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Miniaturized Antennas and Metamaterial-Based Transmission Line Components in Microwave Circuits Applications

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UNIVERSITY OF CALIFORNIA
Los Angeles
Miniaturized Antennas and Metamaterial-Based
Transmission Line Components in Microwave Circuits
Applications
A dissertation submitted in partial satisfaction of the
requirements for the degree Doctor of Philosophy
in Electrical Engineering
By
Pei-Ling Chi
2011
UMI Number: 3472614
All rights reserved
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UMI
Dissertation Publishing
UMI 3472614
Copyright 2011 by ProQuest LLC.
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unauthorized copying under Title 17, United States Code.
ProQuest LLC
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© copyright by
Pei-Ling Chi
2011
The dissertation of Pei-Ling Chi is approved.
V^
Frank M. C. Chang
Yuanxun Ethan Wang
/ZTatsuo Itoh, Committee Chair
University of California, Los Angeles
2011
ii
Table of Contents
Chapter 1
1.1
Introduction
1
Basics of Metamaterials
1
1.1.1
Background and the Extraordinary Properties
1
1.1.2
Composite Right/Left-Haned Transmission Lines
4
1.1.3
Dispersion Engineering Technique for the Cimposite Right/Left-
Hnaded Transmission Lines
1.2
7
Bascis of Slow Wave Structures
11
1.2.1
Background and the Properties
11
1.2.2
Periodically Loaded Structures and the Slow Wave Enhancement
Factor
13
References
Chapter 2
16
Composite Right/Left-Hnaded Transmission Line Hybrid Couplers and
Their Applications
18
2.1
Introduction
18
2.2
Miniaturized and Arbitrary Dual-Band Hybrid Couplers Based on the
Composite Right/Left-Handed Transmission Lines
21
2.2.1
Phase Engineering of the Dual-Band Couplers
2.2.2
Design Pmciple of the Compact and Dual-Band 180° Coupler ... 23
2.2.3
Design Pmciple of the Compact and Dual-Band 90° Coupler
iii
21
31
2.3
Application of the CRLH Hybrid Couplers to the Dual-Band Beam Pattern
Diversity Systems
2.3.1
38
Implementation Principle of Dual-Band Beam Pattern Diversity
Uisng the Hybrid Couplers
2.3.2
38
Implementation of the Compact Dual-Band CRLH-Based Delay
Line
39
2.3.3
Implementation of the Dual-Band Antenna
2.3.4
Experimental Demonstration of the Three Types Dual-Band Beam
Pattern Diversity Systems
2.4
45
Application of the CRLH Hybrid Couplers to the Microwave Diplexers. 54
2.4.1
Introduction
54
2.4.2
Diplexer Based on the Single-Band 180° Coupler and the CRLH
Phase-Delay Line
2.4.3
56
Diplexer Based on the Dual-Band 90° Coupler and the CRLH
Phase-Advance Line
60
References
Chapter 3
42
65
Antenna Miniaturization Based on the Slow Wave Enhancement Factor
from the Loaded/Unloaded Transmission Line Models
3.1
Introduction
3.2
Design Procedure of the Capacitive-Loaded Antenna with Fexible Size
68
68
Reduction Using the Slow Wave Enhancement Factor
iv
70
3.3
Example I: The Miniaturized Slot Loop Antenna and the Implementation
of the Wideband Impedance Matching Network
3.3.1
The Capcitor-Loaded and Miniaturized HF Slot-Loop Antenna
with Z-Section Matching Circuit
3.3.2
77
77
The Proposed Filter-Type Matching Network for the Bandwidth-
Improved HF Slot-Loop Antenna
85
3.4
Example II: The Miniaturized Planar Inverted F Antenna (PIFA)
90
3.5
Example III: Compact and Tunable Slot Loop Antenna
95
3.5.1
Introduction
95
3.5.2
Slow Wave Antenna
97
3.5.3
Diode Modeling
101
3.5.4
Simulation, Experiments, and Discussions
103
References
Chapter 4
108
Conclusion
115
v
List of Figures
Figure 1-1 Illustrations of wave propagation in the conventional material (s, // >0) and in
the artifial left-handed material (s, ju <0)
3
Figure 1-2 Dispersion curves and the equivalent circuit models for the ideal homogenous
(a) purely right-handed transmission lines and (b) purely left-handed transmission
lines
3
Figure 1-3 Dispersion curve and the equivalent circuit model for the LC network CRLH
transmission structures
5
Figure 1-4 (a) Phase superposition of the balanced CRLH transmission line, and (b) the
LC network implementation of the balnaced CRLH transmission line by cascading
the right-handed transmission line with the the left-handed transmission line
9
Figure 1-5 Physical realization of the CRLH transmission line. Three unit cells are
illustrated in this case
11
Figure 1-6 Dispersion diagram of the slow wave structres
12
Figure 1-7 (a) Substrate loading, and (b) reactive loading using a capacitor (including the
substrate loading)
13
Figure 1-8 Schematic of the capacitor-loaded slow wave structre
15
Figure 2-1 Schemaic of the CRLH dual-band 180° hybrid coupler
24
Figure 2-2 Four possible CRLH transmission phase solutions of the 180° coupler. The
dashed and solid lines represent <p\ and q>i, respectively
vi
25
Figure 2-3 Phase implementation for the proposed compact dual-band 180° hybrid
coupler at (a) 1 GHz and (b) 2 GHz, where Z0= 50 Q
26
Figure 2-4 Simulated magnitude responses of the proposed compact dual-band 180°
hybrid coupler: (a) from the 2 port and (b) from the A port
27
Figure 2-5 Photograph of the fabricated compact dual-band 180° hybrid coupler. The
radius and width of the ring are 30.51 mm and 0.78 mm, respectively
29
Figure 2-6 Measured magnitude responses of the proposed compact dual-band 180°
hybrid coupler: (a) from the 2 port and (b) from the A port
Figure 2-7 Schematic of the CRLH dual-band 90° hybrid coupler
29
33
Figure 2-8 Six possible CRLH transmission phase solutions of the 90° coupler. Each
curve can be used as q>\ (35.36 Q) or q>i (50 Q)
34
Figure 2-9 Phase implementation for the proposed compact dual-band 90° hybrid coupler
a t ( a ) l GHz and (b) 2 GHz
35
Figure 2-10 Simulated (a) magnitude and (b) phase responses of the proposed compact
dual-band 90° hybrid coupler
35
Figure 2-11 Photograph of the fabricated compact dual-band 90° hybrid coupler. /35.36n=
39.48 mm, W35.36Q= 2.51 mm, /5otr= 38.26 mm, and w>5on= 1.35 mm
36
Figure 2-12 Measured (a) magnitude and (b) phase responses of the proposed compact
dual-band 90° hybrid coupler
37
Figure 2-13 The conceptual schematic of the proposed dual-band CRLH-based delay line.
qh and (pi are the phase responses of the CRLH and microstrip lines, respectively. 40
vii
Figure 2-14 Phase implementation for the proposed dual-band delay line at (a) 1 GHz and
(b)2GHz
41
Figure 2-15 Photograph of the fabricated compact dual-band CRLH delay line. The port
distance for each transmission line is /deiay= 20 mm
41
Figure 2-16 Measured and simulated return losses and phase differences {(p\- q>i) of the
proposed compct dual-band delay line
42
Figure 2-17 Configuration of the dual-band antenna, The fabricted dimnesions are as
follows: /n=/i2 = 12.5 mm, h\=h2= 26.5 mm, d\=d-f^ 1.5 mm, l\= 48.25 mm, h=
18.25 mm, w\= 1.5 mm, W2= 7 mm, /gnd= 60 mm, and wgn(i=150 mm
43
Figure 2-18 Measured and simulated radiation patterns of the dual-band antenna at 1
GHz
44
Figure 2-19 Measured and simulated return losses of the dual-band antenna
44
Figure 2-20 Schematic illustration of the Type-I dual-band beam pattern diversity at (a)
2.4 GHz (b) 5.2 GHz
46
Figure 2-21 Measured H-plane radiation patterns of the Type-I beam pattern diversity
system at (a) 2.4 GHz and (b) 5.2 GHz
47
Figure 2-22 Measured input isolation improvement of the Type-I system between the
cases of array with and without the 180° coupler
47
Figure 2-23 Schematic illustration of the Type-II dual-band beam pattern diversity at (a)
2.4 GHz (b) 5.2 GHz
49
Figure 2-24 Measured H-plane radiation patterns of the Type-II beam pattern diversity
system at (a) 2.4 GHz (b) 5.2 GHz
50
viii
Figure 2-25 Measured input isolation improvement of the Type-II system between the
cases of array with or without the mode decoupling network (MDN)
51
Figure 2-26 Schematic illustration of the Type-Ill dual-band beam pattern diversity at (a)
1 GHz (b) 2 GHz
52
Figure 2-27 Measured and simulated H-plane radiation patterns of the Type-Ill beam
pattern diversity system at (a) 1 GHz (b) 2 GHz
53
Figure 2-28 Measured input isolation improvement of the Type-Ill system between the
cases of array with or without the mode decoupling networks (MDNs)
53
Figure 2-29 Schematic illustration of the proposed ring-hybrid -based diplexer at (a) 1.9
GHz (b) 2.4 GHz
57
Figure 2-30 Photograph of the proposed ring-hybrid -based diplexer at 1.9 GHz and 2.4
GHz
58
Figure 2-31 Measured and simulated insertion losses of the proposed ring-hybrid -based
diplexer
59
Figure 2-32 Measured and simulated input return losses and ouput isolations of the
proposed ring-hybrid-based diplexer
59
Figure 2-33 Schematic illustration of the proposed quadrature-hybrid -based diplexer at
(a) 1 GHz (b) 2 GHz
61
Figure 2-34 Photograph of the proposed quadrature-hybrid -based diplexer at 1 GHz and
2 GHz
62
Figure 2-35 Measured and simulated insertion losses of the proposed quadrature-hybrid based diplexer
63
IX
Figure 2-36 Measured and simulated input return losses and ouput isolations of the
proposed quadrature-hybrid -based diplexer
63
Figure 3-1 Illustration of a capacitor-loaded slow wave antenna in the k-fi diagram. The
unit cell is shown as an inset
71
Figure 3-2 (a) The SWE ifiip^) versus loaded shunt capacitance for the capacitor-loaded
unit cell. The capacitance sweep is from 10 pF to 100 pF with a fixed Zsi0t= 75.44 Q
and a load interval d%\JX^= 7.6 degrees at 300 MHz, (b) the corresponding
frequency responses of the capacitor-loaded unit cell versus /3d.
72
Figure 3-3 Variation of the Bloch impedance for the capacitor-loaded unit cell. The
capacitance sweep is from 10 pF to 100 pF with a fixed Zsiot= 75.44 Q and a load
interval ds\JX%= 7.6 degrees at 300 MHz
74
Figure 3-4 Calculated input VSWRs of the CPW-fed capacitor-loaded slot-loop antennas
(with an inset) with 5 cases of different ZBs. The corresponding quality factors (Qs)
are included in the figure. The slot width, load period, substrate thickness and
dielectric constant of the antennas are 2 mm, 20 mm, 0.508 mm, and 4.5,
respectively
75
Figure 3-5 (a) The configuration of the proposed capacitor-loaded HF slot-loop antenna
with the Z-section matching circuit, (b) Photograph of the fabricated antenna
79
Figure 3-6 SWE investigation for the capacitor-loaded HF slot-loop antenna (a) SWE vs.
load capacitance (b) SWE vs. load period (c) SWE vs. characteristic impedance of
the slot line
79
Figure 3-7 Measured and simulated \Su\ of the loaded HF slot-loop antenna with and
without the Z-section matching circuit
81
Figure 3-8 Calculated radiation gains of the loaded HF slot-loop antennas with the Zsection and four-pole filter-type impedance matching networks, respectively
Figure 3-9 Predicted radiation efficiency rjr with respect to the size reduction
81
84
Figure 3-10 (a) Illustration and (b) corresponding implementation of the impedance
matching network using filter design techniques for the loaded HF slot-loop antenna.
Four-pole prototype matching circuit (including the antenna) is used in this case... 86
Figure 3-11 Measured and calculated \Sn\ of the loaded HF slot-loop antenna with the
filter-type imprdance matching network. The measured |5n| of the HF slot-loop
antenna with Z-section matching circuit is included for comparison
88
Figure 3-12 The configuration of the proposed capacitor-loaded PIFA with an inset of its
unit-cell model
91
Figure 3-13 SWE investigation for the capacitor-loaded PIFA (a) SWE vs. load
capacitance (b) SWE vs. load period (c) SWE vs. characteristic impedance of the
microstrip line
91
Figure 3-14 Photograph of the fabricated capacitor-loaded PIFA
92
Figure 3-15 Measured and calculated \Su\ for the loaded and unloaded PIFAs
92
Figure 3-16 Measured and calculated radiation patterns for the (a) loaded and (b)
unloaded PIFAs
95
Figure 3-17 Schematic of the proposed tunable slot-loop antenna. The microstrip line
(dashed line) is on the opposite side of the substrate with respect to the slot loop
xi
(bold line). Eight varactor diodes are periodically loaded across the slot in the
positions where the gap width is reduced as indicated. All dimensions are in mm.. 97
Figure 3-18 Comparison between the slow wave enhancement factor /?//?o and
miniaturization factor fr0/fr for the proposed tunable slot-loop antenna
100
Figure 3-19 The extracted junction capacitance C} and series resistance R& in the
equivalent lumped-element model versus the bias voltage. The parasitic capacitance
Cp and parasitic inductance Zp are assumed as 0.06 pF and 0.2 nH, respectively.. 100
Figure 3-20 Photographs of the fabricated tunable slot-loop antenna, (a) Top view of the
structure showing the microstrip feed line and the LC low-pass bias network (the
detail is shown in the inset), and (b) back view of the structure showing the slot loop
periodically loaded by the 8 varactor diodes
Figure 3-21 The meausred |5n| for the proposed tunable slot-loop antenna
102
102
Figure 3-22 Comparison between measured and simulated reflection coefficients \Sn\ for
the proposed tunable slot-loop antenna biased at (a) 22 volts, (b) 20 volts, (c) 15
volts, and (d) 4 volts
103
Figure 3-23 Measured radiation patterns for the proposed tunable slot-loop antenna
biased at (a) 20 volts, (b) 15 volts, (c) 10 volts, (d) 4 volts
105
Figure 3-24 Measured and simulated radiation gains for the proposed tunable slot-loop
antenna
107
xii
List of Tables
Table 2-1 Measured performances of the proposed 180° coupler at £ port
30
Table 2-2 Measured performances of the proposed 180° coupler at A port
30
Table 2-3 Simulated performances of the microstrip 180° coupler at 1 GHz
31
Table 2-4 Measured performances of the proposed 90° coupler
37
Table 3-1 Full-wave miniaturization factor versus SWE for the loaded slot-loop antenna...
77
Table 3-2 Lumped-element parameters in the matching circuit for the loaded slot-loop
antenna
86
Table 3-3 Calculated radiation efficiency for the proposed tunable antenna under
different bias voltages
105
xni
Acknowledgments
I would like to give my sincerest gratitude to my advisor, Professor Tatsuo Itoh,
for his guidance and support during my Ph. D. study, and the members of my committee,
Professors Frank Chang, Huan Huang, and Ethan Wang, for the time they have spent in
improving this dissertation. In addition, I received help from Dr. Rod Waterhouse, who
advised me many precious comments on the materials presented in Chapter 3.1 could not
have made it without the help from my fellow lab-mates and visiting scholars: Dr.
Catherine Allen, Dr. Anthony Lai, Dr. Darren Goshi, Dr. Cheng-Jung Lee, Yuandan
Dong, Michael Chung-Tse Wu, Prof. Eisuke Nishiyama, and Prof. Young Kim.
Furthermore, I send many thanks to my best friend, Tao Yang, for his consideration and
encouragement at all times. Finally, to my beloved family, thank them for their
thoughtfulness and endless support all the way in my life.
xiv
VITA
March 25, 1982
Bom, Taichung, Taiwan
2004
Student Member of The Phi Tau Phi
Scholastic Honor Society of The Republic of
China
2004
Research Creativity Award,
National Science Council
2004
B.S., First Place
Department of Communication Engineering
National Chiao Tung University, Hsinchu,
Taiwan
2004
Master Entering Fellowship, First Place
National Chiao Tung University
2006
M.S., First Place
Department of Communication Engineering
National Chiao Tung University, Hsinchu,
Taiwan
2006
Ph.D. Entering Fellowship
University of California, Los Angeles
PUBLICATIONS
P. -L. Chi and T. Itoh, "Miniaturized dual-band directional couplers using composite
right/left-handed transmission structures and their applications in beam pattern
diversity systems," IEEE Trans. Microw. Theory Tech., vol. 57, no. 5, pp. 12071215, May 2009.
P. -L. Chi, R. Waterhouse, and T. Itoh, "Antenna miniaturization using slow wave
xv
enhancement factor from loaded transmission line models," IEEE Trans.
Antennas Propag., to be published
P. -L. Chi, R. Waterhouse, and T. Itoh, "Compact and tunable slot-loop antenna," in
IEEE Trans. Antennas Propag., to be published
P. -L. Chi and Y. -D. Lin, "Tapered bent folded monopole for dual-band wireless local
area network (WLAN) Systems," IEEE Antennas Wireless Propag. Lett., vol. 4,
pp. 355-357, 2005.
P. -L. Chi and T. Itoh, "Dispersion engineering with CRLH metamaterials," in IEEE
RFITInt. Symp., December 2009, pp. 128-131.
P. -L. Chi and T. Itoh, "Novel diplexer synthesis using the composite right/left-handed
phase-advance/delay lines," in IEEE MTT-S Int. Microw. Symp. Dig., June 2009,
pp. 117-120.
P. -L. Chi and T. Itoh, "Metamaterial-based components for a compact dual-band beam
pattern diversity system," in Proc. 38th Eur. Microw. Conf, October 2008, pp.
555-558.
P. -L. Chi, C. -J. Lee, and T. Itoh, "A compact dual-band metamaterial-based rat-race
coupler for a MIMO system application," in IEEE MTT-S Int. Microw. Symp.
Dig., June 2008, pp. 667-670.
P. -L. Chi, K. Leong, R. Waterhouse, and T. Itoh, "A miniaturized CPW-fed capacitorloaded slot-loop antenna," in IEEE ISSSE Int. Symp Dig., July 2007, pp. 595598.
P. -L. Chi, S. - S . Wu, and Y. -D. Lin, "Integrated antennas and diplexers for dual-band
xvi
wireless local area network (WLAN) system," in Proc. 17
Asia-Pacific
Microw. Conf., December 2005.
C. -K. Liao, P. -L. Chi, and C. -Y. Chang, "Microstrip realization of generalized
Chebyshev filters with box-like coupling schemes," IEEE Trans. Microw.
Theory Tech., vol. 55, no. 1, pp. 147-153, January 2007.
T. Yang, P. -L. Chi, and T. Itoh, "Compact quarter-wave resonator and its applications
to miniaturized diplexer and triplexer," IEEE Trans. Microw. Theory Tech., to be
published
T. Yang, P. -L. Chi, and T. Itoh, "High isolation and compact diplexer using the hybrid
resonators," IEEE Microw. Wireless Compon. Lett., vol. 20, no. 10, pp. 551-553.
T. Yang, P. -L. Chi, and T. Itoh, "Lumped isolation circuits for improvement of
matching and isolation in three-port balun band-pass filter," in IEEE MTT-S Int.
Microw. Symp. Dig., May 2010, pp. 584-587.
T. Yang, M. Hashemi, P. -L. Chi, and T. Itoh, "A new way of bandpass filter design
based on zeroth-order and negative-order resonance modes," in 2009 AsiaPacific Microw. Conf, December 2009, pp. 163-166.
xvn
ABSTRACT OF THE DISSERTATION
Miniaturized Antennas and Metamaterial-Based
Transmission Line Components in Microwave Circuits
Applications
by
Pei-Ling Chi
Doctor of Philosophy in Electrical Engineering
University of California, Los Angeles, 2011
Professor Tatsuo Itoh, Chair
This dissertation presents two diversities of miniaturization approaches to the
antennas and microwave passive circuit components. The first approach is based on the
unique metamaterial transmission line structures. The metamaterial structure or the lefthanded structure is an artificial structure that is dispersion engineerable from its
constituent parameters. By means of the left-handed transmission lines or the composite
right/left-handed (CRLH) transmission lines to replace the conventional microstrip lines,
xviii
microwave circuit components can be miniaturized via controlling the phase responses at
the frequencies of interest, which saves the footprint size. Specifically, this idea was
implemented on the dual-band 180° and 90° hybrid couplers and both of them
demonstrate considerable size reductions in the experiments. On the other hand, the
second methodology leading to miniaturization is taking advantage of the slow wave
structures. The slow wave structures presented in this dissertation are formed using the
capacitive loading periodically. The effective propagation constant f3 is enhanced by
increasing the effective shunt capacitance in the equivalent circuit model derived from
the conventional transmission line theory. The associated guided wavelength is therefore
decreased and the same physical structure is capable of operating at lower frequencies.
The slow wave structures are employed for compact antenna applications. In particular,
the slow wave enhancement factor (SWE), which is defined as the ratio of the loaded to
the unloaded propagation constants (fliPo), is investigated using the loaded unit cell of the
equivalent transmission line model and utilized as a design tool for an arbitrary size
reduction. It is shown that the SWE agrees very well with miniaturization factor, and
therefore load parameters in the circuit model can be readily obtained when a specific
size reduction is attempted. Slow wave antennas will be exemplified in the third chapter
in this dissertation.
The subject of the second chapter is CRLH-based and miniaturized dual-band
hybrid couplers (both the 180° and 90° couplers) and their applications in beam pattern
diversity systems as well as to microwave diplexers. To ensure compactness, all possible
phase solutions of the CRLH-based transmission lines, which comprise the couplers, are
xix
considered and compared in terms of the physical length. This design methodology will
be elaborated and given in the second chapter. The focus of the remaining chapter will be
the applications of the CRLH-based dual-band couplers as the mode decoupling networks
(MDNs) in the beam pattern diversity systems to demonstrate antenna pattern diversity in
dual bands, and as the building elements of the microwave diplexers.
The subject of the third chapter is the compact antennas based on the slow wave
structures developed by periodically capacitive loading. In this chapter, the design
principle of the slow wave antenna with an arbitrary size reduction is proposed by taking
advantage of the SWE, which is shown to be equivalent to the miniaturization factor.
Two small radiators, the high-frequency (HF) slot-loop antenna and planar inverted F
antenna (PIFA), are examples to achieve the desired size reductions. Furthermore, the
adverse effects on the impedance bandwidth (VSWR<2) and radiation efficiency from
miniaturization are discussed and improved subsequently. A compact impedance
matching circuit derived from the filter design techniques is proposed to alleviate the
narrow impedance bandwidth to a degree. By the same token, antennas employing
varactor diodes are able to attempt desired size reductions while exhibiting considerable
effective bandwidths across the tunable frequency range. A varactor-loaded slot-loop
antenna was implemented to illustrate this idea.
xx
Chapter 1
Introduction
1.1
Basics of Metamaterials
1.1.1
Background and the Extraordinary Properties
Metameterials are referred to materials that do not exist and may exhibit unusual
electromagnetic properties that do not occur in nature. Particularly, metamaterilas that
present the specific property of simultaneous negative permittivity (<s) and permeability
(ju) are of great interest. In 1968, a Russian physicist, Veselago, studied the physical
properties of such substance and brought up the concept of double negative materials [1]
as compared to the conventional materials characterized by both the positive permittivity
and permeability. The first realization of the negative permeability materials was,
however, implemented thirty years later. Pendry et al. in [2] used an array of split ring
resonators (SRRs) to implement the negative permeability phenomenon. Shortly after,
Smith et al. successfully demonstrated the first observation of the negative refractive
index by combining a matrix of the metallic wires and split ring resonators [3]-[5]. The
unique characteristics of the novel and artificial materials that contradict the basic laws of
physics, such as the Snell's Law and Doppler Effect, attract great interest in the
community of physics and engineering to seek the advantages in all kinds of applications.
1
The artificial structure-based material that exhibits effective double negative
permittivity and permeability has different electromagnetic features in general. For
example, the group velocity and phase velocity, in this type of material, travel in opposite
directions. Opposite to the well-known right-handed triad practiced in the conventional
substances, the vector orientations of the E-field, the H-field, and the phase velocity form
a left-handed triad, leading to the term left-handed materials. The formulations
describing the wave propagation in the respective materials can be deduced as follows [6]:
fixE
+co\/u\H —> £,/U>0
-CO
(1.1a)
\jLl\H^>£,/J<0
-a>\ s\ E-*s,/u>Q
+co\s\E ^>£,/J<0
(Lib)
where /? is the wave vector and points out the direction of the plane of constant phase
travels, which lies in the same orientation of the phase velocity vp. Please note that (1.1)
is derived based on the time dependence e+Jtut. It is clear that from the equation, the triad
formed by E,H, and J3 will be left-handed if e, // < 0 while the triad is right-handed if e,
// > 0. In contrast to the phase velocity vp, the group or energy velocity vg is not
dependent on the constituent parameters and will still be determined by the right-handed
triad in order to obey the causality. Thus, the phase velocity vp and the group velocity vg
are anti-parallel in the left-handed materials. Furthermore, when an oblique signal is
incident upon the left-handed materials, the negative refraction is observed [5], [7] as a
result of the effective negative refractive index n. Therefore, the term negative refractive
materials arises and is referred to the same substances as the double negative/left-handed
2
materials. Fig. 1-1 summaries the properties for the left-handed materials and meanwhile,
illustrates the discrepancies between the right-handed and left-handed materials.
Figure 1-1 Illustrations of wave propagation in the conventional material (s, p.> 0) and in
the artificial left-handed material (e, p. < 0).
\
-f f '
I
\
L^Az
I
\
I
I
j
/
+ CR'Az
+P
(a)
if
'
*•
Az
CL7Az
•9h
ZL7Az
Az
+P
(b)
Figure 1-2 Dispersion curves and the equivalent circuit models for the ideal homogeneous (a)
purely right-handed transmission lines and (b) purely left-handed transmission lines.
3
1.1.2
Composite Right/Left-Handed Transmission Lines
The left-handed structure presented in the preceding section, which is composed
of the metallic wires and split rings, is lossy and bandwidth-limited. Therefore, an
alternative structure that can remedy the problems is needed. The transmission line
approach proposed by Caloz et al. [8] and Eleftheriades et al. [9] provides a practical
solution to implement an artificial structure that is able to behave as a left-handed
structure at certain frequency range, and has the potential to be less lossy, bandwidthenhanced, and more compact.
The derivation of this transmission line structure is essentially based on the
equivalent circuit model of the left-handed materials. The equivalent circuit model of the
left-handed structures is the combination of the purely right-handed (PRH) and purely
left-handed (PLH) circuit models. Fig. 1-2 shows the dispersion curves of the ideal
homogeneous PRH and PLH transmission lines, respectively, as well as their
corresponding infinitesimal circuit models. The dashed lines in the dispersion diagram
indicate the air lines, which divides the space into the fast wave region (a> > ft or vp > c)
and slow wave region (co < (3 or vp < c). Note that the PLH transmission line is a
theoretical stmcture that does not exist in nature. The circuit model of the PLH
transmission line consists of a series capacitance CL /Az and a shunt inductance ZL /Az
when the unit length Az -> 0, and therefore it behaves as the dual circuit from the PRH
circuit. In contrast to the linear and all-positive dispersion relation for the PRH
4
transmission line, the dispersion curve of the PLH transmission line is non-linear and
supports the traveling wave with a negative propagation constant (/?< 0). While the phase
velocity vp = col/3 is negative, the group velocity vg = /p,o is positive, indicating that
they are anti-parallel in the PLH stmcture. The left-handed materials or structures can be
artificially made from the inspiration of the PLH circuit model.
LH region
egion
^R
*
Cjt
1L,
R
Figure 1-3 Dispersion curve and the equivalent circuit model for the LC network CRLH
transmission structures.
Fig. 1-3 shows the LC network model of the left-handed stmcture or the
composite right/left-handed (CRLH) transmission stmcture. Essentially, the model
consists of the series capacitance CL and shunt inductance ZL to provide the left-handed
characteristics whereas the series inductance ZR and shunt capacitance CR present the
consequence of the inevitably parasitic effect and are used to account for the current flow
in the metallization and the voltage gradient developing between the signal traces and the
5
ground plane, respectively. Therefore, the dispersion curve of the CRLH stmcture is lefthanded at the lower frequencies where the propagation constant /3 < 0; on the other hand,
the right-handed property will dominate as the frequency exceeds the stop-band gap
where /3 = 0. Since the ideal homogeneous CRLH transmission line structure is not
readily available from nature, only in a restricted frequency range the artificial structure
(with the unit cell length d) will be effectively homogeneous and thus the LC network
implementation of the CRLH transmission lines presents cutoff frequencies^1111 andycLH
at the ends of the dispersion curve, limiting the usable frequency range. In addition, as
observed in Fig. 1-3, a band gap that is determined by/ s e and^h exists in-between the
right-handed and let-handed regions. The stop band presents the unique feature of the
CRLH transmission line where the propagation constant f3 = 0 (infinite wavelength) at
frequencies above the zero frequency. Furthermore, a s ^ e =fh=fo,
the gap is closed and
the left-handed and right-handed regions are connected at the transition frequency f
where a propagating wave with a constant field distribution is supported. Thereafter, the
CRLH transmission line becomes a balanced structure and the characteristic (Bloch)
impedance Zc is independent of the frequency. The four frequencies determining the
passbands of the CRLH transmission stmcture are described as follows:
r-LH
j-RH
c
1
4x^JLLCL '
1
7f
/ =
z
n4 R R
1
=
S
2K^LRCL
I
L C
2xyJLLCR
-'<iLycL=f/c„
6
< L3 >
where the fse and fh represent the resonant frequencies of the series and shunt LC
resonators, respectively. Note that Zc in the balanced case only depends on the circuit
parameters, which is particularly useful for the wideband impedance matching. As
aforementioned, the balanced CRLH transmission line at the transition frequency is able
to support a uniform amplitude and phase field distribution, and this property lends itself
to the applications of the in-phase power divider and zeroth-order resonators [10].
1.1.3
Dispersion Engineering Technique for the Composite Right/Left-Handed
Transmission Lines
In the preceding section the dispersion relation of the general (unbalanced) CRLH
transmission line was illustrated and the dependence on the circuit parameters (ZR, CR, Z L ,
CL) was briefly addressed. In this section, the dispersion engineering technique that is
applied for dispersion tailoring of the CRLH transmission line will be introduced. Note
that the focus of the dissertation will be on the balanced stmctures as they exhibit useful
properties in many applications. An important feature of the balanced case is that, as it
can be proved, the phase response fa of the balanced CRLH transmission structure
composed of A7 unit cells (as shown in Fig. 1-3) is the sum of the phase delay ^R and the
phase advance fa,
&(/->/oW*+&
= -N2?rfJLRCR
7
+
^ —
(L4)
Therefore, for a net CRLH phase effect, the balanced CRLH transmission line can be
implemented by simply cascading the right-handed or conventional transmission line
with the quasi- left-handed lines. Fig. 1-4 illustrates the phase superposition of a balanced
CRLH line from both the phase-lagging fa that is linear with respect to the frequency and
phase-leading fa that is non-linear versus the frequency. The periodic LC network
implementation of the balanced CRLH transmission line is included as well.
The remaining part of this section will focus on the dual-band dispersion
engineering as the methodology is required to carry out the dual-band CRLH components.
As suggested previously, the dispersion curve or the phase response of a CRLH
transmission line is determined by the constituent circuit parameters ZR, CR, ZL, and CL.
Therefore, to fulfill a specific phase requirement <f>\ and fa atf and/j, respectively, the
four circuit parameters need to be determined by solving (1.4). Furthermore, the balanced
CRLH transmission lines are preferable in terms of the practical advantages. First,
impedance matching to the termination, usually 50 Q, can be simply accomplished by
controlling the ratio of the inductance to the capacitance, as indicated in (1.3). Second, in
the balanced case, the band gap vanishes and the operative passband extends from the
high-pass cutoff frequency fhii
to the low-pass cutoff frequency f™. Having all the
information, the four circuit parameters can be obtained by solving the following
equations:
8
N
A=*c<jx>-mxfxjmci+ 2nf ^L C
x
fa=fa(f2)=-N2xf2y[LR~CR~
+
L
L
N
2nf2<jLLCL
(1.5)
Z = p L = 1 ^ = 50
Note that N is the number of unit cells used in the CRLH transmission line and for a
given JV, exact one solution can be acquired from (1.5). In practice, the numerical solution
that is feasible and results from a smaller number N is preferable as the length of the
transmission line is proportional to the number of unit cells that comprise the CRLH
transmission lines. The choice of the unit-cell number with regards to the practicability
and compactness of the balanced CRLH transmission lines will be discussed in detail in
Chapter 2.
LHTL
RHTL
•91—r-^h-
(b)
Figure 1-4 (a) Phase superposition of the balanced CRLH transmission line, and (b) the LC
network implementation of the balanced CRLH transmission line by cascading the righthanded transmission line with the left-handed transmission line.
9
As the left-handed stmctures or the CRLH transmission lines need to be
artificially fabricated, it is crucial to employ a configuration that is able to provide the
unique properties and satisfies other specifications, such as the miniaturization and
implementation convenience. Examples of several physical realizations are available in
[6]. Owing to the particular applications of interest in the dissertation, the CRLH
transmission line is carried out using the conventional microstrip line loaded by the chip
inductors and capacitors. Note that the microstrip line is used to preserve the right-handed
characteristics while the lumped elements that are arranged in the left-handed LC ladder
network contribute to the left-handed properties. The chip capacitor that acts as a series
CL is in series connection with the microstrip line and the chip inductor is in parallel
connection to the ground by a via-hole, acting as a shunt ZL. Fig. 1-5 illustrates such a
physical realization of the CRLH transmission line. Due to the compact size of the
surface mount chips, the length of the CRLH transmission line can be intentionally
reduced by simply controlling the microstrip line as it represents the majority of the
transmission line length. Furthermore, the required microstrip line length is determined
by the phase response of the CRLH transmission line. Therefore, the phase response is a
critical factor in the overall length, and the design methodology of the phase solution that
leads to a length reduction will be elaborated in Chapter 2. Finally, based on the LCloaded microstrip structures, the design difficulty is alleviated as the right-handed and
left-handed components are independent. The usable frequencies of the CRLH
transmission lines or the circuits based on them are, however, limited due to the
application of the lumped elements.
10
Microstrip line
2C
C
C
I
w
2C
Microstrip line
H I^L
Figure 1-5 Physical realization of the CRLH transmission line. Three unit cells are
illustrated in this case.
1.2
Basics of Slow W a v e Structures
1.2.1
Background and the Properties
Slow wave stmctures are notable for the capability of size reduction. Similar to
the principle applied to the left-handed metamaterials, the dispersion relation of the slow
wave structure is intentionally tailored to exhibit an increased propagation constant J3,
leading to a slower phase velocity vp along the stmcture as its name suggests. By doing so,
the same physical stmcture becomes electrically larger and is capable of operating at
lower frequencies, indicating the potential for miniaturization. A slow wave stmcture,
when described in the dispersion diagram, represents a curve beneath the air line k = j3.
Fig. 1-6 illustrates the typical dispersion diagram of slow wave stmctures. Three
dispersion curves with the propagation constants fi\, p\, and /%, respectively, are depicted
in the region to the right of the dashed line k = /3. This region is defined as the slow wave
region where (3 > k or vp < c. As the propagation constant /? of the stmcture is increased,
the curve is bent toward the abscissa, as /3\ < p\ < p\ in the dispersion diagram.
11
In order to enhance the propagation constant J3 of the stmcture, substrate loading
and reactive loading are the most popular approaches as shown in Fig. 1-7. In Fig. 1-7 (a),
a metallic patch is loaded by the substrate as the conventional patch antenna is
implemented and therefore, the propagation constant /? is increased and proportional to
the square root of the dielectric constant yj£r of the substrate; moreover, by adding a
capacitive loading at the end of the patch as shown in Fig. l-7(b), the propagation
constant /3 can be increased even better, depending on the value of the capacitance.
Corresponding to the dispersion diagram in Fig. 1-6, the dispersion curve that is closer to
the abscissa represents the heavily loaded case with respect to that closer to the air line.
For example, when the structure in Fig. l-7(b) corresponds to the dispersion curves p\ in
Fig. 1-6, the substrate-loaded patch may map to the dispersion curve f3\.
k=p
i
I
/
Slow Wave
Region
Figure 1-6 Dispersion diagram of the slow wave structures.
12
Figure 1-7 (a) Substrate loading, and (b) reactive loading using a capacitor (including the
substrate loading).
1.2.2
Periodically Loaded Structures and the Slow Wave Enhancement Factor
In the previous section, the patch loaded by a reactance component is exemplified
as a slow wave stmcture. In practice, to attempt a considerable size reduction, such an
implementation is less effective. The periodically loaded slow wave stmcture may be a
good candidate. As the structure is periodically populated by loads, the stmcture can be
loaded heavily, leading to a substantial miniaturization. Furthermore, the periodically
loaded structure can be well analyzed by applying the periodic boundary conditions to the
equivalent loaded transmission line model, which provides a reliable analysis approach
comparable to the rigorous method, such as the full-wave analysis.
Fig. 1-8 shows the schematic of a capacitor-loaded slow wave stmcture, which is
best suited for the antenna implementations of interest and will be employed throughout
this dissertation. The equivalent circuit model of a capacitor-loaded slow wave structure
is composed of an equivalent transmission line that describes the property of the
unloaded stmcture in terms of the characteristic impedance ZQ and the unloaded
13
propagation constant p\, and capacitors C that mount the stmcture at a period d. The
loaded propagation constant /3 can be expressed as follows [11]:
cos(fid) = cos(fi0d) - 7rfCZQ sin(fi0d)
(1.6)
where/is the frequency. As observed, the loaded propagation constant /?is a function of
the load period d and the load capacitance C for a given unloaded structure. Further
investigation on (1.6) shows that as the load period decreases or/and the load capacitance
increases, the loaded propagation constant (3 will increase correspondingly. The slow
wave enhancement factor (SWE), defined as the ratio of the loaded to the unloaded
propagation constants as follows
SWE = i L ,
(1.7)
A
is of particular interest. It is well known that the miniaturization factor is proportional to
the SWE. In Chapter 3 of the dissertation, the SWE will be studied through the developed
circuit model of the loaded structure and moreover, it is observed that the SWE is in
excellent agreement with the degree of size reduction. Antenna examples will be
experimentally demonstrated to verify the claim. In the design point of view, this
conclusion conveys the advantage of the equivalent circuit model. In other words, the
load parameters in the model, such as the load period d and load capacitance C, can be
readily accessed for a desired SWE or equivalently, miniaturization.
The derivation of the equivalent circuit model of any periodically loaded slow
wave stmcture will be addressed in detail in Chapter 3. In addition, a design procedure
based on the SWE to attempt a specific size reduction will be provided.
14
• • • ••
/
<
V
d
Figure 1-8 Schematic of the capacitor-loaded slow wave structure.
15
References
[1]
V. G. Veselago, "The electrodynamics of substances with simultaneously
negative values of £-and //," Sov. Phys. Usp., vol. 10, no. 4, pp. 509-514, Jan.-Feb.
1968.
[2]
J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from
conductors and enhanced nonlinear phenomena," IEEE Trans. Microw. Theory
Tech., vol. 47, no. 11, pp. 2075-2084, Nov. 1999.
[3]
D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nassar, and S. Schultz,
"Composite medium with simultaneously negative permittivity and permeability,"
Phys. Rev. Lett., vol. 84, no. 18, pp. 4184-4187, May 2000.
[4]
D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials,"
Phys. Rev. Lett., vol. 85, no. 14, pp. 2933-2936, Oct. 2000.
[5]
R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a
negative index refraction," Science, vol. 292, pp.77-79, Apr. 2001.
[6]
C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory
and Microwave Applications. New York: Wiley, 2005.
[7]
J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett., vol. 85,
no. 18, pp. 3966-3969, Oct. 2000.
16
[8]
C. Caloz and T. Itoh, "Application of the transmission line theory of left-handed
(LH) materials to the realization of a microstrip "LH line"," in IEEE AP-S Int.
Symp., Jun. 16-21, 2002, vol. 2, pp. 412-415.
[9]
A. K. Iyer and G. V. Eleftheriades, "Negative refractive index metamaterials
supporting 2-D waves," in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2-7, 2002,
vol. 2, pp. 1067-1070.
[10]
A. Lai, K. M. K. H. Leong, and T. Itoh, "Applications of infinite wavelength
phenomenon," in Proc. 36th Eur. Microw. Conf, Sept. 10-15, 2006, pp. 937-939.
[11]
D. M. Pozar, Microwave Engineering, 2 nd ed., John Wiley & Sons, 1998.
17
Chapter 2
Composite Right/Left-Handed
Transmission Line Hybrid Couplers and Their
Applications
2.1
Introduction
As the development of communication systems moves toward compactness and
multi-frequency operation, the integral components that comprise the entire system are
essential to meet the demand correspondingly. For example, small and dual-band
components find many applications in nowadays communication systems, such as the
wireless local area network (WLAN). Due to the low cost and easy fabrication,
microstrip circuit elements are a popular choice. In particular, microstrip hybrids are one
of the essential components in many communication systems that require equal power
split and in-phase or quadrature or anti-phase excitation for the next stage. Systems that
are made of these microstrip couplers, however, suffer from the inherent limitation on the
operating frequencies. Due to the linear dispersion property of the microstrip lines, the
second operating frequency of the couplers is three times of the fundamental frequency.
Thus, an alternative or a dispersion-controllable transmission line capable of arbitrary
dual-band operation is highly desired.
18
The CRLH transmission lines are suited for this requirement. Over the past ten
years, extensive studies on the implementation of the CRLH-based antennas and circuit
components were conducted, and have demonstrated the unique feature and superior
performance from the experimental results. In particular, the guided-wave applications
that take advantage of the phase engineering property of the CRLH transmission lines are
found useful with regards to the size reduction and bandwidth control, which are the
focus of the dissertation. The CRLH-based phase shifters in [1] present the phase leading
or lagging responses via controlling the lumped-element values, which alleviates the
phase dependence exclusively on the length of the conventional transmission lines, and
reduces the overall lengths. Furthermore, the broadband implementations of the
Wilkinson balun [2] and bandstop filter [3] demonstrate the phase engineerable feature of
the CRLH transmission lines by matching the phase slopes of a pair of transmission lines.
The arbitrary dual-band operation of the AJ4 CRLH transmission line that acts as the
basic building block for the dual-band 90° and 180° couplers [4] shows an important
application to dual-band circuit components. The XIA CRLH transmission line is
composed of lumped elements in the center and microstrip lines on both sides, as shown
in Fig. 1-5, to produce the 90° phase-delay response. Since the phase increment from the
lumped-element arrangement (series capacitance CL and shunt inductance ZL) will cancel
the phase-delay contribution from the microstrip lines, the JU4 CRLH transmission line is
physically longer than a simple microstrip line with the same phase delay. Therefore, the
CRLH couplers in [4] are larger than the microstrip counterparts operating in the first
band of the dual-band operation. Subsequently, implementation of the CRLH
19
transmission lines with phase-advance responses is considered for compactness. The
single-band 180° hybrid proposed in [5] is miniaturized by replacing one arm of the
microstrip ring coupler with the 90° phase-advance CRLH transmission line. Compared
to the microstrip 180° coupler, this coupler saves much footprint from the replacement of
the conventional 270° phase-delay line by the 90° phase-advance CRLH transmission line.
The operating frequencies are, however, not arbitrary because not all of the transmission
lines in the coupler are realized based on the CRLH transmission lines.
In Section 2.2, the design methodology that enables both arbitrary dual-band
operation and miniaturization for the 180° and 90° hybrid couplers is introduced [6].
Basically, a thorough consideration of the dual-band phase solutions of the constituent
CRLH transmission lines is made in terms of the physical length. The length reduction or
the size reduction of the couplers is therefore assured from this comparison. Experimental
results verify the feasibility. In Section 2.3, the hybrid couplers will serve as the dualband (radiation) mode decoupling networks (MDNs) when connected to an antenna array
to demonstrate three types of dual-band beam pattern diversities. Furthermore, using
specific phase responses of the CRLH phase-advance or delay lines to excite the sum or
the difference port of the CRLH couplers at different frequencies, microwave diplexers
can be easily implemented without employing two filters as observed in the conventional
realization. The implementation principle of the CRLH-based diplexers taking advantage
of the hybrid couplers will be presented in Section 2.4.
20
2.2
Miniaturized and Arbitrary Dual-Band Hybrid Couplers
Based on the Composite Right/Left-Handed Transmission Lines
2.2.1
Phase Engineering of the Dual-Band Couplers
As aforementioned, the most remarkable feature of the artificial CRLH
transmission line is that their dispersion or phase characteristics are determined and can
be tailored by the lumped circuit parameters ZR, CR, ZL, and CL- Furthermore, in Section
1.1.3, one important application that relies on the phase fulfillment in arbitrary dual bands
is brought up and provided with (1.5), which is essentially the design formula for dualband components based on the CRLH transmission lines that require specific phase
responses fa fa at respective frequencies f\, f while maintaining fixed characteristic
impedance Zc. These properties exactly meet the requirements for realizing an arbitrary
dual-band 180° or 90° coupler. It will be discussed later that both of the above couplers
impose particular phase and impedance requirements on the constituent transmission
lines in order for proper operation. To this end, given a set of desired phase responses
$(/i), fafi) at the specific frequencies f and f2, and characteristic impedance Zc, the
required lumped circuit parameters are of importance for practical realization, which can
be solved from (1.5)
21
J1 ,
\J2
LR=-
- C =-
2xN
J\J
f
f2 2
_J\f^
\J\
J2 )
2TTNZ.
\Ji
J2 j
yf
J2 y
ZN
LL =
\J2
(2.1)
N
MM-M'
,CL =
yJ\
J2 J
2nZc{<kf2-^fx)
where N is the number of unit cells for each CRLH transmission line. Note that the
balanced condition
(ZRCL=ZLCR)
is assumed in (2.1) and balanced CRLH transmission
structures will be employed throughout the dissertation. From (2.1) it is observed that for
a given unit-cell number N, exactly one solution corresponds to the phase and impedance
conditions as shown in (1.5). In practice, the choice of the unit-cell number TV is subject
to two aspects. First, choose N as small as possible. Increasing the unit-cell number iV
indicates a longer physical length of the CRLH transmission line, which needs to be
avoided especially when the miniaturization is concerned. Second, numerical solutions
resulted from certain JVs may fail to implement. As pointed out in 1.1.2, the cutoff
frequencies f^11 andycLH, as shown in (1.2), exist for the LC network implementation of
the CRLH transmission line. In some occasions, the occurrence of either f™ or fLH
resulted from the numerical solution produces the stopband covering the frequency of
RTJ
interest. It is therefore important to examine the corresponding cutoff frequencies f
and /CLH for the feasibility of a solution. Furthermore, when this implementation failure
takes place, the number of unit cells N needs to be increased correspondingly until the
solution is realizable.
22
2.2.2
Design Principle of the Compact and Dual-Band 180° Coupler
As shown in Fig. 1-5, the CRLH transmission lines are developed using surface
mount lumped elements in the center that contribute to the left-handed property and
microstrip lines at both ends that present the right-handed property. The primary
advantages of employing lumped elements include their small sizes and ease of
implementation; however, the maximum usable frequency is sacrificed to avoid the self
resonance from the lumped elements. It is shown that in [7], the characteristic impedance
of the arms of the ring coupler, which operates at 2.4 GHz and 5.2 GHz, has to be
adjusted in order to compensate for the resonance effect. It should be pointed out that,
this design complication is a consequence of operating lumped elements at higher
frequencies and the design formula provided in (2.1) still holds. Therefore, to
accommodate for the proper operation of the lumped elements, the operational bands of
the couplers are chosen at 1 GHz and 2 GHz without loss of the generality.
In order to realize an arbitrary dual-band and compact 180° hybrid coupler, the
requirements for proper operation need to be deduced first and a complete comparison of
all solutions that satisfy the requirements needs to be made subsequently to ensure an
optimal implementation. Basically, at either frequency the dual-band 180° coupler should
behave exactly as a single-band coupler and the operating principles of the latter can
therefore be applied. Fig. 2-1 illustrates a dual-band 180° coupler composed of three
CRLH transmission lines with phase response <p\ and a CRLH transmission line with
phase responses (pi. Four basic limitations imposed on the characteristics of these
transmission lines are summarized as follows:
23
output
port 1
Figure 2-1 Schematic of the CRLH dual-band 180° hybrid coupler.
1) At either frequency q>\ and (pi must be odd multiples of 90°. Furthermore, they
can be either phase advance {(p\, (pi> 0) or phase delay (<pi, (pi< 0) based on the CRLH
transmission lines.
2) At either frequency the phase difference between (p and (pi must be the odd
multiples of 180°. This requirement ensures the ideal isolation between the Z and A ports.
3) At either frequency the characteristic impedance for the ring line is kept to be
70.71 (V2x50) fi.
4) The absolute phase responses of q>\ and (pi is confined to 270°, \q>\, <pi\< 270°.
Even though this confinement is not the necessary condition for operation, practical
considerations of reducing the microstrip lines (<p\, (pi> -270°) and the validity when
24
applying (1.4) (<pi, (pi < 270°) lead to such a conclusion. Combining all above
considerations, <pi and <p2 at either frequency can be expressed as follows:
| qh= m90°, (pi= m90° ± 180°|< 270°
(2.2)
where m is an odd integer, including the negatives. In addition, the synthesized
transmission line with phase (p\ should be physically shorter than that with <pi since the
former contributes to the majority of the coupler size. In this manner, four possible phase
solutions for q>\ and q>i are depicted in Fig. 2-2. In each subfigure, dashed and solid lines
stand for the phase variation of (p\ and <pi with respect to the frequency, respectively.
1.5
Frequency (GHz)
1.5
Frequency (GHz)
(b)
2.0
(a)
a> 270
c
o
Q
au
-— 90
«
<u ua ft
*** o>
a a -90
J5
£
*
-270
1.5
Frequency (GHz)
1.5
Frequency (GHz)
2.0
(d)
(c)
Figure 2-2 Four possible CRLH transmission phase solutions of the 180° coupler. The
dashed and solid lines represent q\ and g>i, respectively.
In order to achieve compactness, the length of microstrip lines that dominate the
overall size in the CRLH transmission line should be maintained as short as possible,
25
which leads to positive phase increment. Therefore, phase-advanced CRLH transmission
lines are preferred for size reduction. Furthermore, it is found that the length of the
microstrip lines in the CRLH structure is increased with the phase difference at dual
frequencies. In addition, it should be noted that (1.4) provides a good approximation
when the operational frequencies are close to^o, the transition frequency where the phase
response is zero. It follows that, in practice, a solution to (1.5) whereto is not close
enough to or within the operational bands is difficult to satisfy the desired phase
responses in dual bands. From above discussion, the conclusion leads us to choose the
phase solution (d) for implementation.
output
port t
output
port 1
Figure 2-3 Phase implementation for the proposed compact dual-band 180° hybrid coupler
at (a) 1 GHz and (b) 2 GHz, where Z0= 50Q.
Based on the phase solution in Fig. 2-2(d), the proposed compact and dual-band
180° coupler was implemented using three CRLH transmission lines with phase <pi and
one CRLH transmission line with phase (pi. Fig. 2-3 summarizes the implemented phases
26
for q>\ and <pi at 1 GHz and 2 GHz, respectively. The phase transition of q>\ is from 90° to
-90° while <pi is from -90° to -270°. Each CRLH transmission line is made up of seriescapacitor shunt-inductor lumped elements in the center and microstrip lines at both ends.
The symmetrical layout is arranged and is useful for impedance matching. By applying
(2.1), the left-handed circuit parameters used for this coupler are: (ZL;(pi=10.6nH,
Ch,(s>\=2.5p¥, ZLj(p2=32.7nH, CL>(p2=6pF). Fig. 2-4 shows the simulated results of this
coupler. In order to obtain better accuracy, a through-reflect-line (TRL) calibration
method has been applied to extract the two-port S-parameter at both ends of lumped
elements. From the magnitude simulation, the dual-band characteristic is obvious as
expected.
Frequency (GHz)
Frequency (GHz)
(a)
(b)
Figure 2-4 Simulated magnitude responses of the proposed compact dual-band 180° hybrid
coupler: (a) from the E port and (b) from the A port.
The CRLH-based 180° hybrid coupler was built on FR4 substrate with thickness
0.787 mm and £t=4A. Fig. 2-5 shows the photograph of the fabricated compact dual-band
27
180° hybrid coupler. This ring coupler has a radius of 30.51 mm, which demonstrates a
43.7% size reduction compared to the microstrip coupler with a radius of 40.66 mm at 1
GHz. The 4-port measurement was taken with the Agilent 8515A network analyzer. Fig.
2-6 shows the measured magnitude responses at 2 and A ports, respectively. They exhibit
excellent agreement with simulated results in Fig. 2-4. In these figures, the dual
operational bands are highlighted for clarity. In order to investigate the performance of
this coupler, summaries are given in Tables 2-1 and 2-2 for the measurements at S and A
ports, respectively. Furthermore, a performance summary of the microstrip 180° coupler
at 1 GHz is also reported in Table 2-3 for comparison. As we can observe, a significant
bandwidth improvement is observed in two aspects, one is the isolation and the other one
is the output magnitude balance. The size reduction of the proposed dual-band 180°
hybrid is found to be more than that of the proposed dual-band 90° hybrid (see Section
2.2.3). This results from the fact that the length reduction of the CRLH transmission line
with phase (pi in the 180° coupler (with phase variation from -90° to -270°) compared to a
3/1/4 microstrip line is much higher than that with q>\ (with phase variation from 90° to 90° which are the phase responses used for the 90° coupler) compared to a XI4 microstrip
line. Thus the proposed 180° coupler is relatively smaller than the 90° coupler compared
to their respective microstrip counterparts. Moreover, it should be noted that this coupler
suffers more loss at the outputs due to chip components than the insertion loss shown in
[5], because the lumped elements are included for each transmission line of the ring
hybrid for the operational capability of arbitrary dual bands. Distributed CRLH
transmission structures or low-loss commercial lumped elements can be employed to
28
reduce the loss at the expense of the design complexity in parametric optimization or the
cost. These measured results conclude that the proposed design methodology is feasible
to realize a compact dual-band 180° hybrid coupler based on CRLH transmission lines.
X port
.Output
A:
• 3%*tJ
til V\
V
•
* .Y*. «;«}£&
. ^ /-•.r-V-VS'V*
••&&£•••:• -z-
Figure 2-5 Photograph of the fabricated compact dual-band 180° hybrid coupler. The
radius and width of the ring are 30.51 mm and 0.78 mm, respectively.
I/I
w
o
_i
c
o
«
\ /"V-—.•^.y
x< ^*,*r ™ **" "
X?
*v
A
*
\
-10 Sr i t \
/ ! ' \
<i vf I
\\
// \1 '*
»? ;* 1
*
a
1
1
1*
\
-20
c
j
-30
S
V) CO
EE
s1s
o —' -40
/
ft
*'
f
/ "
t '
VV
\. i
S2E
3 (3
% O
a: J2 -50
/
/
^v»
A.
i I--V<"p\s
Vx1 s
(0
•*. « ^ ^ ^ r
.
0.5
1.0
SAE
2.0
1.5
2.5
Frequency (GHz)
3.0
Frequency (GHz)
(a)
(b)
Figure 2-6 Measured magnitude responses of the proposed compact dual-band 180° hybrid
coupler: (a) from the 2 port and (b) from the A port.
29
Table 2-1 Measured Performances of the Proposed 180" Coupler at Z Port
Measurement
Operating
1 GHz
2 GHz
Frequency
-19.85 dB
-21.74 dB
Return Loss (Szz)
26%
27%
BW<-i5dB
-28.52
dB
-22.18
dB
Isolation (SAT)
139%
70%
BW<_20dB
Insertion Loss 1
-4.05 dB
-3.27 dB
Pis)
Insertion Loss 2
-3.62 dB
-4.5 ldB
Pa)
Magnitude
Imbalance
BW<i.5dB
Phase Imbalance
BW<±io
0.43 dB
1.24 dB
195%
1.8°
65%
98%
5.9°
38%
Table 2-2 Measured Performances of the Proposed 180° Coupler at A Port
Operating
Frequency
Return Loss (SAA)
BW<.i5dB
Isolation (SIA)
BW<_20dB
Insertion Loss 1
Insertion Loss 2
(SIA)
Magnitude
Imbalance
BW<i.5dB
Phase Imbalance
BW<i8o ±io
1GHz
2 GHz
-17.06 dB
30%
-28.51 dB
140%
-20.52 dB
16%
-21.6 dB
70%
-3.56 dB
-4.79 dB
-4.01 dB
-3.26 dB
0.45 dB
1.53 dB
43%
3.2°
56%
*
4.1°
38%
No applicable BW for magnitude imbalance less than 1.5 dB at 2 GHz (1.53 dB).
30
Table 2-3 Simulated Performances of the Microstrip 180° Coupler at 1 GHz
Operating
Frequency 1 GHz
Return Loss (S^z,
Simulation
PortZ
Port A
-30.32 dB
-35.2 dB
40%
-41.48 dB
32%
-3.43 dB
81%
-41.48 dB
32%
-3.53 dB
-3.33 dB
-3.43 dB
0.1 dB
0.1 dB
37%
0.7°
70%
37%
0.8°
28%
SAA)
BW<.i5dB
Isolation (SAZ)
BW<-20dB
Insertion Loss 1
(Siz, S\A)
Insertion Loss 2
(S2Z,
S2A)
Magnitude
Imbalance
BW<i.5dB
Phase Imbalance
BW<(±io , 180 ±10 )
2.2.3
Design Principle of the Compact and Dual-Band 90° Coupler
Applying the same artificial structure as shown in the preceding section, the
constituent transmission lines for the proposed 90° hybrid is made up of microstrip lines
and lumped elements to contribute to the right-handed and left-handed properties,
respectively.
The 90° hybrid coupler is basically composed of four transmission lines of two
different characteristic impedances. Two out of four transmission lines are of
characteristic impedance 35.36 (50/v2) Q with phase response (p\ and the rest are of
characteristic impedance 50 Q with phase response (pi as shown in Fig. 2-7. To operate
the dual-band 90° coupler properly, it is concluded that two requirements are necessary as
follows:
31
1) The phase response q>\ or (pi needs to be at odd multiples of 90° at either
frequency. Since the coupler is composed of CRLH transmission lines, they can be either
phase advanced (q>\, (pi> 0) or phase delayed (<pi, <pi<0).
2) The characteristic impedances of transmission lines with phase responses <p\
and <pi are 35.36 Q and 50 Q, respectively.
3) The absolute phase responses cp\ or (pi at dual frequencies are confined to 270°,
\q>\, (pi\< 270° for the purpose of reducing microstrip lines (q>\, (pi > -270°) and the
proper usage of the (1.4) (<pi, (pi < 270°). The same restriction is applied to the dual-band
180° coupler.
Based on the aforementioned concerns, six phase solutions that satisfy the
requirements are considered and exhibited in Fig. 2-8. Here, q)\ and (pi can be any curve
in (a) - (f) independently. For example, the solution (a) is a phase realization of a 35.36 Q
or 50 Q CRLH transmission structure with 90° at 1 GHz and -90° at 2 GHz. These phases
are odd multiples of 90° and their absolute values are restricted to 270°.
In order to realize compactness, the lengths of microstrip lines should be as short
as possible since they dominate the overall size, which leads to positive phase increment.
Therefore, phase-advanced CRLH transmission lines are preferred for miniaturization.
The performance of the 90° hybrid coupler is sensitive to the individual transmission
lines of two different characteristic impedances and thus its bandwidth is mainly
restricted by the phase responses of each branch. This property makes wideband
implementation difficult and inevitably leads to narrow bandwidth. In order to increase
the operational bandwidth, one can use a transmission structure with phase delay, for
32
example, the solution (f). However, this realization requires longer microstrip lines, since
there is a trade-off between compactness and bandwidth. This paper focuses on
compactness first. In addition, it should be noted that (1.4) is derived under the
assumption that the operational frequencies are close tofo, the transition frequency where
the phase response is zero. In other words, a solution whereto is not close enough to or
within the operational bands is difficult to achieve the desired responses at dual
frequencies using the values obtained in (2.1). Therefore, the optimal solution for all
considerations is the solution (a) in Fig. 2-8.
Figure 2-7 Schematic of the CRLH dual-band 90° hybrid coupler.
Based on the phase solution in Fig. 2-8(a) for both <pi and (pi, the proposed
compact dual-band 90° coupler was implemented using CRLH transmission structures
with (p\ and (pi as shown in Fig. 2-9 at 1 GHz and 2 GHz, respectively. The phase
transitions of q>\ and (pi are both from 90° to -90°. Each CRLH transmission structure is
composed of series-capacitor shunt-inductor lumped elements in the center and
symmetric microstrip lines at both ends. By applying (2.1), the left-handed circuit
parameters used for this coupler are: (ZL,35.36n= 6.2 nH, CL,35.36n= 4.2 pF, ZL,5on= 8.6 nH,
33
CL,5OH=
3 pF). Three unit cells are used in this realization. Fig. 2-10 shows the simulated
results of this coupler. In order to obtain higher accuracy, a through-reflect-line (TRL)
calibration method has been applied to extract the two-port ^-parameters at both
terminals of lumped elements. The magnitude simulation demonstrates the dual-band
characteristic.
1J
Frequency p i )
Fretprteypi)
w
M
is
i m
U
i
Frequency P i )
Fr#qu#ncy P i )
1.5
2
fretpjicyPz)
FrtqumcyPi)
M
I
ffl
Figure 2-8 Six possible CRLH transmission phase solutions of the 90° coupler. Each curve
can be used as ^(35.36 Q) or (pi (50 Q).
34
35.360
35.360
port! port!
90°~~"1
5on|90°
| r -90°
SOQIUO0
90° won
35,360
-90°||»A
3536 Q
(a)
(b)
Figure 2-9 Phase implementation for the proposed compact dual-band 90° hybrid coupler at
(a) 1 GHz (b) 2 GHz.
Frequency (GHz)
Frequency (GHz)
(b)
(a)
Figure 2-10 Simulated (a) magnitude and (b) phase responses of the proposed compact
dual-band 90° hybrid coupler.
The CRLH-based 90° hybrid coupler was built on a FR4 substrate with thickness
0.787 mm and £v=4.4. Fig. 2-11 shows a photograph of the fabricated compact dual-band
90° hybrid coupler. The dimensions for this coupler are as follows: the length (/35.36Q^5on)
and width (w35.36n/w50Q) of the 35.36 Q and 50 Q transmission structures are /35.36n=
39.48 mm, w35.36Q= 2.51 mm,
ISQQ=
38.26 mm, and W 50 Q= 1.35 mm. It therefore shows a
35
10% size reduction (39.48 mm x 38.26 mm) compared to the 1 GHz microstrip coupler
using the same substrate with the area 40.26 mm x 41.35 mm. The 4-port measurement
was taken with the Agilent 8515A network analyzer. Fig. 2-12 shows the measured
magnitude and phase responses. Excellent agreement with simulated results is achieved.
The dual operational bands are highlighted for clarity. For detailed performance of this
coupler, a summary is given in Table 2-4. Moderate bandwidth is observed in the
measured results. One benefit is that the bandwidth of output magnitude balance is
improved, which nearly doubles the bandwidth of the conventional microstrip coupler.
These measured results verify that the proposed design methodology is feasible to realize
a compact dual-band 90° hybrid coupler based on CRLH transmission lines.
Figure 2-11 Photograph of the fabricated compact dual-band 90° hybrid coupler, hs^ri^
39.48 mm, vf35.36n= 2.51 mm, /son= 38.26 mm, and w5on= 1.35 mm.
36
1.2
1.4 1.6
Frequency (GHz)
(a)
1.4
1.6
1.8
2.2
Frequency (GHz)
(b)
Figure 2-12 Measured (a) magnitude and (b) phase responses of the proposed compact dualband 90° hybrid coupler.
Table 2-4 Measured Performances of the Proposed 90" Coupler
Operating
Frequency
Return Loss (Su)
BW<.15dB
Isolation (1S41)
BW<_i5dB
Insertion Loss 1
(S21)
Insertion Loss 2
(S31)
Magnitude
Imbalance
BW<l.5dB
Phase Imbalance
BW<±io
Measurement
1GHz
2 GHz
-20.38 dB
7%
-19.03 dB
6%
-4.29 dB
-24.19 dB
7%
-27.22 dB
9%
-3.80 dB
-4.33 dB
-4.54 dB
0.04 dB
0.74 dB
69%
2.0°
11%
>16%
0.6°
16%
37
2.3
Application of the C R L H Hybrid Couplers to the Dual-Band
Beam Pattern Diversity Systems
2.3.1
Implementation Principle of Dual-Band Beam Pattern Diversity Using
the Hybrid Couplers
When connected to a two-element antenna array, directional couplers are capable
of decoupling two orthogonal modes at two isolated ports [8]. It follows that the
corresponding radiation patterns of the decoupling modes are uncorrelated and thus a
pattern diversity mechanism takes place by using such a configuration. Examples in [8, 9]
are the microstrip 180° and 90° hybrid couplers utilized, respectively, to form single-band
pattern diversity systems. Apparently, the replacement of the conventional directional
couplers by the proposed CRLH hybrids provides two benefits. First, this assembly is
capable of dual-band operation and demonstrating dual-band pattern diversity when
incorporating a dual-band antenna array. Second, the pattern diversity system can be
miniaturized using the proposed compact 180° or 90° coupler. In the dissertation, three
types of the dual-band beam pattern diversities will be demonstrated by manipulating the
phase excitations for the dual-band antenna array through the CRLH delay line combined
with the proposed CRLH hybrids. The first type of pattern diversity demonstrates the
orthogonal sum and difference patterns at dual frequencies (Type I) using the CRLHbased 180° coupler and a compact antenna array [7]. Next, an alternative dual-band
pattern diversity system from which two kinds of beam patterns at different frequencies
are created by taking advantage of the CRLH-based 180° coupler, the dual-band CRLH
38
delay line, and a compact antenna array [10]. The CRLH delay line introduces additional
phase progression at dual frequencies and when combined with the CRLH 180° coupler,
the resulting in-phase and anti-phase excitations at the lower frequency, and quadraturephase excitations in the higher band help the array exhibit sum and difference orthogonal
patterns at the lower frequency, but endfire orthogonal patterns at the higher frequency
(Type II). On the other hand, the third type of the beam pattern diversity, which
corresponds to the endfire orthogonal patterns at the lower frequency and sum and
difference pattern diversity in the higher band (Type III), is implemented by employing
the proposed CRLH 90° hybrid coupler, a CRLH delay line, and two-element planar
antenna array. The operation mechanism for each type will be detailed in Section 2.3.4.
2.3.2
Implementation of the Compact Dual-Band CRLH-Based Delay Line
For arbitrary dual-band operation, the proposed dual-band delay line is realized
based on the CRLH transmission lines. It is composed of a CRLH transmission structure
with phase (p pairing with a microstrip line with phase (pi as shown in Fig. 2-13, and is
implemented by introducing additional phase progression in one path relative to the other
path. This means that q>\- <pi matters.
The phase responses q)\- (pi of the delay line are designed as 0° and -90° at 1 GHz
and 2 GHz, respectively. In addition, the CRLH delay line needs to be of the same
characteristic impedance in order not to cause the unwanted reflection, usually 50 Q.
Based on (2.1), the four circuit parameters (LR, CR, Z,L, CL) can then be determined with
(q>\- (pi)\GR-L= 0°, (q>\- (pi)iGKz= -90°, and Zo=50 Q. The phase implementation of the
39
proposed delay line is shown in Fig. 2-14. The phase lags of the CRLH transmission
structure with respect to the microstrip line are 0° and 90° at 1 GHz and 2 GHz
respectively. The left-handed circuit parameters used in the delay line are LL,deiay= 15 nH
and CL,deiay= 6 pF. Two unit cells are cascaded in this realization because the low-pass
cutoff frequency f™ occurs within the operational bands when using a single unit cell
(see Section 2.2.1). The CRLH-based delay line was built on a FR4 substrate with
thickness 0.787 mm and £f= 4.4 as shown in Fig. 2-15. Fig. 2-16 shows the measured and
simulated return losses and phase differences ((p\- <pi). As observed, a 50 Q impedance
matching is obtained for both transmission lines and excellent agreement for phase
differences are achieved in dual bands.
Figure 2-13 The conceptual schematic of the proposed dual-band CRLH-based delay line.
q>i and 02 are the phase responses of the CRLH and microstrip lines, respectively.
40
<pr(p2=-90°
0>,-0V=O°
-i
(p\
,
CRLH
transmission
structure
CRLH
transmission
structure
Microstrip
Figure 2-14 Phase implementation for the proposed compact dual-band delay line at (a) 1
GHz and (b) 2 GHz.
port 1
port 3
Figure 2-15 Photograph of the fabricated compact dual-band CRLH delay line. The port
distance for each transmission line is /dciav= 20 mm.
41
£
O
f -40
3 -60
-70
._--—.
-80
i
0.8
1.0
-60
Meas - corrf|i^site
yeas - microstrip^
Sim - composite
Sim - microstrip
Meas - phase
Sim - phase
c
1
1.2
1
1
1.4
1.6
1
1.8
;o
o
o
c
£
-80
^ t J -100
re
-120
'"" r
2.0
O
(0
2.2
Frequency (GHz)
Figure 2-16 Measured and simulated return losses and phase differences (<p\-fa)of the
proposed compact dual-band delay line.
2.3.3
Implementation of the Dual-Band Antenna
A printed dual-band antenna with compact size and an omnidirectional pattern in
a principal plane is desirable for integration into the proposed beam pattern diversity
system. The dual-band antenna topology proposed in [11] is a suitable candidate. In the
dissertation, a similar antenna configuration is employed and designed at 1 GHz and 2
GHz. Fig. 2-17 shows the geometry of the dual-band antenna. This antenna is fed by a 50
Q microstrip line with a ground plane on the backside of the substrate and is composed of
two T-shaped geometries which individually account for each resonance. At the lower
frequency, an equivalent quarter wavelength from point A to point B dominates the
resonance and the length is approximately equal to l\\ (In) + l\. Similarly, the distance
from point A to point C is responsible for the higher band resonance and the resonance
length is h\ (hi) + h- This particular T-shaped configuration is employed instead of a
42
straight line for size miniaturization.
11
12
1
B
1
C
dJ 1
1
'a
'22
W
'1
2
•
•
A
microstrip
W
gnd
and
ground
W>
Figure 2-17 Configuration of the dual-band antenna. The fabricated dimensions are as
follows: /11=/12=12.5 mm, /2i=/22=26.5 mm, di=d2=l.5 mm, /i=48.25 mm, /2=18.25 mm, ^1=1.5
mm, Wi=7 mm, /gnd=60 mm, and 1^^=150 mm.
This printed antenna is basically a X/4 monopole, which has an omnidirectional
radiation pattern in its H plane. Fig. 2-18 shows the measured and simulated radiation
patterns at 1 GHz. The monopole-like radiation modes are observed in the principal
planes. Measured patterns agree well with simulated results. Similar monopole-like
radiation patterns can be observed at 2 GHz. The omnidirectional radiation pattern in the
H plane simplifies the pattern multiplication when an array made of omnidirectional
elements is considered. We will demonstrate experimentally that the patterns in the
proposed beam pattern diversity system are mainly determined by the array factor. Fig. 219 plots the measured and simulated return losses for the single-element dual-band
43
antenna based on the configuration in Fig. 2-17. Good agreement is observed.
270
180
— ^ — • Meas_xzplane
mum mum
yeas_yzplane
•»•«»••»• Sim_xzplane
«.„„„.,.». sim_yzplane
Figure 2-18 Measured and simulated radiation patterns of the dual-band antenna at 1 GHz.
c
-20
Measurement
- - - - - Simulation
-25 ^
-30
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
Frequency (GHz)
Figure 2-19 Measured and simulated return losses of the dual-band antenna.
44
2.3.4
Experimental Demonstration of the Three Types Dual-Band Beam
Pattern Diversity Systems
As aforementioned, the basic elements in the proposed dual-band beam pattern
diversity systems include the CRLH 180° or 90° coupler, the CRLH delay line, and the 2element antenna array. The 180° or 90° coupler acts as the mode-decoupling network
(MDN), which separates two orthogonal radiation modes or excite the antenna array to
radiate independent mode patterns even though the strong interference exists between the
antennas. In addition, with the aid of the CRLH delay line, various beam patterns can be
implemented, leading to varieties of beam pattern diversities. In this section, the
formation of the three types beam pattern diversities will be demonstrated.
Type I:
Pattern orthogonality of the Type-I pattern diversity at 2.4 GHz and 5.2 GHz is
illustrated in Fig. 2-20. Due to the element proximity to the other, it is observed that the
array patterns remain almost omnidirectional when the array is in-phase excited.
Conversely, if the array is out-of-phase excited, the H-plane patterns show nulls in the
broadside direction, as expected. Fig. 2-21 shows the measured H-plane radiation patterns
when the array is excited at the S or A port, respectively, at 2.4 GHz and 5.2 GHz. Note
that the out-of-phase excitation pattern measured at 2.4 GHz is less symmetrical
compared to that at 5.2 GHz because there exists larger phase imbalance at 2.4 GHz.
Used as a mode decoupling network (MDN) for receiving orthogonal radiation
modes, Fig. 2-22 shows the input port isolation improvement by the introduction of the
coupler. In the first case, the measurement is taken at the input ports of the antenna array.
45
In the second case, the measurement is taken at the input ports of the coupler when the
output ports are connected to the antenna array. The isolation has been improved by 21
dB and 25 dB at 2.4 GHz and 5.2 GHz, respectively, from the first case to the second
case.
S-Port
A-Port
E-Port
A-Port
(b)
(a)
Figure 2-20 Schematic illustration of the Type-I dual-band beam pattern diversity at (a) 2.4
GHz (b) 5.2 GHz.
46
300
300
270
270
240
240
180
180
in-phase
out-of-phase
in-phase
out-of-phase
(a)
(b)
Figure 2-21 Measured H-plane radiation patterns of the Type-I beam pattern diversity
system at (a) 2.4 GHz (b) 5.2 GHz.
4
5"
Frequency (GHz)
Figure 2-22 Measured input isolation improvement of the Type-I system between the cases
of array with and without the 180° coupler.
Type II:
47
Radiation based on the Type-I pattern diversity system where the 2-element
antenna array is in-phase or out-of-phase excited exhibit sum and difference beam
patterns at both frequencies. In certain applications when endfire radiation patterns are
preferable, the configuration of the Type-I system needs modification. We consider a
situation in which the endfire patterns are obtained in the higher band while the sum and
difference modes are maintained in the lower band. This can be implemented simply by
introducing a CRLH delay line into the Type-I pattern diversity system and is defined as
the Type-II beam pattern diversity.
The Type-II pattern diversity system includes a compact CRLH-based dual-band
180° coupler, a CRLH delay line, and a dual-band 2-element planar antenna array with
the element distance 15 mm (XI4 at 5.2 GHz). The delay line adds extra phase delay of 0°
and 90° at 2.4 GHz and 5.2 GHz, respectively, to the lower path with respect to the upper
one. The schematic of the overall system is illustrated in Fig. 2-23. At 2.4 GHz the
measured H-plane patterns in Fig. 2-24(a) remain omnidirectional (sum radiation mode)
when the array is excited in-phase. On the contrary, if the array is excited out-of-phase,
the H-plane patterns exhibit nulls in the broadside direction (difference radiation mode),
as is demonstrated for the Type-I pattern diversity. These two radiation modes are
orthogonal to each other and thus achieve pattern diversity. At higher frequency, the
excitation currents at the input ports of the antenna array are with quadrature phase
difference and equal magnitude. Therefore, when the element spacing is XI4, the radiation
patterns show the endfire patterns, which are demonstrated in Fig. 2-24(b). This set of
endfire radiation patterns has maximum beams in the opposite directions and thus forms
48
pattern diversity in higher band. Note that the pattern directivity of quadrature-phase
excitation from the S-port is less obvious because at the backward direction its phase
deviation from the out-of-phase requirement is larger than that from the A-port. Fine
tuning of the delay line can be applied to reduce this deviation.
E-Port
0"
uuL
X-Port
O
0°
A-Port
A-Port
CRLH
delay line
CRLH
delay line
X-Port
S-Port
A-Port
A-Port
CRLH
delay line
CRLH
delay line
(b)
(a)
Figure 2-23 Schematic illustration of the Type-II dual-band beam pattern diversity at (a)
2.4 GHz (b) 5.2 GHz.
49
300
300
270 90
240
120
270
240
180
in-phase
out-of-phase
quadrature-phase (E-port)
quadrature-phase (A-port)
(a)
(b)
Figure 2-24 Measured H-plane radiation patterns of the Type-II beam pattern diversity
system at (a) 2.4 GHz (b) 5.2 GHz.
When working in the receiving mode, the 180° coupler together with the delay
line operates as a mode decoupling network (MDN) for splitting orthogonal radiation
modes. Therefore, there needs to be low correlation between the two input ports of the
system. Fig. 2-25 shows the measured input port isolation improvement compared
between two cases: with or without the mode decoupling network. In the first case, the
measurement is taken at the input ports of the antenna array. In the second case, the
measurement is taken at the input ports of the mode decoupling network when the output
ports are connected to the antenna array. The isolation has been improved by 22.6 dB and
11.2 dB at 2.4 GHz and 5.2 GHz, respectively, from the first case to the second case.
50
0
Frequency (GHz)
Figure 2-25 Measured input isolation improvement of the Type-II system between the cases
of array with or without the mode decoupling network (MDN).
Type III:
The proposed Type-Ill beam pattern diversity system includes a compact CRLH
dual-band 90° coupler, a CRLH-based delay line, and a dual-band two-element planar
antenna array with the element spacing of 75 mm (XI4 at 1 GHz) as shown in Fig. 2-26.
Fig. 2-27 presents the measured and simulated H-plane radiation patterns of the Type-III
beam pattern diversity system at dual frequencies. At 1 GHz, the excitations for the two
antennas have equal magnitude and quadrature phase difference. Along with the XI4
element distance at this frequency, two opposite endfire radiation patterns are expected
from different input excitations as shown in Fig. 2-27(a). At 2 GHz, on the other hand,
the array elements are excited with the same power but are either in-phase or anti-phase.
Therefore, the constructive interference will be in the broadside direction with in-phase
excitation. To the contrary, two main beams in the endfire directions are shown in Fig. 2-
51
27(b) due to the anti-phase excitation. These two radiation patterns are defined as the sum
or difference radiation modes and are orthogonal to each other. Good agreement is
observed in Fig. 2-27.
Portl
i/4
Dual-Band ^
90° Coupler! :
^
0
90°
Port 2
0°
CRLH
delay line
90"
^ p |—i—I J.™
Portl
Dual-Band
90° Coupler
J
Port 2
0"
0°
_
.
mmm.
.
— I
CRLH
delay line
(a)
-90°
-90'
Portl
Dual-Band
90° Coupler
Port 2
_l
-90°
0°
CRLH
delay line
-180°
-1-90»-| j j '
Portl
Dual-Band ^
90° Coupler
Port 2
m
^
_:
I
o°
o°
CRLH
delay line
(b)
Figure 2-26 Schematic illustration of the Type-Ill dual-band beam pattern diversity at (a) 1
GHz (b) 2 GHz.
52
300
270 90
240
270
120
—
---_._._.
..........
——«—» Meas_Port1
« - Meas_Port2
Sim_Port1
——— Sim Port2
180
Meas Portl
Meas Port2
Sim Portl
Sim_ Port2
(b)
(a)
Figure 2-27 Measured and simulated H-plane radiation patterns of the Type-Ill beam
pattern diversity system at (a) 1 GHz (b) 2 GHz.
m
H, -io
"\
1
*.*
c
1 -20
o
w
Q. -30
c
V
— —
w/o MDN
Type II MDN
(180° coupler)
.»,-»,«.
Type III MDN
{90° coupler)
-40
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
Frequency (GHz)
Figure 2-28 Measured input isolation improvement of the Type-Ill system between three
cases of array with or without the mode decoupling networks (MDNs).
Fig. 2-28 shows the measured input isolation improvement. The comparison is
made between three cases. The first case is the coupling measured at the input ports of
53
the antenna array without connecting the mode decoupling network. The second and third
measurements were taken at the input ports of mode decoupling networks when the
output ports are connected to the antenna array, which correspond to the set of the 180°
coupler with the delay line (Type II) and the set of the 90° coupler with the delay line
(Type III), respectively. As shown in Fig. 2-28, input port isolation improves for both
cases with mode decoupling networks. Moreover, the second measurement (Type II) is
found to have better capability of reducing the input coupling. This results from the
superior isolation performance of the proposed 180° coupler. The input isolation has been
improved by 22.7 dB and 10 dB at 1 GHz and 2 GHz, respectively, from the first case to
the second case.
2.4
Application of the C R L H Hybrid Couplers to the Microwave
Diplexers
2.4.1
Introduction
Diplexers are essential elements in the transceiver modules of modern
communication systems that often require dual-band operation. For decades, studies on
diplexers have attracted many researchers and were reported extensively. Almost all of
these diplexers are based on two bandpass filters, each of which is responsible for the
respective frequencies in dual-band schemes. In [12, 13], diplexers made up of
waveguide filters were fabricated. Although low insertion loss and high isolation were
obtained, parametric optimization on the three-port junction connecting the filters and
performance tuning are time-consuming. In addition, in order to suppress higher-order
54
harmonics of filters, stepped-impedance resonators (SIRs) were utilized [14, 15]. The
harmonic spurious responses are controlled at the expense of design complexity. Channel
isolation in diplexer design can be enhanced but usually requires connecting extra circuit
elements, such as tapped open stubs [16], and XI4 microstrip lines in front of the filters
[17].
CRLH transmission lines are shown to be engineerable by the constituent circuit
parameters. Therefore, they can be realized with desirable characteristic impedances and
phase responses at the frequencies of interest. In the preceding section, the capability of
the CRLH delay lines contributing to the dual-band beam pattern diversities was
demonstrated. In this section, diplexer application by utilizing the unique phasecontrollable feature of the CRLH phase-advance or delay lines will be implemented.
Instead of employing two bandpass filters, the proposed diplexer is composed of a singleband Wilkinson power divider, CRLH phase-advance or delay lines, and a CRLH-based
directional coupler. The power divider acts as a three-port matched junction, halving
signals to the connected CRLH phase-advance or delay lines. The CRLH transmission
line is phase manipulated at dual frequencies to excite the subsequent directional coupler
such that frequency selection takes place at output ports of the coupler. Based on this
concept, two diplexers were fabricated. The first one demonstrates a diplexer with closer
passbands at 1.9 GHz and 2.4 GHz using a single-band CRLH 180° hybrid and a CRLH
delay line with 0° and -180° phase responses, respectively. The other diplexer exhibits the
diplexing phenomenon at 1 GHz and 2 GHz using the dual-band CRLH 90° hybrid and a
CRLH phase-advance line with 90° and 90° phase responses, respectively. It is shown
55
that based on this topology, the aforementioned design complexities are reduced.
Feasibility of these novel diplexers are verified by experiments.
2.4.2
Diplexer Based on the Single-Band 180° Coupler and the CRLH Phase-
Delay Line
The proposed diplexer based on the ring hybrid includes a single-band Wilkinson
power divider, the CRLH phase-delay line, and the single-band CRLH 180° hybrid.
Schematic illustration is shown in Fig. 2-29. The two-way Wilkinson power divider acts
as a three-port junction, which provides the subsequently connected CRLH phase-delay
line with in-phase and even power split. The easy construction and three-port impedance
matching make the Wilkinson divider the best candidate as the interconnection junction.
The dual-band CRLH delay line is used for exciting the 180° coupler with in-phase or
anti-phase input at the respective frequencies. This delay line is based on CRLH
transmission structures with regards to arbitrary dual-band operation, and is designed to
have 0° and -180° phase responses at 1.9 GHz and 2.4 GHz, respectively, with a
characteristic impedance 50 Cl. As shown in Fig. 2-29(a), at 1.9 GHz the phase
progression along two paths of the delay line are identical, which helps signal
construction at the £ port. On the other hand, the anti-phase signals from the delay line
cause signals at 2.4 GHz to appear at the A port as indicated in Fig. 2-29(b). Therefore,
the frequency selective mechanism is achieved.
56
delay line
(a)
(b)
Figure 2-29 Schematic illustration of the proposed ring-hybrid -based diplexer at (a) 1.9
GHz (b) 2.4 GHz.
The phase nonlinearity and controllability of the CRLH structures make arbitrary
dual-band and compactness of the hybrid possible. Since the present application deals
with rather narrow frequency split, a single-band 180° hybrid is used for diplexing
adjacent passbands. A remarkable advantage of employing a single-band 180° hybrid is
that the footprint size can be reduced significantly. This proposed single-band coupler
operates at 2.15 GHz, which is the mid-band of the two frequencies of the diplexer. It is
made up of three identical CRLH transmission arms with phase-advance response 90°
and a microstrip line with phase -90° at 2.15 GHz. The 90° and -90° transmission
structures replace the corresponding conventional XI4 and 3X14 microstrip lines. This
arrangement leads to a significant size reduction. Based on the topology using chip
components and microstrip lines contributing to left- and right-handedness, respectively,
a miniaturization of 86.2% is accomplished compared to the single-band microstrip 180°
coupler. Two unit-cell lumped elements are used and the shunt inductance and series
capacitance are
(ZL=5.1
nH,
CL=1
pF) in the CRLH transmission structures.
57
The CRLH delay line is characterized to have phase responses 0° and -180° at 1.9
GHz and 2.4 GHz, respectively. These phase responses are implemented as the phase
differences between two paths connected to the hybrid. Pairing a CRLH transmission
structure with a microstrip line is used for this delay line. In order to maintain the
impedance matching, a characteristic impedance of 50 Cl is considered for both lines. At
1.9 GHz and 2.4 GHz the phase lag of the CRLH structure is 0° and 180° relative to the
microstrip line, respectively. In order to fulfill such a phase specification, the required
right-handed microstrip lines in the CRLH transmission structure are relatively long. This
is caused by the fact that the length of the microstrip line in the synthesized CRLH
structures is proportional to the rate of phase descending. Therefore, physically long
microstrip lines are necessary for the 180° phase decrease at two close frequencies. Thus,
the delay line dominates the overall diplexer dimensions. Five unit-cell lumped elements
are used. The shunt inductance and series capacitance are (ZL= 3.9 nH, C\j= 1.2 pF) in the
CRLH transmission structures.
Figure 2-30 Photograph of the proposed ring-hybrid -based diplexer at 1.9 GHz and 2.4
GHz.
58
m
2 , -10
<A
(0
0 -20
_l
c
o -30
*rf
1—
o -40
(0
c
-50
«»«»«»«* Meas -SA-ini
- . - . - = Sim - Ss-in
•••••••••• Sim - S^-in
1.6
1.8
2.0
2.2 2.4 2.6 2.8
Frequency (GHz)
Figure 2-31 Measured and simulated insertion losses of the proposed ring-hybrid -based
diplexer.
CD -10
T3
(0
tf>
-20
O -30
_J
C
3
+*
:irr40 o
-40
O
Of -50
• ^ • • • • • t
Sim - Sjn-in
—f»««»<umm—Sim - S ^ E
-60
1.6
1.8
2.0
2.2
2.4
2.6
-50
-60
2.8
Frequency (GHz)
Figure 2-32 Measured and simulated input return losses and output isolations of the
proposed ring-hybrid -based diplexer.
Fig. 2-30 shows the photograph of the proposed diplexer using a single-band
Wilkinson power divider, a CRLH delay line, and a single-band CRLH ring hybrid. This
diplexer was built on a Duroid/RT 5870 substrate with /z=0.787 mm and £}=2.33. The
measured insertion loss is -0.7 dB and -0.6 dB at 1.9 GHz and 2.4 GHz, respectively, as
59
shown in Fig. 2-31. The channel rejection effectively filters out the other unwanted
frequencies. Excellent agreement is achieved between simulation and measurement. In
addition, the measured and simulated return losses and output isolations are demonstrated
in Fig. 2-32. At the frequencies of interest, -27 dB and -20 dB were obtained for the
measured return losses. Meanwhile -27 dB and -23 dB are the isolations at 1.9 GHz and
2.4 GHz, respectively. The experimental results support our idea that the proposed
diplexer synthesis method is feasible and simple. Namely, using this synthesis method is
free of concerns about the interconnection junction optimization, spurious response
suppression, and isolation improvement by adding extra elements. Furthermore, the
measured three-port return losses are matched at all ports as expected. Note that the
overall circuit can be miniaturized if substrates of high dielectric constants are employed
or a denser layout is configured.
2.4.3
Diplexer Based on the Dual-Band 90° Coupler and the CRLH Phase-
Advance Line
The second example, the proposed 90° hybrid -based diplexer, includes a singleband Wilkinson power divider, a CRLH phase-advance line, and a dual-band CRLH 90°
hybrid. Fig. 2-33 illustrates the frame of this diplexer. The two-way Wilkinson power
divider eases the junction design complexity and bisects signals evenly into the
subsequent CRLH phase-advance line. The CRLH phase-advance line is designed to
exhibit same 90° phase-advance to excite the dual-band 90° coupler at 1 GHz and 2 GHz.
This is ascribed to the phase responses of the dual-band CRLH 90° coupler. As shown in
60
Fig. 2-33(a), at 1 GHz the phase progression along each branch of the 90° coupler is 90°
phase advanced, and thus the constructive signal shows up at port 2. To the contrary,
signals at 2 GHz will come out at port 1 when the 90° phase delay is assigned to each
branch of the coupler as in Fig. 2-33(b). The set of 90° and -90° phase responses at
operating frequencies is employed to consider the compactness. Therefore, the
combination of a 90° phase-advance CRLH line at either frequency with the quadrature
hybrid with the phase variation from 90° to -90° is able to act as a diplexer at frequencies
of interest.
phase-advance
phase-advance
(b^
line
line
Figure 2-33 Schematic illustration of the proposed quadrature-hybrid -based diplexer at (a)
1 GHz (b) 2 GHz.
As mentioned, a dual-band CRLH 90° hybrid with phase responses of 90° and -90°
at 1 GHz and 2 GHz, respectively, is utilized. For miniaturization, transmission lines with
phase advance are considered in this coupler. It is composed of two kinds of CRLH
transmission structures of characteristic impedances 50 Cl and 50/V2 Cl. For each branch,
the phase responses are 90° phase advanced at 1 GHz and -90° phase delayed at 2 GHz.
In place of the traditional XI4 microstrip lines, this proposed quadrature hybrid is compact
61
and capable of dual-band operation. By use of the CRLH structures, the size reduction of
11.6% compared to the microstrip 1-GHz 90° coupler is accomplished. Three unit-cell
lumped elements are used and the shunt inductances and series capacitances for the two
kinds of transmission structures are (LL,5o=9.4 nH, CL,5o=2.8 pF, LU50N2=6.2
nH, CL,50/v
2=4.2 pF). The CRLH phase-advance line is designed to have the same phase responses
of 90° at both frequencies. This requirement is realized by pairing a CRLH transmission
structure with a microstrip line so that the CRLH transmission structure is phase
advanced by 90° at both frequencies. The characteristic impedance of 50 Q is used for
both lines. Two unit-cell lumped elements are used. The shunt inductance and series
capacitance are (£L=15 nH, CL=6 pF) in the CRLH phase-advance line.
Figure 2-34 Photograph of the proposed quadrature-hybrid -based diplexer at 1 GHz and 2
GHz.
62
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Frequency (GHz)
Figure 2-35 Measured and simulated insertion losses of the proposed quadrature-hybrid based diplexer.
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Frequency (GHz)
Figure 2-36 Measured and simulated input return losses and output isolations of the
proposed quadrature-hybrid -based diplexer.
Fig. 2-34 shows the photograph of the proposed diplexer using a single-band
Wilkinson power divider, a CRLH phase-advance line, and a dual-band CRLH 90°
hybrid. This diplexer was built on a Duroid/RT 5870 substrate with /z=0.787 mm and
£^=2.33. The measured insertion losses are -1 dB and -0.9 dB at 1 GHz and 2 GHz,
63
respectively, as shown in Fig. 2-35. As observed in Fig. 2-35, the channel rejection is
higher than 22 dB. Measured and simulated responses agree well. Fig. 2-36 shows the
measured return loss and output isolation. At the frequencies of interest, -19 dB and -15
dB were observed for the input return losses, and meanwhile -22 dB and -20 dB are the
isolations at 1 GHz and 2 GHz respectively. The input return loss of this diplexer can be
improved by employing a dual-band Wilkinson power divider operating at 1 GHz and 2
GHz at the expense of design complexity. Nevertheless, this example verifies the
feasibility and simplicity of the proposed diplexer synthesis method as the first example.
Again, the measured return losses are matched at all ports as expected. Note that the
overall size can be reduced using substrates of high dielectric constants.
64
References
[1]
M. A. Antoniades and G. V. Eleftheriades, "Compact linear lead/lag metamaterial
phase shifters for broadband applications," IEEE Antennas Wireless Propag. Lett.,
vol. 2, no. 1, pp. 103-106, 2003.
[2]
M. A. Antoniades and G. V. Eleftheriades, "A broadband Wilkinson balun using
microstrip metamaterial lines," IEEE Antennas Wireless Propag. Lett., vol. 4, pp.
209-212, 2005.
[3]
C. -J. Lee, K. M. K. H. Leong, T. Itoh, "Metamaterial transmission line based
bandstop and bandpass filter designs using broadband phase cancellation," in
IEEE MTT-S Int. Microw. Symp. Dig, Jun. 2006, pp. 935-938.
[4]
I. -H. Lin, M. DeVincentis, C. Caloz, and T. Itoh, "Arbitrary dual-band
components using composite right/left-handed transmission lines," IEEE Trans.
Microw. Theory Tech., vol. 52, no. 4, pp. 1142-1149, April 2004.
[5]
H. Okabe, C. Caloz, and T. Itoh, "A compact enhanced-bandwidth hybrid ring
using an artificial lumped-element left-handed transmission-line section," IEEE
Trans. Microw. Theory Tech., vol. 52, no. 3, pp. 798-804, March 2004.
[6]
P. -L. Chi and T. Itoh, "Miniaturized dual-band directional couplers using
composite right/left-handed transmission structures and their applications in beam
65
pattern diversity systems," IEEE Trans. Microw. Theory Tech., vol. 57, no. 5, pp.
1207-1215, May 2009.
[7]
P. -L. Chi, C. -J. Lee, and T. Itoh, "A compact dual-band metamaterial-based ratrace coupler for a MIMO system application," in IEEE MTT-S Int. Microw. Symp.
Dig, Jun. 2008, pp. 667-670.
[8]
T. -I. Lee and Y. E. Wang, "Mode-based beamforming with closely spaced
antennas," in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2007, pp. 1723-1726.
[9]
C. B. Dietrich, Jr., K. Dietze, J. R. Nealy, and W. L. Stutzman, "Spatial,
polarization, and pattern diversity for wireless handheld terminals," IEEE Trans.
Antennas Propag., vol. 49, no. 9, pp. 1271-1281, September 2001.
[10]
P. -L. Chi and T. Itoh, "Metamaterial-based components for a compact dual-band
beam pattern diversity system," in Proc. 38th Eur. Microw. Conf, Oct. 27-31,
2008, pp. 555-558.
[11]
Y. -L. Kuo and K. -L. Wong, "Printed double-T monopole antenna for 2.4/5.2
GHz dual-band WLAN operations," IEEE Trans. Antennas Propag., vol. 51, no.
9, pp. 2187-2192, September 2003.
[12]
G. Macchiarella and S. Tamiazzo, "Novel approach to the synthesis of microwave
diplexers," IEEE Trans. Microw. Theory Tech., vol. 54, no. 12, pp. 4281-4290,
Dec. 2006.
[13]
D. Packiaraj, M. Ramesh, and A. T. Kalghatgi, "Cavity diplexer using tapped line
interdigital filters," in Proc. of 2005 Asia-Pacific Microwave Conf, vol. 1, Dec.
4-7, 2005.
66
[14]
A. F. Sheta, J. P. Coupez, G. Tanne, S. Toutain, and J. P. Blot, "Miniature
microstrip stepped impedance resonator bandpass filters and diplexers for mobile
communications," in IEEE MTT-S Int. Microw. Symp. Dig., vol. 2, pp. 607-610,
June 17-21, 1996.
[15]
C. -F. Chen, T. -Y. Huang, C. -P. Chou, and R. -B. Wu, "Microstrip diplexers
design with common resonator sections for compact size, but high isolation,"
IEEE Trans. Microw. Theory Tech., vol. 54, no. 5, pp. 1945-1952, May 2006.
[16]
M. -H. Weng, C. -Y. Hung, and Y. -K. Su, "A hairpin line diplexer for direct
sequence ultra-wideband wireless communications," IEEE Microw. Wireless
Compon. Lett., vol. 17, no. 7, pp. 519-521, 2007.
[17]
X. Chen, W. Zhang, and C. Yao, "Design of microstrip diplexer with wide bandstop," in Proc. of 2007 Int. Microw. Millimeter Tech. Conf, April 18-21, 2007.
67
Chapter 3
Antenna Miniaturization Based on
the Slow Wave Enhancement Factor from the
Loaded/Unloaded Transmission Line Models
3.1
Introduction
As communication systems equipment is downsized substantially, their integral
elements need to be reduced accordingly. Antennas usually occupy substantial real estate
in the front-end modules, indicating that their sizes are critical to the overall volume. This
is particularly crucial if the operating frequency is low such as in the high frequency (HF)
band. There have been many techniques employed to attempt size reduction. The
application of high dielectric constant substrates to enhance the effective permittivity is
the easiest way to reduce the guided wavelength and thus the physical size of antennas
[1-3]. Similarly, magnetic materials of high permeability can be utilized for size
reduction [4]. In [5, 6], footprints are reduced with particular antenna layouts, such as
folded and meandered configurations. These complicated antenna structures are not
straightforwardly determined, however, and they involve time-consuming parametric
optimization. One class of miniaturization is to seek for particular materials of higherorder or controllable dispersion relations. For example, degenerate band edge crystals
exhibit 4 order co-ft curves at the band edges and thus resonances can be reduced to
68
lower frequencies [7]. In addition, artificial left-handed metamaterials have been found
capable of tailoring the dispersion characteristics to desired frequency responses by
optimizing the constituent unit cells, which lend themselves to the application of
miniaturization [8, 9].
Alternatively, antennas can be modeled as transmission lines, allowing the
transmission line theory to be applied. In this scenario, a physically short transmission
line can exhibit a considerable electrical length by increasing the equivalent inductance
or/and capacitance per unit length. This results in a slow wave structure with an enhanced
propagation constant. Examples of increasing the effective propagation constants are the
inductive or capacitive elements loaded to the radiating elements [10-13] and the
uniplanar compact photonic bandgap transmission line [14]. Slot-loop antennas have
dipole-like radiation characteristics but provide wider impedance bandwidths [15-18].
Furthermore, capacitive loading is mechanically easier by mounting chip capacitors
across the slot. By taking this advantage, a preliminary work for a slow wave slot loop
has already been reported [19], where shunt capacitors were distributed periodically
along the slot loop and the loaded transmission line model characterizing the slow wave
antenna was briefly addressed. By the same token, the transmission line model was used
to investigate the input impedance of a wideband spiral antenna [20].
In Section 3.2, the complete characterization of the loaded antennas is carried out
by applying periodically loaded transmission line models. An antenna study will be
illustrated regarding the load effect on the propagation constant, characteristic impedance,
and appearance of the stop-band region versus the load parameters. By exploiting the
69
transmission line model, the calculated slow wave enhancement factor as defined in (1.7)
agrees very well with the miniaturization factor. Therefore, antennas can be specifically
miniaturized using those load parameters with the desired slow wave enhancement factor.
In the end, a design procedure that enables miniaturized antennas to be achieved is
outlined. Subsequently, two small radiators, the capacitor-loaded HF slot-loop antenna
and planar inverted F antenna (PIFA), are developed based on this methodology and are
capable of operating at one-eleventh the frequencies of the unloaded antennas. Antenna
gains and impedance bandwidths are, however, deteriorated as a result of miniaturization.
Thereby, the trade-off of the radiation efficiency versus size reduction factor is
investigated in Section 3.3. In addition, Section 3.3 presents an impedance matching
network derived from filter design techniques to increase the impedance bandwidth of the
slot loop antenna. The underlying principle of realizing this matching circuit is to regard
the antenna as a resonant load around resonance, and the elements in the matching circuit
can be determined by specifications as in filter designs [21]. In Section 3.5, a tunable and
loaded slot loop antenna is provided as an alternative solution to compromise the
somewhat conflicting requirements of size limitation and bandwidth enhancement. The
tunable slot loop antenna is able to show a considerable "effective" bandwidth while
occupying a small footprint.
3.2
Design Procedure of the Capacitive-Loaded Antenna with
Flexible Size Reduction Using the Slow Wave Enhancement Factor
In the dissertation, slow wave antennas periodically loaded by shunt capacitors
are employed as the miniaturization prototype to facilitate implementation convenience.
70
As depicted in Fig. 1-6, a capacitor-loaded slow wave antenna represents a line
underneath the air line k=/3 in the dispersion diagram and has a propagation mode with
propagation constant (3 larger than the propagation constant f3o of the unloaded structure.
Note that the dispersion curve for the unloaded antenna can be non-linear, which is the
case when dispersive transmission lines are considered as the host lines, such as the
microstrip lines and slot lines [22]. As shown in Fig. 3-1, the propagation constant fi is a
function of the load capacitance and period for a given host transmission line and as the
entire structure is increasingly loaded by larger capacitance or/and smaller period, the
corresponding /? is increased toward the abscissa and the loaded structure is electrically
longer despite the same physical length.
Pf{cf,m
Figure 3-1 Illustration of a capacitor-loaded slow wave antenna in the k-/3 diagram. The
unit cell is shown as an inset.
The loaded transmission line model with periodic boundary conditions is applied
to characterize the behavior of a periodic loaded antenna and developed in the Advanced
71
Design System (ADS). Note that the loaded propagation constant f3 is obtained from the
ABCD matrix of a loaded unit cell, where the ABCD matrix characterizes the unique
feature of a particular unit cell and therefore it is independent of the termination loads.
Furthermore, when the periodicity is well maintained, the unit-cell model (as the inset
shown in Fig. 3-1) can fully represent the property of the loaded structure, such as its
propagation constant. Therefore, the characteristic impedance Zo of the host transmission
line, the load interval d, and the load capacitance c need to be determined. The
characteristic impedance Z0 is determined by two steps. First, a particular transmission
line best suited to describe the radiating element is assigned as the host transmission line.
Second, the impedance is determined by antenna structural and material parameters. For
example, a slot-loop antenna is represented by a slot line with Z0 depending on the slot
width and substrate. In addition, the load interval and load capacitance are used as
parameters to engineer the loaded propagation constant /?.
~]
0.0
I
|
0.2
I
|
0.4
I
|
0.6
Frequency (GHz)
(a)
72
I
1
0.8
,
1
1.0
i
N*
0.8-
|
0.4- /10 P E / y \ ^ ^ ^ ^ -
t
A
I 0.20 0
stop-bandi
100 pF
i
0.0
11 i
j i
0.5
i i
i j
i I
1.0
I I i
1.5
i
2.0
2.5
3.0
i
3.5
Beta*d
(b)
Figure 3-2 (a) The SWE (filffy versus loaded shunt capacitance for the capacitor-loaded
unit cell. The capacitance sweep is from 10 pF to 100 pF with a fixed ZAoi= 75.44 Q and a
load interval dsiotIXg= 7.6 degrees at 300 MHz, (b) the corresponding frequency responses of
the capacitor-loaded unit cell versus fid.
An example is given here. As mentioned in Section 1.2.2, the slow wave
enhancement factor, SWE = /?//%, is of particular interest due to its proportionality to the
miniaturization factor. Two approaches, viz. increasing the load capacitance and
decreasing the load interval, are found effective to increase the propagation constant f3, or
the SWE as indicated in [23]. Fig. 3-2 investigates the SWE with respect to the load
capacitance of a capacitor-loaded unit cell of a periodically capacitor-loaded slot line.
The characteristic impedance Zs\ot of this unit cell is determined from a 2 mm wide slot
line on a substrate of thickness 0.508 mm and £r= 4.5, and thus is approximated to be
75.44 Q from the numerical equations provided in [24]. In addition, the electrical length
of the unit cell is fixed at 7.6 degrees at 300 MHz (ds\otIXg). As the capacitance c is
increased from 10 pF to 100 pF, the SWE is increased as expected and the unity (J3=J3o)
73
corresponds to the unloaded case (c=0). It is observed from Fig. 3-2(a) the rate of this
enhancement is, however, diminished as the capacitance is continually increased. In
addition, the stop bands are encountered as the structure is increasingly loaded when the
SWE is inversely proportional to the frequency. These stop bands can be easily verified
and occur at frequencies where the product fid is equal to ;ras shown in Fig. 3-2(b). For
implementation, one should avoid stop-band occurrences in the operational range of
interest. The Bloch impedance ZB of the same example is also investigated in Fig. 3-3 and
is continuously decreased at a retarded rate as the capacitive load is increased. From the
transmission line theory, the reduced impedance is expected as a result of the increase in
the effective capacitance per unit cell (length). Moreover, the Bloch impedances
approach zero at frequencies where the respective stop bands occur. In order to
compensate the mismatch factor, a series inductance should be commensurately added as
mentioned in [20].
0.2
0.4
0.6
0.8
1.0
Frequency (GHz)
Figure 3-3 Variation of the Bloch impedance for the capacitor-loaded unit cell. The
capacitance sweep is from 10 pF to 100 pF with a fixed ZsIot= 75.44 Q and a load interval
daJXg= 7.6 degrees at 300 MHz.
74
20
15
or
>
IM i»
t f s if
I
1
If
| | Z 't
=U3Q
B
/
/
|l B =9.32n\
j
ZB=7.24n
•
X
I
X
X
T T T
\
//
1
140
\
Hh
Hh±
T
'
1
Hh
T
V
\
\y
80
«>
60
Li-
40
o
m
\
\
•-.^
4
100 Is
CO
\
\ZB=29.9in
\
I- 120
±Hh
-^. ZT" ZB=49.89Q
20
"—
' .
'****•-.flSBS
30
60
90
120
150
180
Frequency (MHz)
Figure 3-4 Calculated input VSWRs of the CPW-fed capacitor-loaded slot-loop antennas
(with an inset) with 5 cases of different ZBs. The corresponding quality factors (Qs) are
included in the figure. The slot width, load period, substrate thickness and dielectric
constant of the antennas are 2 mm, 20 mm, 0.508 mm, and 4.5, respectively.
In order to optimize antenna performance, the influence of the Bloch impedance
(of a unit cell) on the input impedance is studied. Corresponding to the capacitor-loaded
unit cell of the slot line discussed previously, a slot-loop antenna fed by the 50 Q
coplanar waveguide (CPW) is used. Input VSWRs of different Bloch impedances loops
were calculated by full-wave simulations in the High Frequency Structure Simulator
(HFSS). By periodically loading the slot loop with 1.2 pF, 5 pF, 25 pF, 60 pF, and 100 pF
capacitors at an interval of 20 mm, Bloch impedances ZBS of 49.89 Q, 29.91 Cl, 14.3 Q,
9.32 Cl, and 7.24 Cl are generated. As shown in Fig. 3-4, the impedance matching is not
significantly improved as the Bloch impedance approaches 50 Cl, which manifests the
effect of the excitation mechanism. In addition, antenna miniaturization is observed from
the increased radiation quality factor (Q), defined as the inverse of the 3-dB impedance
75
fractional bandwidth (half-power bandwidth), as the Bloch impedance ZB is gradually
reduced. Most importantly, the miniaturization factor, as the resonance frequency of the
unloaded antenna compared to the respective resonance frequencies of the loaded antenna
in Fig. 3-4, coincides very well with the SWE obtained from the developed circuit model.
Table 3-1 compares the miniaturization factors with SWEs based on the circuit model.
Excellent agreement is achieved which implies the feasibility of the developed
transmission line model. Practically, when a particular size reduction using the loaded
slow wave antennas is attempted, the required structure can be implemented by
employing the corresponding load parameters. In order to facilitate fabrication of the
antenna prototype of interest (the slot-loop and PIFA), only shunt capacitors are
considered in the dissertation. The design procedure of a loaded slow wave antenna with
specific miniaturization is as follows.
Step 1) Establish the equivalent loaded unit cell for the loaded antenna. Three
parameters involved in the model are the characteristic impedance ZQ of the host
transmission line, the unit-cell electrical length d/Xg, and the shunt capacitance c.
Step 2) Investigate the SWE as functions of the load parameters. The SWE is
obtained by taking the ratio of the loaded to the unloaded propagation constants of the
unit-cell circuits.
Step 3) Employ those load parameters resulting in the desired SWE. Disregard
those solutions with stop bands near or at frequencies of interest.
Step 4) Consider other fabrication factors. For example, a small load period would
increase the fabrication difficulty, leading to fabrication errors.
76
Table 3-1 Full-Wave Miniaturization Factor versus SWE for the Loaded Slot-Loop
Antenna
Loaded
capacitance c
(pF)
1.2
5
25
60
100
Miniaturization factor
(unloaded frequency/
loaded frequency in
MHz)
1.6(255.2/163.75)
2.6 (255.2/97.25)
5.5 (255.2/46.7)
8.4 (255.2/30.4)
10.8(255.2/23.65)
SWE
1.5
2.5
5.3
8.8
10.4
In the following sections, two miniaturized antennas based on the loaded slow
wave structure are demonstrated as examples using the SWE approach.
3.3
Example I: The Miniaturized Slot Loop Antenna and the
Implementation of the Wideband Impedance Matching Network
3.3.1
The Capacitor-Loaded and Miniaturized HF Slot-Loop Antenna with L-
Section Matching Circuit
Using predicted
load parameters
from
the unit-cell
circuit model, a
miniaturization of the capacitor-loaded HF slot-loop antenna is demonstrated as follows.
Furthermore, two matching networks are presented to improve the impedance
performance of the small slot-loop antenna, including an Z,-section matching circuit here
and an advanced four-pole matching network based on the filter design techniques in
Section 3.3.2. The antenna prototype used for miniaturization is a X slot loop. Applying
the slot line model to this slot loop, the characteristic impedance Zsiot for the slot line can
be determined from the slot-loop width wsiot, substrate information, and the operating
77
frequency. In this example, shunt capacitors are periodically distributed along the
aperture. Fig. 3-5 illustrates the configuration of the proposed loaded HF slot-loop
antenna. The associated unit-cell model can be referred to the inset in Fig. 3-2(a).
Employing those particular values (wsiot= 2 mm and an £T= 4.5 substrate of thickness
0.508 mm) exemplified in Section 3-2, the SWEs with respect to the load capacitance c,
load period dsiotIXg, and slot line Zsiot are investigated in Fig 3-6. Each investigation is
performed by one variable sweep at a time while the rest are kept as labeled. As expected,
the SWE increases when the structure is increasingly loaded (with increased load
capacitance or decreased load interval). Furthermore, the SWE becomes larger with the
host characteristic impedance. The shunt capacitance c= 100 pF, Jsiot/^-g= 7.6 degrees at
300 MHz (20 mm), and Zsi0t= 75.44 Q corresponds to a SWE of 10.4 as can be observed
in the figure. These values will be used for fabrication later. In viewpoint of
miniaturization design, the slot width is able to engineer the SWE through the
corresponding characteristic impedance Zsiot of the loop. At around several hundred MHz
the wider slot width corresponds to higher characteristic impedance, and therefore the
higher miniaturization effectiveness. The input matching of the antenna is not, however,
benefited by choosing a particular slot width. This is shown already in Section 3.2 where
the input VSWR of a 50 Q Bloch impedance loop is not satisfactory. In addition, from
the antenna figure of merit, the radiation efficiency is almost unchanged with respect to
the slot width. Therefore, in the dissertation, the slot width of the loop is chosen at the
convenience of capacitor placement.
78
g*
HH
Hh
-y H h
slot
gy
Hh
Hh
M> .
cpw
T
T
c„Hh ?"-f
tL
S,CJ)W •
(a)
Figure 3-5 (a) The configuration of the proposed capacitor-loaded HF slot-loop antenna
with the /.-section matching circuit, (b) Photograph of the fabricated antenna.
•
40
60
80
100
0
8
16
C(pF)
(a)
24
(b)
32
40
20
c=100pF,<fe| o l /.) g =7.6deg
40
60
80
100
(c)
Figure 3.6 SWE investigation for the capacitor-loaded HF slot-loop antenna (a) SWE vs.
load capacitance (b) SWE vs. load period (c) SWE vs. characteristic impedance of the slot
line.
Fig. 3-5(b) shows the photograph of the proposed capacitor-loaded HF slot-loop
antenna combined with the Z-section matching circuit. The slot-loop antenna was fed by
CPW and built on an Arlon AR 450 substrate with fr=4.5 and thickness 0.508 mm. The
unloaded slot-loop antenna was designed to have one wavelength resonance at 255.2
MHz and is able to operate at high frequency (HF: 3-30 MHz) after proper size reduction.
79
Here, the Vishay/Dale 1206 SMD 100 pF lumped capacitors are mounted across the slot
and the dimensions for the fabricated slow wave slot-loop antenna are as follows (see
Fig. 3-5(a)): lx= 190 mm, ly= 284 mm, /gx= 264 mm, /gy= 382.8 mm, wsiot=2 mm, ds\0t= 20
mm, wcpw= 4.4 mm, and gcpvi= 0.2 mm. The measurement was taken with the Anritsu
MS2034A vector network analyzer. Fig. 3-7 shows the measured and simulated |Sn| for
the loaded slot-loop with and without the matching circuit. As observed from the figure,
the measured responses agree well with the simulated results. Impedance matching is
significantly improved due to the L matching circuit where a series inductance Zm=864
nH and a shunt capacitance Cm=29.2 pF are used. The matched slot loop has a measured
\Sn\ of-12.04 dB at 24 MHz with a fractional bandwidth 0.38% for VSWR< 2, which is
considerably reduced as expected from its unloaded counterpart with a bandwidth 7.07%.
Lumped elements are exploited for the compactness and easy implementation of the
matching network, which avoids configuring space-consuming and complicated matching
patterns especially in HF bands. From experimental results, the one wavelength resonant
frequency was effectively reduced from the 255.2 MHz to 24 MHz, showing a size
reduction of 10.6. Compared to the predicted SWE of 10.4, this result confirms the
applicability using SWEs in designs of antenna miniaturization.
80
0
^
m
-a
-Sffi-^J^in.SSStm?^?!!
-5
-10
c/)
Meas w/ L ckt
Sim w/ L ckt
Meas w/o matching
Sim w/o matching
-15
-20
20
22
21
23
24
25
26
Frequency (MHz)
Figure 3-7 Measured and calculated l^nl of the loaded HF slot-loop antenna with and
without the Z-section matching circuit.
300
270
240
210
150
180
•»»»»•
•«•»••*
•••••••••
H plane w / L ckt
E plane w/ L ckt
H plane w/filter ckt
E plane w/ filter ckt
Figure 3-8 Calculated radiation gains of the loaded HF slot-loop antennas with the Z-section
and four-pole filter-type impedance matching networks, respectively.
Due to the limited facilities, our chamber can only accommodate radiation
measurements down to 300 - 400 MHz. Therefore only the calculated radiation gains of
81
the proposed loaded HF slot-loop antenna with matching circuits are presented. It should
be noted that the predicted and measured results for the loaded PIFA (see Section 3.4) are
in good agreement. Fig. 3-8 shows the predicted radiation gains of the loaded antenna
where dipole-like radiation patterns are observed as shown in [19]. The E and H principal
planes of this antenna are parallel to the yz and xz planes in Fig. 3-5(a) respectively.
From simulated results, the maximum radiation gain for the loaded slot-loop antenna with
the L matching circuit is -34.9 dBi (with radiation efficiency r/x= 0.08). This is resulted
from the considerable size reduction compared to the unloaded antenna. As a
fundamental trade-off exists between size reduction and antenna radiation efficiency, a
compromise needs to be made when considering size reduction. Fig. 3-9 establishes the
HFSS calculated radiation efficiency with relation to the size reduction for both small
antennas in Sections 3.3 and 3.4. The effect of the matching networks on the radiation
efficiency of the HF slot-loop antenna is investigated as well. Both the conductor and
dielectric losses are considered in our full-wave simulation. The lumped-element loss is
not included here for two reasons. First, based on the comparison at the frequencies of
interest (at around 400 MHz for the capacitors used in the loaded PIFA and at around 25
MHz for all the lumped elements used in the loaded slot-loop) the measured responses of
the lumped elements are in good agreement with those of the respective ideal models.
Second, to the best of the authors' knowledge, the measured S-parameters cannot be
embedded into the HFSS simulation environment. The equivalent loss resistance needs to
be extracted from the measured S-parameters in order to simulate the behavior of a nonideal lumped element in HFSS. Essentially, the radiation efficiency of the loaded HF
82
antenna decreases with size reduction as electrically smaller antennas are well known for
the poor radiation capability. Despite the good agreement between lossless models and
measured results of lumped elements, the measured efficiency of the HF slot-loop
antenna may suffer more losses (as compared to the predicted efficiency) from the
fabrication error and the possible lumped-element loss provided that the nearby cable
radiation is perfectly prevented (see Section 3.4). Furthermore, when the Z-section
impedance matching circuit is used, the radiation efficiency is reduced further. Higher
density of current distribution on the metal surface around lumped elements (of matching
networks) was observed in the model, which invokes increased conductor loss. Several
approaches can be applied to improve the radiation efficiency. For example, antennas
built on thicker substrates are prone to radiate [25]. Similar to the monopole concept,
antennas backed with large ground planes are able to increase the forward directivity [26].
Moreover, stacked structures composed of antenna substrates mounted with a high
dielectric superstrate can be employed [27-29]. All of the above methods, however,
inevitably lead to bulky antenna structures and increasing fabrication expenses.
83
[
•
•
•
•
PIFA
Slot-loop
Slot-loop w/
L matching ckt
Slot-loop w/
filter matching ckt
•
x
•
•
x
•
*
0
2
4
6
m
8
4
m
10
12
Size reduction
Figure 3-9 Predicted radiation efficiency nr with respect to the size reduction.
Due to the large wavelength at HF frequencies, conventional man-portable
antennas that can operate in this band typically have low gains. For example, a 10 foot
monopole has a gain of approximately -24 dBi at 2 MHz [30]. For applications such as
short range communications (less than 0.5 miles) and medium range communications
(less than 12 miles) these levels of gain are acceptable. A new application currently under
consideration for HF communications is for disaster recovery units. Here HF
communications are being considered because of the advantageous propagation
characteristics of this frequency range through concrete and other building materials as
well as tunnels, or obstructed passages. Although exactly fair comparison is not possible,
it is noted that the proposed slot-loop antenna has a lower radiation gain as compared to
that of a size-comparable monopole antenna backed with the same ground plane
dimensions as our antenna at 24 MHz. Our further investigation on the gain shows that
84
the capacitive loading in our structure creates the current discontinuity and introduces the
additional ohmic loss, deteriorating the radiation efficiency. Nevertheless, due to the
planar nature, the loaded slot-loop antenna provides higher portability and integrability
with other components.
3.3.2
The Proposed Filter-Type Matching Network for the Bandwidth-
Improved HF Slot-Loop Antenna
In Section 3.3.1, an Z-section matching circuit improved the impedance matching
significantly. However, the instantaneous bandwidth is greatly limited due to the inherent
property of the electrically small antennas. In order to effectively increase the bandwidth,
in this section, the filter design technique [21] is applied to the realization of an increased
bandwidth matching network for the miniature slot-loop antenna.
The underlying principle of implementing antenna matching circuits based on the
filter design approach is to consider the antenna to be a resonant load around resonance.
In many situations, antennas can be approximated as series or parallel resonators over the
frequency range of interest. Therefore, elements in the matching circuit are conceived as
the remaining components in a band-pass filter and can be determined by the circuit order
n, the maximum in-band attenuation (ZA)max, and the equal-ripple fractional bandwidth
A(o. Using filter-like impedance matching circuits enables a considerable bandwidth
improvement as desired. It is found, however, that the high-g feature of the small
antenna mainly restrict the capability. In addition, the degraded radiation efficiency of the
HF slot-loop due to the lumped elements in filter-type matching circuit will be discussed
85
later.
res. 4
res. 3
res. 2
IT
45
T
ll
'34
Ti
23
TJ
1
J
C
° — [ — I I—I—°
1
o — J
P
r>
(a)
res. 3
res. 4
45
'45
34
^
4
T
I
Ant
12
T
ant ant ant
res. 2
'23
T
1
£ C
2
2
12
Ant
'12
"(b)"
Figure 3-10 (a) Illustration and (b) corresponding implementation of the impedance
matching network using filter design techniques for the loaded HF slot-loop antenna. Fourpole prototype matching circuit (including the antenna) is used in this case.
Table 3-2 Lumped-Element Parameters in the Matching Circuit for the Loaded Slot-Loop
Antenna
Zi2=75 nH
Ci2=29.4 pF C2=959 pF
C 23 =H.7pF C3=971 pF Z3=32 nH
C45=52 pF
C4=930.6 pF Z4=32 nH
Z2=32 nH
C34=17.4pF
Z 45 =1.2uH
The illustration of the impedance matching network under consideration is
exhibited in Fig. 3-10(a). For the slot-loop antenna, it is observed that around resonance
the input admittance locus of the antenna varies along a constant conductance circle and
therefore is best suited to be modeled as a parallel resonator. In order to compensate for
the high-g of the antenna, a filter order n equal to 4 is chosen and further increase in n is
found with diminishing bandwidth improvement. The admittance inverters Jl}s are
86
introduced between stages to allow for input impedance match to Zo, usually 50 Q. Of
many admittance inverter realizations, the particular circuit shown as the inset in Fig. 310(a) is used. Note that the negative shunt capacitance at both sides can be absorbed into
the nearby capacitance in resonators or equivalently equated to an inductance. In other
words, the equivalent Ln in place of the negative shunt Crj (-Jtil(o) is
L u
^ - *
a>lCv coQJy '
(3-1)
where the resonant frequency coo of the antenna is used for narrowband approximation.
Eventually, the corresponding implementation of the impedance matching network is of
the configuration shown in Fig. 3-10(b). The capacitances Cu, C23, C34, and C45 result
from the corresponding capacitances in the center of each inverter realization. The
inductances Zi2 and Z45 come from the negative capacitance equivalences as
aforementioned. Furthermore, the values of C2, C3, and C4need to be adjusted for nearby
negative shunt capacitances. The design specifications of this filter-like matching circuit
are as follows: n= 4, (Z,A)max= 0-1 dB, in-band ripple level (ZA)max-(-£A)min= 0-04 dB, and
Aco(0.04 dB)= 1.64%. Based on these specific terms, lumped-element parameters in the
matching network are determined and can be found using the look-up diagrams in [21].
Table 3-2 lists the element values. We sourced the lumped components for the matching
circuit from Mouser Electronics Inc. The big capacitance or inductance was made up
from several smaller values. Otherwise, exact (or close enough to) lumped element as
shown in Table 3-2 was mounted. Thereby, 17 lumped-element values are employed in
the matching network and as follows: Murata 0805 SMD Monolith 2.4 pF, Xicon 1206
87
Ceramic Chip 470 pF, Vishay/Vitramon 1206 Ceramic 430 pF, Kemet 1206 SMD
Ceramic 51 pF, Vishay/Vitramon 1206 Ceramic 33 pF, Kemet 1206 SMD Ceramic 27 pF,
Murata 0805 SMD Monolith 16 pF, Vishay/Vitramon 1206 Ceramic 15 pF, AVX 1206
SMD Ceramic 0.5 pF, Murata 0805 SMD Monolith 11 pF, Murata 0805 SMD Monolith 9
pF, Xicon 0805 Ceramic Chip 1 pF, AVX 0603 SMD Microwave Thin-F 0.4 pF,
Dielectric Laboratories 0.7 pF, Vishay/Dale 1008 SMD Ind 68 nH, KOA Speer SMD Ind
72 nH, and Vishay/Dale High Current 1.2 uH. Surface mount chip components are used
in the proposed matching circuit due to the compactness and implementation simplicity.
As compared to the distributed and complicated layout in [31], the present HF matching
network is beneficial especially when the space-saving and time-saving (optimization
iterations are reduced) designs are concerned.
I
| _._._.
*
1
20
25
L matching ckt
Sim w/
filter matching ckt
30
35
40
Frequency (MHz)
Figure 3-11 Measured and calculated \Su\ of the loaded HF slot-loop antenna with the filtertype impedance matching network. The measured l^nl of the HF slot-loop antenna with Zsection matching circuit is included for comparison.
88
< Fig. 3-11 shows the measured \Sn\ of the slot-loop antenna with the filter-type
impedance matching circuit, where the photograph of the matching circuit is inserted.
Please note that matching circuit was connected to the antenna in the measurement and
the introduced electrical length between these two is negligible at such a low frequency
(HF). The simulated result is included for comparison. Note that the calculated double
resonances are decreased to a single resonance in the experiment. This is ascribed to the
lowered inter-coupling between resonators and might be resulted from the tolerance of
lumped-element values in the matching circuit. In addition, as mentioned previously,
bandwidth is broadened due to the degraded quality factor from fabrication error. Most
importantly, the instantaneous bandwidth is enlarged significantly as shown in Fig. 3-11,
where the set of antenna \Su\ with the Z-section and filter-type impedance matching
circuits are compared. Note that the higher resonant frequency is obtained for the antenna
with the filter-type impedance matching network. This is a consequence of the addition of
a shunt inductance to the resonant antenna in order for wider fractional bandwidth
implementation. The impedance bandwidth is improved from 0.38% (Z-section circuit) to
1.78% (filter-type circuit) due to the employment of the filter-type matching circuit. The
assembly of the miniaturized slot-loop antenna with the proposed impedance matching
network demonstrates a wider impedance match of 1.78%) while requiring a small area
0.03\X0 x 0.017Ao, where X0 is the free space wavelength at operational frequency.
Radiation patterns of this antenna are calculated and shown in Fig. 3-8 as well.
Compared to the antenna with the Z-section matching network, reduced radiation
efficiency in Fig. 3-9 is observed for the antenna employing the filter-type matching
89
network. This calculated efficiency rjr= 0.07 is further degraded from the previous
antenna with rjr= 0.08. Although ideal lumped elements are modeled in simulation, it
should be noted that current discontinuity due to the increased number of lumped
elements in the matching network (the filter-type circuit) will lead to a higher conductor
loss as compared to the antenna with a simpler matching network (the Z-section circuit).
The inference of dense current distribution around the filter-type matching network is
observed in the full-wave simulation.
3.4
(PIFA)
Example II: The Miniaturized Planar Inverted F Antenna
In this section, a loaded and miniaturized PIFA is given as an example based on
the SWE design methodology. The antenna prototype used for miniaturization is a XI4
patch with shorting pins connected to the bottom ground plane of the substrate at one end.
Applying the microstrip line model to this patch, the characteristic impedance ZpatCh of the
equivalent transmission line can be determined by the geometrical and material
parameters of the patch. In addition, shunt capacitors are mounted in parallel along the
longitudinal direction. Fig. 3-12 depicts the configuration of the proposed capacitorloaded PIFA with its unit-cell model. The SWE as a function of the load capacitance c,
load period dvatCh/Xg, and host-line characteristic impedance ZpatCh was investigated using
the unit-cell model and shown in Fig. 3-13. Each SWE curve is obtained by a respective
parameter sweep when the other two are fixed as indicated in legend. The cross, triangle,
and square symbols are associated with the load capacitance sweep, load period sweep,
90
and host line characteristic impedance sweep, respectively. As before, the SWE increases
when the structure is increasingly loaded (with increased load capacitance or decreased
load period). Furthermore, the SWE increases with the host characteristic impedance. The
combination of shunt capacitance c= 8 pF, Jpatch/^= 10 degrees at 4 GHz (1.5 mm), and
Zpatch= 38.07 Cl provides a SWE of 9.485 and is chosen for implementation.
gy
i
I i 1 1
py
T
T
x
T
T
T
d.
&
i'feed^f^.-.::
° '"''•>:".•':-•••'
.
.
.
ft
! • • . . '
.
i
pakbV-
T T T T T
-""T
,, ground
patch
Figure 3-12 The configuration of the proposed capacitor-loaded PIFA with an inset of its
unit-cell model.
S 8
W
A
A
S
12
C(pF)
(a)
16
20
0
10
d
A
s
A
CO
c= 8pF, Z p a t e h = 38.0712
20
30
40
patchUg( d e 9@ 4 G H z )
(b)
50
4
•
20
c= 8pF, ofp atc h/^g= 10deg
40
z
60
80
100
patch <n>
(c)
Figure 3-13 SWE investigation for the capacitor-loaded PIFA (a) SWE vs. load capacitance
(b) SWE vs. load period (c) SWE vs. characteristic impedance of the microstrip line.
91
-'
••;.
fr
*
J
' '" ; i*
' 'it-t
•'
-fe
."i"'
r'sa,.
<# *'
Loading capacitors^
.A
Figure 3-14 Photograph of the fabricated capacitor-loaded PIFA.
00
8
f it
CO
Meas
Meas
Sim Sim -25
0.35
0.40
- loaded
- unloaded!
unloaded 1
loaded
j
M
S• • • - *
0.45 3.00
4.00
5.00
Frequency (GHz)
Figure 3-15 Measured and calculated l^nl for the loaded and unloaded PIFAs.
Fig. 3-14 shows the photograph of the fabricated loaded PIFA fed by a coaxial
cable. The loaded antenna was built on a Rogers RT/Duroid 5880 substrate with ^=2.2
and thickness 3.175 mm. The Murata 0805 SMD Monolith 8 pF shunt capacitors are
mounted laterally in the direction of XI4 resonance. The dimensions for this slow wave
92
PIFA are as follows (see Fig. 3-12): /patch= 10.3 mm, wpatch= 14.82 mm, dpatch= 1-5 mm,
and /gx= /gy= 50 mm. Please note that the loaded PIFA has identical dimensions as the
unloaded PIFA, except loaded by capacitors. The measurement was taken with the
Anritsu MS2034A vector network analyzer. Fig. 3-15 depicts the measured and simulated
liSnl for both the loaded and unloaded antennas. The experimental results show good
agreement with the simulated data. The unloaded PIFA has a measured \Sn\ of-16.7 dB
at 3.98 GHz with a fractional bandwidth 4.07% for VSWR< 2 while the |5n| of the
loaded PIFA is -11.2 dB at 0.374 GHz with a fractional bandwidth 0.15%. The
significantly reduced bandwidth is the typical feature of electrically small antennas.
Moreover, the measured impedance bandwidths for both cases are wider than the
simulated results. In other words, a lowered quality factor is resulted from the experiment
and may be ascribed to the extra loss from the fabrication error. The skewed |5n|
response at around 0.4 GHz may be ascribed to two reasons. First, the experimental
period of the capacitors placement may be less than that (1.5 mm) in simulation, which
increases the miniaturization factor due to a heavier loading. Second, the tolerance from
the shunt capacitors will also lead to a resonance frequency shift. As observed from the
responses, the XI4 resonant frequency was effectively reduced from the 3.98 GHz to
0.374 GHz, which shows a size reduction of 10.6. The loaded PIFA occupies a small
footprint of 0.013Ao
x
0.018/io at 0.374 GHz. The excellent approximation to
experimental miniaturization verifies the effectiveness of using the circuit-based SWE for
loaded and miniaturized antenna designs. Furthermore, normalized radiation patterns of
the proposed loaded and unloaded PIFAs were measured and compared to the calculated
93
results in Fig. 3-16. Good agreement is observed. The E and H principal planes of this
antenna are parallel to the yz and xz planes in Fig. 3-12, respectively. Note that the
shielding effect on the backward radiation is reduced notably in the loaded situation since
the electrical size of the ground plane is shrunk accordingly with operating frequency
reduction. In order to prevent radiation from the coaxial cable, the ferrite beads were
connected to prevent current flowing on the cable. The measured maximum radiation
gain for this loaded antenna is -22.6 dBi, which is accurately predicted in the full-wave
simulation with a peak radiation gain of -24.1 dBi (rjr= 0.0024). The measurement
accuracy for the small antennas might have contributed to the gain deviation. As
mentioned previously, though ferrite beads were used during the measurement, there still
can be some that leaks through the cable. Moreover, the broadening of the \S\\\ response
might contribute to additional radiation gain. In addition, this loaded antenna is operating
near the performance edge of our chamber (400 MHz). The calculated radiation
efficiency of the loaded PIFA is also shown in Fig. 3-9 and it drops significantly
compared to the loaded slot-loop antenna. This can be attributed to the significant
conductor loss associated with the PIFA, which has much higher current density on the
small patch.
94
-10
-15 :
60
300
60
-20 ]
-25
2 90
-30
90 f V fi -\£ 15-20-2§-30-25-20-15^0 -*J
-20
-15
120
240 120
-10
r# •
150
^^^»
••••
»•••
••••••
210
180
Meas - E plane
Meas - H plane
Sim - E plane
Sim - H plane
150
210
180
Meas - E plane
Meas - H plane
Sim - E plane
Sim - H plane
(a)
(b)
Figure 3-16 Measured and calculated radiation patterns for the (a) loaded and (b) unloaded
PIFAs.
3.5
Example III: Compact and Tunable Slot Loop Antenna
3.5.1
Introduction
Compact and wideband antennas are highly desired nowadays for communication
terminals as they occupy limited space and can interface with various communication
standards. Miniaturization techniques that increase the effective permittivity or/and
permeability of the structure and therefore decrease the guided wavelength are wellknown. The development of these slow-wave antennas, however, is usually at the
expense of considerably reduced bandwidth, which makes them difficult to be used for
multiple systems. For most wireless communication systems, the instantaneous
bandwidth is relatively narrow and therefore if we can tune the frequency of the antenna
over the entire operational bandwidth (defined as the effective bandwidth), we may be
95
able to meet the somewhat conflicting requirements of a small radiator and a large
bandwidth of operation. Thus, an electrically tunable antenna may provide an alternative
solution.
Over the past few decades, there have been extensive studies on tunable antennas.
One class of the tunable antennas takes advantage of PIN diodes to create multiple
current paths and therefore resonant frequencies depending on the on or off diode state
[32-34]. In order to configure multiple paths, tunable antennas using PIN diodes are
typically layout-complicated and unable to present continuous frequency tunability.
Recently, RF MEMS varactors and switches [35-38] find many applications in tunable
antennas as they demonstrate great tuning potential in terms of the low power
consumption, better linearity, and a large capacitance ratio. In spite of these superior
features, the fabrication technology is relatively costly and the MEMS devices are
therefore not as accessible as the commercial tuning elements. Alternatively, loading
varactor diodes to resonant antennas to demonstrate frequency or polarization agility has
been widely employed [39-44]. In [40], the independent control of orthogonal
polarizations using four varactor diodes was presented. By properly choosing the varactor
locations, the frequency tuning ratio, the second to the first resonant frequencies, can be
significantly increased in dual-band slot antennas [42]. As far as the miniaturization is
concerned, embedding one or two varactor diodes to reduce the antenna operating
frequency, as is generally observed in the literature [43, 44], is less effective. Based on
our previous study [19], a slot loop periodically loaded by capacitors shows ability to
attempt considerable size reduction and moreover, can be easily analyzed by applying the
96
periodic boundary condition. As aforementioned, the instantaneous bandwidth is,
however, adversely reduced for this capacitor-loaded slow-wave antenna.
Therefore, in this section, a slot loop evenly loaded with eight varactor diodes is
applied to create a miniaturized antenna with a considerably increased effective
bandwidth. With regard to the impedance matching across the tunable frequencies, the
electromagnetically coupled feed using the microstrip line beneath the slot loop is
considered to provide more design parameters as compared to the direct CPW feed
employed in [19]. In addition, in order to isolate the RF signal from the bias line,
influencing the radiation characteristics, a LC low-pass circuit is included in the bias
network.
Figure 3-17 Schematic of the proposed tunable slot-loop antenna. The microstrip
line (dashed line) is on the opposite side of the substrate with respect to the slot loop (bold
line). Eight varactor diodes are periodically loaded across the slot in the positions where the
gap width is reduced as indicated. AH dimensions are in mm.
3.5.2
Slow Wave Antenna
Fig. 3-17 shows the proposed varactor-loaded slot-loop antenna. The square slot
loop (8.1 mm x 8.1 mm) is excited by a microstrip line, which is located on the other side
97
of the substrate. In order to enable the antenna to operate over the tunable frequency
range, a feed line composed of two sections of different widths was used for more
degrees of freedom in optimization. It was found that compared to the CPW-fed slot-loop
antenna [19], the microstrip-coupled excitation configuration makes it easier to achieve
wideband impedance matching. The slot is mounted with varactors at a 45° load period
where the perimeter of the loop is one wavelength at 9 GHz. At the load positions,
reduced gap widths are especially arranged in layout for soldering varactors, which are
smaller than the slot width itself. The bias circuitry is arranged as follows. To bias the
diodes across the slot, the DC power applied to the center patch is injected from the other
side through a via-hole whereas the surrounding metal plane is grounded. Furthermore, a
LC low-pass circuit is used to isolate the RF current flowing on the center patch from the
pulled bias line to avoid affecting antenna radiation characteristics from the latter (see Fig.
3-20).
By periodically loading the varactor diodes across the slot, the guided wave is
slowed down as a result of an increased effective propagation constant. The propagation
constant fi of a loaded structure in terms of the unloaded propagation constant fi\ is as
follows [23]:
fi=±-cos-\cos(fiQd)"
a
*"/ CZ o s i r W ) ) ,
(3.2)
where fi Zo, d, and C are the frequency, characteristic impedance of the host structure,
load period, and load capacitance, respectively. The ratio of the propagation constant fi to
fio, or the slow wave enhancement factor filfio, was shown in good agreement with the
98
miniaturization factor in [45]. In this scheme, given the fixed load period, the degree of
the miniaturization is determined by the capacitance tuning ratio of varactors. Fig. 3-18
plots the slow wave enhancement factor versus the available varactor capacitance Ct
compared with the respective miniaturization factors of the slot loop loaded with
equivalent varactor capacitances. Please note miniaturization is defined as the ratio of the
unloaded to the loaded loop resonant frequencies, frolfi, and is calculated in the full-wave
simulation. The varactor lumped-element model was embedded into the simulation
environment and carried out using the Ansoft Designer 4.0. As observed from Fig. 3-18,
good agreement is achieved and moreover, approximately twice the resonant frequency
can be reduced from Ct~ 0.2 pF to Ct~ 1.4 pF, which is the case for the proposed slotloop antenna with frequency tunable range from 2.34 GHz to 4 GHz. Please note that
each miniaturization factor is calculated with respect to the unloaded one wavelength
resonant frequency of the microstrip-fed slot loop antenna that occurs at 6.34 GHz and
can be read from Fig. 3-18.
99
Figure 3-18 Comparison between the slow wave enhancement factor fi/fio and
miniaturization facto r/r0//"r for the proposed tunable slot-loop antenna.
Bias (volts)
Figure 3-19 The extracted junction capacitance Cs and series resistance Rs in the equivalent
lumped-element model versus the bias voltage. The parasitic capacitance Cp and parasitic
inductance Lp are assumed as 0.06 pF and 0.2 nH, respectively.
100
3.5.3
Diode Modeling
In order to improve the simulation accuracy, the characterization technique
provided in [46] is applied to extract the equivalent lumped-element parameters of a
varactor diode. The Microsemi MPV 2100 surface mount varactor diode is used [47].
From the manufacturer's datasheet, the parasitic inductance Lv and parasitic capacitance
Cp are assumed as 0.2 nH (the worst case) and 0.06 pF in the model. Instead of mounting
the diode at the open-end of a known transmission line, which is ordinarily used for diode
characterization in the past, the proposed configuration in [46] especially incorporates the
impedance matching circuit to improve the extraction accuracy. Because of the close
proximity to the edge of the Smith chart, the real part of the impedance of the varactor is
very sensitive to the calibration plane where the diode is mounted, which increases the
possibility of extraction error based on the former implementation. Furthermore, while
the DC voltage is applied to the cathode of the diode through the high impedance line in
the bias network, the impedance matching circuit in [46] provides the ground voltage to
the anode from the shorted stub. Thus, a bias tee is not required in this bias scheme. Fig.
3-19 shows the extracted junction capacitance C} and series resistance i?s biased at several
voltage points. The equivalent lumped-element model is included as an inset. As
observed, the junction capacitance and series resistance are decreased with the bias
voltage as expected for the reverse-biased varactor diodes.
101
(a)
lb)
Figure 3-20 Photographs of the fabricated tunable slot-loop antenna, (a) Top view of the
structure showing the microstrip feed line and the LC low-pass bias network (the detail is
shown in the inset), and (b) back view of the structure showing the slot loop periodically
loaded by the 8 varactor diodes.
-10
CD
-a
oo
-20
-30
& # * & & & $ & & s-&
1
22 volts
20 volts
15 volts
10 volts
4 volts
Ovolt
2
3
4
5
Frequency (GHz)
Figure 3-21 The measured \Sn\ for the proposed tunable slot-loop antenna.
102
T
o.«
m
B. -10
< —
———
-20
Meas 22 volts
Calc 22 volts
00
S. -10
to
u
«8B88S8¥*S5Bft
-20
I
-l
Meas 20 volts
Calc 20 volts
l(b)
(a)
.30
-30
2
3
2
4
3
4
Frequency (GHz)
Frequency (GHz)
If
ll
»
m
•o -10
f
1
— — » Meas 4 volts
«•«— Calc 4 volts
Meas 15 volts
Calc 15 volts
-20
(d)
-30
1
2
3
4
5
1
2
Frequency (GHz)
3
4
5
Frequency (GHz)
Figure 3-22 Comparison between measured and simulated refection coefficients \Sn\ for the
proposed tunable slot-loop antenna biased at (a) 22 volts, (b) 20 volts, (c) 15 volts, and (d) 4
volts.
3.5.4
Simulation, Experiments, and Discussions
The proposed varactor-loaded slot-loop antenna was built on a Duroid 5880
substrate of ^ = 2.2 and thickness 1.57 mm. Fig. 3-20 shows photographs of the
fabricated antenna. Eight MPV 2100 varactor diodes are periodically mounted across the
slot. Two wires are pulled from the center patch (with the L= 22 nH and C= 8 pF lowpass circuit in-between) and the ground plane, respectively, to bias the diodes. The entire
footprint is 40 mm x 38.97 mm. The return loss measurement was taken with an Agilent
8515A network analyzer and is illustrated in Fig. 3-21. From 4 volts to 22 volts (close to
the breakdown voltage VB), the resonant frequency is tuned from 2.34 GHz to 4 GHz
with better than -7.5 dB reflection coefficient. The measured impedance bandwidth for
103
VSWR< 2 is about 22.2%, ranging from 3.2 GHz to 4 GHz. Furthermore, simulated and
measured results are compared in Fig. 3-22. The antenna refection coefficients for
varactor diodes biased at 4 volts, 15 volts, 20 volts, and 22 volts are presented in this
figure. Simulation results show that the impedance matching better than -14 dB was
obtained across the tunable frequency range from 1.87 GHz to 4.14 GHz, which
manifests the advantage of the chosen excitation configuration. Compared to the
simulation results, good agreement is observed for the V& > 15 volts. The discrepancy at
4 volts may be ascribed to two reasons. First, at the resonant frequency (2.34 GHz) when
4-volts reverse bias is applied, the slot-loop antenna is electrically small and therefore the
measurement of an electrically small antenna, as is known, is susceptible to nearby
objects. Please note that, an electrically small antenna (as well as the radiation capability)
is determined by its physical dimension with respect to the free space wavelength at
frequency of interest and thus an antenna given a fixed physical size will become
electrically smaller as the operating or resonant frequency decreases. On the other hand,
the resonance occurs as long as the resonant condition is satisfied for the antenna
resonator at the frequency, which can be decreased significantly by artificially loading
the radiator itself such as the substrate loading and reactive element loading. Our
proposed tunable antenna (or any other slow-wave antenna in the literature) is such an
example. By simultaneously applying both loading approaches, the resonant frequency is
decreased considerably at the expense of degraded radiation efficiency (see Table 3-3).
Second, the error tolerance of the parameter extraction at lower bias voltage is increased.
Please note that in Fig. 3-19 the slopes of Cj and Rs curves are steeper at lower bias
104
voltages.
Table 3-3 Calculated Radiation Efficiency for the Proposed Tunable Antenna under
300
60
290
240
120
300
60
290
240
120
Figure 3-23 Measured radiation patterns for the proposed tunable slot-loop antenna biased
at (a) 20 volts, (b) 15 volts, (c) 10 volts, and (d) 4 volts.
Normalized radiation patterns were measured and are shown in Fig. 3-23. The
105
radiation patterns were measured in an anechoic chamber. As observed, the typical
radiation patterns (solid curve for the H-plane and dashed curve for the E-plane) for the
slot-loop antenna are maintained across the frequency tunable range. The E-plane and Hplane of the slot loop is parallel to the xz and yz planes in Fig. 3-17, respectively.
Furthermore, the pattern ripples in the measurement may be due to the bias wires. The
measured maximum gain versus the bias voltage is plotted in Fig. 3-24. The radiation
gain is lowered with the decreased bias voltage when the varactor capacitance is
increased. Three reasons may contribute to this outcome. First, the antenna itself becomes
electrically smaller and the antenna radiation capability is deteriorated as a result [48].
Second, the resistance loss from the varactor diode increases at lower bias voltages (see
Fig. 3-19). Third, the increased return loss when biased at a lower voltage degrades the
antenna gain. The measured maximum gain at 20 volts is 1.71 dBi while the value drops
to -8.25 dBi at 4 volts. Compared to numerical calculation, the measured gains are less by
approximately 1.6 dBi. The fabrication inaccuracy and measurement error might
contribute to the discrepancy. The antenna radiation efficiency was calculated and
tabulated in Table 3-3, where the decreasing radiation efficiency at the lower resonant
frequencies indicates the electrically smaller size of the loop antenna. Since the measured
antenna gain is less than its simulation counterpart, it should be noted that, the measured
radiation efficiency is expected to be lower than the simulated result.
106
O
•
-
ik
A
CQ
JO
.E -3 0
A
•
•
•
•
-9
0
5
Meas
Calc
1
1
10
15
20
Bias (volts)
Figure 3-24 Measured and simulated radiation gains for the proposed tunable slot-loop
antenna.
107
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114
Chapter 4
Conclusion
Two miniaturization approaches are utilized and investigated in this dissertation.
The first method is to take advantage of the metamaterial-based transmission lines or the
CRLH transmission lines that are dispersion engineerable. Implementation of microwave
components that rely on particular phase responses at frequencies of interest is suitable
for size reduction based on the CRLH transmission structures. The CRLH transmission
line is able to support backward wave propagation (vp< 0 or fi< 0) below the transition
frequency and, its non-linear dispersion relation can be controlled through the equivalent
circuit parameters. These unique features show the potential for operating the arbitrary
dual-band and miniaturized components, such as the dual-band 180° and 90° hybrid
couplers. On the other hand, miniaturization utilizing the reactive loading is the focus of
second approach. By periodically loading reactive elements into the original structure, the
frequency behavior of a slow wave structure can be easily analyzed and therefore,
facilitates the realization. In spite of the well known contribution to size reduction, few
studies are concentrated on the development of a design procedure that enables arbitrary
miniaturization factor. In the dissertation, the design procedure based on the slow wave
enhancement factor is given to implement capacitor (varactor)-loaded slow wave
structures. The complete characterization of the loading effect on the frequency response
is made, and the design trade-off is discussed. Antenna examples of the capacitor-loaded
115
slot-loop antenna, the capacitor-loaded planar inverted F antenna, and the varactor-loaded
tunable slot loop are provided to demonstrate the feasibility.
In Chapter 2, the application of CRLH transmission lines to the arbitrary dualband and miniaturized 180° and 90° couplers are implemented. The critical factor that
contributes to the size reduction is to take advantage of the phase leading responses of the
CRLH transmission line that satisfy the phase requirement and moreover, save the
footprint size. In addition, by constructing the artificial CRLH structure from the specific
topology shown in the dissertation, it is found that the couplers can be miniaturized
further and the design process can be much simplified. Applications of the dual-band
couplers are addressed afterward, including serving as the dual-band mode decoupling
networks (MDNs) in the beam pattern diversity systems and the frequency selectors for
the diplexers.
In Chapter 3, a design procedure based on the slow wave enhancement factor
(SWE) is proposed. The slow wave enhancement factor, defined as the loaded to the
unloaded propagation constants of the structure, demonstrates excellent agreement with
the miniaturization factor. This property implies an important advantage that provides a
systematic approach to attempt arbitrary size reduction. Specifically, the periodically
capacitor-loaded slow structures are investigated in the dissertation. To verify the
practicability of this SWE approach, the high-frequency (HF) slot-loop antenna and
planar inverted F antenna (PIFA), are examples of small radiators to achieve the desired
size reductions. In addition, a miniature impedance matching network based on the filter
design techniques is presented to remedy the narrow band as a result from the inherent
116
property of small antennas. Before closing this chapter, a varactor-loaded slot loop is
implemented as an alternative of a small antenna while exhibiting a considerably
effective bandwidth.
117
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