.
(e)
(g) P ,:P X=1:0.8,
(i) P y:Px= l:0 .4 , ^ = 6 2 °.
(j)
Py:Px= 1:0.2, ip=72°. (k) P y:Pa= l:0 , v?=90°..........................................
87
4.15 ip rad iatio n angles for leaky-wave antenna of Fig. 4.8; Eq. (4.6)
versus FEM for /?=28.55 rad /m , /3=47.43 ra d /m , and (3=72.50
r a d /m .................................................................................................................
88
4.16 Far-field m easurem ent setup, (a) Front view of m ounted antenna.
(b) Back view of m ounted antenna showing feeding network. . . .
89
4.17 E xperim ental 2-D far-field plots for /= 3 .2 GHz (backward scan,
0=-61°), /= 4 .2 GHz (broadside, 0= 0°), and /= 5 .1 GHz (forward
scan, 0=4-60°); Py :Px= 0:1...........................................................................
90
4.18 E xperim ental versus numerical dispersion diagram .............................
91
4.19 M easured 3-D far-field p attern s (normalized dB-scale) of th e CRLH
leak-wave anten n a a t /= 3 .8 0 GHz. (a) Py:Px—0.16:1. (b) Py:Px= 0A :l.
(c) Py :Px= 1:1..................................................................................................
92
4.20 E xperim ental ip versus numerical ((4.6) and FEM ) tp for /3=24.69 rad /m . 93
4.21 C om puted far-field polarization com ponents for Py :Px = 1Z90°:1Z0°. 94
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L is t o f T a b l e s
2.1
2.2
Sum m ary of num erical input im pedance and corresponding reso­
n an t frequency of proposed an tennas.......................................................
41
E xperim ental results for two, four, and six unit-cell antennas.
45
xiv
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. .
A cknow ledgm ents
I would like to express my sincere g ratitu d e to my advisor, Professor Tatsuo Itoh
for his sup p o rt and guidance through my graduate program . I would especially
like to th an k Dr.
C hristophe Caloz and Dr.
Kevin M.K.H. Leong for their
valuable advice and discussions. In addition, I wish to express my appreciation
to th e m em bers of my com m ittee, Professor Troy C arter, Professor Harold R.
Fetterm an, Professor E th an Y. Wang, and Professor Tatsuo Itoh, for offering their
valuable tim e and comments. I would also like to th an k Mrs. Celina Liebeman
for her wonderful adm inistrative work. I could not have m ade it so far w ithout
the help and sup p o rt of my fellow group members, Dr. I-Hsiang Lin, Dr. Asushi
Sanada, Dr. Tetsuya Ueda, Dr. Naobumi M ichishita, K atie Allen, Eric Ash,
B randon Choi, A lexandre Dupuy, Tim othy Fujishige, D arren Goshi, Cheng-Jung
Lee, Sungjoon Lim, and Wei-Yang Wei. Last b u t not least, I would like to thank
my family and friends for their support in all my endeavors.
xv
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V it a
1979
Born, Hong Kong.
1998
Research A ssistant, Electrical Engineering D epartm ent, K ing’s
College, London, England.
2001
B.E. (Electrical Engineering), Cooper Union, New York, NY.
2001-2003
Network Engineer, Barclays C apital, New York, NY.
2005
M.S. (Electrical Engineering), UCLA, Los Angeles, CA.
2007
Sum m er Intern, Ansoft C orporation, Irvine, CA.
2003-present
G rad u ate Student Researcher, Electrical Engineering, UCLA,
Los Angeles, CA.
P u b l ic a t io n s a n d P r e s e n t a t io n s
A. Lai, Left-Handed M etam aterial Design Using A n so ft D esigner and HFSS,
P ittsb u rg h , PA: A nsoft C orporation, 2007.
N. M ichishita, A. Lai, and T. Itoh, “Dielectric resonator-based dual band lefthanded transm ission line,” Asia Pacific Microwave Conference, Bangkok, T hai­
land, Dec. 2007.
xvi
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N. M ichishita, A. Lai, and T. Itoh, “Proxim ity coupled interconnect using zeroth
order resonant m ushroom stru ctu re,” European Microwave Conference, Munich,
Germany, Oct. 2007.
T. Ueda, A. Lai, N. M ichishita, and T. Itoh, “Leaky-wave radiation from lefthanded transm ission lines composed of a cut-off parallel-plate waveguide loaded
w ith dielectric resonators,” IE IC E Trans. Electron., vol. e-90c, no. 9, pp. 17701775, Sep. 2007.
N. M ichishita, A. Lai, T. Ueda, and T. Itoh, “Tunable dielectric resonator-based
left-handed leaky wave antenna,” International Sym posium on A ntennas and
Propagation, N iigata, Japan, Aug. 2007.
N. M ichishita, A. Lai, T. Ueda, and T. Itoh, “Recent progress of dielectric
resonator-based left-handed m etam aterials,” International Sym posium on Sig­
nals, System s and Electronics, M ontreal, Quebec, C anada, Jul. 2007.
N. M ichishita, T. Ueda, A. Lai, and T. Itoh, “Evanescent-m ode dielectric m eta­
m aterial stru ctu re excited by NRD guide and its application to leaky wave an­
ten n a,” IE E E A P -S /U R S I I n t ’l Symp., Honolulu, HI, Jul. 2007.
A. Lai, K.M .K.H. Leong, and T. Itoh, “Dual-mode m etam aterial w ith backward
and forward wave selectivity,” IE E E -M T T I n t ’l Sym p., Honolulu, HI, Jun. 2007.
T. Ueda, A. Lai, and T. Itoh, “D em onstration of negative refraction in a cutoff
parallel-plate waveguide loaded w ith 2-D square lattice of dielectric resonators,”
xvii
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IE E E Trans. Microw. Theory Tech., vol. 55, no. 6, pp. 1280-1287, Jun. 2007.
A. Lai, K.M .K.H. Leong, and T. Itoh, “Infinite wavelength resonant antennas
w ith m onopolar radiation p a tte rn based on periodic stru ctu res,” IE E E Trans.
A ntennas Propag., vol. 55, no. 3, pp. 868-876, Mar. 2007.
W.Y. Wu, A. Lai, C.W . Kuo, K.M .K.H. Leong, and T. Itoh, “Efficient FD TD
m ethod for analysis of m ushroom -structure based left-handed m aterials,” IE T
Microw. A ntennas Propag., vol. 1, no. 1, pp. 100-107, Feb. 2007.
K.M .K.H. Leong, A. Lai, and T. Itoh, “Power combining oscillator array using
m etam aterial based injection locking coupling network,” A sia Pacific Microwave
Conference, Yokohama, Japan, Dec. 2006.
T. Ueda, A. Lai, N. M ichishita, and T. Itoh, “Leaky-wave radiation from lefthanded transm ission lines composed of a cut-off parallel-plate waveguide loaded
w ith dielectric resonators,” A sia Pacific Microwave Conference, Yokohama, Japan,
Dec. 2006.
T. Ueda, A. Lai, and T. Itoh, “Negative refraction in a cut-off parallel-plate
waveguide loaded w ith two-dimensional lattice of dielectric resonators,” European
Microwave Conference, M anchester, UK, Sep. 2006.
A. Lai, K.M .K.H. Leong, and T. Itoh, “Leaky-wave steering in a two-dimensional
m etam aterial stru ctu re using wave interaction,” IE E E -M T T I n t ’l Sym p., San
Francisco, CA, Jun. 2006.
xviii
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A. Lai, K.M .K.H. Leong, and T. Itoh, “Dual-mode com pact m icrostrip antenna
based on fundam ental backward wave,” Asia Pacific Microwave Conference, Suzhou,
China, Dec. 2005.
K.M .K.H. Leong, A. Lai, and T. Itoh, “A pplication of a series coupler based on
infinite wavelength phenom ena,” Asia-Pacific Microwave Conference, Suzhou,
China, Dec. 2005.
A. Lai, K.M .K.H. Leong, and T. Itoh, “Novel series divider for antenna arrays
w ith a rb itrary element spacing based on a com posite rig h t/left-handed transm is­
sion line,” European Microwave Conference, Paris, France, Oct. 2005.
W.Y. Wu, A. Lai, K.M .K.H. Leong, C.W . Kuo, B. H oushm and, and T. Itoh,
“Efficient FD T D m ethod for analysis of left-handed m ushroom stru ctu re using
system identification m ethod,” European Microwave Conference, Paris, France,
Oct. 2005.
C. Caloz, A. Lai, and T. Itoh, “The challenge of hom ogenization in m etam ateri­
als,” New Journal o f Physics, vol. 7, no. 167, pp. 1-15, Aug. 2005.
A. Lai, W .Y. Wu, K.M .K.H. Leong, T. Itoh, and C. Caloz, “Q uasi-optical m a­
nipulations of microwaves using m etam aterial interfaces,” IE E E A P -S /U R S I I n t ’l
Symp., W ashington D.C., Jul. 2005.
A. Lai, K.M .K.H. Leong, and T. Itoh, “A novel N -port series divider using infinite
wavelength phenom ena,” IE E E -M T T I n t ’l Sym p., Long Beach, CA, Jun. 2005.
xix
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A. Lai, C. Caloz, and T. Itoh, “Com posite right/left-handed transm ission line
m etam aterials,” IE E E Microwave Magazine, vol. 5, no. 3, pp. 34-50, Sep. 2004.
C. Caloz, A. Lai, and T. Itoh, “Wave interactions in a LH m ushroom stru ctu re,”
IE E E A P -S U S N C /U R S I N ational Radio Science M eeting, Monterey, CA, Jun.
2004.
A. Lai, “Left-H anded M etam aterial-B ased Microwave Devices,” Presented at
Raytheon, Tuscon, AZ, Sep. 2007.
A. Lai, K.M .K.H. Leong, T. Itoh, and C. Caloz, “Analysis and design of lefthanded m etam aterial lenses using Ansoft HFSS,” Presented at Ansoft Converge
Workshop, Los Angeles, CA, Oct. 2005.
xx
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A b s t r a c t o f t h e D is s e r t a t io n
O ne- a n d T w o -D im e n sio n a l M icro w a v e D e v ic e s
B a se d o n L eft-H a n d ed M e ta m a te r ia ls
by
A n th on y Lai
D octor of Philosophy in Electrical Engineering
University of California, Los Angeles, 2007
Professor Tatsuo Itoh, Chair
The analysis, design, and application of novel one- and two-dim ensional lefthanded (LH) m etam aterial microwave devices are presented. T he concept of LH
m aterials is discussed and a general transm ission line approach tow ards th e re­
alization of practical LH m aterials is presented. In particular, it is shown th a t a
com posite rig h t/left-h an d ed (CRLH) m etam aterial is a general model of a prac­
tical LH m etam aterial th a t includes parasitic effects. These parasitic effects are
not detrim ental, b u t rath er provide th e unique characteristics of th e CRLH m eta­
m aterial such as supporting infinite wavelength modes, negative refractive index,
and fundam ental leaky-waves. Several microwave devices based on exploiting the
CRLH m etam aterial’s characteristics are described in this dissertation.
T he fundam ental infinite wavelength supported by th e CRLH m etam aterial
is used to realize a IV-port series divider.
This A/"-port series divider evenly
divides power in m agnitude and phase to an arb itrary num ber of o u tp u t ports; the
divider’s perform ance is not dependent on its length or th e location of its output
ports. T he C R LH ’s infinite wavelength is also used to realize size independent
planar resonant antennas. It is shown th a t the supported infinite wavelength
xxi
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gives rise to a m onopolar radiation p attern . Numerical and experim ental d ata
are used to verify th e iV-port series dividers and infinite wavelength resonant
antennas.
By modifying th e CRLH unit-cell for even-/odd-m ode excitation, a mode
selective m etam aterial is dem onstrated.
This dual-m ode CRLH m etam aterial
can have either a negative or positive refractive index w ithin th e same frequency
band.
A one-dim ensional prototype of this novel dual-m ode m etam aterial is
realized and th e dual-m ode concept is extended to two-dimensions by numerical
simulation. D ual-m ode wave steering and re-focusing/de-focusing w ith th e twodimensional dual-m ode m etam aterial are presented.
The fundam ental leaky-wave mode supported by the CRLH m etam aterial is
used to realize a two-dim ensional CRLH leaky-wave antenna. Elevation scan­
ning of th e resulting leaky-wave radiation is achieved by varying th e operational
frequency of th e antenna. By applying a novel orthogonal feeding m ethod to
the CRLH leaky-wave antenna, azim uth steering of the leaky-wave radiation is
achieved w ithout utilizing phase-shifters. The theory behind th e orthogonal feed­
ing m ethod is presented. Numerical and experim ental results are used to validate
the orthogonal feeding m ethod.
xxii
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CHAPTER 1
L eft-H a n d ed M e ta m a te r ia ls
1.1
In tro d u ctio n
Over th e last century, researchers have used m etam aterials to engineer elec­
trom agnetic properties not readily available in nature.
These electrom agnetic
m etam aterials are effectively homogeneous artificial structures whose lattice con­
stants are much sm aller th a n the applied electrom agnetic wave. In particular,
researchers have used m etam aterials to tailor a m aterial’s p erm ittiv ity (e) an d /o r
perm eability (/x). U ntil recently, only double positive (s > 0, //, > 0), single neg­
ative electric (e < 0), and single negative m agnetic (/x < 0) m etam aterials, as
shown respectively in quadrant I, II, and IV of Fig. 1.1, have been investigated.
The com bination of q u ad ran t III was not investigated since no natu rally occurring
double negative (e < 0, jn < 0) m aterial has yet to be discovered. The Russian
scientist, V ictor Veselago, is credited to being th e first person to have speculated
about th e existence of double negative materials; in his 1967 paper entitled “The
electrodynam ics of substances w ith sim ultaneously negative values of e and /x,”
Veselago discussed th e unique phenom ena occurring for an electrom agnetic wave
in a double negative m aterial [1]:
1. Electric field, m agnetic field, and wavevector form a left-handed (LH) triad.
2. Negative refractive index leads to reversal of Snell’s Law, Doppler Effect,
1
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and Vavilov-Cerenkov radiation.
3. Frequency dispersion.
f l (Perm eability)
1
plasm a
air
wire structure
air
conventional
(RH)
k
/T > 0.//> 0
n-
N o transm ission
+ £
IV
LHMs
air
/ ; < 0 , //< ()
air
(Permittivity)
ferrites
split rings structure'
i: s-ti, it ■'()
No transm ission
Figure 1.1: e - n diagram [1],
1.1.1
B ackw ard W aves
Since an electrom agnetic wave in a double negative m aterial forms a LH triad,
double negative m aterials are generally referred to as LH m aterials. A LH triad
means th a t power flows away from th e source (group velocity is positive) while
the phase front travels tow ards the source (phase velocity is negative). Therefore,
LH m aterials support backward waves; waves w ith anti-parallel group and phase
velocities. This backw ard wave phenom enon can be observed in Fig. 1.2, which
shows th e electric field m agnitude plot of an air-filled rectangular waveguide with
its middle section filled w ith a fictional LH m aterial of er= -l and jir= -1. The
m agnitude plot shows th a t power is transferred from the in p u t to th e ou tp u t of
the waveguide, while th e phase front travels backwards.
2
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RH |
LH | RH
Figure 1.2: Effective m edium LH m aterial sim ulation [2] in Ansoft HFSS. R ect­
angular waveguide w ith middle section filled w ith LH m aterial (er = - l, p r = -l);
backward wave can be observed by observing phase front for different phases.
1.1.2
N eg a tiv e R efractive Index
Since e and // are negative, th e refractive index of a LH m aterial is negative.
The sign of th e refractive index is usually taken as positive, however, Veselago
showed th a t if a m edium has bo th negative p erm ittivity and negative perm eabil­
ity, th e negative sign m ust be taken:
n
\J (
£ y )(
(J>r)
\ / Erl-I>r ■
( I ’-O
This negative refractive index means th a t an obliquely incident wave from
a conventional (i.e.
right-handed (RH)) m aterial onto a LH m aterial will be
negatively refracted as shown in Fig. 1.1. T he Ansoft HFSS sim ulation of an
effective m edium LH m aterial flat lens [5] is shown in Fig. 1.3, which dem onstrates
the negative refraction as a direct result of Snell’s Law:
3
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riiH sin(0LH ) =
(1.2)
n R H s i n ( 6 n H )-
A negative angle of refraction occurs because ulh has a negative value.
RH Material
..
,
A *.
LH Material
' v.
-v .
V
focus
4 s o u r c e '•
jP '
—?RJ)'
Sp
BLH k> N
'
(a)
(b)
Figure 1.3: A nsoft HFSS sim ulation of negative refraction using effective medium,
(a) F lat lens model consisting of a RH m aterial interfaced w ith a LH m aterial;
cylindrical wave source excited in RH m aterial, (b) M agnitude plot of electric
field showing focusing in LH m aterial.
1.1.3
Frequency D ispersion
Veselago also stated th a t a LH m aterial will have frequency dispersion, which
means th a t its propagation constant (8) is a nonlinear function of frequency.
Therefore, a LH m aterial will not have constant values of e and // over a wide
frequency range unlike RH m aterials [1]. Instead, e and fi vary depending on the
frequency of operation. In Section 1.3, this frequency dispersive natu re of LH
m aterials is fu rther discussed.
4
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1.2
R ealization : R eson an t A pproach
In his paper, Veselago also stated th a t although LH m aterials do not exist
in nature, they can be artificially constructed. In particular, Veselago concluded
th a t th e realization of a LH m etam aterial will be possible w ith th e discovery or
construction of an isotropic negative )i m aterial. W hen Veselago published his
paper, m aterials w ith n < 0 were not known to exist.
For 30 years, Veselago’s paper and its theory was not investigated any fur­
ther. Interest in Veselago’s paper and LH m aterials begin to m aterialize when
Professor P endry a t Im perial College dem onstrated the first non-ferrite negative
fj, m etam aterial based on split ring resonators (SRRs) in 1998 [6 ]. P en d ry ’s SRR
was th e cornerstone of th e first bulk LH m etam aterial realization by a group at
University of California, San Diego (UCSD) in 2000 [7]. T he U CSD ’s LH m eta­
m aterial was based on combining a SRR (-/i) w ith a m etal wire (-£•). T he UCSD’s
LH m etam aterial unit-cell is shown in Fig. 1.4(a). By periodically cascading the
unit-cell in three-dim ensions, th e UCSD group constructed a bulk LH m etam ate­
rial, shown in Fig. 1.4(b), to confirm negative refraction. It should be noted th a t
periodicity is not a requirem ent to realize a m etam aterial; only average cell size
m atters in term s of macroscopic param eters [3], periodicity allows for analytical,
com putational, and fabrication simplicity.
SRR-based LH m etam aterials only exhibit LH properties around the reso­
nance of th e SRR, Therefore, realization of LH m etam aterials using SRRs are
known as th e resonant approach. In term s of microwave engineering applica­
tions, th e resonant approach towards LH m etam aterials is not practical for the
following reasons:
• Bulky, not applicable to planar microwave circuits.
5
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(b)
(a )
Figure 1.4: SRR-based LH m etam aterial; m etal wire provides negative e and
SRR provides negative fx. (a) Unit-cell, (b) Two-dimensional SRR-based LH
m etam aterial.
• N arrow -band due to requirem ent of operation near SR R resonance.
• Lossy due to requirem ent of operation near SRR resonance.
1.3
R ealization : T ransm ission Line A pproach
To overcome th e drawbacks of SRR-based LH m etam aterials for microwave
engineering applications, several researchers [8 ]-[10 ] soon realized th a t a backward
wave transm ission line can be used to realize a non-resonant LH m etam aterial.
This transm ission line approach towards LH m etam aterials is based on th e dual
configuration of a purely RH /conventional transm ission line (TL). T he homoge­
neous model of a purely RH (PRH) and purely LH (PLH) lossless TL are shown
in Fig. 1.5(a) and 1.5(b), respectively. The PR H TL can be used to model a RH
m aterial, while th e PLH TL can be used to model a LH m aterial. As depicted
in Fig. 1.5(a), th e PR H TL can be represented as th e com bination of a per-unit
length series inductance L'R and a per-unit length shunt capacitance C'R. The
PLH TL is th e com bination of a tim es-unit length series capacitance C'L and a
tim es-unit length shunt inductance L'l as shown in Fig. 1.5(b).
6
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C'l/A z
L'r AZ
o-----
o
-o
if
■o
L'l/A z
=r
o
o
■o
Az
■o
(a)
Figure 1.5: Equivalent circuit model, (a) Homogeneous P R H TL. (b) Homoge­
neous PLH TL.
T he propagation constant of a T L 1 is defined as 7 = jf3 — V Z 'Y ' , where
Z’ and Y ’ are th e per-unit length im pedance and per-unit length adm ittance,
respectively. In th e case of th e PRH TL, th e propagation constant is
PRH
>PRH
1 PRH = j/3PRH = \] ( ju L 'R) (jujC'R) = ju j ^ L 'RC'R,
(1.3)
while for th e PLH TL, th e propagation constant is
,PLH = j pPLH
By p lotting a uo—(3 diagram , commonly referred to as a dispersion diagram , the
group velocity (vg = cLu/d(3) and phase velocity (vp = oj//3) of a circu it/m aterial
can be directly observed. T he dispersion diagram of th e PR H and PLH TL are
shown in Fig. 1.6(a) and 1.6(b), respectively.
The group velocity and phase velocity of these TLs can be inferred from their
dispersion diagram . The dispersion diagram s of Fig. 1.6 show th a t vg and vp of
the PR H TL are parallel (vgvp > 0), while vg and vp for a PLH TL are antipar­
allel (vgVp < 0). In addition, the PLH T L ’s dispersion diagram shows th a t vg
approaches infinity as uj increases. However, this is not physically possible since it
1Lossless case considered for simplicity.
7
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G>
CO
/ +pc
,+Pc
-p c \
(3
P
(a)
(b)
Figure 1.6: Dispersion diagram s for th e TLs of Fig. 1.5. (a) PR H TL [3]. (b)
PLH TL [3].
violates E instein’s special theory of relatively. Consequently, a PLH TL does not
exist in n atu re and since RH parasitic effects are unavoidable, a synthetic PLH
TL is not possible. Instead, the unit-cell model of Fig. 1.5(b) has to be modified
to account for unavoidable parasitic effects w ith any practical realization of a LH
TL. To see w hat these parasitic effects are, a distributed realization of a RH and
LH TL is first considered. A RH m icrostrip TL is shown in Fig. 1.7(a) and consists
of a ground plane and trace separated by a dielectric substrate. The current flow
along th e trace of th e m icrostrip line gives rise to a series inductance, while the
voltage gradient between th e trace and ground plane gives rise to a shunt capaci­
tance. Therefore, th e RH unit-cell circuit model can accurately model a RH TL.
Fig. 1.7(b) is a m icrostrip im plem entation of a m icrostrip LH TL, which is based
on th e Sievenpiper m ushroom unit-cell [11]. T he edge coupling between adjacent
m etal patches contributes to th e series capacitance, while th e via connecting the
m etal patch to th e ground plane provides th e required shunt inductance. Besides
these LH contributions, RH parasitic effects also occur w ith th e im plem entation
of th e LH TL; series inductance due to current flow on th e m etal patch and shunt
8
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capacitance from th e voltage gradient between th e m etal patch and the ground
plane. Therefore, th e LH unit-cell circuit model of Fig. 1.5(b) does not take into
account th e unavoidable RH effects th a t occur w ith any practical realization of
a LH TL.
perspective view
perspective view
series capacitance
series inductance
shorting post (via)
side view
side view
shunt capacitance
shunt inductance
(b)
(a )
Figure 1.7: D istributed realization of unit-cells shown in Fig. 1.5 [4], (a) RH
m icrostrip TL. (b) LH m icrostrip TL consisting of periodic cascade of Sievenpiper
mushroom unit-cells.
1.3.1
C om p osite R ig h t/L eft-H a n d ed Transm ission Line
A PLH TL cannot be physically realized due to RH parasitic effects.
As
a result, a PLH TL is a more general model of a com posite right/left-handed
(CRLH) TL, which also includes RH attrib u tes. T he general model of a CRLH
TL is shown in Fig. 1.8 and consists of a series RH inductance L'R, a series LH
capacitance C'L, a shunt RH capacitance C'R, and a shunt LH inductance L'l .
Therefore, Z’ and Y ’ are defined as
9
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Z l ---------------------,
;
z cy/Az j
II
!
!
1
H i
U
1
iC'nAZzj—
vi
J
Ly/Az j
T
5---------------------------- --------0
Az
Figure 1.8: Equivalent circuit model of homogeneous CRLH TL.
Z ' (w) = j ( u L'r -
,
(1.5)
r
(co) = j { u C ’R -
.
Following th e sam e procedure as for th e PR H and PLH TL, th e dispersion
relation for th e CRLH TL is
7
C RL H
jP(<v) = s (u > )jJ u 2L'RC'R +
C'r.
( 1 .6 )
where
-1
if
lu <
cnri = min(
s(ui) = <
(1.7)
+1
if
d
> cor 2 = m ax(-
A = ).
r >rv '
E xam ination of (1.6) reveals th a t th e phase constant /? can be real or imag­
inary.
A pass-band is present in th e frequency range where f3 is purely real
(7 = jP )- O n th e other hand, in the frequency range where (3 is purely im aginary
10
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(7 = a ), a stop-band occurs. In addition, th e characteristic of th e CRLH TL can
be inferred from (1.6). For low frequencies, th e LH attrib u tes are dom inant and
the RH a ttrib u tes are dom inant for high frequencies. The dispersion diagram of
a CRLH TL is shown in Fig. 1.9, which is based on (1.6). This diagram shows
th a t th e CRLH TL has an LH {vgvp < 0) region a t low frequencies and a RH
(VgVp > 0) region a t high frequencies. In addition, th e pass-band and stop-band
m entioned above can be observed; the stop-band is a unique characteristic of the
CRLH TL which does not appear in th e PR H or PLH TLs.
0)
-P c
+pc
Figure 1.9: D ispersion diagram for the homogeneous CRLH TL (unbalanced).
T he stop-band of th e CRLH TL can be elim inated when th e series and shunt
resonances are equal. This is known as the balanced case and occurs when
L'r C'l = L'l C'r ,
( 1 .8 )
which m eans th a t th e LH and RH attrib u tes exactly balance each other at a
specific frequency.
T he more general case of th e CRLH TL is known as the
unbalanced case where th e series and shunt resonances are not equal. It can be
shown th a t under th e balanced condition, ( 1 .6 ) reduces to
11
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where j3 is separated into th e RH phase constant
and th e LH phase constant
/3 l■ T he dual n atu re of th e CRLH TL is clearly illustrated by (1.9). In addition,
a seamless tran sitio n from LH-ness to RH-ness occurs since @ is always purely
real; uj0 = tu n = ojv2 for th e dispersion diagram of Fig. 1.9. T he seamless LH to
RH tran sitio n occurs at
unbalanced
balanced
i/L 'RC'RL'LC'L
^U C '
( 1 .1 0)
where uiQ is known as th e transition frequency. At this tran sitio n frequency, a
traveling wave (vg ^ 0) w ith an infinite wavelength ( \ g = 2ir/\(3\, j3 = 0) is
supported.
Therefore, in th e balanced case, phase advance occurs in th e LH
region, phase stagnation occurs at the transition, and phase delay occurs in the
RH region.
T he equivalent CRLH TL model can be related to the constitutive param eters
of a CRLH m aterial (i.e. /i, e). First, equating th e propagation constant of a
TL ( 7 = j/3 = V Z 'Y ') w ith th e propagation constant of a m aterial (/3 =
allows th e following to be setup
- oj2/i £ = Z 'Y '.
( 1 . 11 )
N ext, th e characteristic im pedance (Z 0 — \ j Z ' / Y ') of th e CRLH TL needs
to be defined, which is
unbalanced
balanced
12
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( 1 . 1 2 a)
Z L = \l-p jr,
(1.12b)
,LI
yR
Z r = \ I ^ T~V(>
( 1 .1 2 c )
where Z l and Z r are th e PLH and PRH characteristic im pedances, respectively.
Now, th e
T L ’s characteristic im pedance can be related to th e m aterial’s intrinsic
im pedance (77 = \Z fi/e ) by the following relationship
Z 0 = V or
~
Y
= -.
£
(1.13)
E quations (1.11) and (1.13) can be used to relate the perm eability and per­
m ittivity of a m aterial to th e im pedance and adm ittance of its equivalent TL
model,
lx = J ^ = L 'R ~ Z p c rL '
(L14a)
e=
(1.14b)
=
13
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1 .3 .1 .1
P h y s ic a l R e a liz a tio n
T he above section discussed homogeneous CRLH TLs, which do not appear to
exist in n atu re. However, CRLH TLs th a t are effectively homogenous 2 in a certain
range of frequencies can be realized [3]. By cascading the LC unit-cell shown in
Fig. 1.10 in a nonperiodic or periodic fashion, an effectively homogeneous CRLH
TL of length d can be formed. In general, periodicity is preferred for com putation
and fabrication convenience.
C n =±=
A0
Figure 1.10: LC model of CRLH unit-cell.
T he unit-cell of Fig. 1.10 is dimensionless unlike the increm ental model shown
in Fig. 1.8. However, a physical length p will be associated w ith th e capacitors
and inductors used. In th e lim it p = A z —> 0, th e LC unit-cell is equivalent
to th e increm ental model.
Therefore, by cascading th e LC unit-cell w ith the
homogeneity condition, p —*■0, a CRLH TL of length d can be constructed. In
practice, th e hom ogeneity condition can be defined as
2The electrom agnetic wave’s guided wavelength is much larger th a n the discontinuities of
the structure.
14
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T he hom ogeneity condition of (1.15) ensures th a t th e electrical length of the
unit-cell is sm aller th a n n /2 . As a result, th e CRLH TL appears homogeneous
to th e propagating electrom agnetic wave.
By applying Bloch-Floquet periodic boundary conditions (PBCs) [3] to the
LC unit-cell of Fig. 1.10, th e LC dispersion relation
^ H
= “ cos“ 1
+
>
(L16)
is obtained, where th e series im pedance (Z ) and shunt adm ittance (Y ) of the LC
unit-cell are given by
z
M =j
(u L r
-
,
(1.17)
Y ( U) = j ( u C R - zf c ) .
U nder th e hom ogeneity condition, th e Taylor approxim ation cos(/3p) m 1 —
{(ip)2/2 can be applied and Eq. 1.16 becomes
0M
= sM
^ LsCr + - j J
_ _
(Y l + 2 s ) ,
(1.18)
which is identical to th e homogeneous dispersion relation of (1.6) w ith L'R =
Lr/p,
C'r = C r / p , L'l = L Lp , and C'L = CLp.
This result shows th a t the
LC-based CRLH TL is equivalent to th e homogeneous CRLH TL under th e ho­
mogeneity condition.
To physically realize th e LC CRLH unit-cell of Fig. 1.10 either lum ped com­
ponents, d istrib u ted technology, or a com bination of th e two can be used. Sev­
eral common im plem entations of CRLH unit-cells are shown in Fig. 1.11.
15
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In
general, d istrib u ted im plem entation is preferred over lum ped com ponent imple­
m entation for fabrication simplicity and for use in radiative applications. The
interdigital capacitor-based unit-cell of Fig. 1.11(b) is com monly used to realize
one-dim ensional CRLH m etam aterial, while th e Sievenpiper m ushroom unit-cell
of Fig. 1.11(c) is commonly used to realize two-dimensional CRLH m etam aterials.
capacitors
n~n
r|
m etal pads
™ (provides RH effects)
inductor
'v ia to gnd
P
(a)
(b)
(c)
Figure 1.11: Physical realization of LC CRLH unit-cell shown in Fig. 1.10. (a)
Lum ped com ponents based on surface m ount technology, (b) D istributed imple­
m entation on m icrostrip technology; series capacitance from interdigital capacitor
and shunt inductance from shorted stub, (c) D istributed im plem entation on mi­
crostrip technology using Sievenpiper m ushroom structure.
16
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CHAPTER 2
In fin ite W a v elen g th D e v ic e s
2.1
In tro d u ctio n
In this chapter, th e fundam ental infinite wavelength (/3 = 0, uj / 0) supported
by th e CRLH m etam aterial is discussed. This infinite wavelength phenom enon
can be used to realize microwave devices not possible before w ith RH m aterials
alone.
To d em onstrate th e unique properties of this infinite wavelength phe­
nomenon, several microwave devices have been realized. In particular, IV-port
series dividers [12 ] and infinite wavelength resonant antennas w ith monopolar
p attern s [13] are presented in this chapter. A pplications of these novel microwave
devices are also discussed.
2.2
In fin ite W avelen gth T h eory
In Section 1.3.1, th e unique dispersion characteristics of th e CRLH m etam ate­
rial was discussed. It was m entioned th a t a tran sitio n from LH to RH dispersion
occurs. A t th is transition, (5 is zero at a non-DC frequency; this m eans th a t an
infinite wavelength can be supported by th e CRLH m etam aterial TL. In general,
the series and shunt resonance of th e CRLH unit-cell are not equal. Therefore,
a stop-band appears between th e LH and RH ranges as illu strated in Fig. 1.9
which results in two infinite wavelength frequency points. These two points are
17
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
determ ined by th e series (case) and shunt (ujsh) resonance of th e CRLH unit-cell
which are defined as
1
and
1
Ush
^ c jr L
(2 . 1)
T he CRLH m etam aterial TL supports a wave w ith an infinite wavelength at
bo th loy\ and u>r2 , where u'ri= m in(u;se.; a;s/l) and cur2=m ax(u;se, Lush)-
2.2.1
Z eroth Order R esonance
An infinite wavelength w ith a non-zero group velocity can be supported by
a balanced (cuse = cush) CRLH m etam aterial TL. W hile for th e unbalanced case
(cuse ^ ujsh), a stop-band occurs which does not allow for guided wave propagation.
For either th e balanced or unbalanced case, th e CRLH m etam aterial TL can be
used as a infinite wavelength resonator. The microwave devices discussed in this
chapter are based on th e CRLH infinite wavelength resonator.
To u n d erstan d th e infinite wavelength resonance and th e resonance conditions
of th e CRLH m etam aterial TL, a review of resonator theory is presented. A
conventional (i.e. RH) open- or short-circuit TL of physical length, I, can be
used to realize a resonator w ith resonance condition described by
mr
Pn =
( 2 .2 )
where 0 n is th e phase constant of resonance mode n [14]. For th e conventional
TL resonator, n has to be a non-zero, positive integer. In th e case of a CRLH
TL resonator, n can also be a negative integer or even zero. Fig 2.1(a) shows
a CRLH m etam aterial TL of length, L= N p w ith its resonance modes shown
18
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
in Fig. 2.1(b). From (2.2), a CRLH TL resonator w ith n = 0, referred to as a
zeroth order resonator (ZOR), is able to support an infinite wavelength which is
independent of th e T L ’s physical length, L [14].
1
2
3
N
CRLH TL
m -T i
1—►
L=N*p
(a)
CO
CD
CD
CD,
n
(b)
Figure 2.1: CRLH resonator, (a) CRLH resonator consisting of N unit-cells. (b)
Dispersion diagram of CRLH resonator showing resonance modes; u se and ojsh
can be reversed.
As shown in Fig. 2.1(b), there exists two infinite wavelength points for the
unbalanced CRLH m etam aterial.
The n = 0 m ode for th e unbalanced case is
determ ined by th e boundary condition applied to the in p u t an d o u tp u t of the
CRLH m etam aterial resonator. In th e case of short-circuit boundary conditions,
as shown in Fig. 2.2(a), th e shunt com ponents of th e CRLH unit-cell are elim­
inated. Therefore, th e series resonance (ojse) determ ines th e n = 0 resonance for
short-circuit boundary conditions. The input im pedance for short-circuit bound-
19
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ary conditions is given by
/3^0
Zin,a.c. — - j Z 0tan((3L) « - j Z 0j3L = N Z .
(2.3)
In th e case of open-circuit boundary conditions, as shown in Fig. 2.2(b), th e series
com ponents of th e CRLH unit-cell are elim inated. Therefore, th e shunt resonance
(ojsh) determ ines th e n = 0 resonance for open-circuit boundary conditions. The
input im pedance for th e case of open-circuit boundary conditions is given by
/3 -0
Z in,0.c. = ~ j Z 0 cot(f3L)
c l/ n
short-circuit
(2.4)
- J Z J P L = 1/N Y .
n *l r
CRLH TL
+ -►
(a)
open-circuit
CRLH TL
.Lm
0
O" ......................
W*CR
O
(b)
Figure 2.2: Infinite wavelength resonance boundary conditions, (a) Short-circuit
boundary condition w ith equivalent circuit, (b) O pen-circuit boundary condition
w ith equivalent circuit.
20
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2.3
N -P o r t Series D ivid er
Power dividers of various types are regularly used in microwave applications
such as signal dividing for amplifier chains, an ten n a array feeds, or distribution to
sub-systems. There are two classes of dividers, parallel or series, each having their
own advantages and disadvantages [15]. B oth topologies are generally scalable
to accom m odate an N num ber of divisions.
This usually comes w ith added
complexity and larger size. Due to the parallel divider’s fundam ental three port
shape, parallel divider based feed networks are usually large in com parison to
series divider based feed networks [16]-[17]. Series dividers are usually used over
parallel dividers in applications where power needs to be equally divided to a large
num ber of elem ents and where th e physical area of the feed network is limited.
For example, series dividers can be used to feed antenna arrays.
In order to
ensure th a t each an ten n a element w ith a predefined element spacing is fed with
an equal am plitude and equal phase signal, a m eander line is usually used such
th a t power can be tap p ed from the series feed line at locations which are integer
multiples of th e guided wavelength. This m eander line adds com plexity to the
series divider design and places spacing restrictions on th e anten n a elements in
the array.
To address th e size and design complexity of conventional power dividers for
equal m agnitude and phase division, a novel A -p o rt series divider based on the
CRLH infinite wavelength resonator is presented in this section. In particular,
there is no lim itation on th e num ber of ports or th e location of th e ports along the
divider for equal am plitude and equal phase power division. T he concept behind
the proposed divider is illustrated in Fig. 2.3; th e m agnitude and phase at all
points along a CRLH TL supporting an infinite wavelength are identical. As a
result, th e physical length of th e divider or th e position of th e power tap s has no
21
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
effect on th e phase and power balance between each o u tp u t p ort. Furtherm ore,
the divider can be easily expanded to accom m odate an N num ber of ports.
i
©H
d,
t
d2
□
t
d3
E3u
'
t
’ '
t
E2
CRLH TL with
■*i
Figure 2.3:
Infinite wavelength Af-port series divider,
(d i,d 2,d,3 , ...) and physical length (L) is arbitrary.
2.3.1
element spacing
C R LH U n it-C ell
An open-circuit CRLH TL resonator com parable to th e one presented in [14]
is used to design th e novel iV-port series divider. The unit-cell used to realize the
CRLH TL is depicted in Fig. 2.4(a) w ith a period, p=11.6 mm. T he interdigital
capacitor provides C l and th e short stub provides L l while th e RH capacitance
(Cr) is a ttrib u te d to th e parallel plate natu re of th e interdigital capacitor and
the RH inductance ( Lr ) is a ttrib u ted to th e current flow on th e conductor [3].
The su b strate used is Rogers R T /D uroid 5880 w ith dielectric constant er=2.2 and
thickness h = 1.57 mm. These dimensions are chosen to create a CRLH TL w ith an
infinite wavelength frequency around 2.3GHz ~ 2.4 GHz. P aram eter extraction
yields LC values of C l= 1 .27 pF, C r= 1 .45 pF, L l = 3.27 nH, and L ^=3.21 nH
corresponding to f sh=2.31 GHz and / se=2.49 GHz. The dispersion diagram of
this unit-cell is shown in Fig. 2.4(b).
By cascading N unit-cells of Fig. 2.4(a), a CRLH TL of length, L= N p can
be realized. Eight unit-cells of Fig. 2.4(a) are cascaded to realize th e CRLH TL
resonator shown in Fig. 2.5(a). Coupling capacitors w ith values of 0.5 pF are
22
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
j series
interdigitai ca p a citor
4.8 mm
9.9 mm
10.4 mm
shunt stub to ground
via (radius: 0.12 mm)
(a)
6
5
4
>»
3
1
0
0.0
0.2
0.4
0.6
0.8
1.0
Pp/n
(b)
Figure 2.4: CRLH TL unit-cell, (a) Unit-cell details; w idth of fingers are 0.3 mm,
w idth of stu b is 1.0 mm, and gaps are all 0.2 mm. (b) D ispersion diagram of
unit-cell obtained from extracted circuit param eters.
23
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used to increase th e transferred power since weak coupling is not of interest for
the divider design.
Cftpsng capacitor* -
PTT
3
(a)
n=0
f=2.28 GHz
n=-1
f=1.86 GHz
n=-2
f=1.56GHz
-10-
IF'
■o
-2 0 -
- - MoM
— Exp.
-3 0 -
0.5
1.0
1.5
2.0
2.5
3.0
F requency (GHz)
(b)
(c)
Figure 2.5: CRLH TL resonator, (a) 8 unit-cell realization of CRLH resonator,
(b) E-field plots of CRLH TL at different resonant modes (c) Num erical versus
experim ental resonance peaks.
In addition, M ethod of M oment (MoM) sim ulations are used to confirm
Fig. 2.5(a)’s CRLH nature.
A 2.28 GHz and 2.32 GHz infinite wavelength
frequency is obtained by MoM and m easurem ent, respectively.
These results
show good agreem ent between the predicted resonant frequency of 2.31 GHz and
M oM /experim ental results.
T he numerical and experim ental resonances from
1.0 GHz to 3.0 GHz of th e CRLH resonator are shown in Fig. 2.5(c). In ad­
dition, Fig. 2.5(b) shows th e CRLH natu re of the im plem ented CRLH TL; at
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
n = 0 an infinite wave is supported and for n < 0 , th e wavelength is proportional
to frequency.
2.3.2
4-P ort Series D ivider
To d em onstrate th e novel series divider, th e CRLH TL resonator of Fig. 2.5(a)
was modified as shown in Fig. 2.6 in order to sim ultaneously maximize power to
the o u tp u t p o rts and not to detrim entally affect th e resonance condition. P o rt 1
is used as th e feed p o rt and th e other three ports are o u tp u t ports. A 1.5 pF
coupling capacitor is used at th e feeding p ort to maximize th e transferred power
to th e o u tp u t ports.
4.8
mm
H i- ,,,
b
q
“ 1.4 mm
0.2 pF SMT
capacitor
4.8
25 mm
mm
Hl
1.5 pF SMT
capacitor
103 mm
Figure 2.6: Layout of 4-port series divider.
As seen in Fig. 2.6, th e o u tp u t ports are connected to th e CRLH TL at the
stub ends w ith 0.2 pF capacitors. Currently, th e only lim itation on p o rt location
is th e size of th e unit-cell used to realize th e CRLH TL. In th e lim it th a t the
unit-cells are infinitesim ally small, th e p o rt locations can be tru ly arbitrary. A
quarter-wave length transform er was used for th e o u tp u t p o rts in order to m atch
the high im pedance of th e divider to th e 50 f2 o u tp u t ports. Three o u tp u t ports
were connected a t th e second, fourth, and sixth unit-cells of th e CRLH TL. This
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
port d istribution was chosen in order to connect SMA connectors to th e 50 ft
o u tp u t ports.
Fig. 2.7(a) and Fig. 2.7(b) respectively show the o u tp u t p o rts’ m agnitude
and phase responses. T he MoM results were obtained from Ansoft Ensemble and
the m easured results were obtained from an Agilent 8510C network analyzer.
At /= 2 .3 7 GHz, th e 3-port divider has th e following m easured m agnitude re­
sponses: Ids'll| =-10.02 dB, |*S,2i|= -6 .6 4 dB, |5,3 i|=-6.42 dB, and |S,4 i|=-6.42 dB. In
addition, th e corresponding m easured phase responses at /= 2 .3 7 GHz are: S 2 1 —93.01°, *S3i = - 9 4 .3 3 °, and <S4i=-93.07°. The shift of th e infinite wave frequency is
a ttrib u ted to th e coupling capacitors at the ports. T he associated loss a t this fre­
quency due to radiation, capacitor, conductor, and dielectric losses is -1.12 dB.
The m agnitude and phase responses also show th a t the 4-port series divider’s
ou tp u t p o rts are nearly equal from 2.34 GHz to 2.52 GHz, corresponding to a
180 MHz bandw idth.
26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-5
----|S2il
Exp.
IS31I Exp.
........IS41I Exp.
—
CO
l®211 MoM
IS31I MoM
........IS41I MoM
- -
CD
~o
3
'c
O)
cc
2.20
2.25
2.30
2.35
2.40
2.45
2.50
2.55
2.60
Frequency (GHz)
(a)
S 21 Exp.
- S 31 Exp
«CD
<D
D)
a3>_
'T
-50
to
-100-
TO
S 41 Exp
S 21 MoM
S 31 MoM
S 41 MoM
-150
2.20
2.25
2.30
2.35
2.40
2.45
2.50
2.55
2.60
Frequency (GHz)
(b)
Figure 2.7: Sim ulation and experim ental results for th e 4-port divider of Fig. 2.6.
(a) M agnitude response, (b) Phase response.
27
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2.3.3
6-P ort Series D ivider
In order to d em onstrate th a t th e novel divider presented has no lim itation on
the num ber and location of o u tp u t ports, th e 4-port series divider presented in
Section 2.3.2 is modified to create a 6-port series divider as shown in Fig. 2.8.
0.2 pF SM T
cap ac ito r
1.5 pF SM T
cap ac ito r
161 mm
Figure 2.8: Layout of 6-port series divider.
T he 6-port series divider of Fig. 2.8 is composed of th irteen unit-cells and has
five o u tp u t p o rts unevenly distributed along th e CRLH TL. P o rt 1 is used as the
feed p o rt and th e other five ports are o u tp u t ports. The experim ental m agnitude
and phase responses of th e 6-port series divider respectively shown in Fig. 2.9(a)
and Fig. 2.9(b) confirm th e proposed idea presented in this paper.
A t /= 2 .3 7 GHz, th e 6-port divider has the following m easured m agnitude re­
sponses: |S'n|=-10.39 dB, |S'2i|= -8.32 dB, |5'3i|= - 8 :56 dB, |5 41|=-8.48 dB, |S,5i|= 8.31 dB, and |S,6 i|=-8.26 dB. In addition, th e corresponding m easured phase
responses a t /= 2 .3 7 GHz are: 5 2i=-96.04°, S31=-100.17°, 5 41= - 102.36°, S5i= 101.89°, and 5,6 i=-100.59°. As m entioned in Sec. 2.3.2, th e shift in resonance
frequency can be attrib u te d to the coupling capacitors. T he associated loss at
this frequency due to radiation, capacitor, conductor, and dielectric losses is 0.90 dB. T he m agnitude and phase responses also show th a t th e 6-port series
divider’s o u tp u t p o rts are nearly equal from 2.34 GHz to 2.40 GHz, correspond-
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ing to a 60 MHz bandw idth.
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-8-
9-
-10-
c
05
TO
2
------|S
-12-13
2.20
2.25
2.30
2.35
2.40
2.45
2.50
2.55
2.60
2.50
2.55
2.60
Frequency (GHz)
(a)
50
<
/)
<D
£
O)
0
S
$ -100(0
-C
-
-
CL
-
150-
2.20
2.25
2.30
2.35
2.40
2.45
Frequency (GHz)
(b)
Figure 2.9: E xperim ental results for th e 6-port divider of Fig. 2.8 (a) M agnitude
response, (b) P hase response.
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2 .3 .4
A p p lic a tio n s
A ntenna array and power combining applications of th e iV-port series divider
are presented in th e following subsections.
2.3.4.1
Sparse A n ten n a A rray Feed
T he A -p o rt series divider can be used in place of conventional antenna array
feeds especially in th e case of sparse arrays where nonuniform spacing is required
[18].
T he m ain benefits of th e proposed feed network over conventional feed
networks for sparse array designs are ease of scalability and design simplicity. In
the case of conventional parallel or series equal feed networks, further complexity
needs to be introduced in order to achieve non-uniform spacing of elements. These
complexities include proper design of the non-uniform spaced dividers such as
adding curved lines for phase com pensation to achieve equal excitation in the
parallel case. In addition, th e o u tp u ts of some dividers may need to be loaded
w ith ju st a m atched load to achieve th e required spacing. As a result, th e input
power will not be efficiently used. Since in th e series case th e element spacing is
lim ited to integer m ultiples of th e guided wavelength, th e feed line may need to be
curved or m anipulated to accomplish equal excitation and non-uniform spacing.
A nother m ajor draw back of these conventional feed networks for equal excitation
and non-uniform spacing is th a t the feed networks have to be custom tailored
according to th e num ber of elements.
To dem onstrate th e application of the A -p o rt series divider as a sparse array
feed network, th e 6-port, thirteen unit-cell divider of Fig. 2.8 is used to feed
five identical quasi-Yagi antennas. Quasi-Yagi antennas were chosen because of
their inherent broadband response. The quasi-Yagi antennas were fabricated on
on Rogers R T /D u ro id 6010 (er =10.2, h=1.27m m ) and one antenna is shown in
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Frequency (GHz)
(a )
(b )
Figure 2.10: Quasi-Yagi antenna, (a) Top-view of fabricated antenna, (b) Ex­
perim ental retu rn loss.
Fig. 2.10(a) w ith its experim ental retu rn loss shown in Fig. 2.10(b). Fig. 2.10(b)
confirms th e broadband response ( |5 n | < -10.0 dB) from 2.07 GHz to 2.80 GHz.
T he quasi-Yagi antennas are connected to th e o u tp u t ports of th e series di­
vider of Fig. 2.8, th e com pleted sparse array is shown in Fig. 2.11(a). W ith the
quasi-Yagi antennas connected, th e infinite wavelength frequency is shifted to
/= 2 .3 8 GHz since each an ten n a’s im pedance is not exactly 50 fb T he measured
radiation p a tte rn of th e series-fed antenna array a t /= 2 .3 8 GHz is com pared with
the theoretical p a tte rn of an equally excited antenna array w ith th e same spacing
between elements in Fig. 2.11(b). In addition, th e m easured radiation p attern
of th e an ten n a array a t /= 2 .6 3 GHz is also plotted in Fig. 2.11(b) to show th a t
broadside radiation does not occur once th e elements are out-of-phase w ith each
other.
32
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Quasi-Yagi Ante
2
3
4
5
6
T h e o re tic a l (f= 2.38 G H z)
E x p erim e n ta l (f= 2.38 G H z)
E x p erim e n ta l (f= 2.63 G Hz)
1 4
-25
-80
•60
-40
-2 0
20
40
60
80
Theta (degrees)
(a)
Figure 2.11: Sparse antenna array, (a) Top view; spacing between 2 and 3:
0.184A, spacing between 3 and 4: 0.184A, spacing between 4 and 5: 0.276A,
spacing between 5 and 6: 0.184 A, where f = 2.38 GHz. (b) Theoretical and
experim ental radiation patterns.
2.3.4.2
Pow er C om bining
T he A -p o rt series divider can also be used as a combiner. The power com­
bining function was dem onstrated by connecting two free running oscillators to
the o u tp u t p o rts of a th irteen unit-cell series combiner in [19]. A simple tra n ­
sistor oscillator was designed using a NEC GaAs M ESFET device to have a free
running oscillation frequency of 2.36 GHz.
Two tran sisto r oscillators were connected to th e ports along th e length of
the CRLH TL and th e combined power was m onitored at th e end p ort of the
combiner. DC bias was provided separately to th e two oscillators and tuned to
achieve m utual frequency locking between th e two oscillators.
A djustm ent of
the coupling between oscillators was tuned by changing th e value of coupling
capacitors to 1.3 pF in order to facilitate m utual frequency locking. A eight u n it­
cell com biner (combiner A) was fabricated w ith in p u t ports placed 23.2 mm and
33
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4
4
osc. 1
osc. 2
(b)
Figure 2.12: Fabricated power combiners (a) Combiner A. (b) Com biner B.
46.4 mm away from th e o u tp u t p ort as shown in Fig. 2.12(a). Fig. 2.13 shows
the o u tp u t spectrum observed using combiner A. M axim um power of 12.0 dBm
was observed. This is less th a n th e 13.3 dBm expected by simply doubling the
power of a single oscillator. This may be caused by the loss from th e combiner
a n d /o r th e non-optim ized synchronization between th e oscillators.
A second
th irteen unit-cell com biner (combiner B)w ith in p u t ports placed 23.2 mm
and
104.4 m m away from th e o u tp u t p ort was fabricated and is shown in Fig. 2.12(b).
Because th e p o rt position on th e CRLH TL does not affect transm ission phase or
power coupling between th e o u tp u t po rt and oscillator ports, th e power combining
results of com biner B are alm ost identical w ith th a t of com biner A.
E xternal injection locking was also applied to bo th combiners by using an HP
83621 frequency synthesizer through an external -10.0 dB directional coupler.
Fig. 2.14(a) shows th e spectrum of combiner A ’s o u tp u t w ith -5.0 dBm locking
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
; ,s| ,
'i 1,:ii| I .i ----SL.tr* q I
2.35874
2,35889
2.35924
2,35949
F re q u e n c y \G Hz]
Figure 2.13: E xperim ental o u tp u t power spectrum w ith m utual frequency locking
of combiner A.
power w ith a m axim um power of 10.5 dBm. P hase noise of -61.33 dBc, -75.5 dBc,
and -80.0 dBc was m easured for offset frequencies of 10 KHz, 100 KHz, and
1 MHz, respectively. Fig. 2.14(b) shows th e spectrum of com biner B ’s o utput
w ith -5.0 dB m locking power. M aximum power was m easured to be 10.88 dBm for
combiner B. P hase noise of -58.0 dBc, - 70.33 dBc, and -76.33 dBc was measured
for offset frequencies of 10 KHz, 100 KHz, and 1 MHz, respectively.
1
... J
F re q u e n c y
[GHz]
*
4E !
Frequency [GHz]
(a)
(b)
Figure 2.14: Experim ental o u tp u t power spectrum w ith external injection lock­
ing. (a) Com biner A. (b) Combiner B.
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.4
In fin ite W avelen gth R eson an t A n ten n a
T he backw ard wave property of th e CRLH TL and other LH-based TLs has
been used to realize novel, small half-wavelength resonant antennas [20]-[21], In
this section, th e analysis and design of resonant, planar antennas based on the
fundam ental infinite wavelength property of th e CRLH TL is presented. Since an
infinite wavelength occurs when th e propagation constant is zero, th e frequency
of th e proposed anten n a does not depend on its physical length, b u t only on the
reactance provided by its unit-cell. Therefore, th e physical size of th e proposed
antenna can be arbitrary; this is useful to realize electrically small or electrically
large antennas. By properly designing th e unit-cell, the radiation p a tte rn of the
antenna at th e infinite wavelength frequency can also be tailored. In particular,
the CRLH TL unit-cell is th e general model for th e required unit-cell which con­
sists of a series capacitance, a series inductance, a shunt capacitance, and a shunt
inductance. T he CRLH TL unit-cell’s shunt resonance determ ines th e infinite
wavelength frequency and thus the an ten n a’s operational frequency. By modify­
ing th e equivalent shunt capacitance a n d /o r shunt inductance circuit param eters
of th e unit-cell, th e operational frequency and th e physical size of th e realized
antennas can be controlled. Furtherm ore, th e unique ’’equal am plitu d e/p h ase”
electric-field distrib u tio n of an infinite wavelength excited on th e antenna gives
rise to a m onopolar radiation pattern.
2.4.1
M onopolar R adiation
By using an open-ended resonator th a t supports an infinite wavelength, an
infinite wavelength resonant antenna w ith an operational frequency independent
of its physical size can be realized. Such an antenna can be m ade electrically large
or small, th e la tte r of which was dem onstrated in [22] w ith a patch-like p attern.
36
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In contrast to [22], electrically large and small infinite wavelength antennas w ith
m onopolar rad iatio n p attern s are dem onstrated.
Various low-profile monopo­
lar antennas have been realized [23]-[26] based on reactive loading w ith shorting
pins. However, th e placem ent and num ber of shorting pins for these monopolar
antennas were strictly based on numerical studies. T he presented periodic design
m ethodology offers a straight-forw ard design approach based on th e character­
istics of a single CRLH unit-cell. In order to discuss th e radiation mechanism
behind th e proposed antenna, first consider the conventional m icrostrip patch
antenna as shown in Fig. 2.15(a).
*•
m icrostrip
an te n n a
(a)
(b)
Figure 2.15: M icrostrip patch antennas w ith dimensions p x p m m 2; resonant
length along y-direction. (a) Conventional supporting half-wavelength, (b)
CRLH supporting infinite wavelength.
T he patch an ten n a can be modeled as a square cavity w ith perfect magnetic
conductor (PM C ) walls. A t its fundam ental mode, the patch antenna supports
a half-wavelength along its resonant length. Therefore, th e non-zero equivalent
m agnetic current density at each radiating edge is given by
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
M s = —2h x E ,
(2.5)
where h is th e u n it norm al to the edge, E is th e electric field a t th e edge, and
the factor of 2 is due to the ground plane [27]. It is th e two equivalent m agnetic
current densities at th e radiating edges of th e patch antenna th a t contribute
to its rad iatio n p attern . Next consider the proposed CRLH antenna shown in
Fig. 2.15(b). Since th e CRLH TL can support an infinite wavelength, th e field dis­
tributions along th e perim eter of th e CRLH anten n a are in-phase when operated
at its infinite wavelength frequency. Therefore, th e equivalent m agnetic current
densities a t th e edges described by (2.5) form a loop as shown in Fig. 2.15(b). It
is this equivalent m agnetic loop th a t produces th e m onopolar radiation pattern;
a m agnetic loop is an ideal electric dipole by duality. As a result, th e proposed
infinite wavelength antennas are polarized in th e theta-direction.
2.4.2
P ro p o sed A n ten n a D esign
In this section, infinite wavelength antennas consisting of two, four, and six
unit-cells w ith m onopolar radiation p attern s are realized. T he CRLH unit-cell for
the proposed antennas are based on a modified Sievenpiper m ushroom unit-cell
[11]; th e m etallic patch does not need to be a square, but can be rectangular. The
size of th e patch, th e dielectric constant, th e period of th e unit-cell, th e radius
of th e shorting post, and th e num ber of unit-cells are all factors th a t control
the dispersion curve of th e unit-cell and in effect th e resonant frequencies of the
antenna [28]. T he general model for th e proposed infinite wavelength antenna
is shown in Fig. 2.16(a), which shows th a t proxim ity coupling is used as the
feed network for th e antenna. However, th e feeding m ethod varies depending on
the num ber of unit-cells (N ) as discussed below. To dem onstrate th e resonant
38
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length independence, antennas consisting of two, four, and six CRLH TL unitcells are realized. All th e antennas are fabricated on Rogers R T /D u ro id 5880 with
dielectric constant er~2.2 and thickness h —1.57 mm. T he CRLH TL unit-cell
measures 7.3 x 15 m m 2 w ith a period of 7.5 mm. The radius of th e shorting post
is 0.12 mm.
Port 1
CRLH TL unit-cell
*
CRLH resonator
Figure 2.16: Infinite wavelength antenna composed of A unit-cells. (a) Model
of proposed design, (b) Dispersion diagram of CRLH unit-cell used to realize
antennas.
The calculated dispersion diagram the CRLH unit-cell is shown in Fig. 2.16(b)
along w ith experim ental resonant peaks of a five unit-cell open-ended resonator
39
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im plem entation. The infinite wavelength frequency for th e CRLH TL unit-cell
is 3.65 GHz as predicted by applying periodic boundary conditions on a single
unit-cell.
In contrast, th e five unit-cell resonator im plem entation predicts an
infinite wavelength frequency of 3.51 GHz th e CRLH TL unit-cell. By modifying
the patch area or th e radius of th e shorting post of th e unit-cell, th e infinite
wavelength frequency can be controlled.
The input im pedance (Zin= R + j X Q) of each antenna im plem entation is
com puted using Ansoft HFSS. A 50
line was directly attach ed to th e input
edge of each an ten n a and deembeded to calculate th e input im pedance. The real
part and im aginary com ponent of the input im pedance for th e antennas are shown
in Fig. 2.17(a) and 2.17(b), respectively. T he input im pedance and corresponding
infinite wavelength resonant frequency obtained from HFSS for th e antennas are
sum m arized in Table 2.1. The resonant frequency is defined as th e frequency
where th e resistance reaches a maximum, independent of th e value of reactance
[2 9 ]-
1200-1
600-
£
~2 unit-cells
*4 unit-cells
■*6 unit-cells
800-
«
— 2 unit-cells
- -4 unit-cells
■— 6 unit-cells
400-
JS
o 200-
600-
C .200-
400-
- 600-
3-5
3.0
3.0
4.0
3.5
4.0
fre q u e n c y (GHz)
fre q u e n c y (GHz)
(a)
(b)
Figure 2.17: CRLH an ten n a input impedance, (a) Real p a rt (R). (b) Imaginary
p art (X ).
From Table 2.1, it can be observed th a t th e infinite wavelength frequency in-
40
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antenna
resonant frequency
Zin—R + j X (G)
2 unit-cells
4 unit-cells
6 unit-cells
3.47 GHz
3.53 GHz
3.55 GHz
1060.1+j0.0
410.0-j 15.0
253.0-j 73.0
Table 2.1: Sum m ary of num erical input im pedance and corresponding resonant
frequency of proposed antennas.
creases slightly as th e num ber of unit-cells increases. This is due to th e additional
m utual coupling between th e unit-cells, which affects th e resonance frequency. It
can also be observed from Fig. 2.17 and Table 2.1 th a t th e in p u t im pedance fol­
lows th e tren d predicted by 2.4; th e input im pedance decreases as th e num ber of
unit-cells increases.
2.4.3
T w o U n it-C ell A n ten n a R ealization
The input im pedance for th e two unit-cell CRLH an ten n a is quite high for
quarter wavelength m atching. Therefore, proxim ity coupling is used to m atch the
antenna to a 50
line as shown in Fig. 2.16(a) w ith wq=15.0 m m and w2= 0.2 mm.
The num erical and experim ental retu rn loss of th e two unit-cell CRLH antenna
is shown in Fig. 2.18. For th e CRLH based antenna an experim ental retu rn loss
of -12.34 dB is obtained a t /o= 3.38 GHz. T he electrical size of th e antennas is
A0/6 x A0/6 x A0/5 7 a t / 0. T he result shows th a t th e two unit-cell antenna is not
m atched exactly a t th e predicted infinite wavelength frequency of Table I. This
is due to th e high input im pedance of th e antenna.
T he electric-held distribution underneath th e two unit-cell CRLH antenna for
the n = - l (/?/=-180°) and n = 0 mode are shown in Fig. 2.19(a) and Fig. 2.19(b),
respectively. A nsoft HFSS was used to obtain these held plots. T he n = - 1 mode
distribution shows th a t th e electric-held is 180° out-of-phase corresponding to
41
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F re q u e n c y (GHz)
Figure 2.18: N um erical and experim ental retu rn loss of th e two unit-cell antenna.
a half-wavelength. As a result, th e equivalent m agnetic current densities along
the perim eter of th e antenna for th e n = - 1 m ode form a distrib u tio n com parable
to Fig. 2.15(a) and th e radiation p attern will be similar to a conventional patch
antenna. T he n = 0 distribution shows th a t the electric-held is in-phase verifying
th a t an infinite wavelength is supported.
Therefore, th e equivalent magnetic
current densities along th e perim eter of th e antenna for th e n = 0 mode form a
loop com parable to Fig. 2.15(b) and a m onopolar radiation occurs.
(b)
(a)
Figure 2.19: Electric-held distribution underneath two unit-cell CRLH antenna
obtained via Ansoft HFSS. (a) Half-wavelength, n —- 1 mode, (b) Inhnite wave­
length, n = 0 mode.
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T he num erical and experim ental radiation p attern s of th e two unit-cell CRLH
antenna is shown in Fig. 2.20 and reveal th e expected m onopolar radiation p a t­
tern. A m axim um gain of 0.87 dBi is experim entally obtained for th e CRLH based
antenna. In addition, th e x-y plane radiation p a tte rn and cross-polarization (nor­
malized relative to co-polarization) of th e CRLH antenna are shown in Fig. 2.20(c)
and Fig. 2.20(d), respectively. Fig. 2.20(c) illustrates the om ni-directional cover­
age in th e x-y plane provided by th e m onopolar antenna, while Fig. 2.20(d) shows
th a t th e cross-polarization is less th a n th e co-polarization. These p attern s verify
th a t th e anten n a is polarized in th e theta-direction as discussed in Section 2.4.1.
43
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z
z
o
o
330
-1
0-
-2
0-
330
-10
300
300
-20
-3 0 -
-30
-4
0 - 270
-3
0-
-2
0-
90 X
-40
270
-30
-20
240
120
-10-
240
120
-10
210
num.
150
210
- - exp.
180
num.
150
- - exp.
180
(a)
(b)
X
0
330
300
-2
330
0
- d~v
-10-
-10
300
0-
-20
-3
0-
-4
0 - 270
-30
-40 270
-30
-3 0 -2
-20
0240
120
-10-
210
150
180
-10
o
num.
30
60
240
120
210
180
- - exp.
— x-zp'ane
y-z plane
x-y plane
(c)
(d)
Figure 2.20: Two unit-cell CRLH antenna radiation patterns, (a) P h i= 0 ° (x-z
plane), (b) P hi= 90° (y-z plane), (c) T heta= 90° (x-y plane), (d) Experim ental
cross-polarizations norm alized to co-polarizations.
44
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2.4.4
E ffects o f Increasing th e N um ber o f U n it-C ells
A dditional unit-cells are added along th e y-direction to create four and six
unit-cell antennas as depicted in Fig. 2.16(a). A single section q u arter wavelength
transform er is used to m atch each four and six unit-cell an ten n a to a 50 Q line.
Only th e real p a rt of th e input im pedance shown in Table I is considered in
the m atching. T he experim ental infinite wavelength frequency, retu rn loss, and
gain of th e two, four, and six unit-cell antennas are displayed in Table 2.2. The
electrical size of th e four unit-cell antennas is A0/6 x A0/3 x A0/5 3 at /o and the
electrical size of th e six unit-cell antennas is A0/6 x Ac/2 x A0/5 3 at / q. Although
the antennas become physically larger, the infinite wavelength frequency remains
approxim ately constant.
In addition, gain increases as th e antenna becomes
physically larger. T he x-y plane and cross-polarization of th e four and six u nit­
cell CRLH antennas are similar to those of th e two unit-cell CRLH antenna and
therefore are not shown.
antenna
resonant frequency
retu rn loss
peak gain
2 unit-cells
4 unit-cells
6 unit-cells
3.38 GHz
3.52 GHz
3.55 GHz
-12.34 dB
-17.33 dB
-11.17 dB
0.87 dBi
4.50 dBi
5.17 dBi
Table 2.2: Experim ental results for two, four, and six unit-cell antennas.
T he predicted infinite wavelength frequencies of Table 2.1 show good agree­
m ent w ith th e m easured infinite wavelength frequencies of Table 2.2. The num er­
ical and experim ental radiation p attern s for th e four unit-cell CRLH antennas
are shown in Fig. 2.21. W hile, th e numerical and experim ental radiation p a t­
terns for th e four unit-cell CRLH antennas are shown in Fig. 2.22. T he expected
m onopolar p a tte rn is obtained. However, th e p a tte rn is asym m etrical in th e y-z
plane. This can be attrib u te d to the feed and th a t th e an ten n a is operated in
45
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the fast-wave region [30], which means th a t th e unit-cell is inherently radiative.
This asym m etry can be elim inated by using a coaxial feed a t th e center of the
antenna.
Z
o
Z
o
330
0
330
■10
-10
300
300
-20
-20
-30
•40
-30
270
-40
-30
270
90
y
-30
-20
-20
240
120
-10
120
240
-10
0
210
150
180
num.
- - exp.
210
(a)
num .
150
- - exp.
180
(b)
Figure 2.21: Four unit-cell CRLH antenna radiation p attern s, (a) P hi= 0° (x-z
plane), (b) P hi= 90° (y-z plane).
Z
o
Z
o
330
330
-10
-10
300
-20
-20
-30
-40 270
-30
-30
-40
300
270
-30
-20
•20
240
120
-10
210
150
180
-10
num .
90 y
240
120
150
210
180
- - exp.
(a)
nUin
exp.
(b)
Figure 2.22: Six unit-cell CRLH antenna radiation patterns,
plane), (b) P hi= 90° (y-z plane).
(a) P hi= 0° (x-z
46
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2 .4 .5
R a d ia tio n P a tte r n D iv e r sity
Only th e infinite wavelength frequency of th e unit-cell, corresponding to the
n = 0 resonance mode, was used to im plem ent th e antennas discussed in Sec­
tions 2.4.3 and 2.4.4. However, th e other resonances m odes are quite different;
the fundam ental m ode of th e CRLH TL supports a backward mode below the
infinite wavelength frequency.
As a result, a dual-m ode an ten n a [28] w ith a
m onopolar p a tte rn a t one frequency and a patch-type p a tte rn a t a lower fre­
quency can be obtained by using the CRLH unit-cell. This anten n a can address
com m unication system s which require com pact antennas w ith radiation p attern
selectivity such as terrestrial com m unication system s w ith satellite uplinks and
wireless local-area-netw orks (WLANs).
T he m onopolar p a tte rn of th e dual-m ode antenna is a ttrib u te d to th e n ~ 0
resonance m ode of th e unit-cell, while th e patch-type p a tte rn is due to th e n=1 resonance m ode of th e CRLH TL. At th e n = - 1 mode, th e antenna supports
a half-wavelength field distribution and only two edges contribute to th e radi­
ation resembling th e dom inant mode of a classical patch anten n a as shown in
Fig. 2.15(a) and Fig. 2.19(a).
o
o
330
330
-10-2
.
300
-10-
60
-2
0-
-20-10-
0-
-3 0 -
3 0 - 270
-2
120
240
180
270
0-
-10-
150'- - Phi=0°
210
300
240
120
150
210
Phi=90°
180
(a)
Phi=0°
Phi=90°
(b)
Figure 2.23: E xperim ental radiation p attern s of dual-m ode antenna, (a) n —0
mode showing m onopolar radiation, (b) n = - 1 m ode showing patch-like p attern.
47
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The operational frequencies of the proposed dual-m ode anten n a are not har­
monics of each other because of th e CRLH T L ’s nonlinear dispersion relation.
Since th e unit-cell’s dispersion relation is determ ined by its unit-cell, th e oper­
ational frequencies of th e antenna can be controlled by modifying th e unit-cell
an d /o r th e num ber of unit-cells.
The proposed dual-m ode antenna is based on Fig. 2.16(a) and consists of three
CRLH unit-cells each m easuring 4.8 x 15 m m 2 w ith a period of 5.0 mm. The
radius of th e shorting post is 0.12 mm. A retu rn loss of -10.21 dB and -9.2 dB
are experim entally obtained at /o = 4.00 GHz and at / _ i= 3 .5 7 GHz, respectively.
The anten n a size is A0/5 x A0/5 x Ao/5 0 at /o and th e an ten n a size is A0/5 .7 x
A0/5 .7 x A0/5 4 a t / _ i. The experim ental radiation p attern s at /o and a t / _ \ are
shown in Fig. 2.23(a) and Fig. 2.23(b), respectively. A m axim um gain of 2.3 dBi
w ith an efficiency of 75% was achieved at /o, while a m axim um gain of -2.5 dBi
w ith an efficiency of 25% was achieved at / _ i.
48
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CHAPTER 3
D u a l-M o d e C R L H M e ta m a te r ia l
3.1
In tro d u ctio n
T he concept of a dual-m ode CRLH m etam aterial [31] is presented in this
chapter. This m ode selective m etam aterial supports either forward or backward
waves w ithin th e same frequency bandw idth.
T he choice between dispersion
operations is based on th e mode excitation applied to th e m etam aterial. A one­
dim ensional m icrostrip prototype of this novel dual-m ode CRLH m etam aterial is
realized and characterized. The dual-m ode concept is exfended to two-dimensions
by num erical sim ulations w ith th e p ro to ty p e’s experim ental results. T he num er­
ical sim ulations are perform ed to dem onstrate electrom agnetic wave steering and
spatial m ultiplexing at a fixed frequency based on dispersion selectivity.
3.2
D u a l-M o d e C oncep t
Recently, there has been a growing interest in m etam aterials and photonic
crystals for guiding and focusing electrom agnetic waves [32]-[33]. In th e m eta­
m aterial approach, negative refractive index flat lenses and wedges are used to
focus point sources and negatively refract waves, respectively. Presently, proposed
m etam aterials such as th e CRLH m etam aterial TL can only support either a for­
ward (VgVp > 0) or backward (vgvp < 0) wave for a given frequency region. To
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
change from LH to RH dispersion characteristics, th e operational frequency of
the CRLH m etam aterial has to be changed. If fixed frequency dispersion control
is required varactor diodes can be em bedded into th e CRLH unit-cell for voltage
controlled operation [3]. In addition, anisotropic m etam aterials [3] can also be
used for fixed frequency operation; th e incident wave in th e m etam aterial will ex­
perience different dispersion characteristics depending on its direction of travel.
However, th e varactor diode and anisotropic m ethod for fixed frequency opera­
tion either require active devices or only works for a one-dim ensional propagation,
respectively.
To illustrate th e frequency dependent wave-steering of a conventional CRLH
m etam aterial, a CRLH prism w ith two incident waves w ith different frequencies,
J a and f s are shown in Fig. 3.1(a) and 3.1(b), respectively. This CRLH prism
can be engineered to have a refractive index of + 1 a t frequency / a and a refractive
index of -1 a t frequency f s , where //i > J'b - T he direction of th e refracted wave is
determ ined by applying 1.2. A t / a , the CRLH m etam aterial supports a backward
wave resulting in a negative refractive index, while a t /# th e CRLH m etam aterial
supports a forward wave resulting in a positive refractive index. If a free-space
incident wave w ith frequency J a enters th e prism th e resulting refracted wave will
simply pass through. In contrast, if an incident wave w ith frequency / b enters
the prism it will be negatively refracted and th e resulting wave will be directed
in an orthogonal direction.
A lthough th e CRLH m etam aterial can support bo th backward and forward
waves it cannot do so w ithin the same frequency band. Fig. 3.2 shows the pro­
posed concept for dual-m ode m etam aterial th a t is able to select between positive
or negative refractive index depending on th e excitation m ode of th e incident
wave w ithout dependence on the wave’s frequency. This dual-m ode m etam ate-
50
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incident wave
with frequency, fA
incident wave
with frequency, fB
refracted
wave
refracted 111
w ave H I
(b)
(a)
Figure 3.1: CRLH prism w ith incident wave; 45° angle, (a) Incident wave with
J a \ CRLH has refractive index of +1. (b) Incident wave w ith /# ; CRLH has
refractive index of -1.
rial can be engineered to have a refractive index of +1 for m ode 1 operation and
a refractive index of -1 for m ode 2 operation. W hen an incident wave w ith fre­
quency. f 0 and m ode 1 enters the dual-m ode m etam aterial prism it will simply
pass through. In contrast an incident wave w ith th e same frequency b u t of mode
2 enters th e prism it will be negatively refracted.
In order to realize th e dual-m ode wave-steering concept of Fig. 3.2, the pro­
posed m etam aterial is engineered to have a dispersion diagram sim ilar to Fig. 3.3.
Under one mode, th e m etam aterial would support a forward wave, where the re­
fractive index is positive. U nder another mode, th e m etam aterial would support
a backw ard wave and therefore would have a negative refractive index. Such a
dual-m ode m etam aterial can be used for wave steering in which under forward
mode operation, an incident wave will be positively refracted, while under back­
ward m ode operation, th e wave will be negatively refracted.
51
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incid en t w ave
with fr e q u e n c y ,^
m ode 1
incident w ave
with freq u en cy, f Q
m ode 2
refracted
w ave
refracted I
w ave
▼
Figure 3.2; D ual-m ode m etam aterial wave-steering concept.
+Pc
-p c
w ave
backward
wave >
mode 1
mode 2
Figure 3.3: Proposed dispersion characteristics for dual-m ode CRLH m etam ate­
rial.
52
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3.3
M o d e S electiv e U n it-C ell
To realize th e dispersion diagram shown in Fig. 3.3, a m ode selective m eta­
m aterial unit-cell has to be engineered; depending on the wave’s mode, th e dual­
mode unit-cell will appear like a CRLH unit-cell or a RH unit-cell as illustrated in
Fig. 3.4. T he CRLH unit-cell serves as th e basis for the design of th e dual-m ode
unit-cell since it supports a fundam ental backward wave. To realize th e mode
selective dispersion characteristics shown in Fig. 3.3, the LH circuit com ponents
(C l and L l ) of th e conventional CRLH TL model has to be either elim inated or
introduced depending on th e excitation mode.
Backward-Wave
LR
Forward-Wave
mode selective
unit-cell
Figure 3.4: M ode selective unit-cell concept.
E ven-/odd-m ode excitation is used as th e excitation for th e m etam aterial. The
dual-m ode m etam aterial is engineered so th a t under odd-m ode excitation it will
support a backw ard wave and under even-mode excitation it will support a for­
ward wave.
Therefore, th e CRLH unit-cell has to be engineered so th a t it is
applicable to even-/odd-m ode excitation.
T he CRLH unit-cell is can be modified such th a t th e shunt inductance lies
in th e sym m etry plane of th e unit-cell as shown in Fig. 3.5. W hen odd-mode
excitation is applied to th e unit-cell, a virtual short is created and the shunt
53
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sym m etry plane
Figure 3.5: Modified CRLH unit-cell for even-/odd-m ode excitation; LH series
capacitance exists for b o th excitation modes.
inductance is tu rn ed on. T he resulting stru ctu re supports a backward wave as
expected. W hen even-mode excitation is applied, a v irtual open is created, and
the shunt inductance is turn ed off. T he resulting stru ctu re supports a forward
wave. However, because of th e series capacitance, th e even-m ode’s forward wave
cannot occur in th e same frequency band as th e odd-m ode’s backwards wave.
Therefore, a m ethod to tu rn on/off th e series capacitance is required.
One way to tu rn on/off th e series capacitance w ith even-/odd-m ode excitation
is to connect th e series capacitor in a parallel configuration as shown Fig. 3.6(a).
T he series capacitor is not directly connected to th e rest of th e unit-cell b u t rather
it is coupled to th e unit-cell. Therefore, when odd-m ode excitation is applied, a
virtual short occurs along th e sym m etry plane and bo th th e series capacitance
and shunt inductance are present as shown in Fig. 3.6(b).
U nder even-mode
excitation, b o th LH com ponents are elim inated and the equivalent circuit model
is shown in Fig. 3.6(c).
54
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couple se r ie s
capacitan ce
sy m m e try plane
w
(a )
--
Odd-M ode Excitation
n
o'•ill
tee
n
t t /
iUUU t
r
sym m etry plane
U
XuuJ
O T irc
1|_a_A-Aj T
(b)
Even-M ode Excitation
71
1
‘J
1
J
sym m etry plane
V
+ o-
XuuJJ"
luuJ”
(c)
Figure 3.6: Modified CRLH unit-cell w ith parallel coupled series capacitance, (a)
C ircuit model applicable to even-/odd-m ode excitation, (b) O dd-m ode excitation
equivalent circuit, (c) Even-m ode excitation equivalent circuit.
55
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3 .3 .1
P h y s ic a l R e a liz a tio n
M icrostrip technology is used to physically realize th e dual-m ode unit-cell
of Fig. 3.6(a). In order to accomplish th e required series capacitor coupling, the
concept of ap ertu re coupled m icrostrip lines [34] was employed. Fig. 3.7(a) shows
two m icrostrip lines sharing a common ground plane in which an aperture slot
is cut. Because of th is apertu re slot, coupling occurs between th e two m icrostrip
lines.
As a result, th e b ottom m icrostrip stru ctu re is serially coupled to the
top structure. T he equivalent circuit for the aperture coupled m icrostrip lines
is shown in Fig. 3.7(b), where th e aperture coupling can be modeled as an ideal
transform er coupling w ith tu rn s ratio n. The tu rn s ratio is given by
(3.1)
where Z™trip and Z f A are the m icrostrip and slot characteristic impedances,
respectively.
T he physical realization of th e dual-m ode circuit model is shown in Fig. 3.8.
The perspective view of th e circuit shows th a t th e circuit consists of two mi­
crostrip stru ctu res w ith a shared ground plane between them . This structure
is sym m etric along th e x-z plane and even-/odd-m ode excitation is applied to
P ort 1 /P o rt 3 or P ort 2 /P o rt 4. The m icrostrip lines on th e to p su b strate pro­
vide th e required RH com ponents (C r and L r ) of th e circuit model, th e stubs
connecting th e two m icrostrip lines provide th e shunt inductance (L r ), and the
m icrostrip line w ith surface m ount technology (SMT) capacitors on the bottom
su b strate provide th e series capacitance (C l )- The LH series capacitance on the
b ottom layer of th e circuit is coupled to th e top m icrostrip stru ctu re by th e aper­
ture slots on th e shared ground plane. The equivalent half-circuit model for the
56
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z
microstrip .
coupled line
ideal
transformer coupling
y
2
coupling
aperture
ground
plane
aperture
slots
4
microstrip
feed line
(a)
(b)
Figure 3.7: A perture coupled m icrostrip lines, (a) Physical model consisting of
two su b strates sharing common ground plane w ith aperture slot, (b) Equivalent
circuit model; ap ertu re slot modeled as ideal transform er.
realized dual-m ode CRLH m etam aterial is shown in Fig. 3.9. The ap ertu re slots
are modeled as two ideal back-to-back transform ers separated by TLs characterized by im pedance Z f ot and electrical length j3slotd, where d is th e length of
the slot [35]. Since th e m agnetic field is continuous in th e plane of th e slot, the
b ottom m icrostrip stru ctu re is serially coupled to th e top m icrostrip structure.
The w idth of th e slot is proportional to th e am ount of coupling and is inversely
proportional to th e coupling bandw idth. T he length of th e slot determ ines the
frequency of m axim um coupling. The bandw idth of this type of transform er sets
the m ain constraint on bandw idth of th e entire unit-cell realization.
57
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P o rt 2
Top Side
P ort 4
ort
ort
a p e rtu re
Bottom Side
f
0.6 pF SMT
cap ic a to r
ground
p lan e >
SM T C a p a c ito r
(a)
Figure 3.8: Model of realized dual-m ode CRLH unit-cell, (a) Perspective view;
era=era= 2.33, da=c?b=0.784 mm. (b) D etailed view; Zi=15 mm, /2=19.34 mm,
1 3 = 9 .4 mm, Z
4=11.6 mm, l$ = 24 mm, Ze=10.66 mm, d= 20 mm, w i = w 4=2.33 mm,
W2=0.3 mm, u;3=0.5 mm.
3.3.2
N um erical and E xperim en tal R esu lts
The unit-cell shown in Fig. 3.8 was sim ulated in Ansoft Designer, a MoM fullwave solver. T he four-port S-param eters were obtained and th en th e even-/oddmode excited tw o-port S-param eters were calculated using Agilent Advanced De­
sign System (ADS). T he MoM even-/odd-m ode dispersion diagram for th e u nit­
cell of Fig. 3.8 is shown in Fig. 3.10. In addition, th e dispersion diagram obtained
by using th e circuit model of Fig. 3.9 is also plotted against th e MoM results in
Fig. 3.10. To verify th e transm ission properties of th e proposed m etam aterial,
five unit-cells were cascaded to form a TL and were num erically sim ulated using
MoM and th e circuit model. The insertion and retu rn loss for th e five unit-cell
TL is shown in Fig. 3.11.
T he results of Fig. 3.10 and 3.11 show th a t under even-mode excitation, the
58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ideal transformer
coupling
2%
2%
2%
even-mode: o.c.
odd-mode: s.c.
Ideal TLs: A p e rtu re S lo ts
2*C,
2*C,
Figure 3.9: Equivalent half-circuit model of even- and odd-m ode excited m eta­
m aterial of Fig. 3.8.
N
CD 3
o
S '
dual-mode BW: 1.80 - 1.95 GHz
c
0
§ - 2
0
even-m ode (MoM )
- even-m ode (circuit)
- - odd-m ode (MoM)
odd-m
ode (circuit)
1
,--------------------------- ,—
2
3
p*p (rad)
Figure 3.10: Num erical dispersion diagram for unit-cell of Fig. 3.8.
59
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1.80 GHz
1.95 GHz
0 even-mode
-10
(MoM)
[2 -304
1.5
2.5
2.0
frequency (GHz)
odd-mode
-10
S21 (MoM)
(circuit)
S21 (circuit)
-20
-30
1.5
2.5
2.0
frequency (GHz)
Figure 3.11:
N um erical in sertio n /retu rn
even-/odd-m ode excitation.
loss
of five
unit-cell
TL
for
unit-cell supports a forward wave and under odd-m ode excitation, th e unit-cell
supports a backw ard wave w ithin the frequency range of 1.80 GHz - 1.95 GHz.
This narrow -band operation is m ainly due to th e apertu re slot transform er. In
addition, th e good agreem ent between circuit model and full-wave results confirms
the model of Fig. 3.9,
T he unit-cell in Fig. 3.8 was fabricated using two pieces of Rogers RT/'Duroid
5870 w ith dielectric constant er =2.33 and thickness /).—0.784 mm. The aperture
slots were etched off th e ground planes of each su b strate and th e two substrates
are pieced together w ith conductive epoxy. A four-port m easurem ent was per­
formed on a tw o-port H P 8720ES network analyzer. The experim ental even-/oddmode dispersion diagram of th e unit-cell is displayed in Fig. 3.12. T he differences
between th e num erical and experim ental results are due to alignm ent errors and
also to th e im perfect loads used to obtain th e four-port S-param eters [36]. The
experim ental results show th a t th e RH and LH bands coexist in th e frequency
60
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range of 1.86 GHz - 2.00 GHz.
N
I
o
✓
.
S s 'dual-mode BW: 1.85 - 2.00 GHz
'•*
/
______
even-m ode (Exp.)
even-m ode (circuit)
odd-m ode (Exp.)
odd-m ode (circuit)
1
0
2
1
3
P*p (rad)
Figure 3.12: Experim ental dispersion diagram for unit-cell of Fig. 3.8.
3.4
D u a l-M o d e W ave-S teering D em o n stra tio n
T he proposed concept of m ode selective m etam aterials brings about possi­
bilities for interesting wave steering applications in signal routing and spatial
m ultiplexing. It has been dem onstrated th a t using m etam aterials, wavefronts
can be steered in a two-dim ensional stru ctu re based on excitation frequency [37].
In some cases th e frequencies need to be widely separated to observe a prom inent
effect. Using th e proposed dual-m ode CRLH m etam aterial th e same concept of
spatial m ultiplexing can be realized under fixed frequency operation.
To d em onstrate fixed frequency wave-steering, th e one-dim ensional unit-cell
in Fig. 3.8 is extended to two-dimensions in circuit sim ulation. The setup for
the wave-steering sim ulation is shown in Fig. 3.13(a), w ith Region I consisting
61
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of 19x11 RH cells as shown in Fig. 3.13(b) and Region II consisting of 19x11
dual-m ode CRLH cells shown in Fig. 3.13(c)1. U nder even-mode excitation, the
dual-m ode m etam aterial is RH and an oblique incident wave from Region I is
positively refracted. U nder odd-m ode excitation, th e dual-m ode m etam aterial is
LH and th e oblique incident wave from Region II is negatively refracted. The
RH cell in Fig. 3.13(b) consist of four RH unit-cells connected together w ith an
eight-port junction. The RH unit-cell circuit model is illustrated in th e inset of
Fig. 3.13(b). T he dual-m ode cell of Fig. 3.13(c) consists of four dual-m ode unitcells connected together w ith an eight-port junction. T he junction consists of
two equal four-port resistive dividers such th a t a signal from p o rt A1 gets evenly
divided into p o rts B \ , C \ , and D\ and a signal from p ort A-2 gets evenly divided
into p o rts B 2. C2, and D 2.
A 45 degree incident plane wave is excited on B oundary A of th e stru ctu re
shown in Fig. 3.13(a), while B oundary B, C, and D are term in ated w ith m atched
loads (Z b )•
T he excitation setup for generating the oblique incident wave is
shown in Fig. 3.14 [38]. Each of th e RH cells along boundary A is excited with
a phase delay. In addition, even-mode excitation is achieved by using a 0 degree
phase shifter and odd-m ode excitation is achieved by using a 180 degree phase
shifter. T he operational frequency of 1.92 GHz was chosen. For Region I, num er­
ical d a ta was used for th e RH unit-cells and th e RH cell was designed to provide
a propagation constant of 0.342 radians w ith Z b = 50 H. Experim ental d a ta was
used for th e dual-m ode unit-cell, for which under odd-m ode excitation a prop­
agation constant of -0.34 radians w ith Z b = 31 Q is obtained and a propagation
constant of 1.46 radians w ith Z b = 63 0, is obtained under even-mode excitation.
The resulting voltage phase plots for even-mode and odd-m ode excitation in the
xT he cells shown in Fig. 3.13(b)and 3.13(c) are drawn such th a t the overlap between adjacent
R H /dual-m ode unit-cells are accounted for, i.e., one row of Region I is represented by RH-JR H -J-RH -J-... and one row of Region II is represented by LH-J-LH-J-LH-J-...
62
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sim ulated stru ctu re is shown in Fig. 3.15(a) and 3.15(b), respectively. Under
even-mode excitation, th e incident wave is positively refracted and under odd­
mode excitation, th e incident wave is negatively refracted.
63
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Boundary B
Boundary D
(a)
B 1 B2
Bi B2
■xi ■
RH
J
RH
Ci
RH
D„ D
Di D2
(b)
(c)
Figure 3.13: Wave steering simulation,
(b) RH cell, (c) D ual-m ode cell.
(a) Numerical sim ulation space setup,
64
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V Ajepunog
65
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Figure 3.14: Excitation setup on boundary A for wave steering dem onstration.
0 Ajepunog
(a)
(b)
Figure 3.15: Voltage phase distribution for wave-steering dem onstration,
Even-m ode excitation, (b) Odd-m ode excitation.
66
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(a)
3.4.1
D u a l-M o d e W ave F o cu sin g D e m o n str a tio n
To dem onstrate wave focusing, the sim ulation setup of Fig. 3.13(a) is modified
for point source excitation as shown in Fig. 3.16. B oundary A, B, C, and D are
m atched to Z b of th e contacting cells and a point source is placed in Region I, four
cells away from th e Region I /I I interface. T he operational frequency of 1.90 GHz
was chosen for th e sim ulation2. The RH unit-cells are modified to provide a
propagation constant of 0.50 radians w ith Z b = 50 fi. Experim ental d a ta was used
for th e dual-m ode unit-cell, for which under odd-m ode excitation a propagation
constant of -0.40 radians w ith Z B= 36 Q is obtained and a propagation constant
of 1.43 radians w ith Z b = 62 Q is obtained under even-mode excitation.
Boundary B
o
Z
(0
■o
C
3
O
CQ
Boundary D
point source located
4 cells away from interface
Figure 3.16: Dual-mode flat lens sim ulation setup.
U nder odd-m ode excitation, th e stru ctu re behaves like a flat lens [5] since the
effective refractive index of Region II is th e negative of Region I. In contrast, the
stru ctu re sim ply diverges th e point source in th e case of even-mode excitation
2T he operation frequency was changed from 1.92 GHz to 1.90 GHz for clearer visualization
of the wave refocusing; a smaller propagation constant for the dual-m ode unit-cell (odd-mode)
translates to smaller wavelength
67
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since th e effective refractive index of Region I and II are b o th positive.
The
resulting voltage phase distributions in the stru ctu re for even-mode and odd­
mode excitation are shown in Fig. 3.17(a) and 3.17(b), respectively.
Mil PL
n h ■”
(a)
(b)
Figure 3.17: Voltage phase distribution for flat lens dem onstration, (a) Even­
mode excitation, (b) O dd-m ode excitation.
68
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CHAPTER 4
T w o -D im e n sio n a l C R L H L e a k y -S te e r in g
4.1
In tro d u ctio n
Tw o-dim ensional beam scanning antennas are very im p o rtan t for radar, quasioptical, and satellite systems.
dim ensional beam spanning.
There are several m ethods for achieving twoThe simplest m ethod is mechanical scanning in
which th e an te n n a /a rra y is placed on a mechanical platform . However, m echan­
ical scanning is bulky and not practical for planar microwave systems. Phaseshifters can be used in a planar antenna array to achieve two-dim ensional electronicbased beam scanning; separate sets of phase-shifters are used for azim uth and
elevation scanning. However, these phased arrays are typically cost-, power-, and
space-inefficient due to th e complexity of th e phase-shifters and th e associated
feed network [39]-[40]. T he required num ber of phase-shifters can be reduced
by one-dim ension w ith th e use of leaky-wave antennas [41] in place of resonant
antennas. This one-dim ensional phased leaky-wave antenna array was first pro­
posed in [42]; by varying th e operational frequency, elevation scanning is achieved,
while azim uth scanning is performed by phase-shifters. By using coupled oscilla­
tors [43]-[44] and leaky-wave antennas, a phase-shifterless two-dim ensional beam
scanning array was realized in [45]. By controlling th e free-running frequency of
each leaky-wave element, th e m ain beam can be scanned in th e azim uth plane.
A lthough th e leaky-wave array of [45] elim inates th e use of phase-shifters, each
69
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leaky-wave an ten n a requires its own oscillator.
In this chapter, a novel phase-shifterless technique for beam scanning is com­
bined w ith a leaky-wave antenna to accomplish two-dim ensional beam scanning.
This phase-shifterless technique is based on an orthogonal feeding m ethod [46]
applied to a two-dim ensional stru ctu re as shown in Fig. 4.1. By varying th e power
ratio between th e two orthogonal feed ports, th e net average Poynting vector and
therefore th e net power-flow w ithin the stru ctu re can be controlled. By applying
this technique to a two-dim ensional leaky-wave antenna, th e resulting leakage
power can be controlled in th e azim uth plane while elevation scanning is per­
formed by varying th e operational frequency. By varying th e in p u t power ratio
to th e two feeds and varying th e operational frequency, azim uth (0° < 90 < 90°)
and elevation (-90° < 0 < +90°) scanning can be respectively achieved, suggest­
ing interesting new possibilities in realizing full two-dim ensional phase-shifterless
beam scanning. In th e following sections, th e orthogonal feeding m ethod is ex­
plained and is th en applied to a two-dimensional CRLH leaky-wave antenna. A
CRLH leaky-wave an ten n a is used because of its ability to scan b o th backward
and forward elevation angles [47] while being operated at its dom inant-m ode.
B oth num erical and experim ental results are presented to dem onstrate this novel
phase-shifterless two-dim ensional beam scanning technique.
4.2
O rth ogon al F eeding T h eory
By feeding a two-dim ensional stru ctu re w ith an orthogonal feed, th e net
power-flow w ithin th e stru ctu re can be controlled by sim ply varying the power
ratio between th e feeds [48].
This concept is based on th e fact th a t th e net
average Poynting vector, Sav, in th e stru ctu re will have an x-com ponent and a
y-com ponent which are proportional to th e input powers. By varying th e power
70
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71
\
1 /
p t
y
Figure 4.1: O rthogonal feeding m ethod concept.
ratio, Py:Px, th e resulting average Poynting vector’s angle can be controlled as
shown in Fig. 4.1.
For example, if th e applied power in the y-direction is increased, th e ycom ponent of th e average Poynting vector also increases and th e azim uth angle
of th e resulting average Poynting vector increases. To determ ine th e relation­
ship between th e azim uth angle and the power ratio, th e fields incident to the
homogeneous, isotropic stru ctu re are considered TEM w ith their electric fields
polarized in th e z-direction as shown in Fig. 4.2 w ith
E i = az E i e 1X
(4.1a)
Hi = - a yH i e - ^ x,
(4.1b)
E 2 = azE 2e
(4.1c)
H 2 = axH 2e-™.
(4-Id)
71
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(^"2
Figure 4.2: TE M incident waves on a homogeneous, isotropic structure.
where 7 =a+j(3 and th e tim e-dependence factor ex p (+jj3t) is om itted. Therefore,
the average Poynting vector of th e resulting to ta l field w ithin th e stru ctu re is given
by
Sav
=
=
=
{ a z (E\e~lx + E 2e-™) x (axH 2e
- ayH
^ {ax [E\Hi co sh a(2 x ) + E 2Hi c o sh a (x + y) cos j3(x —y)]} +
- {ay [E2H 2 cosha(2y) + E i H 2 c o sh a (x + y) cos[3(x — y)]}
Assuming a is negligible, (4.2) can be reduced to
72
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(4.2)
sav
“= °
^ { a x [E1H 1 + E 2H 1c o s p ( x - y ) } } +
^ {ay [E2H 2 + E i H 2 c o s /? ( x - y)}} ,
(4.3)
and th e azim uth angle of the resulting average Poynting vector is determ ined by
ip = arctan (
),
(4.4)
-'aVjX
where Sav y and
SaV)X
are th e net y-com ponent average Poynting vectors and
net x-com ponent average Poynting vectors, respectively. Therefore, (4.4) can be
w ritten as
,
^
arC an
( j k IL,y
~ v)) dA\
\ A ^ a I L , y ( E 1H 1 + ^ 2 # 1 COS (3{x
-
y)) d A J '
W ith th e input powers defined as Px = P\H\ and Py = E 2H 2, (4.5) can be
rew ritten as
( p y + y/KPy
f f Xty cos 0 ( x - y ) d A \ \
tp = arctan I ---------,---------------------------------- .
\ P x + y fK P y
(4.6)
f f XiV c o s f i ( x - y ) d A j J
From 4.6, it can be inferred th a t th e azim uth angle of th e net power-flow
is not sim ply determ ined by th e power ratio between th e orthogonal feeds, but
also from th e stru c tu re ’s propagation constant and size. In th e lim iting cases,
the stru ctu re is electrically small or the propagation constant is relatively small,
then (4.6) can be reduced to th e following
73
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p
~
H i? )
arctan (
y
\P* +VPZ\J
— arctan (
,
(4.7)
V p*J
or if th e stru c tu re ’s physical size is an integer m ultiple of a wavelength, (4.6)
simplifies to
p
«
arctan ( ^
J , n = 1,2,3... .
(4.8)
Fig. 4.3 shows th e plot of possible azim uth angles versus power ratios using
(4.6) and th e two lim iting cases, (4.7) and (4.8).
c/)
40
-
30
-
tan 1
0
0
5?
20-
^
10 -
tan
0.0
0.2
0.4
0.6
0.8
1.0
Py: Px
Figure 4.3: P lo t of (4.7) and (4.8); shaded region represents all possible azim uth
angles versus power ratios as determ ined by (4.6).
74
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4 .2 .1
N u m e r ic a l S im u la tio n
To d em onstrate and verify th e orthogonal feeding m ethod for steering th e net
power-flow in a stru ctu re, a parallel plate waveguide (P P W G ) was sim ulated using
the commercial Finite-Elem ent-M ethod (FEM ) full-wave solver, Ansoft HFSS.
The P P W G has an area of 50x50 m m 2, height of 2.54 mm, and £r =10.2; the
top and b o tto m plates are assigned w ith copper and th e four sides are assigned
as waveports. T he sim ulated P P W G is illustrated in Fig. 4.4. Sim ulations were
done at three different frequencies, 1.0 GHz, 1.5 GHz, and 2.0 GHz correspond­
ing to propagation constants of /3=23 rad /m , /?=78 ra d /m , and /?=118 rad /m ,
respectively. For th e sim ulations, th e power ratio between w aveports A and B
were varied, while w aveports C and D were set to 0 W.
7
X
Figure 4.4: A nsoft HFSS sim ulation setup for orthogonal feeding dem onstration
using P PW G ; w aveports applied to four sides for sym m etric boundary conditions.
T he Poynting vector field distribution in th e P P W G a t /= 1 .0 GHz w ith
/5=23 ra d /m were p lotted for several power ratios as shown in Fig. 4.5. The
plots of Fig. 4.5 illustrate th e directional dependence of th e net power-flow on
the power ratio between waveports A and B.
75
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waveport B=0 W
waveport B=0.167 W
(a)
waveport B=0.286 W
waveport B=0.375 W
(c)
(d )
*i
,
5
U1
o
II
<
t
o
a
<u
>
re
5
•:
waveport 8=0.444 W
waveport B=0.5 W
(0
(e)
Figure 4.5: Poynting vector plot for different power ratios (Py:Px)-, 0=23 rad /m .
(a) P ^ P ^ O i l .
(b) Py:Px= 0.2:1. (c) Py:Px=0A:l.
( d ) . P„:Pa= 0 .6 :l.
(e)
P
-P
0.8:1.
(f)
Py:Px=
l:
l.
1y 1a
76
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T he x- and y-com ponents of th e average Poynting vector distribution in the
sim ulated P P W G were obtained using HFSS and then th e net power-flow az­
im uth angle was calculated for different power ratios by using (4.4) for th e three
sim ulated frequencies. These FEM predicted azim uth angles are plotted against
the theoretical values obtained by (4.6) in Fig. 4.6; good agreem ent can be seen
between th e FEM and theoretical results. T he results of Fig. 4.5 and 4.6 vali­
date th e orthogonal feeding m ethod for azim uth steering of th e net power-flow
w ithin a structure. In Section 4.4, this orthogonal feeding m ethod is applied to a
two-dimensional CRLH m etam aterial leak-wave antenna for azim uth steering of
its rad iated field.
40-
^cn
cp«tan
30-
CD
CD
(p ~tan
§? 20^
p- 23 rad/m (eqn.)
p=78 rad/m (eqn.)
p=118 rad/m (eqn.)
3
9- 1 0
-
/? = 23 rad/m (FEM)
AP
=7Qrad/m (FEM)
• p- 118 rad/m (FEM)
P:P
y
x
Figure 4.6: P lot of net average Poynting vector azim uth angle versus power ratio
for different propagation constants of the P P W G shown in Fig. 4.4.
77
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4.3
B ea m -S ca n n in g A p p lica tio n
Tw o-dim ensional beam -steering performed by a two-dim ensional leaky-wave
stru ctu re was first proposed in [3]. In [3], th e authors proposed using a twodim ensional CRLH m etam aterial w ith m ultiple edges (i.e. polygon) as shown
in Fig. 4.7.
Elevation scanning is achieved by changing th e frequency, while
azim uth scanning is achieved by feeding th e stru ctu re a t a different edge. For
example, when power is fed to th e edge depicted in Fig. 4.7, power flows along
the <p—45° plane and th e resulting radiated beam will also occur along th e same
plane. However, this single edge feeding technique is not practical since it requires
a com plicated feeding network and th e num ber of possible azim uth angles are
dependent on th e num ber of edges.
y
Figure 4.7: Single edge feeding of a two-dim ensional leaky-wave stru ctu re for
two-dim ensional scanning.
By applying th e proposed orthogonal feeding m ethod to a square-shaped,
two-dim ensional CRLH m etam aterial, two-dim ensional beam scanning can be
accomplished w ithout using phase-shifters. By operating th e CRLH m etam a­
terial in th e fast-wave region, it can be used as a dom inant-m ode leaky-wave
78
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antenna. A zim uth scanning of th e resulting leaky-wave radiation is determ ined
by th e power ratio of th e orthogonal feeds calculated by (4.6), since a leaky-wave
an ten n a’s power leakage occurs in the direction of the guided power-flow. Un­
like th e proposed anten n a of [3], th e num ber of scanned azim uth angles can be
arbitrary. Elevation scanning of th e resulting radiation is perform ed by varying
the operational frequency. T he two-dimensional CRLH leaky-wave anten n a w ith
orthogonal feeding is illustrated in Fig. 4.8. In Section 4.4, th e analysis, design,
and verification of this antenna for two-dimensional beam -scanning is presented.
■v ■
"-L - j f r - . '
*4
A
V -
/
Figure 4.8: Illustration of orthogonally fed, two-dim ensional CRLH leaky-wave
antenna operating in th e forward fast-wave region.
79
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4.4
T w o -D im en sio n a l C R LH Leaky-W ave A n ten n a
In th is section, th e orthogonal feeding m ethod is applied to a two-dimensional
CRLH m etam aterial leaky-wave antenna. Numerical sim ulations are used to ana­
lyze, design, and verify th e CRLH m etam aterial leaky-wave antenna. In addition,
num erical sim ulation and experim ental m easurem ents are used to verify th e az­
im uth (0° < <p < 90°) and elevation (-90° < 6 < +90°) scanning capabilities of
the proposed phase-shifterless antenna.
4.4.1
U n it-C ell A nalysis
The unit-cell of th e proposed two-dimensional CRLH m etam aterial is based
on th e Sievenpiper m ushroom structure, which in general consists of a square
m etal patch connected to th e ground plane by a via. T he im plem ented CRLH
unit-cell is shown in Fig. 4.9(a) w ith period p and its equivalent circuit model
is shown in Fig. 4.9(b). Surface m ount capacitors w ith values of 0.75 pF were
used to provide C l in order to create a balanced stru ctu re (L l C l = L r C r ) so th a t
v g is nonzero a t ( 3 = 0 for broadside radiation1. P aram eter extraction [49] of the
im plem ented CRLH unit-cell yielded C l —0 . 75 pF, L l = 0.70 nH, C r = 2.00 pF,
and L r = 2.10 nH. A Bloch im pedance of 32 f2 is obtained for th e unit-cell. In
order to characterize th e two-dimensional unit-cell, its dispersion diagram has to
be p lo tted along th e two-dimensional Brillouin zone [50] as shown in Fig. 4.10
where T (k xp = kyp = 0), X ( k xp = 7r, kyp = 0), and M (k xp = kyp = tt) represent
the high-sym m etry points.
Fig. 4.11 shows th e calculated dispersion diagram s of th e CRLH unit-cell
shown in Fig. 4.9(b). Several numerical m ethods were used to generate the disxIn practice th e band-gap between LH and RH pass-bands is difficult to eliminate, b u t a
quasi-balanced stru ctu re can still achieve broadside radiation when operated a t (3 ss 0
80
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>X
.vA-
------
i ( y y y -i
PEC
2C|
capacitance (2 CL)
(a)
(b)
Figure 4.9: 2-D CRLH unit-cell, (a) Im plem ented 2-D CRLH unit-cell w ith p = 5.2
mm, u q = 1 .0 mm , w 2=W3—0.2 mm, and via diam eter, d=0.24 mm on Rogers
R T /D uroid 6010 (h= 1.27 mm, £r =10.2). (b) Equivalent circuit model.
7ilp
nip
-nip
Figure 4.10: Brillouin zone for plotting 2-D dispersion diagram ; T — X — M —F
represents th e irreducible Brillouin zone.
81
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£
^ -----a irlin e
O-O^
0
r
x
M
r
P'P (rad)
Figure 4.11: N um erical 2-D dispersion diagram s for unit-cell of Fig. 4.9(b) using
several num erical m ethods.
persion diagram s. PB C s were used in HFSS to generate th e dispersion diagram
for an infinite stru ctu re, while th e resonance condition of a single unit-cell were
used to generate th e dispersion diagram for a finite stru ctu re [4]. In addition,
the dispersion diagram was also generated w ith th e extracted circuit model (LC)
values by using
(4.9)
(M - T) : kXtV
where th e angular frequencies are defined as
82
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1
(4.10a)
“L
1
UR
y/L^C~R
1
^
(4.10b)
(4.10c)
y /L & l
1
(4.10d)
All three num erical m ethods agree well below / = 7.0 GHz. Since th e struc­
ture is to be effectively homogeneous, it is operated in th e regions satisfying the
homogeneity condition, p < A<,/4. In th e fast-wave region (\f3\ < kQ), th e CRLH
stru ctu re is able to support leaky-waves and the radiation angle is determ ined by
arcsm
(4.11)
T he P B C results show th a t th e dom inant TM mode couples to th e air-line
in the fast-wave region, which indicates th a t an infinite stru ctu re is not able to
support backw ard leaky-waves. However, in practice this air-line coupling does
not exist for two-dim ensional structures w ith finite size. T he P B C results pre­
dict air-line coupling because th e eigenmode solver takes into account radiation
attenuation, a.
4.4.2
A n ten n a R ealization
By periodically cascading th e CRLH unit-cell of Fig. 4.9(b) in two-dimensions,
a 8x8 unit-cell CRLH m etam aterial is realized. The perspective view of th e CRLH
m etam aterial an ten n a is shown in Fig. 4.8 and th e top-view of th e completed
83
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antenna w ith one feeding network is shown in Fig. 4.12. Two orthogonal edges
of th e stru ctu re are used as feeds. Each feed edge consists of eight m icrostrip
transm ission lines connected to a unit-cell by a capacitor of 2-Cl - A 32 Q-to-50 C
tap er is used to connect th e eight input ports at each edge to an 8:1 m icrostrip
corporate feed network; th e ta p er is used to m atch th e CRLH unit-cell’s Z b = 32 S2
to th e feeding netw ork’s Z o=50 Q. For linear polarization of th e radiated field,
bo th feed edges are fed in-phase and only th e m agnitude of th e in p u t power is
varied. Section 4.4.5 will discuss th e case when one feed p o rt is out-of-phase with
the other feed-port. The unit-cells at th e non-feeding edges are term inated with
50 Q, loads to minimize reflections.
50 Q loads— ►,,i
,j
Figure 4.12: P hoto g rap h of realized orthogonally fed, two-dim ensional CRLH
leaky-wave antenna.
By varying th e input power ratio (Py:Px), th e net power-flow of th e resulting
field distrib u tio n in th e stru ctu re can be steered along th e x-y plane. W ith only
two feeding edges, th e resulting leaky-wave rad iatio n ’s <p is determ ined by (4.6)
and can range from 0° to 90°. While, the resulting leaky-wave rad iatio n ’s 6 is
determ ined by (4.11) and can range from -90° to +90°. In addition, since the
84
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CRLH unit-cell is balanced, th e CRLH antenna can also scan a t broadside (6= 0°).
4.4.3
N um erical R esu lts
N um erical sim ulation of th e 8x8 CRLH m etam aterial anten n a w ith orthogonal
feeding was perform ed in Ansoft HFSS. To verify th e 9 scanning capability of the
antenna, several frequencies in th e fast-wave region was sim ulated. T he resulting
2-D far-held plots for /= 3 .2 GHz (0 < 0), /= 4 .0 GHz ((3 = 0), and /= 5 .1 GHz
{0 > 0) are shown in Fig. 4.13 w ith Py:Px= 0:1. T he far-held plots of Fig. 4.13
verify th e leaky-wave radiation scanning of th e CRLH antenna.
Z
0
0
-5
330
7'~
300
-10
-15- 270
-
10 -
-5-
0
240
120
- ~ f = 3.2 GHz
210
180
150 _ _ f = 4.o G Hz
f = 5.1 GHz
Figure 4.13: N um erical 2-D far-held plots for /= 3 .2 GHz (backward scan,
0=-4O°), /= 4 .0 GHz (broadside, 0=0°), and f —5.1 GHz (forward scan, 0=+ 45°);
P y 'P x —O T -
N ext, th e sim ulated results for /= 3 .2 GHz (0 —72.50 ra d /m ) were used to
verify th e <p scanning capability of th e orthogonal feed applied to th e antenna.
This was done by varying Py:Px and plotting th e resulting 3-D far-held p attern
at /= 3 .2 GHz. Fig. 4.14 shows th e 3-D far-held p attern s as Py :Px is varied from
0:1 to 1:0 w ith 0.2 increm ents. The azim uth angle versus power ratio for the
85
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FEM sim ulation a t /= 3 .2 GHz are plotted in Fig. 4.15 along w ith th e theoretical
values obtained from (4.6). Good agreement can be seen between th e FEM and
theoretical results. In addition, the FEM and theoretical azim uth angle versus
power ratio for f = 3.35 GHz (/3—47.43 rad /m ) and f —3.50 GHz (/3=28.55 rad /m )
are also p lo tted in Fig. 4.15. Discrepancies between th e FEM and theoretical
results can be a ttrib u te d to th e lim ited mesh density of th e FEM sim ulation
a n d /o r negligence of th e an ten n a’s a in th e theoretical calculations of (4.6).
86
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------ >X
(a)
(0
(e)
(c)
(d )
(g)
(h )
-+x
Utirm
-*X
w
(i)
0)
(k)
Figure 4.14: Far-field radiation plots for different power ratios (Py:Px):
f —3.20 GHz w ith f3=72.5 ra d /m and 0=~4O°. (a) Py :Px= 0:1, <p=0°. (b)
Py:Px= 0.2:1, <p=18°. (c) P y:Pa= 0 .4 :l, <p=28°.
(d) Py:Px= 0.6:1, <p=34°. (e)
P B:Pa= 0 .8 :l, <p=40°. (f) P ^ P ^ H l , <p=45°. (g) P„:Pa= l:0 .8 , <p=50°. (h)
Py:Px= 1:0.6, ip—56°. (i) P„:Pa= l:0 .4 , <p=62°.
(j) P„:Pa= l:0 .2 , <p=72°. (k)
P S:PX=1:0, tp= 90°.
87
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— /?= 28.55
- - p = 47.43
—• p —72.50
■ p = 28.55
a /?= 47.43
• p = 72.50
rad/m
rad/m
rad/m
rad/m
rad/m
rad/m
(eqn.)
(eqn.)
(eqn.)
(FEM)
(FEM)
(FEM)
Figure 4.15: ^ radiation angles for leaky-wave antenna of Fig, 4.8; Eq.
versus FEM for /?=28.55 rad /m , /3=47.43 rad /m , and /?—72.50 rad /m .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(4.6)
4 .4 .4
E x p e r im e n ta l R e su lts
T he fabricated an ten n a was placed in an Nearfield Systems spherical near-field
cham ber in order to obtain 3-D far-held radiation patterns. Fig. 4.16(a) shows
the com pleted an ten n a w ith feeding networks m ounted in an antenna chamber;
Fig. 4.16(b) shows th e feed network incorporated in the backside of th e antenna.
W ilkinson
pow er divider
W ilkinson
pow er divider
Figure 4.16: Far-held m easurem ent setup, (a) Front view of m ounted antenna,
(b) Back view of m ounted antenna showing feeding network.
To verify th e capability of the antenna to scan in th e 6 direction, th e antenna
was fed w ith Py :Px= 0:1. Fig. 4.17 shows th a t th e antenna can scan from backhre
to endhre and is capable of broadside radiation. Similar results were obtained
when th e an ten n a was fed w ith Py :Px= 1:0 and Py:Px= l: 1 w ith th e exception th a t
the an ten n a is polarized in another plane. B oth endhre and backhre radiation is
observed, indicating th a t b o th RH and LH leaky modes exist. In th e LH region,
as th e frequency is decreased from 4.2 GHz to 3.2 GHz, 6 decreases from 0° to
-61°, and th e rad iated beam scans tow ard backhre. In th e RH region, as the
frequency is increased 4.2 GHz to 5.1 GHz, 6 increases from 0° to +60°, and the
89
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radiated beam scans tow ard endfire.
z
0-i
0
3
3
0
^
—~ r -^ 3 0
90 x,y
-
10-
^
180
150
_ _ .f = 3.2 GHz
f = 4.2 GH z
f = 5.1 GHz
Figure 4.17: E xperim ental 2-D far-field plots for /= 3 .2 GHz (backward scan,
#=-61°), /= 4 .2 GHz (broadside, 6= 0°), and /= 5 .1 GHz (forward scan, #=+ 60°);
Py-.PX= 0:1.
By m easuring th e 6 of th e resulting radiated beam , th e propagation constant
of the CRLH unit-cell can be verified w ith th e use of (4.11). T he m easured and
experim ental dispersion diagram are shown in Fig. 4.18. T he deviation of the
m easured dispersion diagram to th e calculated diagram can be a ttrib u ted to the
im plem ented 0.75 p F capacitors, which have a tolerance of ±0.25 pF.
Therefore by controlling th e frequency, elevation (9) scanning is achieved. By
varying th e power ratio, Py '.Px , azim uth (ip) scanning can be achieved. T he power
ratio was changed by using atten u ato rs a t the o u tp u t p o rts of th e W ilkinson
power divider shown in Fig. 4.16. To dem onstrate azim uth scanning, Py.Px was
varied and th e 3-D far-held was measured. Fig. 4.19 shows th e m easured 3-D farheld p attern s for various power ratios at /= 3 .8 0 GHz (/?=24.69 rad /m ). W hen
Py:Px= 0.16:1, th e rad iated beam occurs at ip=3°, 8= -15°. W hen Py :Px= 0.4:1,
the rad iated beam occurs at <p=33°, #=-15°. W hen Py:Px= 1:1, th e radiated beam
90
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c
/
oO<D
g)
/
/
J
*
°0
-----LC Model (T - X)
- - LC Model (r - M)
— 64 Cells (2-D LWA)
— air-line
_
I !
30
60
90
120
(3p (degrees)
Figure 4.18: Experim ental versus num erical dispersion diagram .
occurs at tp=43°, 9—- 15°. These results are in agreem ent w ith the azim uth and
elevation angles predicted by (4.6) and (4.11), respectively. T he azim uth angles
versus power ratio for th e experim ental results are plotted along w ith th e FEM
and theoretical predicted azim uth angles in Fig. 4.20. D eviations between the
FEM and theoretical results can be a ttrib u ted to m ism atch at th e term inated
edges of th e CRLH stru ctu re and th e im plem ented 0.75 pF capacitors.
91
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dB
dB
dB
-5 .0 d B
-7 .0 d B
-9 .0 d B
-1 1 .0 d B
-1 3 .0 d B
- 1 5 .0 d B
-1 5 0
-1 0 0
-5 0
0
50
100
15 0
0 (degrees)
(a)
H
-150
-1 0 0
-5 0
0
50
100
0 dB
-1 .0 d B
-3 .0 d B
-5 .0 d B
-7 .0 d B
-9 .0 d B
- 1 1 .0 d B
-1 3 .0 d B
- 1 5 .0 d B
150
0 (degrees)
(b)
0 dB
-1 .0 d B
-3 .0 d B
-5 .0 d B
-7 .0 d B
-9 .0 d B
- 1 1 .0 d B
- 1 3 .0 d B
-1 5 .0 d B
-150
-1 0 0
-5 0
0
50
100
150
0 (degrees)
(c)
Figure 4.19: M easured 3-D far-field p attern s (normalized dB-scale) of th e CRLH
leak-wave an ten n a a t /= 3 .8 0 GHz. (a) P y ' - P x =0.16:1. (b) P y : P x = 0 A : l . (c)
P , Px=
1:1.
92
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50
40-
c/)
0
0L_
30-
05
■g 2010
-
experimental
numerical (eqn.)
numerical (FEM)
0.0
Figure 4.20: E xperim ental
f3=24.69 rad /m .
0.2
0 .4
0.6
0.8
1.0
versus num erical ((4.6) and FEM )
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tp for
4 .4 .5
P o la r iz a tio n D iv e r sity
In th e case of azim uth scanning, the input power to each feed was in-phase.
However, if one p o rt has a fixed phase offset from the other p o rt, polarization
diversity can also be achieved. For example if Py:Px=1 Z 90°:1Z 0 °, then the re­
sulting rad iated field will be left-hand circular polarized (LH CP). Therefore, a
LHCP beam can be scanned in 9 w ith p = 45°. This is verified by FEM simula­
tion of th e stru ctu re w ith Py:Px = 1Z90°:1Z0° and operation in th e backward
wave region; th e num erical far-held plots (p = 45°, 9 = -180° —> +180°) for dif­
ferent polarization com ponents are shown in Fig. 4.21 and confirm th a t LHCP
is achieved. If th e m agnitude of th e input powers have an offset then elliptical
polarization can be achieved a t a fixed >p angle.
o
330
-5-
300
10-
-15- 270
-10
240
120
150
210
180
Figure 4.21:
1Z90°:1Z0°.
C om puted
far-held
polarization
LHCP
RHCP
- — X-Linear
Y-Linear
com ponents
for
94
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Py :Px —
CHAPTER 5
C o n clu sio n
Novel one- and two-dimensional CRLH microwave devices not possible with
conventional m aterials were presented.
T he analysis, design, and verification
of these CRLH microwave devices were discussed. In particular, these devices
exploited th e CRLH m etam aterial’s infinite wavelength resonance, negative re­
fractive index, and fundam ental leaky-wave mode.
T he infinite wavelength resonance of th e CRLH m etam aterial was used to
realize a novel JV-port series divider which evenly divides power in m agnitude
and phase to an a rb itrary num ber of o u tp u t ports. In addition, it was shown
th a t th e novel series divider’s performance is not dependent on th e location of
its o u tp u t ports.
Since an infinite wavelength is supported, all points along
the CRLH m etam aterial TL have th e same m agnitude and phase.
A 4-port
series divider consisting of a eight unit-cell CRLH m etam aterial TL was shown
to exhibit 0.22 dB m axim um m agnitude difference and 1.32° m axim um phase
difference between o u tp u t ports a t its infinite wavelength frequency. In addition,
a 6-port series divider consisting of a thirteen unit-cell CRLH m etam aterial TL
was fabricated and shown to exhibit 0.30 dB m axim um m agnitude difference and
6.3° m axim um phase difference between o u tp u t p o rts at its infinite wavelength
frequency. B oth num erical and experim ental results were shown to validate the
divider’s perform ance. A pplications of this novel divider for sparse array antenna
feed and for power combining were also presented.
95
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T he infinite wavelength phenom enon of th e CRLH m etam aterial was also
used to realize size-independent planar resonant antennas. Since th e phase shift
is zero for a unit-cell th a t supports an infinite wavelength, th e physical size of
the anten n a can be arbitrary; th e an ten n a’s size is independent of th e resonance
phenomenon. T he an ten n a’s operational frequency depends only on its unit-cell
and th e an ten n a’s physical size depends on th e num ber of unit-cells. It was also
shown th a t th e supported infinite wavelength can be used to generate a monopolar
radiation p attern . To dem onstrate these concepts, six antennas w ith different
num ber of unit-cells were numerically and experim entally realized w ith th e CRLH
unit-cell. A lthough, th e an ten n a’s resonant length is increased by 200%, only a
4.7% frequency shift was obtained for th e six unit-cell antenna in comparison
to th e two unit-cell antenna. By using th e infinite wavelength and supported
backward wave of th e CRLH m etam aterial TL, a dual-m ode com pact antenna
was realized. This anten n a is capable of m onopolar radiation a t one resonant
frequency and patch-like radiation at another resonant frequency. Numerical and
experim ental results of a three unit-cell CRLH resonant anten n a were presented
to validate th e concept.
A m ode selective m etam aterial which supports either forward or backward
waves w ithin th e sam e frequency bandw idth was also presented. This dual-m ode
m etam aterial was based on a modified CRLH. T he choice between dispersion
operations is based on th e mode excitation applied to th e dual-m ode CRLH
m etam aterial. A dem onstration m icrostrip prototype of this dual-m ode CRLH
m etam aterial was realized and characterized. T he m etam aterial possess a positive
refractive index under even-mode excitation and possess a negative refractive
index under odd-m ode excitation in th e 1.86 GHz - 2.00 GHz frequency range.
C ircuit sim ulations w ith th e num erical and experim ental results of th e dual-m ode
CRLH m etam aterial are performed to dem onstrate electrom agnetic wave steering
96
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and spatial m ultiplexing a t a fixed frequency based on dispersion selectivity.
Next, th e fundam ental leaky-wave supported by th e CRLH m etam aterial was
used to realize a two-dim ensional CRLH leaky-wave antenna. This CRLH leakywave an ten n a is com bined w ith an orthogonal feeding stru ctu re to realize a novel,
dom inant-m ode leaky-wave antenna w ith spatial diversity w ithout th e use of any
phase-shifters. By varying th e m agnitude of th e input power to two orthogonal
edges of th e CRLH m etam aterial, th e net power-flow direction can be controlled.
A zim uth scanning is achieved by varying th e m agnitude of th e input power at the
two orthogonal edges of th e structure, while elevation scanning is m ade possible
by varying th e operational frequency. Numerical sim ulations were used to validate
the orthogonal feeding m ethod for azim uth steering of th e leaky-wave. Experi­
m ental radiation p attern s of th e stru ctu re were m easured and dem onstrated an
elevation scanning range of -61° to +60° and an azim uth scanning range of 0° to
+90° w ith orthogonal two-edge feeding. In addition, polarization diversity of the
orthogonally fed CRLH antenna was also presented.
97
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R eferen ces
[1] V. G. Veselago, “T he electrodynam ics of substances w ith sim ultaneously
negative values of e and //,” Soviet Physics Uspekhi, vol. 10, no. 4, pp. 509..
514, Jan. 1968.
[2] C. Caloz, C. C. Chang, and T. Itoh, “Full-wave verification of th e fundam en­
ta l properties of left-handed m aterials in waveguide configurations,” Applied
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