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Development of design approaches for passive RF and microwavecircuits using periodical structures

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Development of Design Approaches for Passive RF and
Microwave Circuits Using Periodical Structures
A DISSERTATION
SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL
OF THE UNIVERSITY OF MINNESOTA
BY
Ho Saeng Kim
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Advisor: Rhonda R Franklin
August 2009
UMI Number: 3373404
Copyright 2009 by
Kim, Ho Saeng
All rights reserved
INFORMATION TO USERS
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______________________________________________________________
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Е Hosaeng Kim 2009
ACKNOWLEGEMENTS
First of all, I would like to thank God for giving me the strength, courage, and
means to complete this dissertation.
I would like to thank my advisor, Dr. Rhonda R. Franklin, for her constant
support and invaluable guidance over this six year journey. Inspiration drawn from the
insightful ideas and fruitful discussions with her has helped me overcome plenty of
difficulties encountered during my Ph.D. study. I have also learned much from her
insights into science, industry, and her philosophy of research. I would also like to thank
my committee members, Dr. Anand Gopinath, Dr. Stephen A. Campbell, and Dr.
Tianhong Cui, for their time and effort in serving on my committee.
I would like to extend special thanks to all current and graduated MPACT group
members: Young Seek Cho, Casey Murray, Jordan Alstad, Dr. Swagata Riki, Dr. Isaac
Itotia, Ethan Miller, Emile Davies-Venn, Napol Chaisilwattana, and Chenglin Zheng.
They gave me a lot of help in many aspects and made my time at the University of
Minnesota enjoyable. I feel very lucky to have worked with them.
I also appreciate the help that I received from all the staff in the Nanofabrication
centers and the Characterization Facility. The staff, Suzanne Miller, Mark Fisher, Kevin
Roberts, Tony Whipple, and John Nelson helped me many times with equipment and
processing problems.
I gratefully thank my parents and parents in law, Young Cheol Kim, Uh Yeon
Eom, Yong Kyun Oh, and Kwan Sim Jun, for their love, care, and prayer. I owe them a
-i-
huge debt of gratitude for their selfless support and encouragement. I would also like to
thank my sister, Jeong Ae Kim, for her support.
Last but not least, I would like to thank my wonderful wife and lifelong friend,
Sook Kyoung Oh, for her love, faith, support, and encouragement. Without all of these
wonderful supporters, I could not have made it through my Ph. D. study.
- ii -
To my loving wife, Sook Kyoung Oh
- iii -
ABSTRACT
This thesis deals with several design and analysis techniques for RF/microwave
passive circuits such as interconnects, filters, and antennas that offer circuir size
reduction and lower fabrication cost associated with future integrated communication
systems. Presented are new design approaches to enhance performance of passive circuits
and offer the ability to reduce size, minimize mismatch, reduce group delay variation, and
alleviate unwanted odd-mode excitation. This work is developed by exporing and using
periodic structure behavior in coplanar waveguide (CPW) designs. Periodic structures are
known to have bandgaps such as those seen in electromagnetic bandgap (EBG) designs.
Circuit based models were developed to predict the stop-band frequency range and to
reduce computational time associated with full wave models. To reduce circuit size slowwave designs can be employed. Thus, periodic structures in the form of interdigitated
designs can be used to achieve this function when operating well below the bandgap
frequency range. Herein, interdigitated coplanar waveguide designs are developed by
increasing both inductance and capacitance per unit length to reduce circuit size, control
signal phase, and match signal velocity. Geometrical characteristics of the proposed
structures are analyzed with the S-paramters, effective dielectric constant, and attenuation
constant. Design guidelines, which relate the effective dielectric constant to geometrical
parameters, are also developed. To suppress slot-line mode excitation in circuits with
structures, namely right-angle bends, slow wave structures can be used. In this work,
novel designs for wire-bond free circular interdigitated bends are presented and compared
- iv -
to circuits with right-angle bends. Also shown is a novel alternative approach which
presents a fast-wave design method and exploits it for suppression of slot-line mode
excitation. In filter design, the interdigitatated approach is used to (1) reduce the size of a
standard EBG based stopband filter by approximately 45% and (2) reduce the size of an
ultra-wide band (UWB) bandpass filter by 40% when combined coupled line with
meandered slot. Lately, annular ring slot antennas are miniaturized by leveraging the
periodic nature of meander geometry to reduce the surface area of single- and dual-band
annular ring slot antennas by 40% and 35%, respectively. The performance of all
structures is evaluated by comparing modeled designs to the measured one in this thesis.
-v-
TABLE OF CONTENTS
иииииииииииииииииииииииииииииииииии
i
ииииииииииииииииииииииииииииииииииииииииииииииииииии
iii
ABSTRACT и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
iv
TABLE OF CONTENTS и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
vi
LIST OF FIGURE
иииииииииииииииииииииииииииииииииииииииии
x
LIST OF TABLES
иииииииииииииииииииииииииииииииииииииииии
xix
ACKNOWLEDGEMENT
DEDICATION
ииииииииииииииииииииииииииииииииииии
xxi
I. INTRODUCTION и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
1
LIST OF APPENDICES
CHAPTER
1.1
Thesis Overview и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
3
II. ELECTROMAGNETIC BANDGAP (EBG)
STRUCTURE
5
2.1
Geometry
ииииииииииииииииииииииииииииииииии
6
2.2
Dispersion Diagram и и и и и и и и и и и и и и и и и и и и и и и и и и и и
7
2.3
LC Circuit Modeling и и и и и и и и и и и и и и и и и и и и и и и и и и и
11
2.4
ADS and HFSS Simulation и и и и и и и и и и и и и и и и и и и и и и и
13
2.5
Measurement Results и и и и и и и и и и и и и и и и и и и и и и и и и и и
18
2.5.1
Fabrication и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
18
2.5.2
S-Parameters и и и и и и и и и и и и и и и и и и и и и и и и и и и
20
Summary и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
22
2.6
III.
ииииииииииииииииииииииииииииииииииии
и и и и и и и и и и и
23
3.1
Coplanar Waveguide (CPW) и и и и и и и и и и и и и и и и и и и и и и
24
3.2
Slow-Wave Coplanar Waveguide (CPW) и и и и и и и и и и и и и
26
3.2.1
26
SLOW WAVE COPLANAR WAVEGUIDE
Design и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
- vi -
IV.
3.2.2
Geometry и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
30
3.2.3
Fabrication and Measurement и и и и и и и и и и и и и и и и
32
3.2.4
Characterization и и и и и и и и и и и и и и и и и и и и и и и и и
33
3.2.4.1
S-Parameter и и и и и и и и и и и и и и и и и и и и и и и и
33
3.2.4.2
Effective Dielectric Constant и и и и и и и и и и
35
3.2.4.3
Attenuation и и и и и и и и и и и и и и и и и и и и и и
35
3.2.4.4
Ultra Broadbadn Characteristic и и и и и и и и и
37
3.2.4.5
Impact of Size of CPW on Effective
Dielectric Constant and Attenuation и и и и и
40
3.3
Design Guidelines for Slow Wave CPWs и и и и и и и и и и и и и
42
3.4
Scale-Up of Slow Wave CPWs to PCB Circuit Size и и и и и и
43
3.5
Summary и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
45
и и и и и и и
47
Slow Wave Technique for CPW Right Angle Bends и и и и и
50
4.1.1
Design и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
50
4.1.1.1
Suppression of Slot-Line (Odd) Mode и и и
50
4.1.1.2 Radius of Circular Bend и и и и и и и и и и и и и
51
4.1.1.3
Design Guidelines и и и и и и и и и и и и и и и и и
52
Simulation and Measurement Results и и и и и и и и и и и
53
RIGHT ANGLED COPLANAR WAVEGUIDE
4.1
4.1.2
4.1.2.1
90░ Circular Bend with Slow Wave
Compensation и и и и и и и и и и и и и и и и и и и и
4.1.2.2
4.2
53
Back-to-Back 90░ Circular Bend with Slow
Wave Compensation и и и и и и и и и и и и и и и и
56
4.1.2.3
Fabrication and Measurement и и и и и и и и и и
58
4.1.2.4
Surface Current Distribution и и и и и и и и и и и
59
4.1.2.5
Measurement Results и и и и и и и и и и и и и и и
61
Fast Wave Technique for CPW Right Angle Bends и и и и и и
66
4.2.1
66
Design и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
- vii -
4.2.2
4.2.1.1
Fast Wave Coplanar Waveguide и и и и и и и и
4.2.1.2
90░ Circular Bend with a Trench in Longer
68
Slot и и и и и и и и и и и и и и и и и и и и и и и и и и и
69
Simulation and Measurement Results и и и и и и и и и и и
71
4.2.2.1
Single Bend: 90░ Circular Bend with Fast
Wave Compensation и и и и и и и и и и и и и и и и
71
4.2.2.2
Back-to-Back CPW Bend Structure и и и и и
73
4.2.2.3
Fabrication Process and Measurement
Setup и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
74
4.2.2.4
Surface Current Distributions и и и и и и и и и и
79
4.2.2.5
S-Parameters и и и и и и и и и и и и и и и и и и и и и
79
Summary и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
81
V. FILTER DESIGN и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
82
5.1
Electromagnetic Band-Gap (EBG) Filter и и и и и и и и и и и и и и и и и и и
83
5.1.1 Introduction и и и и и и и и и и и и и и и и и и и и и и и и и и и и
83
5.1.2
Conventional CPW EBG Structure и и и и и и и и и и и и и
84
5.1.3
Size Reduction Principle и и и и и и и и и и и и и и и и и и и и
86
5.1.4
Characterization of Slow Wave Structure и и и и и и и и
87
5.1.5
Design of New CPW EBG Structures и и и и и и и и и и и
89
5.1.6
Fabrication and Measurement и и и и и и и и и и и и и и и и
90
5.1.7
Simulation and Measurement Results и и и и и и и и и и и
93
Ultra-Wide Band (UWB) Bandpass Filter и и и и и и и и и и и и и
95
5.2.1 Introduction и и и и и и и и и и и и и и и и и и и и и и и и и и и и
95
5.2.2
96
4.3
5.2
Design и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
5.2.2.1
Conventional UWB Bandpass Filter of
CPW Type и и и и и и и и и и и и и и и и и и и и и и и и и
5.2.2.2
97
Modified Open-Ended Multiple Mode
Resonator (MMR) и и и и и и и и и и и и и и и и и
- viii -
101
5.2.2.3
Compact Coupled Line и и и и и и и и и и и и и и
104
Simulation and Measurement Results и и и и и и и и и и и
106
Summary и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
109
VI. MINIATURIZED ANNULAR RING SLOT
ANTENNAS
6.1
Ring Slot Antenna и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
110
5.2.3
5.3
6.2
6.3
6.4
111
Single-Band Meandered Annular Ring Slot Antenna и и и и и
115
6.2.1
Design и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
115
6.2.2
Fabrication и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
117
6.2.3 Return Loss и и и и и и и и и и и и и и и и и и и и и и и и и и и и
118
6.2.4
Size Reduction и и и и и и и и и и и и и и и и и и и и и и и и и и
119
6.2.5
Far-Field Radiation Patterns и и и и и и и и и и и и и и и и и
121
Dual-Band Annular Ring Slot Antenna using Meandered
Slots и и и и и и и и и и и и и и и и и и и и и и и и и и и ии и и и и и и и и и и и и и и и
122
6.3.1
Design и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
123
6.3.2
Simulation and Measurement Results и и и и и и и и и и и
125
6.3.2.1
Fabrication of Test Antennas и и и и и и и и и и
125
6.3.2.2
Return Losses и и и и и и и и и и и и и и и и и и и и
126
6.3.2.3 Far-Field Radiation Patterns и и и и и и и и и и и
129
Summary и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
131
и и и и и и и и и и и и и
132
Future Work и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
134
BIBLIOGRAPHY и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
136
APPENDICES и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
140
VII.
CONCLUSION AND FUTURE WORK
7.1
- ix -
LIST OF FIGURES
Figure
Top view and cross-sectional view of the unit cell of the modified EBG
structure и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
7
The top views of (a) the original EBG structure in [5] and (b) the
modified EBG structure и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
8
Dispersion diagrams of the EBG structure for wave propagating in (a)
x-direction, (b) y-direction, and (c) diagonal direction respectively и и и
10
Top views of the unit cell without the top metal divided into 16 sections
in (a) x-direction and (b) y-direction. R=3mm in each case. и и и и и и и и и и
11
Circuit Modeling of the unit cell of the EBG structure. (a) Unit cell. (b)
Cross section of an element of the unit cell. (c) Lossless lumped element
circuit model of the element shown in (b). R=3mm in each case. и и и и и и
12
ADS simulation results of EBG structures based on the lossless lumped
element circuit model. Input and output ports are terminated with
50hom. (a) Return loss of 1x1, 1x2, 1x4, 1x8, and 1x16 unit cells
connected in series. (b) Insertion and return losses of the EBG structure
of 2, 4, 6, and 8 rows (1 row = 1x8 unit cells) и и и и и и и и и и и и и и и и и и и и и
14
Simulation results of an 8x8 EBG structure with port impedance
matched (1.8 ohm). (a) The 8x8 EBG structure. (b) Comparison of ADS
and HFSS simulation results и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
16
Three different 1x8 cell EBG structures. (a) original 1x8 cell EBG
structure, (b) the modified 1x8 EBG structure I, and (c) the modified
1x8 EBG structure II и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
17
2.9
Configuration of the 1x8 EBG structure I и и и и и и и и и и и и и и и и и и и и и и и и
18
2.10
Picture of the two modified EBG structures (a) I and (b) II и и и и и и и и и и
19
2.11
Microstrip fixture и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
19
2.12
Comparison of the measured and simulated S parameters. (a) Return
loss (S11) and insertion loss (S21) и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
20
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
-x-
Cross sectional view of a finite ground coplanar waveguide on a
substrate, where S is the signal line width, G is the gap width, Wg is the
ground plane width, and h is the height of the substrate и и и и и и и и и и и и и
24
Figure 3. 2. Electrical and magnetic field distribution of (a) the evenmode and (b) the odd mode on a coplanar waveguide и и и и и и и и и и и и и и
25
3.3
Circuit models of (a) a conventional CPW and (b) a slow wave CPW и
27
3.4
Top views and cross-sectional views of (a) a regular finite ground
coplanar waveguide and (b) a finite-ground slow-wave coplanar
waveguide и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
29
Top view of two unit sections of slow wave CPWs with geometric
parameters и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
30
SEM picture of the slow wave CPW 3 fabricated on a high resistivity
silicon wafer with thickness of 400?m и и и и и и и и и и и и и и и и и и и и и и и и и и
32
The return loss (S11) and the insertion loss (S21) of the slow wave
CPWs and a reference CPW и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
33
3.1
3.2
3.5
3.6
3.7
3.8
The measured effective dielectric constant of the slow wave CPWs with
signal line width (S) of 225?m, gap width (G) of 130?m, and ground
plane width (Wg) of 1335?m и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
34
The measured attenuation per unit centimeter of the slow wave CPWs
with signal line width (S) of 225?m, gap width (G) of 130?m, and
ground plane width (Wg) of 1335?m и и и и и и и и и и и и и и и и и и и и и и и и и и и
36
The simulated insertion loss (S21) and return loss (S11) of the slow
wave CPW 3 and 6 и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
37
3.11
The effective dielectric constant of the slow wave CPW 3 and 6 и и и и и и
38
3.12
Variation of the effective dielectric constant of the slow wave CPW
developed from CPWs of several different sizes for various S1 и и и и и и
39
Variation of the attenuation of the slow wave CPW developed from
CPWs of several different sizes for various S1 и и и и и и и и и и и и и и и и и и и и
39
Relationship between S1 and FL2. The FL1 is equal to the subtraction
of S1 from S, and FW1, FW2, and U are fixed at 40?m, 40?m, 120?m
respectively и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
42
3.9
3.10
3.13
3.14
- xi -
3.15
3.16
4.1
4.2
4.3
4.4
4.5
4.6
Top view of (a) a reference CPW and a slow wave CPW with
dimensions. The substrate for the CPW and the slow wave CPW is FR4
epoxy with thickness of 59mil (1.5mm) и и и и и и и и и и и и и и и и и и и и и и и и и
43
The simulated S parameters of (a) the reference CPW and (b) the slow
wave CPW shown in Figure 3. 15 и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
44
Wire-bond techniques and dielectric overlay techniques for CPW rightangle bends: (a) conventional CPW right-angle bend with air bridges,
(b) chamfered CPW bend with air bridges, (c) step compensated CPW
bend with air bridges, and (d) the right-angle bend with dielectric
overlay on the inner slot и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
48
Wire-bond free techniques for CPW right-angle bends: (a) 90░ circular
bend with slow wave compensation and (b) 90░ circular bend with fast
wave compensation и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
49
Various CPW bend structures without air bridges: (a) Right-angle bend,
(b) 90░ circular bend, and (c) 90░ circular bend with slow wave
compensation. The arc radius (R) of a 90║ circular bend is defined as the
distance from the origin of a 90║ circular bend to the center of the signal
line. The physical length of inner and outer slots is denoted by L1 and
L2 respectively и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
51
The ratio of the outer slot length to the inner slot length versus the arc
radius (R) and the desired effective dielectric constant at the inner slot
versus the circular bend radius. The effective dielectric constant at the
outer slot is assumed to be 6.45 и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
52
Relationship between geometrical parameters (S1, FL2) and effective
dielectric constant of a slow wave CPW with signal width (S) of
225?m, gap width (G) of 130 ?m, and ground width (Wg) of 1335?m.
The value of the other geometric parameters of the 50 ? slow wave
CPW: FW1=40 ?m, FD1=80 ?m, FL1=(S-S1)*0.5, FW2=40 ?m,
FD2=80 ?m и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
53
Simulated S-parameters of a single right-angle bend structure, single
90░ circular bend structure with slow wave compensation (CB-SW)
shown in Fig. 2(a) and (c) respectively, and reference straight CPW
whose length is the same as the slow wave compensated bend structure.
Geometric parameters: S= 225?m, G=130 ?m, Wg=1335?m, R=1500
?m, FD1=80 ?m, FL1=52.5 ?m, FD2=80 ?m, FW2=40 ?m, FL2=
107.5 ?m, and ?=4.5░ и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
55
- xii -
Total Losses of a single right-angle bend structure, single 90░ circular
bend with slow wave compensation, and reference straight CPW и и и и и
56
4.8
Top view of a back-to-back 90░ circular bend structure и и и и и и и и и и и и и
57
4.9
The scanning electron microscopy (SEM) picture of a back-to-back 90║
circular bends with a 4 mm straight CPW section. The arc radius is
1500?m. The reference plane for the measurement is located right
before the circular 90║ bend by TRL calibration и и и и и и и и и и и и и и и и и и и
58
The surface current distribution on (a) a back-to-back right-angle bend
structure, (b) back-to-back 90║ circular bend structure, and (c) back-toback 90║ circular bend structure with slow wave compensation at the
frequency of 50 GHz. Each structure has a straight CPW section of 4
mm between two bend structures и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
60
The S-parameters measured of back-to-back right-angle bend structures
without air bridges, back-to-back 90║ circular bend structures with slow
wave compensation (CB-SW), and reference straight CPW lines. The
arc radius (R) of the 90║ circular bends is 1500 ?m for all the cases. (a)
The insertion and (c) return losses of the back-to-back structures
without a straight section of 4 mm. (b) The insertion and (d) return
losses of the back-to-back structure with a straight section of 4mm и и и
62
The S parameters measured of back-to-back circular 90║ circular bend
structures with slow wave compensation (CB-SWs) with three different
arc radii (R=500 ?m, 1000 ?m, and 1500?m) and a reference straight 50
? CPW line corresponding to the back-to-back 90║ circular bendwith
slow compensation with R=1500 ?m and ?L=4 mm и и и и и и и и и и и и и и и
65
Several types of CPW bend structures designed for a 400?m thick
silicon wafer. (a) Right-angle bend. (b) Circular bend without a outer
trenched slot. (c) Circular bend with a outer trenched slot. The arc
radius (R) is defined as distance from the origin of circular bend to the
center of signal line. The outer slot width (G2) of the circular bend is
determined based on the arc radius (R) of the circular bend. The
conductor thickness (T) is 3um и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
67
Cross-sectional view of the line A-A? of the 90░ circular bend with a
trench in the longer (outer) slot shown in Figure 4. 13(c) и и и и и и и и и и и и
67
Cross-sectional view of a fast wave CPW that has trenches between
signal line and ground planes и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
68
4.7
4.10
4.11
4.12
4.13
4.14
4.15
- xiii -
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
5.1
5.2
The velocity of electromagnetic wave of a coplanar waveguide with
S=225?m and Wg=1335?m and the trench depth TD. Slot width (G2)
varies from 130?m to 50?m и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
69
Relationship between geometrical parameters, the gap width (G2)
between signal line and ground planes and the depth of trenches (TD),
of a trenched CPW with signal line width of 225?m and ground plane
width of 1335?m shown in Figure 4.15. The trench depth (TD) is
optimized for characteristic impedance of 50? и и и и и и и и и и и и и и и и и и и и
70
Simulated (a) insertion (S21) and (b) return losses (S11) of the three
bend structures: right angle bend, 90░ circular bend without a trench,
and 90░ circular bend with a trench и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
72
Back-to-back 90░ circular bend with fast wave compensation. A straight
CPW line of 4mm long is placed between two bends и и и и и и и и и и и и и и и и
73
Fabrication processes of the test back-to-back CPW bend structures.
The crosssectional view is located in the line A-A? shown in Figure 4.
14.(a) Deposition of a seed layer of Ti/Au/Ti (=400┼/1500┼/400┼), (b)
photolithography for defining CPW bend circuits, (c) Etching of the top
titanium layer, (d) gold electroplating, (e) removal of the photoresist
and etching of the seed layer, (f) photolithography for defining
trenches, (g) deep trench etching, and (h) removal of the photoresist и и и
75
SEM pictures of the back-to-back 90░ circular bend with fast wave
compensation. (a) Top view of a 90░ circular bend with trench
compensation, (b) Cross sectional view of a 90░ circular bend with
trench compensation at the section AA? и и и и и и и и и и и и и и и и и и и и и и и и и
77
The surface current distribution of (a) right-angle bend, (b) circular
bend without trenched slots, and (c) circular bend with trenched slots at
the frequency of 50GHz и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
78
Measured (a) insertion and (b) return losses of the test back-to-back
CPW bend structures и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
80
Configuration of a conventional electromagnetic band-gap (EBG)
structure и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
84
Figure 5. 2 Top view of a 1D CPW EBG structure which is
implemented on a high resistivity silicon wafer (>2000?иcm) with
thickness of 400?m. и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
84
- xiv -
The simulated insertion and return losses of a 1D CPW EBG structure
shown in Figure 5. 1 и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
85
Three different types of slow wave coplanar waveguides (CPWs). (a) 50
? CPW with finger-shaped patterns (slow wave structure I), (b) 75?
CPW with finger-shaped patterns (slow wave structure II), and (c) 50?
CPW with finger-shaped patterns and air trenches (slow wave structure
III) и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
86
Top view of one unit section of a slow wave coplanar waveguide with
trenches with geometrical parameters и и и и и и и и и и и и и и и и и и и и и и и и и и и
87
5.6
Effective dielectric constant of the slow wave structures и и и и и и и и и и и и
89
5.7
The proposed miniaturized one-dimensional CPW EBG structures. (a)
CPW EBG structure I and (b) CPW EBG structure II и и и и и и и и и и и и и и и
90
5.8
SEM pictures of the proposed CPW EBG structure (a) I and (b) II и и и и
91
5.9
ADS circuit models of the conventional CPW EBG structure based on
physical T-line models и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
92
The insertion loss (S21) and return loss (S11) of the conventional CPW
EBG structure and the two proposed CPW EBG structures I and II.
Each plot compares the S parameters of the proposed CPW EBG
structures with a conventional CPW EBG structure. (a) CPW EBG
structure I and (b) CPW EBG structure II и и и и и и и и и и и и и и и и и и и и и и и и
94
Schematic of the compact UWB bandpass filter fed by coplanar
waveguides with geometrical parameters и и и и и и и и и и и и и и и и и и и и и и и и
96
Conventional UWB bandpass filter designed based on coplanar
waveguides и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
97
(a) Geometry and (b) equivalent circuit network of the open-ended
CPW multiplemode resonator (MMR) и и и и и и и и и и и и и и и и и и и и и и и и и и
99
5.14
(a) Geometry and (b) equivalent circuit model of an edge-coupled line
100
5.15
Schematic and geometric parameters of the modified open-ended
multiple mode resonator (MMR) using the slow wave structure
(w4=0.8mm, g5=0.2mm) и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
102
5.3
5.4
5.5
5.10
5.11
5.12
5.13
- xv -
(a) Geometry of a slow wave CPW and (b) slow wave factor of the
reference CPW and slow wave CPW developed и и и и и и и и и и и и и и и и и и и
103
The first three resonant frequencies of the modified open-ended slow
wave MMR for different geometric sizes. The electrical length of the
middle section is about double of that of the side sections even though
the physical length of both sections is the same и и и и и и и и и и и и и и и и и и и
104
Schematic of two modified interdigitated coupled lines with meandered
slots for different lengths based on part B in Fig. 1 (S=2mm, G=0.9mm,
Wg=5mm,
FL1=FL2=0.65mm-w3,
w1=0.4mm,
w2=0.2mm,
g1=0.15mm). (a) Design 1: L1=2.95mm and (b) Design 2: L1=2.25mm
105
Lower and upper 3-dB cut-off frequencies of the two modified coupled
lines shown in Figure 5.18 и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
106
5.20
Photograph of the fabricated UWB bandpass filter and a penny и и и и и и и
107
5.21
Simulated and measured insertion and return loss of the UWB bandpass
filter и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
108
5.22
Simulated and measured group delay of UWB bandpass filter и и и и и и и и
108
6.1
Comparison of (a) microstrip ring and (b) slot ring structures и и и и и и и и
112
6.2
A slot ling antenna with a sinusoidal electric field distribution at the
first resonance и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
112
Transmission line equivalent circuit of slot-ring antenna. (a) With
magnetic wall across slot ring. (b) Resulting transmission equivalent
circuit и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
114
6.4
Three possible feed configuration for the slot ring resonator и и и и и и и и и
114
6.5
Geometries of the antenna designed in this study и и и и и и и и и и и и и и и и и и
116
6.6
Photograph of the fabricated test antennas (Antenna 1 ~ 5) и и и и и и и и и и
118
6.7
The measured return loss of the meandered annular ring slot antennas
with different meandered slot lengths и и и и и и и и и и и и и и и и и и и и и и и и и и и
119
6.8
Photograph of the fabricated antenna 5 (right) and 6 (left) и и и и и и и и и и и
120
6.9
Measured return loss of the antenna 5 and 6 и и и и и и и и и и и и и и и и и и и и и и
120
5.16
5.17
5.18
5.19
6.3.
- xvi -
6.10
Measured x-y plane and y-z plane radiation patterns for Antenna 5 and
6. (a) Antenna 5 (f=2.82GHz) and (b) Antenna 6 (f=2.79GHz) и и и и и и и
121
Geometry of the proposed dual-band CPW-fed annular ring slot antenna
with meandered slot и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
123
6.12
Picture of the test antenna 6 fabricated on FR4 epoxy material и и и и и и и
125
6.13
Measured return losses of the reference antenna and test antennas и и и и и
127
6.14
The first two resonant frequencies and its frequency ratio for different
values of FL и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
128
Measured radiation patterns of (a) the reference antenna (FL=0mm) and
(b) antenna 6 (FL=4mm) и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
129
Metallo-dielectric EBG structure and its unit cell. The metal plates place
on the top and bottom of the dielectric material и и и и и и и и и и и и и и и и и и и
141
Linked boundary condition and phase relationship fro HFSS
eigensolution analysis. (a) Phase relation between master and slave
boundary conditions. (b) Master 1 and Slave 1. (c) Master 2 and Slave 2
142
Perfect E boundaries are assigned to the top and bottom face of the
substrate и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
142
Solution setup for calculating resonance frequencies of the EBG
structure и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
143
A.5
Setup sweep analysis of Optimetrics и и и и и и и и и и и и и и и и и и и и и и и и и и и
143
A.6
The dispersion diagrams of the EBG structure shown in Figure A.1
about x an y directions. (a) X direction. (b) Y direction и и и и и и и и и и и и и
145
B.1
LPKF ProtoMat C60 milling machine и и и и и и и и и и и и и и и и и и и и и и и и и и
147
B.2
Assembly of the parallel plate EBG structure и и и и и и и и и и и и и и и и и и и и и
148
C.1
HP 8510C network analyzer with Cascade MicroTech probe station
used for on-wafer devices и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
154
EBG waveguide placed in the microstrip fixture и и и и и и и и и и и и и и и и и и и
155
6.11
6.15
A.1
A.2
A.3
A.4
C.2
- xvii -
C.3
Inter-Continental Microwave calibration kit и и и и и и и и и и и и и и и и и и и и и и
155
C.4
TRL calibration standards for on-wafer circuits и и и и и и и и и и и и и и и и и и и
157
C.5
The sinusoidal response of three delay line. y ? sin ? ? ldelay lines 1,2,3 ? и и и и и
157
C.6
Antenna test set-up. (a) Configuration of the anechoic chamber system
and (b) AUT mounted on the turn-table which is connected a LNA и и и и
159
Alignment of the AUT and source to obtain desired polarization
measurements и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
160
Comparison method (gain transfer technique) for gain measurement
using a standard gain antenna и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
161
C.7
C.8
- xviii -
LIST OF TABLES
Table
2.1
2.2
3.1
3.2
4.1
4.2
5.1
Capacitance and inductance of each element of the unit cell divided in x
direction and in y direction respectively и и и и и и и и и и и и и и и и и и и и и и и и и
13
The stopband frequencies of the EBG structures obtained from three
different techniques и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
15
Dimensions of the six slow wave CPWs developed from a conventional
CPW with signal line width of 225?m, gap of 130?m, and ground plane
width of 1335?m. The length of unit section U is 120?m for all the
cases. The effective characteristic impedance of the slow wave CPWs is
50?. The unit of values is micrometers и и и и и и и и и и и и и и и и и и и и и и и и и и
31
Dimensions of the slow wave CPWs developed based on CPWs with
several different sizes. Substrate material for the slow wave CPWs is a
high resistivity silicon wafers with thickness of 400?m. Unit of all
values is micrometers и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
41
The parameter values of the six back-to-back 90░ circular bend
structures with slow wave compensation (CB-SW) и и и и и и и и и и и и и и и и
57
Optimized dimensions of the 90░ circular bend with fast wave
compensation. Unit of all values is micrometers и и и и и и и и и и и и и и и и и и и
71
Dimensions of the three slow wave CPWs. The geometrical parameter
used in this table are described in Figure 5. 5. Unit of all values is
micrometers и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
90
93
5.2
Size comparison of conventional CPW EBG structures and the proposed
CPW EBG structures и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
5.3
Dimensions of the slow wave CPW used in the middle of the CPW
MMR. The geometrical parameters are described in Figure 5. 11. Unit
of all values is millimeters и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
102
Dimensions of the miniaturized UWB bandpass filter shown in Figure
5. 20 и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
107
Dimensions of the five test antennas и и и и и и и и и и и и и и и и и и и и и и и и и и и и
117
5.4
6.1
- xix -
6.2
A.1
Geometric parameters of the test antennas and their frequency
characteristics и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
124
Material parameters и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
141
- xx -
LIST OF APPENDICES
A.
B.
C.
MODELING и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
142
A.1
Dispersion Diagram и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
142
A.1.1 Optimetrics and Eigenmode Solver и и и и и и и и и и и и и и и и и и и
142
A.1.2 3D Model и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
143
A.1.3 Material Setup и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
143
A.1.4 Boundaries/Sources Setup и и и и и и и и и и и и и и и и и и и и и и и и и и
144
A.1.5 Solution Setup и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
145
A.1.6 Dispersion Diagram in X and Y Directions и и и и и и и и и и и и и
146
FABRICATION и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
148
B.1
Parallel Plate EBG Structure и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
148
B.2
Fabrication Recipe #1 и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
150
B.3
Fabrication Recipe #2 и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
152
TEST AND MEASUREMENT и и и и и и и и и и и и и и и и и и и и и и и и и и и и
155
C.1
Measurement Apparatus и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
155
C.2
TRL Calibration и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
158
C.3
Antenna Measurement и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
160
C.3.1 Far-Field Radiation Pattern и и и и и и и и и и и и и и и и и и и и и и и и и
160
C.3.2 Gain Measurement и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и и
162
- xxi -
CHAPTER 1
INTRODUCTION
With the emergence of multiple wireless applications, industry initiatives and
activities have been targeted at enabling wireless access and mobile networking
technologies. Diversified applications using various wireless technologies, such as wide
area cellular networks, personal (hand-held) communication systems and wireless local
area networks (WLANs), have created an increasing demand for handsets and portable
internet access devices, such as 3G cellular phone, PDAs and mobile PCs, that are small
in size and light weight for consumers. This trend has forced wireless systems to have
more functionality, higher performance, smaller size and lower cost. Moreover, with the
increasing demand on higher data rates, the wireless carrier operating frequency is
continuously moving to higher radio and/or microwave frequencies to provide greater
information bandwidth.
Reduction in the size and component count of a wireless system have been
achieved by developments of low- and high-level integration technology including
multilayered circuits using layered board technology and monolithic integrated circuits
(MMIC). Despite many years of research, there are many challenges to further increase
-1-
integration.
Passive components and devices, such as high-Q inductors, capacitors,
varactors, interconnects, filters, and antennas, limits reduction in system size. In a typical
mobile phone design, the passive surface mount devices (SMDs) account for a large
portion of the components and system board area, which increases fabrication cost. In
complex high frequency systems, cost is a linear function of circuit area. As such, the size
associated with passive devices unlike active devices has become a primary issue to
address. While active device size is regularly scaled down in integrated circuit (IC)
technology development, passive devices are not and still present different challenges.
Hence, research is still needed to enhance size reduction of passive components.
A variety of techniques to shrink passive device designs have been developed. One of
these techniques is to increase effective dielectric constant of the substrates using
periodical structures. Periodical structures with large effective dielectric constant, called
slow wave structures, are one method for miniaturization of passive devices. Slow wave
structures offer the ability to reduce circuit size, control signal phase and match signal
velocity. Component level designs include miniature filter and antennas as well as
velocity matched electrical and optical signals in electro-optic modulators. Another
approach to reduce a device?s size is to fold the geometry of the device whiling
maintaining functionality of the device.
In this work, circuit models of a parallel plate electromagnetic bandgap (EBG)
structure are developed to analyze its properties in electric circuits and to reduce analysis
time. Moreover, several design approaches for smaller and cheaper passive devices
(interconnects, filters, and antennas) are presented. Slow wave structures are used to
-2-
shrink the size of filters and are used to suppress the excitation of unwanted modes (slotline) typically achieved with wire-bonds in right-angled CPW bend structures. Fast wave
structures are also developed for the same purpose. Two miniaturized filters (stopband
filter and UWB bandpass filter) are developed and reduced their size using slow wave
structures and coupled-lines with meandered slot. In addition, meandered annular ring
slot antennas are developed.
1.1
Thesis Overview
In chapter 2, lumped element circuit models of a parallel plate type EBG structure
are developed to analyze stopband characteristics of the EBG structure and are discussed
in details. The lumped element circuit models are verified with simulation results by fullwave simulation tools and measurement results of test EBG structures. The lumped
element circuit models are used in designing a waveguiding structure.
In chapter 3, an interdigitated slow wave coplanar waveguide is designed and
developed on high resistivity silicon wafer. Performance of the slow wave coplanar
waveguide is evaluated with S-parameters, effective dielectric constant, and attenuation.
In addition, design guidelines, which relate effective dielectric constant to geometrical
parameters, are presented for design of a new slow wave coplanar waveguide.
Two wire-bond free techniques, slow-wave and fast-wave are used in right-angled
CPW bend structures and are presented in chapter 4. Incorporating a slow wave structure
or fast wave structure in 90░ circular bends suppresses the excitation of slot-line mode in
right angled CPW bends in a similar manner for wire-bonds or air bridges. Simulated and
-3-
measured results are used to demonstrate the performance of the two wire-bond free
techniques.
In chapter 5, two filter designs (a stopband filter and an ultra-wide band (UWB)
filter) are presented and studied. The stopband filter shrinks its size by replacing low- and
high-impedance sections of a conventional stopband filter with slow wave structures, and
the UWB filter size is reduced using slow wave coplanar waveguide and meandered
coupled lines. The details of design and performance of two miniaturized filters are
followed.
Chapter 6 begins with a description of basic theory about slot lines and antennas
as well as recent studies based on slot-ring antennas and their application.
Miniaturization of the ring slot antenna is obtained by meandering the slot feature. After
describing the design of meandered ring slot antennas, geometrical characteristics are
discussed. The performance of meandered ring slot antennas for single- and dual-band
operations is demonstrated using antenna parameters such as return loss, far-field
radiation patterns, and gain.
The thesis is summarized and future works is described on various topics relating
to periodical structures in chapter 7. The appendices contain details about the different
simulations, fabrication processes, and measurement techniques used for the various
circuit discussed in this work.
-4-
CHAPTER 2
ELECTROMAGNETIC BANDGAP (EBG) STRUCTRUE
Electromagnetic bandgap (EBG) structures have become popular because of their
ability to suppress unwanted electromagnetic mode transmission and radiation in
microwave and millimeter waves [1-3]. The EBG structures are periodic structures that
allow greater control over electromagnetic waves than has previously been possible.
These structures block the propagation of electromagnetic waves within particular
frequency bands and allow propagation only in certain spatial directions. They are
scalable and operate a wide range of frequencies. These properties of EBG structures are
very desirable for a variety of applications such as radar, communication devices,
antennas, and noise suppressing ground planes.
Traditionally, the analysis of the electromagnetic properties of EBG structures
relied heavily on the mathematics of infinite periodic structures, similar to that used to
describe crystal diffraction. However, for real applications, the finite dimensions, lattice
defects, and boundaries have to be included in the analysis to account for their impact on
the bandgap characteristics. To accomplish this, various full-wave simulation tools such
-5-
as HFSS, CST, and Sonnet, which give very accurate results, have been used. In contrast,
these full-wave tools require high-performance computer systems and the simulation
times significantly increase as EBG structure size is increased.
In this chapter, lumped element circuit models of a parallel plate EBG structure
are developed to fully understand its properties in electric circuits. Moreover, these
lumped element circuit models significantly reduce simulation time in comparison to fullwave simulation tools. The lumped element circuit models are developed based on
transmission line theory and are verified using full-wave simulation tools and
measurements of test circuits.
2.1
Geometry
Figure 2.1 shows the top view and cross-sectional view of the unit cell of the EBG
structure studied in this chapter. The EBG structure consists of cylindrical air holes with
a radius of 3mm on Rogers RO3010 substrate and conducting metal layers attached to the
top and bottom of the substrate as shown in Figure 2.1. The substrate dielectric constant
is 10.2 with a thickness of 1.15mm, and the lattice spacing is 12.5mm with air holes
arranged in a triangle shape.
This triangle EBG structure design is derived from [1] by changing configuration
of unit cells as shown in Figure 2.2. The parallelogram unit cell of the original EBG
structure is modified into a rectangle with three cylindrical air holes arranged in triangle
shape as shown in Figure 2.2(b) to simplify the EBG structure and to make it easy to
-6-
Figure 2.1. Top view and cross-sectional view of the unit cell of the modified EBG structure.
model the EBG structure into lumped element equivalent circuit models. This design
reduces the coupling effects between unit cells.
2.2
Dispersion Diagram
Dispersion diagrams of the triangle EBG structure are obtained using the
eigenmode solver in HFSS and periodic boundary conditions [5]. The eigenmode solver
in HFSS enables direction calculation of the permitted resonance frequencies for a unit
cell structure, and the computations by the eigenmode solver can be performed over the
entire range of field relationship between linked boundary condition (LBC) pairs by using
-7-
(a)
(b)
Figure 2.2. The top views of (a) the original EBG structure in [5] and (b) the modified EBG
structure.
-8-
Optimetrics. The Optimetrics interface automates the process of altering parametrically
phase relationship of the LBC pair to match each value in a table of desired configuration
setups and executing each resultant solution. The resultant solutions with different phase
relationship form a dispersion diagram of the unit cell of the EBG structure in one
direction.
The dispersion diagrams of the triangle EBG structure for x, y, and diagonal
directions are shown in Figure 2.3. For x direction, the forbidden band of the infinite
periodic EBG structure is from 4.69GHz to 6.20GHz. The y direction has forbidden band
gap frequency range of 5.5GHz and 6.56GHz, and the diagonal direction has forbidden
band gap frequency range of 6.03GHz to 7.9GHz.
12
10
Frequency (GHz)
8
6
4
2
0
mode 1
mode 2
mode 3
0
20
40
60
80
100
Phase (Deg)
(a)
-9-
120
140
160
180
12
10
Frequency (GHz)
8
6
4
2
0
mode 1
mode 2
mode 3
0
20
40
60
80
100
Phase (Deg)
120
140
160
180
(b)
12
Diagonal direction
10
Frequency (GHz)
8
7.9GHz
Forbidden Band
6.03GHz
6
4
Y
2
mode 1
mode 2
mode 3
X
0
0
20
40
60
80
100
Phase (Deg)
120
140
160
180
(c)
Figure 2.3. Dispersion diagrams of the EBG structure for wave propagating in (a) x-direction, (b)
y-direction, and (c) diagonal direction respectively.
- 10 -
RO3010
Y
X
11.66mm
AIR
AIR
AIR
R=3mm
?z
12.5mm
(a)
(b)
Figure 2.4 Top views of the unit cell without the top metal divided into 16 sections in (a) x and
(b) y directions. R=3mm in each case.
2.3
LC Circuit Modeling
The triangle EBG structure is sandwiched between two metal plates and is a
parallel plate structure which can support a TEM mode and other higher-order modes
(TE1, TM1, etc.). The cut-off frequency of the modes TE1 and TM1 of this triangle EBG
structure is between 40.84GHz and 130.43GHz. Thus, higher order modes are outside of
the frequency range of interest. The triangle EBG structure have only TEM mode in
frequency range of interest up to 10GHz. Thus, the triangle EBG structure can be
modeled with lumped elements.
When the triangle EBG structure is modeled into a lumped element circuit, the
EBG structure is divided into smaller sections whose length is less than ?/10 at the
maximum frequency of interest, in this case 10GHz. Figure 2.4(b) shows the unit cell
- 11 -
Figure 2.5. Circuit Modeling of the unit cell of the EBG structure. (a) Unit cell. (b) Cross
section of an element of the unit cell. (c) Lossless lumped element circuit model of the element
shown in (b). R=3mm in each case.
which is divided into 16 element sections in x and y direction. Each element section of
the unit cell is modeled into a distinct LC circuit as shown in Figure 2.5, and all the LC
circuits are combined together to form the overall lumped element circuit model of the
unit cell of the triangle EBG structure. The inductance of each element section is
calculated using the equation L=(?0d/W)?x where d is substrate thickness and the relative
permeability ?r is 1. The total capacitance C of each element section is calculated for the
parallel set of capacitors shown in Figure 2.5. The calculated capacitance and inductance
of each element of the unit cell which is divided in x-direction and in y-direction,
respectively, and is summarized in Table 2.1.
- 12 -
Table 2.1. Capacitance and inductance of each element of the unit cell divided in x-direction and
in y-direction, respectively.
Element
Number
X direction
Y direction
Capacitance
(pF)
Inductance
(pH)
Capacitance
(pF)
Inductance
(pH)
1
0.592
96.82
0.505
84.25
2
0.465
96.82
0.263
84.25
3
0.411
96.82
0.159
84.25
4
0.387
96.82
0.109
84.25
5
0.268
96.82
0.098
84.25
6
0.161
96.82
0.125
84.25
7
0.161
96.82
0.195
84.25
8
0.268
96.82
0.298
84.25
9
0.268
96.82
0.452
84.25
10
0.161
96.82
0.455
84.25
11
0.161
96.82
0.420
84.25
12
0.268
96.82
0.407
84.25
13
0.387
96.82
0.412
84.25
14
0.411
96.82
0.437
84.25
15
0.465
96.82
0.489
84.25
16
0.592
96.82
0.609
84.25
2.4
ADS and HFSS Simulation
Lumped element circuit models of the unit cell of the triangle EBG structure is
developed as explained in the previous section. However, with only one unit cell, the
frequency characteristics of the EBG structure cannot be investigated because of
insufficient periodicity. Figure 2.6 shows the insertion loss of the lumped element circuit
models for 1x1, x2, x4, x8, and x16 unit cells connected in series. As shown in
- 13 -
6.6GHz
0
-10
4.46GHz
S21 (dB)
-20
-30
-40
1x1 Unit Cell
1x2 Unit Cells
1x4 Unit Cells
1x8 Unit Cells
1x16 Unit Cells
-50
-60
-70
2
4
6
8
10
Frequency (GHz)
(a)
0
S11
S11 and S21 (dB)
-10
-20
-30
2 Rows
4 Rows
6 Rows
8 Rows
-40
-50
S21
-60
2
4
6
8
10
Frequency (GHz)
(b)
Figure 2.6. ADS simulation results of EBG structures based on the lossless lumped element
circuit model. Input and output ports are terminated with 50hom. (a) Return loss of 1x1, 1x2, 1x4,
1x8, and 1x16 unit cells connected in series. (b) Insertion and return losses of the EBG structure
of 2, 4, 6, and 8 rows (1 row = 1x8 unit cells)
- 14 -
Figure 2.6(a), the stopband frequencies are saturated into certain frequencies by
increasing the number of unit cells because the lumped element circuit model periodicity
is large enough to show the frequency characteristic of a periodic EBG structure.
Furthermore, the stopband characteristics of the lumped element circuit model of the
EBG structure is improved by considering a two dimensional array with the number of
the rows increasing as shown in Figure 2.6(b). The lumped element circuit model of the
8x8 EBG structure has insertion loss of about 50dB in the stopband.
Figure 2.7(b) compares the ADS simulation results of the lumped element circuit
model for the 8x8 EBG structure with ports matched (1.8ohm) to the full-wave
simulation results by HFSS [6]. As shown in Figure 2.7(b), the insertion and return losses
obtained from the ADS simulation are close to those obtained from the HFSS simulation.
Moreover, both simulation results are consistent with the forbidden band shown in the
dispersion diagrams (Figure 2.3). The stopband frequencies obtained from the lumped
element circuit model simulation and full-wave simulation are close to the forbidden
band frequencies as shown in Table 2.2. The results by the full-wave simulation are
closer to the forbidden band of the EBG structure than those by the lumped element
circuit model as expected.
Table 2.2. The stopband frequencies of the EBG structures obtained from three different
analysis techniques.
Stopband (GHz)
Dispersion Diagram
Full-wave Simulation
Circuit Model
4.69 ~ 6.20
4.64 ~ 6.24
4.65 ~ 6.51
- 15 -
(a)
0
-10
S11 and S21 (dB)
-20
-30
-40
S11(HFSS)
S11(ADS)
S21(HFSS)
S21(ADS)
-50
-60
-70
2
4
6
8
10
Frequency (GHz)
Figure 2.7. Simulation results of an 8x8 EBG structure with port impedance matched (1.8 ohm).
(a) The 8x8 EBG structure. (b) Comparison of ADS and HFSS simulation results.
- 16 -
Several factors affect the difference in the results. First, the 8x8 EBG impedance
varies with frequency of operation. In HFSS, this is accounted for by the termination that
offers variable port impedance compared to the fixed port impedance of the ADS circuit
model. At low frequency, for example, the port impedances of the HFSS 3D models
rapidly decrease with increasing frequency. Second, the wave propagation mode changes
from single below the bandgap to multiple modes above the bandgap. The lumped
element models, developed based on TEM mode, are accurate descriptions of the 8x8
EBG structure at low frequencies whereas the simple lumped element circuit model
doesn?t work above the first stopband because the higher order modes are not included.
HFSS models automatically consider higher order modes. Another minor reason is that
(a)
(b)
(c)
Figure 2.8. Three different 1x8 cell EBG structures. (a) original 1x8 cell EBG structure, (b)
the modified 1x8 EBG structure A, and (c) the modified 1x8 EBG structure B.
- 17 -
the coupling effect between unit cells and fringing fields at the edge are not included thus
far in the current ADS simulation. Despite these differences, this approach using lumped
element circuit models shows fairly good agreement in the EBG structure for single mode
regions.
2.5
Measurement Results
2.5.1
Fabrication
Two symmetric 1x8 EBG structures are developed from an original 1x8 EBG
structure shown in Figure 2.8(a) to verify the developed LC circuit models and are shown
in Figure 2.8(b) and (c) respectively. The modified EBG structure A shown in Figure
2.8(b) has an extra hole with the original 1x8 EBG structure. In the modified EBG
structure B, half of the original 1x8 EBG structure is flipped as shown in Figure 2.8(c).
Figure 2.9. Configuration of the 1x8 EBG structure A.
- 18 -
(a)
(b)
Figure 2.10. Picture of the two modified EBG structures (a) A and (b) B.
Figure 2. 11. Microstrip fixture
- 19 -
Figure 2.9 shows the configuration of the modified EBG structure A fabricated on
Roger?s RO3010 substrate. The 3M copper tape with conductive adhesive is used as the
two metal plates on the top and bottom of the substrate. A milling machine, LPKF C60, is
used to drill air holes and to fabricate microstrip feed lines. The fabricated EBG
structures A and B are shown in Figure 2.10.
2.5.2
S-Parameters
The two modified 1x8 EBG structures are measured form 1GHz to 15GHz with
an Agilent 8510C network analyzer connected to a microstrip fixture shown in Figure 2.
11. TRL calibration technique is used with the Inter-Continental Microwave calibration
kit (ICM TRL-303B).
ADS Circuit
Model
(a)
- 20 -
(b)
Figure 2.12. Comparison of the measured and simulated S parameters. (a) Return loss
(S11) and insertion loss (S21).
Figure 2.12 shows the measured S parameters of the two modified EBG structures.
As shown in Figure 2.12, the EBG structures have the stopband (from 5GHz to 6.2GHz)
which is close to each other. However, in comparison to the simulated S parameters
obtained from the LC circuit models, the measured stopband regions shift approximately
1GHz to lower frequency due to the microstrip feed line. The input and output ports of
the EBG structures used in the LC circuit models are parallel plate waveguides. In
contrast, the test EBG structures have microstrip feed lines, and they may lead to higher
order modes in the transition of the microstrip line to the EBG structure.
- 21 -
2.6
Summary
A triangular EBG structure based on the modified honeycomb lattice of holes in a
solid dielectric substrate, sandwiched between two conducting plates, is designed and
analyzed using HFSS. A circuit model of the triangular EBG cell is developed from the
HFSS data, simulated in ADS and compared with the dispersion diagram. Although, the
lumped element circuit models have some limitation of high-order mode, the simulation
results of the lumped element circuit models are consistent with the dispersion diagram
and the HFSS simulation results in single mode regions of operation.
- 22 -
CHAPTER 3
SLOW WAVE COPLANAR WAVEGUIDE
As described in chapter 1, the miniaturization of circuit size is one of the
important requirements in the design of RF/microwave passive circuits for integrated
circuits. Since coplanar waveguides are mostly used in constructing passive
RF/microwave components in the integrated circuits, dielectric material of large relative
dielectric constant are conventionally used to reduce size. However, the reduction factor
is limited to ? r ,eff . To improve this factor, capacitively-loaded periodic structures, called
by slow wave structures, such as open-circuited stub loaded CPW [7], crosstie and
crosstie overlay CPW [8-10], have been proposed and various reduction factors have
been achieved. These slow wave structures offer the ability to reduce circuit size, control
signal phase and match signal velocity. Thus these approaches are used in component
level designs such as filter and antennas as well as to aid optoelectronic device operation
by velocity match electrical and optical signals in electro-optic modulators [11-13].
- 23 -
Figure 3.1. Cross sectional view of a finite ground coplanar waveguide on a substrate, where S is
the signal line width, G is the gap width, Wg is the ground plane width, and h is the height of the
substrate.
In this chapter, an interdigitated slow wave structure of coplanar waveguide
(CPW) type, which uses both inductive and capacitive loadings, is developed and studied
to achieve effective integration approaches in coplanar waveguide (CPW) based systems.
This chapter focuses on investigation of the characteristics of the interdigitated slow
wave coplanar waveguide in terms of effective dielectric constant and loss performance.
Based on effective dielectric constant of the slow wave coplanar waveguide study, design
guide lines are also developed and will be used in the following chapters.
3.2 Coplanar Waveguide (CPW)
Coplanar waveguides are planar transmission lines which consists of a signal line
and two ground planes as shown in Figure 3.1. The unique feature of this transmission
line is that it is uniplanar in construction, which implies that all of the conductors are on
the same side of the substrate. This attribute simplifies manufacturing and allows fast and
inexpensive characterization using on-wafer techniques. Because, in principle, it is a
three conductor line, it can carry two fundamental modes with zero cut-off frequency: (a)
- 24 -
(a)
(b)
Figure 3.2. Electrical and magnetic field distribution of (a) the even-mode and (b) the odd mode
on a coplanar waveguide.
the ?even-mode,? which has equal potential of the ground planes, and (b) the ?odd
mode,? which has ground potentials of opposite phases but equal magnitude. The CPW
line supports a quasi-TEM mode of propagation due to the presence of a mixed dielectric
region (air and underlying substrate) in which the signal propagates.
Figure 3.2 shows the electric field and the magnetic field distribution of (a) the
even mode (coplanar waveguide mode) and (b) the odd mode (slot-line mode). The even
- 25 -
mode is a quasi-TEM mode with even symmetry with respect to the symmetry plane; its
dispersion is very low, and it is normally used for application in circuit design. The
electric field lines begin at the signal line and end at the ground plane as shown in Figure
3.2(a). The magnetic field lines enclose the center conductor. Because of the low
dispersion of the fundamental ?even mode,? very broadband applications are possible,
making this propagation mode applicable in microwave integrated circuits.
The electric field lines of the odd mode start on one ground plane and end on the
other ground plane, which means that the potential of the two ground planes have
opposite phase. In the case of infinitely wide ground planes the odd mode, like a slot-line
mode, is a hybrid mode and has magnetic field components in longitudinal direction and
its dispersion can be considered large. If the ground plane width is finite, the magnetic
field lines may be closed in the cross section enclosing the ground planes.
3.3 Slow-Wave Coplanar Waveguide (CPW)
3.3.1
Design
Interdigitated slow wave coplanar waveguides (CPWs) which have high effective
dielectric constant are designed using conventional three conductor strip geometric
parameters of a CPW. Two main characteristic parameters of a CPW are the effective
dielectric constant and characteristic impedance. They can be represented by its line
parameters such as R? (resistance per unit length), L? (inductance per unit length), G?
(conductance per unit length), and C? (capacitance per unit length). The lossless circuit
- 26 -
(a)
(b)
Figure 3.3. Circuit models of (a) a conventional CPW and (b) a slow wave CPW.
model of a CPW consist of a series inductance L? and a shunt capacitance C? only as
shown in Figure 3.3(a).
The phase velocity of the CPW and is 1/ L ' C ' , and its characteristic impedance
is
L '/ C ' as shown in Eq. 3.1 and Eq. 3.2. The expression for the effective dielectric
constant shown in Eq. 3.3 can be obtained by changing the form of Eq. 3.1.
vp ?
c
? r ,eff
?
- 27 -
1
L 'C '
Eq. 3.1
Z0 ?
L'
C'
? r ,eff ? c 2 ? L ' C '?
Eq. 3.2
Eq. 3.3
According to Eq. 3.3, the effective dielectric constant is proportional to the production of
L? and C?. Thus the effective dielectric constant can be changed by adding series
reactance in the form of inductance L?, shunt capacitance C?, or a combination of both
inductance L? and capacitance C? as shown in Figure 3.3(b). Another characteristic
parameter, characteristic impedance, also should be considered. The characteristic
impedance of the line can be changed by adjusting the ratio of the inductance per unite
length L? to capacitance per unit length C?. In this study, the characteristic impedance of
the slow wave coplanar waveguide is not changed and is be kept at 50 ohm to interface to
existing 50ohm CPW lines in a system. The effective dielectric constant of CPWs can be
increased by increasing the inductance per unit length L? and the capacitance per unit
length C? at the same ratio while maintaining its characteristic impedance. Thus, the
phase velocity and characteristic impedance of the transmission line which uses both
inductive loading and capacitive loading are
vp ?
1
? L '? ?L ?? C ? ?C '?
- 28 -
Eq. 3.4
(a)
(b)
Figure 3.4 Top views and cross-sectional views of (a) a regular finite ground coplanar waveguide
and (b) a finite-ground slow-wave coplanar waveguide.
Zo ?
L '? ?L '
C '? ?C '
Eq. 3.5
The slow wave characteristics of slow wave CPWs are obtained by creating
interdigitated patterns in the conventional CPW as shown in Figure 3.4. Select portions of
the center strip are reduced to increase inductance per unit length while finger-shaped
patterns are added to the ground planes periodically to increase per unit length. The main
- 29 -
Figure 3.5. Top view of two unit sections of slow wave CPWs with geometric parameters.
features are the ability to vary the effective dielectric constant for a given conventional
CPW impedance and to achieve ultra broadband behavior with low signal dispersion.
3.3.2
Geometry
The original coplanar waveguide used to design slow wave CPWs consists signal
line width of 225?m, gap width of 130?m , and ground plane width of 1335?m and is
fabricated on a high resistivity silicon wafer (>2000 ?иcm) with thickness of 400?m. As
described in the previous section, the finger-shaped interdigitated patterns are introduced
in the CPW to obtain the slow wave characteristics. By increasing inductance and
capacitance per unit length at the same ratio, the characteristic impedance can be
maintained while increasing the effective dielectric constant of the slow wave CPWs. The
geometry of two unit sections of the slow wave CPW is shown in Figure 3.5 with
- 30 -
geometrical parameters. Two geometrical parameters, the width (S1) of the reduced signal
line and the length (FL2) of the finger-shaped patterns on the ground plane, are mainly
used to control the effective dielectric constant. The dimensions of the slow wave CPWs
are determined by parametric simulations of Ansoft?s HFSS. The HFSS model of the
slow wave CPWs are simulated repeatedly with two key geometrical parameters S1 and
FL2 until their return loss (S11) is lower than -20dB. It can be assumed that the effective
characteristic impedance of the slow wave CPWs is close to 50? if its return loss (S11) is
lower -20dB for wave ports with port impedance of 50?. The dimensions of the slow
wave CPWs developed are summarized in Table 3. 1.
Table 3. 1 Dimensions of the six slow wave CPWs developed from a conventional CPW with
signal line width of 225?m, gap of 130?m, and ground plane width of 1335?m. The length of unit
section U is 120?m for all the cases. The effective characteristic impedance of the slow wave
CPWs is 50?. The unit of values is micrometers.
S
G
Wg
S1
FL1
FW1
FL2
FW2
SW CPW 1
225
130
1335
10
107.5
40
192.5
40
SW CPW 2
225
130
1335
20
102.5
40
177.5
40
SW CPW 3
225
130
1335
30
97.5
40
162.5
40
SW CPW 4
225
130
1335
60
82.5
40
147.5
40
SW CPW 5
225
130
1335
90
67.5
40
122.5
40
SW CPW 6
225
130
1335
120
52.5
40
97.5
40
- 31 -
Figure 3.6. SEM picture of the slow wave CPW 3 fabricated on a high resistivity silicon wafer
with thickness of 400?m.
3.3.3
Fabrication and Measurement
Six slow wave CPWs and one conventional CPW design are fabricated on high
resistivity silicon wafers (400?m thick, >2000 ?иcm) using the standard microelectronic
fabrication techniques. A seed layer of titanium/gold/titanium (400/1500/400┼) is
deposited and the circuits are photolithographically defined and Au-electroplated to a
height of 3?m.
The S-parameters of the interdigitated slow wave CPWs are measured on a
Cascade Microtech probe station with Cascade Mictrotech 250?m pitch ground-signalground (GSG) probes using an HP 8510 vector network analyzer (45MHz-50GHz). The
- 32 -
reference plane is shifted to 700 ?m along the feedlines using on-wafer TRL calibration
standards.
3.3.4
Characterization
3.3.4.1
S Parameters: Return Loss and Insertion Loss
Figure 3.7 shows the measured S-parameters of the slow wave CPWs in
comparison to a reference conventional CPW. The return loss (S11) of all the circuits is
below -20dB over the entire frequency range of interest. The insertion loss (S21) of all
slow wave CPWs increases with frequency and with the reduction of signal line width S1
due to increase in conductor loss. As a result, all cases suggest the slow wave CPW lines
are approximately 50? and well matched to the feedlines.
0
S1=10um
S1=20um
S1=30um
S1=60um
S1=90um
S1=120um
CPW
-10
S11 (dB)
-20
-30
-40
-50
-60
-70
0
10
20
30
Frequency (GHz)
(a)
- 33 -
40
50
0.0
S21 (dB)
-0.2
-0.4
-0.6
S1=10um
S1=20um
S1=30um
S1=60um
S1=90um
S1=120um
CPW
-0.8
-1.0
0
10
20
30
40
50
Frequency (GHz)
(b)
Figure 3.7 . The return loss (S11) and the insertion loss (S21) of the slow wave CPWs and a
reference CPW.
35
S1=10um
S1=30um
S1=90um
CPW
Effective Dielectric Constant
30
S1=20um
S1=60um
S1=120um
25
20
15
10
5
0
0
10
20
30
40
50
Frequency (GHz)
Figure 3.8 The measured effective dielectric constant of the slow wave CPWs with signal line
width (S) of 225?m, gap width (G) of 130?m, and ground plane width (Wg) of 1335?m.
- 34 -
3.3.4.2
Effective Dielectric Constant
The effective dielectric constant of the slow wave CPWs are calculated using the
S21 phase information and physical line length of 2400?m as described in Eq. 3.4. Figure
3.8 shows the measured effective dielectric constant of the interdigitated slow wave CPW
lines. As seen in Figure 3.8, the effective dielectric constant value increases from 6 to
approximately 25 based on the geometry dimensions. As the width of the signal line (S1)
is reduced, the effective dielectric constant increases and tends to become slightly
dispersive with increased frequency for small S1 values. The slow wave CPW with
S1=10?m has increase of 12.6% in the effective dielectric constant at 50GHz in
comparison to the lowest value, while the reference regular CPW (S1=225?m) has
increase of 6.1% at 50GHz.
?21 ? ? l ?
2?
?
l?
2?
?0
? l ? ? r ,eff
? ? ?c ?
2? f
?
? l ? ? r ,eff ? ? r ,eff ? ? 21 ?
c
? 2? f ? l ?
2
Eq. 3.6
.
3.3.4.3
Attenuation
The attenuation results of the slow wave are calculated from S parameters data
using Eq. 3.5. The attenuation is calculated in dB/length (L) with Sij as the S-parameters.
? ??
? S S
10
log ?? 12 21
l
? 1 ? S11 S 22
?
??
?
(dB/length)
Eq. 3.7
Figure 3.9 presents a comparison of the attenuation results of the six slow wave
CPWs samples. The attenuation of all slow-wave CPWs increases with frequency due to
- 35 -
7
S1=10um
S1=20um
S1=30um
S1=60um
S1=90um
S1=120um
CPW
6
Loss (dB/cm)
5
4
3
2
1
0
0
10
20
30
40
50
Frequency (GHz)
Figure 3.9. The measured attenuation per unit centimeter of the slow wave CPWs with signal
line width (S) of 225?m, gap width (G) of 130?m, and ground plane width (Wg) of 1335?m.
increase in the conductor loss which is linearly proportional to the square root of
frequency. The metal thickness plays a significant role in the total conductor loss
primarily due to the skin depth. As the frequency increases, the current becomes more
confined to the surface of the conductor thus increasing its resistance. Moreover, the
expected increased in attenuation with decreasing the width (S1) of the reduced signal line
is confirmed due to the increase in resistive loss from the interdigitated structure. In
compared to the reference CPW, the attenuation of the slow wave CPW with S1=10?m is
approximately two times bigger at 50GHz than the reference CPW (S1=225?m).
- 36 -
0
S11 (SW
S21 (SW
S11 (SW
S21 (SW
S11 and S21 (dB)
-10
CPW 3)
CPW 3)
CPW 6)
CPW6)
-20
-30
-40
-50
-60
0
20
40
60
80
100
Freq (GHz)
Figure 3.10. The simulated insertion loss (S21) and return loss (S11) of the slow wave CPW 3
and 6.
3.3.4.4
Ultra Broadband Characteristics (110GHz)
The six slow wave CPWs are simulated and measured up to 50GHz which is
frequency range of interest in the previous sections. The results show that the slow wave
CPW can used as a transmission lines with large effective dielectric constant up to
50GHz. In this section, a couple of the slow wave CPWs are simulated up to 100GHz
using HFSS to evaluate the performance of the slow wave CPWs above 50GHz. The
simulated insertion loss and return loss of the slow wave CPW 3 and 6 are shown in
Figure 3.10, and their effective dielectric constants are plotted in Figure 3.11.
- 37 -
SW CPW 3
SW CPW 6
Effective Dielectric Constant
30
25
20
15
0
20
40
60
80
100
Freq (GHz)
Figure 3.11 The effective dielectric constant of the slow wave CPW 3 and 6.
The insertion losses (S21) increases slowly with frequency, and the return losses
(S11) are below -20dB which shows that the slow wave CPW is matched to 50? as
shown below 50GHz. However, the insertion losses (S21) increase significantly with
frequency above 50GHz and the return losses (S11) become bigger than -20dB. Variation
in the effective dielectric constant for frequency is small below 50GHz but increases fast
with frequency above 50GHz as shown in Figure 3.11. Even though slow wave CPWs
naturally have stop band region in the frequency responses due to its periodicity, the poor
performance in the frequency responses of the slow wave CPWs in frequencies above
50GHz is not due to stop-band region by its periodicity but due to surface wave. The
length of the unit cell of the slow wave CPWs is electrically very small, and the
- 38 -
30
S=50um, G=35um, Wg=400um, simulated
S=100um, G=65um, Wg=700um, simulated
S=150um, G=95um, Wg=1000um, simulated
S=225um, G=130um, Wg=1335um, measured
S=250um, G=144um, Wg=1600um, simulated
S=300um, G=168um, Wg=1900um, simulated
Effective Relative Permittivity
25
20
15
10
5
0
0
50
100
150
200
250
300
350
S1
Figure 3.12. Variation of the effective dielectric constant of the slow wave CPW developed from
CPWs of several different sizes for various S1.
6
S=50um, G=35um, Wg=400um, Simulated
S=100um, G=65um, Wg=700um, Simulated
S=150um, G=95um, Wg=1000um, Simulated
S=225um, G=130um, Wg=1335um, Measured
S=250um, G=144um, Wg=1600um, Simulated
S=300um, G=300um, Wg=1900um, Simulated
Loss (dB/cm)
5
4
3
2
1
0
0
50
100
150
200
250
300
S (um)
Figure 3.13. Variation of the attenuation of the slow wave CPW developed from CPWs of several
different sizes for various S1.
- 39 -
computed stop-band region should be located around 150GHz as oppose to 100GHz as
shown in Figure 3.10.
3.3.4.1
Impact of Size of CPWs on Effective Dielectric
Constant and Attenuation
To find out the effects of size of CPWs on the effective dielectric constant and
attenuation, a variety of interdigitated slow wave CPWs are designed based several
CPWs of different sizes. The dimensions of the slow wave CPWs developed are
summarized in Table 3.2.
Figure 3.12 shows the effective dielectric constant variation of the interdigitated
slow wave CPWs as a function of S1. As S1 increases, the effective dielectric constant
decreases. Simulation results for a variety of slow wave structure sizes are also plotted.
For large conventional CPW signal line widths (S), the effective dielectric constant range
is large compared to smaller values when S1 is varied.
Figure 3.13 shows the variation in the attenuation of the slow wave CPWs at
50GHz for S1 variations. The measured data for S=225?m is compared to simulated
results for S values ranging from 50?m to 300?m. Regardless of the signal line width (S),
the variation of the slow wave CPWs is similar, which means the loss is mainly due to the
S1 dimension of the signal line. For larger effective dielectric constant, the small S1
value is required and thus results in large attenuation
- 40 -
Table 3. 2 Dimensions of the slow wave CPWs developed based on CPWs with several different
sizes. Substrate material for the slow wave CPWs is a high resistivity silicon wafers with
thickness of 400?m. Unit of all values is micrometers.
S
50
100
150
200
250
300
G
35
65
95
120
144
168
Wg
S1
FL1
FW1
FL2
FW2
400
10
20
30
40
40
30
20
10
40
40
40
40
52
40
30
20
40
40
40
40
700
10
30
50
70
90
90
70
50
30
10
40
40
40
40
40
105
90
60
45
20
40
40
40
40
40
1000
10
30
50
90
130
140
120
100
60
20
40
40
40
40
40
150
130
110
80
50
40
40
40
40
40
1300
10
30
50
90
150
190
170
150
110
50
40
40
40
40
40
180
160
150
120
60
40
40
40
40
40
1600
10
30
50
100
150
200
240
220
200
150
100
50
40
40
40
40
40
40
210
180
160
140
110
70
40
40
40
40
40
40
1900
10
30
50
100
150
200
250
290
270
250
200
150
100
50
40
40
40
40
40
40
40
220
210
190
160
140
120
50
40
40
40
40
40
40
40
- 41 -
250
S=50um, G=35um, Wg=400um
S=100um, G=65um, Wg=700um
S=150um, G=95um, Wg=1000um
S=225um, G=130um, Wg=1335um
S=250um, G=144um, Wg=1600um
S=300um, G=168um, Wg=1900um
200
FL2 (um)
150
100
50
0
0
50
100
150
200
250
300
S1 (um)
Figure 3.14. Relationship between S1 and FL2. The FL1 is equal to the subtraction of S1 from S,
and FW1, FW2, and U are fixed at 40?m, 40?m, 120?m respectively.
3.4 Design Guidelines for Slow Wave CPWs
A new slow wave CPW with desired effective dielectric constant can be designed
using the simulated and measured results studied in the previous sections. When the
dimension specifications (S, G, and Wg) of a conventional CPW and its desired effective
dielectric constant are given, the geometric parameter S1 can be determined from Figure
3.12. Once known, FL1, FW1, FL2, and FW2 are easily calculated where FL1 equals S
minus S1, and FL2 is determined from Figure 3.14. Both FW1 and FW2 are fixed at 40?m.
- 42 -
G=50mil
S=100mil
G=50mil
Wg=495mil
//
Wg=495mil
//
GND
Signal
GND
(a)
G=50mil
S=100mil
G=50mil
Wg=495mil
//
Wg=495mil
//
S1=30mil
S1
FW2
FW2=30mil
FL2=60mil
FW1=30mil
FL1=35mil
GND
Signal
GND
(b)
Figure 3. 15. Top view of (a) a reference CPW and a slow wave CPW with dimensions. The
substrate for the CPW and the slow wave CPW is FR4 epoxy with thickness of 59mil (1.5mm)
3.5 Scale-Up of Slow Wave CPWs to PCB Circuit Size
The slow wave CPWs discussed in the previous sections are fabricated on silicon
wafers using standard microelectronic fabrication processes which makes the size of slow
wave CPWs into micrometer scale. In this section, the slow wave CPWs are scaled up to
PCB board size (mil scale) to check if the design of slow wave CPWs work in PCB scale.
The minimum size of PCB circuits is about 4mil or 6mil depending on size of milling
bits. Based on this minimum dimension, a reference CPW with signal line width of
100mil, gap width of 40mil, and ground plane width of 495mil is designed, and a slow
- 43 -
wave CPW is developed from the reference CPW. Parts of the signal line are reduced to
30mil periodically, and the finger-shaped patterns of 60mil long attached to the ground
plane.
The simulated S parameters of the reference CPW and the slow wave CPW are
plotted in Figure 3.16. The return loss (S11) of the reference CPW is larger than -20 dB at
frequencies above 20GHz, and it increases with frequency. The S parameters of the slow
wave CPW is slightly different from those of the reference CPW due to the stop band
region in the frequency response. The slow wave CPW has a stop band above 13GHz
because the unit cell size is large enough to introduce the stop band region within
0
S11 and S21 (dB)
-10
-20
-30
-40
-50
S11
S21
-60
0
5
10
15
Freq (GHz)
(a)
- 44 -
20
25
30
0
S11 and S21 (dB)
-10
-20
-30
-40
-50
S11
S21
-60
0
5
10
15
20
25
30
Freq (GHz)
(b)
Figure 3.16. The simulated S parameters of (a) the reference CPW and (b) the slow wave CPW
shown inFigure 3. 15.
frequency band of interest. Thus, the slow wave CPW designed in PCB scale can be used
as a transmission line with high effective dielectric constant below approximately 8GHz.
3.6 Summary
The characteristics of interdigitated slow wave CPWs have been investigated to
determine effective dielectric constant and attenuation from S-parameter data. The slow
wave CPWs can control the effective dielectric constant without change in the
characteristic impedance, and variation of the effective dielectric constant depends on the
signal line width (S). The attenuation of the slow wave CPWs depends mainly on the S1
geometry in the signal line and tends to be large for large effective dielectric constant
- 45 -
value. These results will be used as guidelines for a new slow wave CPW design in
following chapters.
- 46 -
CHAPTER 4
RIGHT ANGLED COPLANAR WAVEGUIDE
Coplanar waveguides (CPWs) are used in various applications of microwave
integrated circuits (MICs) and monolithic microwave integrated circuits (MMICs) due
the benefits of a uniplanar nature, fabrication ease of circuits, and simple integration of
lumped or active elements [14]. Their use in complex MICs and MMICs, however, has
been limited in the presence of asymmetric discontinuities (i.e. bends, T-junctions, and
cross-junctions) commonly used in integrated circuits due to performance degradation
caused by slot-line mode excitation [15]. The slot-line mode increases the radiation loss
of the circuit.
To suppress slot-line mode effects [16], air-bridge techniques are typically used as
shown Figure 4.1(a). Its role is to suppress the excitation of the parasitic coupled slotline mode even though the air-bridges themselves create parasitic capacitance and limit
the operating bandwidth of the circuit [17]. To enhance the performance of air-bridge
techniques, methods such as chamfered CPW right-angle bend (Figure 4.1(b)), step
compensated CPW right-angle bends (Figure 4.1(c)), and dielectric overlay CPW right- 47 -
Air bridge
Air bridge
Chamfered signal
conductor
(a)
(b)
(c)
(d)
Figure 4.1. Wire-bond techniques and dielectric overlay techniques for CPW right-angle bends: (a)
conventional CPW right-angle bend with air bridges, (b) chamfered CPW bend with air bridges,
(c) step compensated CPW bend with air bridges, and (d) the right-angle bend with dielectric
overlay on the inner slot.
- 48 -
Ground
Signal
Wg
G
Reference
Plane 2
R
Path 1(L1)
Path 2(L2)
S
G
Trench
Wg
Ground
Reference
Plane 1
G2
TW
TG
(a)
(b)
Figure 4.2. Wire-bond free techniques for CPW right-angle bends: (a) 90░ circular bend with
slow wave compensation and (b) 90░ circular bend with fast wave compensation.
angle bends were developed (Figure 4.1(d)) [18-20]. While these methods do improve
bend performance, they also increase fabrication complexity and process steps such as
repeated photolithography or micromachining [21], which can lead to an increase in
fabrication cost. For this reason, a new method is proposed to create a wire-bond (or airbridge) free design approach to conformal CPW circuits with bends, T-junctions, and
cross-overs that can enhance performance without increasing fabrication process steps
and cost.
In this chapter, two wire-bond free techniques, slow-wave technique and fastwave technique, are presented, and geometrical characteristics of 90║ circular bend
structures with slow wave compensation and fast wave compensation are investigated.
These approaches, which are also achieved using the overlay dielectric method [18],
equalize the electrical length of the inner and outer slots in bends. This work uses a slow
wave structure in the shorter slot of the 90║ circular bend structure or a fast wave
- 49 -
structure in the longer slot of the 90║ circular bend structure as shown in Figure 4.2. The
performance of the two different 90░ circular bend structures shown in Figure 4.2 is
evaluated with model and measurement of fabricated test circuits and is compared to the
S-parameters of reference straight CPW lines.
4.1
Slow Wave Technique for CPW Right Angle Bends
In this section, the slow wave technique for suppressing the excitation of slot-line
mode at CPW right angle bends is presented, and its performance is discussed using
simulation and measurement results.
4.1.1
Design
4.1.1.1
Suppression of Slot-Line (odd) Mode
An incident electromagnetic wave of even mode is converted into the slot-line
mode traveling along the right-angle bend, shown in Figure 4.3(a), because inner and
outer slot lengths, L1 and L2, are unequal. Typically, this mode is suppressed using air
bridges or wire bonds. Herein, a 90║ circular bend, shown in Figure 4.3 (b), is used to
suppress the slot-line mode instead of a right angle bend. The 90║ circular bend
minimizes the length difference between the slots and thus reduces the coupling of the
even- and odd (slot-line)- mode observed in a right-angle bend [16]. To compensate for
the remaining length difference in the 90║ circular bends, a slow wave structure is used in
the shorter slot. The slow wave structure applied to the inner slot of the 90║ circular bend
- 50 -
(a)
(b)
(c)
Figure 4.3. Various CPW bend structures without air bridges: (a) Right-angle bend, (b) 90░
circular bend, and (c) 90░ circular bend with slow wave compensation. The arc radius (R) of a 90║
circular bend is defined as the distance from the origin of a 90║ circular bend to the center of the
signal line. The physical length of inner and outer slots is denoted by L1 and L2 respectively.
increases the electrical length by increasing the effective dielectric constant in the inner
slot while maintaining the given characteristic impedance.
4.1.1.2
Radius of Circular Bend
The outer:inner (L2:L1) slot length ratio of a 90║ circular bend is plotted versus the
arc radius (R) in Figure 4.4 for a 50? CPW with signal width of 225?m, gap width of
130?m, and ground width of 1335?m. As the arc radius (R) decreases, the ratio increases
exponentially. Thus, to equalize the electrical length of the inner and outer slots of the 90║
circular bend, the effective dielectric constant of the inner slot should be increased by the
square of the outer:inner length ratio. The variation of the desired effective dielectric
constant in the inner slot for equalizing the electrical length of the inner and outer slots is
shown in Figure 4.4 for designs on a silicon substrate (?r=11.9). As the arc radius
increases, the desired effective dielectric constant in the inner slot decays and saturates to
- 51 -
Signal
1335хm
)
Reference
Plane 2
1(
L1
130хm
80
2
)
4
R
Ground
Pa
th
2(
L
225хm
130хm
1335хm
Reference
Plane 1
3
60
The ratio of outer slot length to
the inner slot length
2
40
1
20
The desired effective dielectric
constant at the inner slot
0
400
600
800
1000
1200
1400
1600
1800
Desired effective dielectric constant at the inner slot
100
Ground
Pa
th
The ratio of the outer slot length to the inner slot length
5
0
2000
Arc radius of a circular bend (R)
Figure 4.4. The ratio of the outer slot length to the inner slot length versus the arc radius (R) and
the desired effective dielectric constant at the inner slot versus the circular bend radius. The
effective dielectric constant at the outer slot is assumed to be 6.45.
The outer:inner (L2:L1) slot length ratio of a 90║ circular bend is plotted versus the arc
radius (R) in Figure 4.4 for a 50? CPW with signal width of 225?m, gap width of 130?m,
and ground width of 1335?m.
As the arc radius (R) decreases, the ratio increases
exponentially. Thus, to equalize the electrical length of the inner and outer slots of the 90║
circular bend, the effective dielectric constant of the inner slot should be increased by the
square of the outer:inner length ratio. The variation of the desired effective dielectric
constant in the inner slot for equalizing the electrical length of the inner and outer slots is
shown in Figure 4.4 for designs on a silicon substrate (?r=11.9). As the arc radius
increases, the desired effective dielectric constant in the inner slot decays and saturates to
- 52 -
30
200
1335хm
130хm
225хm
130хm
1335хm
//
//
S1
25
120хm
40хm
FL2
FL1
GND
Signal
GND
15
100
FL2(?m)
20
Er_eff
150
40хm
10
50
5
0
0
50
100
150
200
0
S1(?m)
Figure 4.5. Relationship between geometrical parameters (S1, FL2) and effective dielectric
constant of a slow wave CPW with signal width (S) of 225?m, gap width (G) of 130 ?m, and
ground width (Wg) of 1335?m. The value of the other geometric parameters of the 50 ? slow
wave CPW: FW1=40 ?m, FD1=80 ?m, FL1=(S-S1)*0.5, FW2=40 ?m, FD2=80 ?m.
approximately 10% of the max value. In this study, three different arc radius sizes are
chosen to investigate the performance of the new 90║ circular bend structure with slow
wave compensation: R=500?m, R=1000?m, and R=1500?m. For an outer slot effective
dielectric constant value of 6.45, the desired inner slot effective dielectric constant values
are 28.5, 13.2, and 10.4 respectively.
4.1.1.3
Design Guidelines
The slow wave structure used to increase the effective dielectric constant of the
inner slot was initially presented and studied in the previous chapter. In this section, the
- 53 -
relationship between geometrical parameters of the slow wave CPW and its effective
dielectric constant obtained from the simulation and measurement results in the chapter 3
is plotted in Figure 4.5.
Three 50 ? slow wave CPWs with different effective dielectric constants (28.5,
13.2, and 10.4) are chosen to compensate wave velocity in the inner slot of the three test
circuits with different arc radii (R) from Figure 4.5. First, the approximate values of the
geometrical parameters corresponding to each effective dielectric constant are determined
from Figure 4.5. Next, the arc angle ? is chosen to equalize the arc length to the unit
length (120 хm) of the straight slow wave CPWs. Lastly, the exact dimensions are
optimized with Ansoft?s HFSS to take account of the effect of circular bend.
4.1.2
Simulation and Measurement Results
4.1.2.1
90░ Circular Bend with Slow Wave Compensation
A right-angle CPW bend structure, 90░ circular bend structure, and 90░ circular
bend structure with slow wave compensation are shown in Figure 4.3(a), (b), and (c),
respectively. Each have characteristic impedance of 50?, and are simulated using Ansoft
HFSS. Even though the characteristic impedance of all bend structures is 50?, both the
right-angle CPW bend and the 90░ circular bend structure have strong resonances shown
in Figure 4.6. The return loss increases with frequency due to the slot-line mode
excitation. As shown in Figure 4.6, only modifying the bend in a 90░ circular shape does
not improve the S-parameter performance. In contrast, the proposed 90░ circular bend
- 54 -
0
Ground
Gr ound
Signal
Ground
Gr ound
Signal
Signal
Ground
Ground
S11 and S21 (dB)
-10
-20
-30
Right angle bend, S11
Right angle bend, S21
o
90 CB, S11
o
90 CB, S21
o
90 CB-SW, S11
o
90 CB-SW, S21
Reference CPW, S11
Reference CPW, S21
-40
-50
-60
0
10
20
30
40
50
Frequency (GHz)
Figure 4.6.Simulated S-parameters of a single right-angle bend structure, single 90░ circular
bend (CB) structure, single 90░ circular bend structure with slow wave compensation (CB-SW)
shown in Fig. 2(a) and (c) respectively, and reference straight CPW whose length is the same as
the slow wave compensated bend structure. Geometric parameters: S= 225?m, G=130 ?m,
Wg=1335?m, R=1500 ?m, FD1=80 хm, FL1=52.5 хm, FD2=80 хm, FW2=40 ?m, FL2= 107.5
?m, and ?=4.5░
with slow wave compensation does not have resonances, and has return loss below -20dB
over the 50GHz frequency range. It is achieved by suppressing the excitation of the slotline mode using slow wave structures. When compared to a reference straight CPW
whose length is the same as the 90░ circular bend with slow wave compensation, both
insertion and return loss responses similar to the reference straight CPW. Thus, the 90░
circular bend with slow wave compensation behaves similar to a regular straight CPW.
The total losses of the right angle bend structure, 90░ circular bend with slow
wave compensation, and reference CPW are compared in Figure 4.7. As expected, the
- 55 -
0.6
Right angle bend
o
90 CB
o
90 CB-SW
Reference CPW
Signal
Ground
Gr ound
Signal
2
Total Loss (1-|S11| -|S21| )
0.5
Ground
0.4
Signal
Ground
2
Gr ound
0.3
0.2
Ground
0.1
0.0
0
10
20
30
40
50
Frequency (GHz)
Figure 4.7. Total Losses of a single right-angle bend structure, single 90░ circular bend (CB),
single 90░ circular bend with slow wave compensation(CB-SW), and reference straight CPW.
right angle bend structure has very large loss due to radiation at the corner of the bend. In
contrast, the 90░ circular bend with slow wave compensation has much smaller loss than
the right angle bend and is similar to the reference straight CPW up to 20GHz. Above
20GHz, it increases due to higher conduction loss in the slow wave structure at the inner
slot.
4.1.2.2
Back-to-Back 90░ Circular Bend with Slow Wave
Compensation
Back-to-back structures are implemented for measurement ease. The first 90░
circular bend structure with slow wave compensation (Figure 4.8) prevents the slot-line
- 56 -
Figure 4.8. Top view of a back-to-back 90░ circular bend structure
mode from propagating along the straight CPW line connecting two bends. The three
designs are chosen to characterize the effects of the arc radius (R) in the 90║ circular bend:
500?m, 1000?m, 1500?m, with two different straight CPW section lengths (?L): 0mm
and 4mm respectively. The geometries of the six designed test circuits are summarized in
Table 4.1.
Table 4.1. The parameter values of the six back-to-back 90░ circular bend structures with slow
wave compensation (CB-SW).
(Unit:?m)
?L
R
?
FD1
FL1
FW2
FL2
CB-SW 1
0
500
18░
80
107.5
40
160
CB-SW 2
0
1000
7.5░
80
67.5
40
130
CB-SW 3
0
1500
4.5░
80
52.5
40
107.5
CB-SW 4
4000
500
18░
80
107.5
40
160
CB-SW 5
4000
1000
7.5░
80
67.5
40
130
CB-SW 6
4000
1500
4.5░
80
52.5
40
107.5
Note: S=225?m, G=130?m, and Wg=1335?m for all six structures
- 57 -
Figure 4.9. The scanning electron microscopy (SEM) picture of a back-to-back 90║ circular
bends with a 4 mm straight CPW section. The arc radius is 1500?m. The reference plane for the
measurement is located right before the circular 90║ bend by TRL calibration.
4.1.2.3
Fabrication and Measurement
Six test structures were fabricated on a high resistivity silicon wafer (~400?m
thick, >2000?иcm) using the standard microelectronic fabrication techniques. After
forming the seed layer of Ti-Au-Ti (400/1500/400┼), the patterns of CPW bend
structures are Au-electroplated to a thickness of 3?m. A scanning electron microscopy
(SEM) picture of a back-to-back 90║ circular bend structure with R=1500?m and
?L=4mm fabricated is shown in Figure 4.9. For comparison, two benchmark straight
- 58 -
CPWs with length of 8.7mm and 4.7 mm respectively were also fabricated that
correspond to the two back-to-back 90║ circular bend structures (R=1500?m) with slow
wave compensation
having straight section lengths of ?L=4 mm and ?L=0 mm
respectively. The S-parameters of the test circuits are measured with an HP 8510 network
analyzer (45MHz - 50GHz) using a Cascade Microtech probe station and Cascade
Microtech ACP250 GSG probes. A TRL calibration is used to eliminate the feed line
section effects.
4.1.2.4
Surface Current Distribution
An electromagnetic wave of even mode is launched at the input of the right-angle
bend, 90║ circular bend (non-compensated 90║ circular bend), and 90║ circular bend with
slow wave compensation as shown in Figure 4.10. In the case of the right-angle bend
without air bridges, the slot-line mode is excited at the right-angle bend and propagates
along the straight CPW section connecting the two bend structures. The effect is
illustrated by the twisted current pattern shown in Figure 4.10 (a). In the 90║ circular bend
case, the slot-line mode at the straight CPW section is weaker than the right-angle bend.
However, the slot-line mode still exists as shown in the less-twisted current pattern in
Figure 4.10 (b). The 90║ circular bend with slow wave compensation, however, maintains
the even-mode throughout the straight CPW section as shown in the balanced current
pattern in Figure 4.10 (c).
- 59 -
(a)
(b)
(c)
Figure 4.10. The surface current distribution on (a) a back-to-back right-angle bend structure, (b)
back-to-back 90║ circular bend structure, and (c) back-to-back 90║ circular bend structure with
slow wave compensation at the frequency of 50 GHz. Each structure has a straight CPW section
of 4 mm between two bend structures
- 60 -
4.1.2.5
Measurement Results
The S-parameters of back-to-back right-angle bend structures without air-bridges
(Figure 4.10 (a)), back-to-back 90║ circular bend structures of the arc radius (R) of 1500
?m with slow wave compensation (Figure 4.10 (c)), and reference straight CPW lines are
compared in Figure 4.11. All back-to-back structures are interconnected with a straight
CPW section of ?L=0 mm or ?L=4 mm. As shown in Figure 4.11, the back-to-back rightangle bend structures have several resonance responses whose strength increase with
frequency due to the slot-line mode excitation, while the back-to-back 90║ circular bend
structures with slow wave compensation barely have resonance responses. The insertion
loss of the back-to-back 90║ circular bend structure with slow wave compensation is very
close to that of the reference straight 50? CPW line with deviation arising above 25GHz.
The return loss of the back-to-back right-angle bend structure with ?L=4mm increases
with frequency and is limited to less than -20dB up to 18GHz. In contrast, the return loss
of the back-to-back 90║ circular bend structures with slow wave compensation is below 20dB over the entire 50GHz frequency range similar to the reference straight CPW lines.
These results indicate that the 90║ circular bend structure with slow wave compensation
successfully suppresses the slot-line mode excitation.
- 61 -
0
-1
S21 (dB)
-2
-3
-4
Reference straight CPW line (L=4.7 mm)
Back-to-back right-angle bend structure ( ?L=0 mm)
o
Back-to-back 90 CB-SW (R=1500 ?m, ?L=0 mm)
-5
-6
0
10
20
30
40
50
Frequency (GHz)
(a)
S21 (dB)
0
-1
4mm
-2
4mm
-3
-4
-5
-6
Reference straight CPW line (L=8.7 mm)
Back-to-back right-angle bend structure (?L=4 mm)
o
Back-to-back 90 CB-SW (R=1500 ?m, ?L=4mm)
0
10
20
30
Frequency (GHz)
(b)
- 62 -
40
50
0
-10
S11 (dB)
-20
-30
-40
-50
Reference straight CPW line (L=4.7 mm)
Back-to-back right-angle bend structure (?L=0 mm)
o
Back-to-back 90 CB-SW (R=1500 ?m, ?L=0 mm)
-60
-70
0
10
20
30
40
50
Frequency (GHz)
(c)
0
4mm
-10
4mm
S11 (dB)
-20
-30
-40
-50
Reference straight CPW line (L=8.7 mm)
Back-to-back right-angle bend structure (?L=4 mm)
o
Back-to-back 90 CB-SW (R=1500 ?m, ?L=4 mm)
-60
-70
0
10
20
30
40
50
Frequency (GHz)
(d)
Figure 4.11. The S-parameters measured of back-to-back right-angle bend structures without air
bridges, back-to-back 90║ circular bend structures with slow wave compensation (CB-SW), and
reference straight CPW lines. The arc radius (R) of the 90║ circular bends is 1500 ?m for all the
cases. (a) The insertion and (c) return losses of the back-to-back structures without a straight
section of 4 mm. (b) The insertion and (d) return losses of the back-to-back structure with a
straight section of 4mm.
- 63 -
Figure 4.11 also show the effect of the delay line placed between two bends.
When the S-parameters of the back-to-back 90║ circular bend structures with slow wave
compensation are compared for two different straight CPW section lengths: ?L=0mm and
?L=4mm, the back-to-back 90║ circular bend structure with slow wave compensation
shows improved performance for non-zero straight sections of CPW lines, as shown in
Figure 4.11. The resonance responses of the back-to-back 90║ circular bend structure with
slow wave compensation having a 4mm straight CPW section are much weaker and
cannot be readily recognized as shown in Figure 4.11 (b). The straight CPW section
interconnected by two CPW bend structures stabilizes the electromagnetic wave coming
out of the 90║ circular bend with slow wave compensation.
In Figure 4.12, the S-parameters of the back-to-back 90║ circular bend structures
with slow wave compensation are compared for three different arc radii: R=500?m,
1000?m, and 1500?m. As the arc radius (R) increase, the frequencies where resonance
responses occur shift down to lower frequencies and the strength of the resonance
responses decreases as shown in Figure 4.12. This behavior is because large arc radius (R)
reduces the outer: inner slot length ratio and thus decrease the coupling of even and odd
mode at the 90║ circular bend. Thus, the insertion loss of the back-to-back 90░ circular
bend structure with slow wave compensation of large arc radius is much smoother that of
small arc radius and the return loss of the back-to-back 90░ circular bend structure with
slow wave compensation of large arc radius is lower than that of large arc radius as
shown in Figure 4.12.
- 64 -
0.0
-0.5
S21 (dB)
Reference CPW line
8.7mm
Back-to-back 90? CB-SW with Radius R
-1.0
4 mm
R
-1.5
-2.0
Reference straight CPW line (8.7mm)
o
Back-to-back 90 CB-SW (R=500 ?m, ?L=4 mm)
o
Back-to-back 90 CB-SW (R=1000 ?m, ?L=4 mm)
o
Back-to-back
90 CB-SW (R=1500 ?m, ?L=4 mm)
Frequency
(GHz)
0
10
20
30
40
50
(a)
0
Reference CPW line
8.7mm
-10
Back-to-back 90? CB-SW with Radius R
4 mm
R
S11 (dB)
-20
-30
-40
-50
Reference straight CPW line (8.7mm)
o
Back-to-back 90 CB-SW (R=500 ?m, ?L=4 mm)
o
Back-to-back 90 CB-SW (R=1000 ?m, ?L=4 mm)
o
Frequency
(GHz)
Back-to-back
90 CB-SW (R=1500 ?m, ?L=4 mm)
-60
-70
0
10
20
30
40
50
Frequency (GHz)
(b)
Figure 4.12. The S parameters measured of back-to-back circular 90║ circular bend structures with
slow wave compensation (CB-SWs) with three different arc radii (R=500?m, 1000?m, and
1500?m) and a reference straight 50 ? CPW line corresponding to the back-to-back 90║ circular
bend with slow compensation with R=1500?m and ?L=4mm.
- 65 -
4.2 Fast Wave Technique for CPW Right Angle Bends
In this section, another design technique that suppresses slot-line mode excitation
in CPW right-angle bends without air-bridges is presented. This design technique
suppresses the slot-line mode by equalizing the travel time of electromagnetic waves
propagating along inner slot and outer slot by trenching the outer slot of CPW bends like
the slow wave technique. The speed of the wave which propagates in the trenched slot is
increased from that of an original slot without slots, and thus it is called as ?fast-wave
technique.? In the slow wave techniques for CPW right angle bend, the compensation
method for length difference of the inner and outer slots is described with effective
dielectric constant of transmission lines. In this section, fast-wave technique, the
compensation method is described by velocity of electromagnetic wave propagating
along slots.
4.2.1
Design
As described in the previous section 4.2, slot-line mode occurs at right-angle bend
shown in Figure 4.13 (a) because of the difference in inner- and outer-slot lengths. The
slow wave technique presented in the previous section compensates the length difference
in the outer and inner slots by introducing slow wave structure in the shorter (inner) slot
of a 90░ circular bend shown in Figure 4.13 (b). In the ?fast-wave? technique, the
excitation of slot-line mode at CPW bends is suppressed by speeding up the
electromagnetic wave that travel in the longer slot and thus by make it come out of the
- 66 -
(a)
(b)
(c)
Figure 4.13. Several types of CPW bend structures designed for a 400?m thick silicon wafer. (a)
Right-angle bend. (b) Circular bend without a outer trenched slot. (c) Circular bend with a outer
trenched slot. The arc radius (R) is defined as distance from the origin of circular bend to the
center of signal line. The outer slot width (G2) of the circular bend is determined based on the arc
radius (R) of the circular bend. The conductor thickness (T) is 3um.
Figure 4.14. Cross-sectional view of the line A-A? of the 90░ circular bend with a trench in the
longer (outer) slot shown in Figure 4.13(c).
bend in phase with an electromagnetic wave that travels in the shorter (inner) slot. To
increase the speed of the electromagnetic wave that travel in the longer (outer) slot and
maintain its characteristic impedance, the dielectric material in the longer slot is removed
and the gap between the signal line and the ground plane is reduced. Removing the
dielectric material in the slot results in decrease in the effective dielectric constant of the
slot.
- 67 -
Figure 4.15. Cross-sectional view of a fast wave CPW that has trenches between signal line and
ground planes.
4.2.1.1
Fast Wave Coplanar Waveguide
A CPW with signal line of 225?m wide, gap of 130?m wide, and ground planes
of 1335?m is fabricated on high-resistivity silicon wafer of 400um thick to evaluate this
design technique. Several types of 50 ohm CPWs with trenched slots shown in Figure
4.15 are developed for various gap widths (G2) (from 130?m to 50?m) with a constant
signal line width (S) of 225um using Ansoft?s 2D extractor. Trench width (TW) is 20?m
smaller than the slot width (G2) for trench fabrication ease. The trench depth (TD) for
each slot width (G2) is determined by parametric sweep simulations using Ansoft?s 2D
extractor for characteristic impedance of 50?.
Figure 4.16 shows the velocity of the electromagnetic wave that propagates along
the CPW with trenched slots for various gap width (G2). As can be seen in Figure 4.16,
the velocity of the electromagnetic wave is increased by a factor of 1.42, corresponding
to a change from approximately 1.2О108m/s and to 1.7О108m/s as the gap width (G2) is
decreased. As can be seen in Figure 4.16, however, the maximum velocity of the
electromagnetic wave is constrained due to geometrical size limitations. Even though the
trench depth is deeper than 130?m, the velocity rarely decreases. This velocity limitation
- 68 -
1.80E+008
Velocity (m/s)
1.60E+008
1.40E+008
1.20E+008
40
60
80
100
120
140
G2 (TW=G2-20um) (um)
Figure 4.16. The velocity of electromagnetic wave of a coplanar waveguide with S=225?m and
Wg=1335?m and the trench depth TD. Slot width (G2) varies from 130?m to 50?m.
should be taken account into when the arc radius (R) of a 90░ circular bend is determined
because the required velocity of the electromagnetic wave at the outer slot is increased as
the arc radius (R) is decreased. Relationship between geometrical parameters (G2 vs TD)
of the 50? trenched CPWs shown in Figure 4.15 is summarized in Figure 4.17. Figure
4.16 and Figure 4.17 will be used as guidelines to design the fast-wave CPW lines.
4.2.1.1
90░ Circular Bend with a Fast Wave Compensation
Eq. 4.1 and Eq. 4.2 describe the relationship between velocities of
electromagnetic waves that travel in the outer and inner slots of a 90░ circular bend with
- 69 -
250
Trench Depth (TD) (um)
200
150
100
50
0
40
60
80
100
120
140
G2 (TW=G2-20um) (um)
Figure 4.17. Relationship between geometrical parameters, the gap width (G2) between signal
line and ground planes and the depth of trenches (TD), of a trenched CPW with signal line
width of 225?m and ground plane width of 1335?m shown in Figure 4.15. The trench depth
(TD) is optimized for characteristic impedance of 50?.
an arc radius R to compensate for length difference between the outer and inner slots. In
test circuits, an arc radius of R=2000?m is chosen, and thus the velocity of the
electromagnetic wave traveling the outer (longer) slot shown in Figure 4.13(c) need to be
approximately 1.45О108m/s to suppress the excitation of slot-line mode at a CPW bend.
Approximate dimensions of the trench width (TW=55?m) and the trench depth
(TD=62?m) of the 90░ circular bend with fast-wave compensation are obtained from
Figure 4.16 and Figure 4.17. According to Figure 4.16 and Figure 4.17, an
electromagnetic wave propagates at velocity of 1.45О108m/s in a trenched CPW with
trench width (TW) of 55?m and trench depth (TD) of 62?m. When this trench is
incorporated in a 90░ circular bend as shown in Figure 4.13 (c), the dimensions of outer
- 70 -
Table 4.2. Optimized dimensions of the 90░ circular bend with fast wave compensation. Unit
of all values is micrometers.
S
G
Wg
R
G2
TW
TD
225
130
1335
2000
85
75
50
slot width (G2), trench width (TW), and trench depth (TD) are optimized with Ansoft?s
HFSS to take an account of effects of circular bend. The exact dimensions of a 90░
circular bend with fast-wave compensation are summarized in Table 4.2.
? Linner slot
Tinner slot ? ?
? vinner slot
?
?
? Louter slot
?? ? Touter slot ?? ?
?
? vouter slot
?
??
?
Eq. 4.1
? Louter slot
vouter slot ? ?
? Linner slot
?
?
? R ? 0.5 ? S ? 0.5 ? G ?
?? ? vinner slot ? ?
? ? vinner slot
? R ? 0.5 ? S ? 0.5 ? G ?
?
Eq. 4.2
4.2.2
Simulation and Measurement Results
4.2.2.1
Single Bend: 90░ Circular Bend with Fast Wave
Compensation
A right angel CPW bend structure, 90░ circular bend structure, and 90░ circular
bend with a trench in the outer (longer) slot are simulated using Ansoft?s HFSS. The
radius of 90░ circular bend structures is 2000?m for all structures. Other geometrical
parameters for the 90░ circular bend with fast wave compensation are used from Table
4.2.
- 71 -
Figure 4.18 is a comparison of the simulated S parameters of three bend structure
designs shown in Figure 4.13. Both right angle bend structure and 90░ circular bend
structure without trench have strong resonances due to excitation of slot-line modes in the
bends, and their strength increases with frequency. The 90░ circular bend with fast-wave
compensation also has resonances at 37GHz and 45GHz, they are very weak and
negligible. Moreover, the insertion loss of the 90░ circular bend with fast wave
compensation is just a half or one third of the insertion loss of the 90░ circular bend
without fast wave compensation, and its return loss is below -20dB in frequency range of
interest (up to 50GHz). The return losses of the other two bend structures without fast
wave compensation increase significantly with frequency as shown in Figure 4.18.
0
-2
Wg
G S
G
Wg
Ref.
Plane 2
A
R G ND
Sign
Trench
al
G2
G ND
TW
TG
A
S21 (dB)
Ref. Pl ane 1
Substrate
-4
Wg
G S
G
Wg
R ef.
P lane 2
GND
Sign
al
GND
Ref. P lane 1
Substrate
-6
Wg
G
S
G
Wg
Ref.
Plane 2
GND
S ignal
GND
Ref. P lane 1
-8
-10
S ubstrate
Right-angle CPW bend
o
90 circular bend without a trench
o
90 circular bend with a trench
0
10
20
30
Frequency (GHz)
(a)
- 72 -
40
50
0
Wg
G S
G
Wg
R ef.
P lane 2
GND
-10
Sign
Wg
G
S
G
al
Wg
Ref.
Plane 2
GND
Ref. P lane 1
GND
Substrate
S ignal
GND
Ref. P lane 1
S ubstrate
S11 (dB)
-20
-30
Wg
-40
G S
G
Wg
Ref.
Plane 2
A
R G ND
Sign
Trench
al
G2
G ND
TW
A
Ref. Pl ane 1
Right-angle CPW bend
o
90 circular bend without a trench
o
90 circular bend with a trench
-50
-60
TG
Substrate
0
10
20
30
Frequency (GHz)
40
50
(b)
Figure 4.18. Simulated (a) insertion (S21) and (b) return losses (S11) of the three bend structures:
right angle bend, 90░ circular bend without a trench, and 90░ circular bend with a trench.
4.2.2.2
Back-to-Back CPW Bend Structure
For the test circuit design, a back-to-back structures with a delay line length of
Figure 4.19. Back-to-back 90░ circular bend with fast wave compensation. A straight CPW line
of 4mm long is placed between two bends.
- 73 -
4mm in a right-angle bend, circular bend without trenched slots, and circular bend with
trenched slots are implemented to evaluate the bend structure performance. A back-toback 90░ circular bend with fast wave compensation is shown in Figure 4.19.
4.2.2.3
Fabrication Process and Measurement Setup
Three back-to-back bend structures and a reference straight CPW line are
fabricated on a high resistivity silicon wafer (400?m thick, >2000?иcm) using the
standard microelectronic fabrication techniques. The reference line has the same length as
the back-to-back 90░ circular bend with fast wave compensation. The details of the
fabrication processes for the four test structures are described in Figure 4.20. After
depositing a seed layer of Ti/Au/Ti (=400┼/1500┼/400┼) using sputter or evaporator, a
first photolithography is performed to define the CPW bend structures and the reference
straight CPW. The patterns of CPW bend structures with thickness of 3?m are formed by
gold electroplating processes. After removing the remaining photoresist and the Ti/Au/Ti
seed layer, a second photolithography is performed to define trenches. Trenches are
created by deep trench etching (Bosh Process). Scanning electron microscopy (SEM)
pictures of trenched regions for the fast wave designs are shown in Figure 4.20.
To evaluate the response, S-parameters of the four test structures are measured
with an HP 8510 network analyzer (45MHz ? 50GHz) using a Cascade Microtech probe
station and Cascade Microtech ACP 250 GSG probes. The TRL calibration is used to
- 74 -
eliminate the feed line section effects and to shift the measurement reference planes away
from the probe point contact.
(a)
(b)
(c)
Electroplated gold
3?m
Silicon
(d)
- 75 -
(e)
(f)
(g)
(h)
Figure 4.20. Fabrication processes of the test back-to-back CPW bend structures. The crosssectional view is located in the line A-A? shown in Figure 4.14.(a) A seed layer of Ti/Au/Ti
(=400┼/1500┼/400┼) is deposited, (b) photoresist is patterned to define circuits, (c) the top Ti
layer is etched, (d) circuits are built through electroplating, (e) the remaining photoresist and seed
layer are removed. (f) photoresist is patterned to define trenches, (g) trenches are formed using a
deep trench etcher with Bosch process, and (h) the remaining photoresist is cleaned.
- 76 -
(a)
(b)
Figure 4.21 SEM pictures of the back-to-back 90░ circular bend with fast wave compensation. (a)
Top view of a 90░ circular bend with trench compensation, (b) Cross sectional view of a 90░
circular bend with trench compensation at the section AA?
- 77 -
(a)
(b)
(c)
Figure 4.22. The surface current distribution of (a) right-angle bend, (b) circular bend and (c)
circular bend with trenched slots at the frequency of 50GHz.
- 78 -
4.2.2.4
Surface Current Distributions
Surface current distribution of three test circuits is plotted in Figure 4.22 to show
the suppression of the slot-line mode at the circular bend with trenched slots. As shown in
Figure 4.22, electromagnetic waves of even mode are fed to port 1 in three test circuits.
In the case of the right-angle bend and circular bend without trenched slots, the slot-line
mode is excited at the bends and exists after passing the bends as a twisted current pattern
as shown in Figure 4.22 (a) and (b). With the inclusion of the trenched slot in the outer a
slot of the bends alleviates the slot line mode propagation and results in a balanced
current pattern as shown in Figure 4.22(c).
4.2.2.5
S-Parameters
The S-parameter performance of the back-to-back circular bend with trenched slots is
compared to the back-to-back right-angle bend, back-to-back circular bend without
trenched slots, and reference straight CPW. The return loss (S11) and insertion loss (S21)
of the back-to-back right-angle bend and the back-to-back circular bend without trenched
slots increase with frequency, and strong resonance responses appear at several
frequencies starting at 10 GHz as shown in Figure 4.23. The insertion loss (S21) of the
back-to-back circular bend with trenched slots is smaller than that of the other structures,
and it does not show the resonance responses. In compared to the reference straight CPW,
the insertion loss (S21) of the 90░ circular bend with trenched slots is close to that of the
reference
- 79 -
0
S21 (dB)
-2
-4
-6
Right-angle bend, measured
o
90 Circular bend, measured
o
90 Circular bend with trench compensation, measured
Reference straight CPW, measured
-8
0
10
20
30
40
50
Frequency (GHz)
(a)
0
S11 (dB)
-20
-40
-60
Right-angle bend, measured
o
90 Circular bend, measured
o
90 Circular bend with trench compensation, measured
Reference straight CPW, measured
-80
0
10
20
30
40
50
Frequency (GHz)
(b)
Figure 4.23. Measured (a) insertion and (b) return losses of the test back-to-back CPW bend
structures
- 80 -
straight CPW as shown in Figure 4.23. Moreover, the return loss (S11) of the back-toback circular bend trenched slots is below -20dB over the entire frequency range of
interest up to 50GHz like the reference straight CPW with characteristic impedance of
50?.
4.3 Summary
In this chapter, two novel design techniques, slow wave technique and fast wave
techniques, for CPW right-angle bends are presented. The excitation of slot-line mode in
CPW right angle bends is suppressed by equalizing the traveling time of the
electromagnetic wave propagating along inner and outer slots with slow wave structure or
fast wave structure. Slow wave structures are incorporated in the shorter slot of a 90░
circular bend to slow down the electromagnetic wave traveling in the shorter slot. In
contrast, fast wave structures (trenches) are incorporated in the longer slot of a 90░
circular bend to speed up the electromagnetic wave traveling in the longer slot.
Measurement and simulation results demonstrate these design techniques work extremely
well for CPW right angle bends.
- 81 -
CHAPTER 5
FILTER DESIGN
Filter circuits are a key component in any high frequency wireless systems.
Modern trends have been to try to move away from analogue filtering as much as
possible and to implement filtering using digital signal processing wherever possible.
However, this is only achievable a lower frequencies where the analogue signal can be
successfully transformed into the digital domain.
RF/Microwave filters have traditionally been built using waveguide and coaxial
lines. Following the enormous expansion in printed circuit technology and modeling
techniques, many of them are now built using printed circuits. Printed circuit filters have
advantages over rectangular or coaxial waveguide filters in terms of low cost,
repeatability, high accuracy, and compact size. By selecting high dielectric constant
substrate, the size of the printed filters can be reduced significantly, which provides
compact size. Printed filters can be designed using microstrip or strip lines. Steppedimpedance, interdigital, and coupled-line filters are the most commonly used forms of
printed filters.
- 82 -
In this chapter, two new designs for compact filter, CPW EBG structure and
UWB bandpass filter, are presented. Miniaturization of these filters is obtained by using
slow wave CPWs and meandered coupled lines. In the following sections, details of
designs and their characteristics are presented, and simulation and measurement results
are discussed.
5.1
Electromagnetic Band-Gap (EBG) Filter
5.1.1
Introduction
Electromagnetic band-gap (EBG) structures for microwave and millimeter
applications are attractive for their frequency selective characteristics and potential to
improve waveguiding functions, radiation mirroring, noise suppressions, etc. In planar
RF/microwave circuits, EBG structures have been used as band-stop filers or highimpedance ground plane [22-24]. However, one major problem in utilizing EBG
structures in planar circuits printed on PCB boards or on silicon wafers is the large size of
EBG structures at microwave and millimeter wave frequencies. Several studies for
reducing EBG structures such as an artificial dielectric material approach using a 2D
array of grounded metallic posts, capacitive loading approach, and rectangular and fractal
patterns approaches have been carried out [25-27].
In this section, a compact one-dimensional (1D) CPW EBG structure used as a
band-stop filter is presented. Miniaturization of the 1D CPW EBG structure is obtained
by replacing low-impedance and high-impedance sections with low-impedance slow
wave CPW and high-impedance slow wave CPW, respectively. Characterization of the
- 83 -
Figure 5.1. Configuration of a conventional electromagnetic band-gap (EBG) structure.
Figure 5.2 Top view of a 1D CPW EBG structure which is implemented on a high resistivity
silicon wafer (>2000?иcm) with thickness of 400?m.
1D CPW EBG structure will include full-wave simulations and experimental validation
of designs. These are also compared to a conventional 1D CPW EBG structure.
5.1.2
Conventional CPW EBG Structure
A conventional one-dimensional EBG structure is formed by alternating low and
high impedance sections as shown in Figure 5.1. Alternating characteristic impedance of
a series of transmission lines leads to a stopband. A large ratio of high impedance to low
impedance makes a deeper stopband null and reduces the number of unit cells. A unit cell
consists of two sections of high and low impedance lines. In this study, the onedimensional EBG structure is implemented in the form of a CPW as shown in Figure 5.2.
- 84 -
0
S11 and S21 (dB)
-10
-20
-30
Return Loss (S11)
Insertion Loss (S21)
-40
10
20
30
40
50
Frequency (GHz)
Figure 5.3 The simulated insertion and return losses of a 1D CPW EBG structure shown in
Figure 5.1.
The CPW EBG structure shown in Figure 5.2 uses a 50? CPW for the low impedance
section and a 75? CPW for the high impedance section. Each section is 120хm long. The
50? CPW is composed of a signal line of 225?m wide, gap of 110?m wide, and ground
planes of 1335?m wide. The 75? CPW is composed of a signal of 225um, gap of
425.5?m, and ground planes of 819.5?m. As seen in Figure 5.3, the CPW EBG structure
has a stop band from 22GHz to 33GHz, and the total length of the CPW EBG circuit is
1320?m long.
- 85 -
(a)
(b)
(c)
Figure 5.4. Three different types of slow wave coplanar waveguides (CPWs). (a) 50 ? CPW
with finger-shaped patterns (slow wave structure I), (b) 75? CPW with finger-shaped patterns
(slow wave structure II), and (c) 50? CPW with finger-shaped patterns and air trenches (slow
wave structure III).
5.1.3
Size Reduction Principle
The stopband characteristics of EBG structure depends highly on cell distance, the
number of unit cells and effective dielectric constant. Especially, the center frequency of
the stopband is determined by the effective dielectric constant (?r,eff) and cell distance (u)
as shown in Eq. 5.1, derived from Bragg?s condition.
1
c
1
?
fc ? ?
2
? eff u
Eq. 5.1
According to Eq. 5.1, the length of EBG structure can be reduced by using a high
permittivity substrate or by increasing the effective dielectric constant of the EBG
structure synthetically. In this study, we increase the effective dielectric constant of the
- 86 -
Figure 5.5. Top view of one unit section of a slow wave coplanar waveguide with trenches with
geometrical parameters.
EBG structure by incorporating a slow wave design. It produces a high effective
dielectric constant value in the 1D CPW EBG structures, which reduce its overall length.
5.1.4
Characterization of slow wave structure
Three slow wave structures to be applied on conventional 1D CPW line are
shown in Figure 5.4. These slow wave structures are formed by adding finger-shaped
metal patterns, and this modification increase both the capacitance and the inductance per
unit length of CPW lines. To maintain the characteristic impedance of the slow wave
CPW, the inductance to the capacitance per unit length is maintained.
In this study, three types of slow wave CPW structures are developed for different
reference characteristic impedance: 50ohm CPW line with finger-shaped metal patterns
(Figure 5.4(a)), 75ohm CPW line with finger-shaped metal patterns (Figure 5.4(b)), and
- 87 -
50ohm CPW line with finger-shaped metal patterns and air trenches (Figure 5.4(c)). The
slow wave structure III shown in Figure 5.4(c) is made by removing the dielectric
material between signal line and ground plane of the slow wave structure I with 50?
characteristic impedance. The air trenches between the signal line and the ground planes
cause a decrease in the line capacitance, whereby the reduced capacitance leads to an
increase in the effective characteristic impedance. Note, the effective characteristic
impedance of the slow wave structure I is 50?, and the effective characteristic impedance
of the other two slow wave structures (II and III) is 75?. The dimensions of the slow
structures are optimized by full wave simulations and are summarized in Table 5.1.
The effective dielectric constant of three types of the CPW slow wave structures
is calculated based on the phase relationship of transmission coefficient. The transmission
coefficient (S21) was obtained from 3D full wave simulations by HFSS. Figure 5.6 shows
Table 5.1. Dimensions of the three slow wave CPWs. The geometrical parameter used in this
table are described in Figure 5.5. Unit of all values is micrometers.
Parameter
Slow wave CPW I
Slow wave CPW II
Slow wave CPW III
U
120
120
120
S
225
225
225
G
110
425.5
425.5
W
1335
819.5
1335
FW1
30
40
30
FL1
97.5
97.5
97.5
FW2
40
40
40
FL2
182.5
350
182.5
FG
25
20
25
TG
5
TD
- 88 -
Effective Dielectric Constant
40
50ohm CPW line
50ohm CPW with finger-shaped metal patterns(Slow wave CPW I)
75ohm CPW with finger-shaped metal patterns(Slow wave CPW II)
50ohm CPW with finger-shaped metal patterns
and air trenches(Slow wave CPW III)
30
20
10
0
0
10
20
30
40
50
Frequency (GHz)
Figure 5.6. Effective dielectric constant of the slow wave structures.
the effective dielectric constant of three CPW slow wave structure designs. As shown in
Figure 5.6, the effective dielectric constant of the slow wave structure III is lower than
the slow wave structure I with only finger-shaped metal patterns due to removal of the
dielectric material between the signal line and the ground planes. The effective dielectric
constant of the standard 50ohm CPW line is about 6, while the CPW line on which slow
wave design is employed have much larger values such as 25, 19, and 12.
5.1.5
Design of New CPW EBG Structures
In this study, two different approaches are used to reduce the size of the
conventional one-dimensional (1D) CPW EBG structure shown in Figure 5.2. Using the
- 89 -
(a)
(b)
Figure 5.7. The proposed miniaturized one-dimensional CPW EBG structures. (a) CPW EBG
structure I and (b) CPW EBG structure II.
CPW slow wave structures studied in the previous section, two types of CPW EBG
structure are formed as shown in Figure 5.7(a) and Figure 5.7(b), respectively. The CPW
EBG structure I consists of 50ohm CPW SW section and 75ohm CPW section, and the
CPW EBG structure II consists of 50ohm CPW SW section and 50ohm CPW SW section
with air trenches. Here, the effective characteristic impedance the 50ohm CPW SW
section with air trenches is about 75ohm. Both EBG structures have 5 unit cells and a
50ohm CPW SW section for symmetry.
5.1.6
Fabrication and Measurement
- 90 -
Three CPW EBG structures (conventional CPW EBG structure and the two
proposed CPW EBG structure I and II) are fabricated on a high resistivity silicon (>2000
ohm-cm, ~400 um thick) substrate using standard fabrication techniques. Circuits are
formed by evaporating of a seed layer of Ti(500┼)/Au(1500 ┼)/Ti(500┼) on silicon
substrate. Then, the patterns of CPW EBG structures are transferred on the seed layer
using standard photolithography and are formed by Au electroplating. The CPW EBG
structure II requires air trenches to be etched between signal line and ground plane using
deep reactive ion etching (DRIE). Figure 5.8 shows the CPW EBG structures I and II
fabricated.
The S-parameters of the EBG CPW structures are measured by HP 8510 network
analyzer on a Cascade Microtech probe station with Cascade Microtech ACP250 groundsignal-ground (GSG) probes. A line-reflect-match (LRM) calibration is used.
(a)
- 91 -
(b)
Figure 5.8. SEM pictures of the proposed CPW EBG structure (a) I and (b) II.
Term
TLINP
Term1
TL12
Num=1
Z=50 Ohm Z=ZFEED
L=LFEED
K=6
TanD=0.002
TLINP
TL1
Z=ZL
L=LL
K=6
TanD=0.002
TLINP
TL2
Z=ZH
L=LH
K=6
TanD=0.002
TLINP
TL4
Z=ZL
L=LL
K=6
TanD=0.002
TLINP
TL3
Z=ZH
L=LH
K=6
TanD=0.002
TLINP
TL6
Z=ZL
L=LL
K=6
TanD=0.002
TLINP
TL8
Z=ZL
L=LL
K=6
TanD=0.002
TLINP
TL7
Z=ZH
L=LH
K=6
TanD=0.002
TLINP
TL10
Z=ZL
L=LL
K=6
TanD=0.002
TLINP
TL9
Z=ZH
L=LH
K=6
TanD=0.002
TLINP
TL11
Z=ZL
L=LL
K=6
TanD=0.002
TLINP
TL13
Z=ZFEED
L=LFEED
K=6
TanD=0.002
TLINP
TL5
Z=ZH
L=LH
K=6
TanD=0.002
Term
Term2
Num=2
Z=50 Ohm
Figure 5.9. ADS circuit models of the conventional CPW EBG structure based on physical T-line
models.
- 92 -
5.1.7
Simulation and Measurement Results
The ADS circuit models for the conventional CPW EBG structure are developed
based on physical T-line models to compare the length of the CPW EBG structures due to
its fast simulation speed. All designs are reformed and verified (CPW EBG structure I
and II) by HFSS [29]. The length and characteristic impedance of the conventional CPW
EBG structures are modified until their simulation results match the S-parameters of the
proposed CPW EBG structures. Figure 5.9 shows the ADS models of the conventional
CPW EBG structures used in this study.
Figure 5.10 compares the S-parameters of the conventional CPW EBG structures
and the proposed CPW EBG structures I and II. As can be seen in Figure 5.10, the ADS
simulation results for the conventional CPW EBG structures agree well with the HFSS
simulation results and measurement results for both proposed CPW EBG structure I and
II as shown in Figure 5.10. This means that proposed CPW EBG structures I and II
perform as stop-band filters like the conventional CPW EBG structures. Moreover, the
proposed CPW EBG structures I and II significantly reduce the overall length by 45.4
and 37.5% respectively for structures I and II. Table 5.2 describes the dimensions of the
various designs.
Table 5.2. Size comparison of conventional (Con.) CPW EBG structures and the proposed CPW
EBG structures
The length of unit cell
Case I
Case II
CPW EBG I
Con. CPW EBG
1200um
2200um
CPW EBG II
Con. CPW EBG
1200um
1920um
- 93 -
Size reduction
45.4%
37.5%
0
S11 and S21 (dB)
-10
-20
-30
S11 CPW EBG structure I(HFSS)
S21 CPW EBG structure I(HFSS)
S11 Conventional CPW EBG structure(ADS)
S21 Conventional CPW EBG structure(ADS)
S11 CPW EBG structure I(Measurement)
S21 CPW EBG structure I(Measurement)
-40
-50
0
10
20
30
40
50
Frequency (GHz)
(a)
0
S11 and S21 (dB)
-10
-20
-30
S11 CPW EBG Structure II (HFSS)
S21 CPW EBG Structure II (HFSS)
S11 Conventional CPW EBG structure (ADS)
S21 Convetiional CPW EBG Structure (ADS)
S11 CPW EBG structure II (Measurement)
S21 CPW EBG structure II (Measurement)
-40
-50
0
10
20
30
40
50
Frequency (GHz)
(b)
Figure 5.10. The insertion loss (S21) and return loss (S11) of the conventional CPW EBG
structure and the two proposed CPW EBG structures I and II. Each plot compares the S
parameters of the proposed CPW EBG structures with a conventional CPW EBG structure. (a)
CPW EBG structure I and (b) CPW EBG structure II.
- 94 -
5.2
Ultra-Wide Band (UWB) Band-pass Filter
5.2.1
Introduction
Numerous studies in ultra-wideband (UWB) communication technology have
been conducted in both academia and industries due to its potential for high speed links
since the Federal Communications Commission (FCC) authorized its unlicensed use for
indoor and hand-held wireless communication in early 2002 [30]. Recently, several types
of UWB bandpass filters, a key component in the UWB system, have been developed
using various design methods and structures such as dual stop-band ring [31], multiplemode resonator (MMR) with two short-circuited ends [32] or two open-circuited ends
[33], MMR with capacitive-end coupling section for spurious harmonic suppression [34],
stub-loaded multiple-mode resonator [35], hybrid microstrip/CPW structure [36], and
shunt stubs with lumped capacitors [37]. Most of these filters are designed in microstrip
structures or in a combined form of microstrip and CPW. There has been not much effort,
however, in developing CPW-type UWB bandpass filters despite a variety of advantages
of CPW such as a uniplanar nature, fabrication ease of circuits, and simple integration of
lumped or active elements [38]. Moreover, CPW-type filters can improve group delay
performance, which is one of the key issues of UWB devices for better signal
transmission, since CPW is less dispersive than the microstrip line [39]. In [33-34],
CPW-based UWB bandpass filters were developed using an open/short ended CPW
MMR and CPW interdigital capacitor. The total length of these filters is equal to about
one guided wavelength (?g) at the center frequency of UWB passband. Note, the MMR
- 95 -
Figure 5.11 Schematic of the compact UWB bandpass filter fed by coplanar waveguides with
geometrical parameters.
determines the length. In this section, a new compact ultra-wide band (UWB) bandpass
filter using modified open-ended slow wave CPW stepped-impedance MMR with
compact coupled line is presented and studied.
5.2.2
Design
Figure 5.11 shows the geometry of the proposed compact UWB bandpass filter in
this study. The proposed filter is composed of a slow wave CPW for a low-impedance
section in the middle of the design and a pair of coupled line structures with meandered
slots for two high-impedance sections at the input and output sides of the design. By
- 96 -
Figure 5.12 Conventional UWB bandpass filter designed based on coplanar waveguides.
using the slow wave CPW and meandered slots, the filter?s length is approximately 0.56
?g at the center of UWB passband and thus is about 40% shorter than the conventional
UWB filters in [33-34]. As a result, the group delay effects are reduced due to shorter
length of the UWB filter.
5.2.2.1
Conventional UWB Bandpass Filter of CPW Type
Figure 5.12 shows the geometry of the conventional UWB bandpass filter on
CPW which consists of an open-ended CPW multiple mode resonator (MMR) and two
edge coupled lines. This MMR has one low-impedance section in middle and two high
impedance sections in two sides. The high impedance sections are edge-coupled with the
signal line whose ground planes are widened as shown in Figure 5.12. To get a UWB
passband, the first three resonant modes are allocated near the lower-end, center, and
- 97 -
high-end of the targeted UWB frequencies, and the quarter-wave edge coupled line excite
two additional poles below and above the UWB's center or 6.85GHz.
Figure 5.13(a) depicts the open-ended CPW stepped impedance MMR. It is
composed of three distinctive sections, one low-impedance section in the middle and two
identical high-impedance sections insides. Figure 5.13(b) is its equivalent transmission
line network model, in which the two CPW step discontinuities are ignored since their
effects in fact rarely affect the UWB bandpass filter behavior. This CPW MMR aims to
make effective use of its lowest multiple resonant modes for wideband filter design. This
MMR resonator is very similar to SIR [40] in geometry and equilvalent topology, but it
should be emphasized here that the so-called SIR only uses the lowest or dominant
resonant mode in the design of narrow band filters with widened upper stopband.
The input admittance (Yin) at the left open-end, looking into the right side, as
indicated in Figure 5.13(b).
Yin ? jY2 ?
2 ? K tan ?1 ? tan ? 2 ?? K ? tan ?1 tan ? 2 ?
K ?1 ? tan 2 ?1 ??1 ? tan 2 ? 2 ? ? 2 ?1 ? K 2 ? tan ?1 tan ? 2
Eq. 5.2
where K=Y1/Y2 is the admittance ratio of two dissimilar sections in this MMR. At the
resonance, Yin=0 is valid. From Eq. 5.2, a set of algebraic equations are established to
solve all the resonant to solve all the resonant frequencies, including the three lowest
ones of interest, i.e. f1, f2, and f3. In this conventional design, electrical lengths of these
two sections are selected as ?1? ?2= ? such that the three separate closed-form equations
- 98 -
(a)
(b)
Figure 5.13. (a) Geometry and (b) equivalent circuit network of the open-ended CPW multiplemode resonator (MMR).
are deduced to individually determine f1, f2, and f3. As can been in Eq. 5.3-Eq. 5.5, the
lower and higher frequencies, f1 and f3, are mainly controlled by K, while the center f2
relies on the selected actual lengths of the three sections in this MMR.
? ? f1 ? ? tan ?1 K
? ? f2 ? ?
Eq. 5.3
?
Eq. 5.4
2
? ? f3 ? ? ? ? tan ?1 K
Eq. 5.5
- 99 -
(a)
(b)
Figure 5.14. (a) Geometry and (b) equivalent circuit model of an edge-coupled line.
Figure 5.14(a) describes the geometry of an edge-coupled line with enlarged
ground-to-ground distance which is a frequency distributed CPW element over 110%
UWB passband. The equivalent circuit model of this edge coupled line is shown in
Figure 5.14(b). The circuit model consists of a J-inverter network with susceptance (J) in
the middle part and two feed lines in the two end-sides as in Figure 5.14(b). The middle
J-network, in relation to the coupling section with finger shape, is represented by a
frequency-dependent J-inverter susceptance (J) and two equal electrical lengths (?1 and
?2). The J-susceptance as well as two electrical lengths are derived in terms of the three
independent parameters of an Y-matrix, B11, B12=B21, and B22.
- 100 -
B12 cos ?2
J
??
cos ?1 ? B11 cos ?1
Y1Y2
tan ??1 ? ?
tan ??2 ? ?
2 ? B11 ? B22 B ?
1 ? B222 ? B112 ? B
2
Eq. 5.7
2
Eq. 5.8
2 ? B22 ? B11 B ?
1 ? B112 ? B222 ? B
Eq. 5.6
where B11=B11/Y1, B22=B22/Y2, B12=B12/?(Y1Y2), and |B|2=B11B22-B122.
The conventional UWB bandpass filter shown in Figure 5.12 is constructed by
combining the open-ended CPW resonator in the middle and an edge coupled CPW at the
two ends. To achieve the specified UWB passband, the three sections of this MMR are
arranged to be approximately, half-, and quarter-wave length, i.e., ?g2/4, ?g1/2, and ?g2/4,
respectively.
5.2.2.2
Modified Open-Ended MMR
The modified MMR replaces the regular 50? CPW for the low impedance section
of the conventional MMR, shown in Figure 5.13(a), with a 50 ? slow wave CPW as
shown in Figure 5.15. This slow wave CPW, used as a low-impedance section, is
designed based on a regular 50? CPW with signal line width of 2mm, gap width of
0.9mm, and ground width of 5mm on Rogers?s Duroid RO3010 (?r=10.2) with thickness
of 1.27mm (50mils). To increase the effective dielectric constant of the slow wave CPW
- 101 -
Figure 5.15. Schematic and geometric parameters of the modified open-ended multiple mode
resonator (MMR) using the slow wave structure (w4=0.8mm, g5=0.2mm).
and to maintain its characteristic impedance, the inductance and capacitance per unit
length are increased for the same ratio as describe in the Chapter 3.
Figure 5.16(b) compares the slow wave factor of the designed 50? CPW
compared to the reference straight CPW which consists of a signal line of 2mm, gap of
0.9mm, and ground planes of 5mm. The length of unit cell of the designed slow wave
CPW 0.7mm. The finger-shaped pattern on the ground plane is 0.2mm x 1.1mm, and the
finger-shaped patterns on the signal line is 0.2mm x 0.9mm. The dimensions of the slow
wave CPW is summarized in Table 5.3. As shown in Figure 5.16, the slow wave factor of
the designed 50? slow wave CPW is in a range from 4.4 to 5 which is approximately
double of the regular CPW fabricated on the same substrate. Therefore, the low
impedance section of the CPW MMR can be reduced in size by approximately 50%. The
estimated length of the slow wave CPW, located in the middle section, is about 4.9mm
(0.5 ?g at 6.86GHz).
- 102 -
Table 5.3. Dimensions of the slow wave CPW used in the middle of the CPW MMR. The
geometrical parameters are described in Figure 5.11. Unit of all values is millimeters.
S
G
Wg
S1
FW1
FW2
FL3
g2
g3
2
0.9
5
0.1
0.2
0.2
1.1
0.5
0.5
6
Slow wave CPW (Part A in Fig. 1)
CPW
5
??k
4
3
2
1
2
4
6
8
10
12
Frequency (GHz)
Figure 5.16. (a) Geometry of a slow wave CPW and (b) slow wave factor of the reference CPW
and slow wave CPW developed.
The three resonant frequencies of the modified open-ended slow wave CPW
MMR shown in Figure 5.17 are controlled by two parameters, the admittance ratio of two
dissimilar sections and the length of three sections, like the conventional open-ended
stepped impedance MMR. To analyze its frequency characteristics, the modified MMR is
simulated for different dimensions. The simulation results are summarized in Figure 5.17.
As the length (L1= L2) of three sections is increased, all three resonant frequencies
decrease as expected. For fixed value of L1 and L2, the second and third frequencies
- 103 -
12
f3
f1, f2, and f3 (GHz)
10
8
f2
6
f1
4
2
0
g4=0.9mm
g4=2mm
g4=3mm
4.0
4.5
5.0
5.5
L1=L2 (mm)
Figure 5.17.The first three resonant frequencies of the modified open-ended slow wave MMR
for different geometric sizes. The electrical length of the middle section is about double of that
of the side sections even though the physical length of both sections is the same.
decrease as the slot width (g4) increases. For UWB filtering performance, three resonant
frequencies have to be placed between the lower and upper end of the UWB passband,
and thus L1=L2=5.1 mm, and g4=1.5 mm are chosen from Figure 5.17.
5.2.2.3
Compact Coupled Line
Figure 5.18 shows a compact coupled line with meandered slots to be used for the
high impedance section. The physical length of the conventional ╝ ?g coupled line is
reduced by meandering the slot of the coupled line. This modified coupled line is
simulated for different dimensions to obtain at least 110% UWB passband. The
relationship between the geometric parameters and upper and lower 3dB cut-off
- 104 -
Figure 5.18. Schematic of two modified interdigitated coupled lines with meandered slots for
different lengths based on part B in Fig. 1 (S=2mm, G=0.9mm, Wg=5mm, FL1=FL2=0.65mm-w3,
w1=0.4mm, w2=0.2mm, g1=0.15mm). (a) Design 1: L1=2.95mm and (b) Design 2: L1=2.25mm.
frequencies are summarized in Figure 5.19. As the slot length is reduced by increasing
the value of w3, both upper and lower cut-off frequencies increase. The upper cut-off
frequencies are more sensitive on both the total slot length and the physical length of the
coupled line than the lower cut-off frequencies. However, both cut-off frequencies barely
change with g4. From the simulation results, L1=2.95mm and w3=0.2mm are chosen.
Finally, a new compact CPW-fed UWB filter shown in Figure 5.11 is constructed by
combining the modified open-ended slow-wave CPW stepped impedance MMR, shown
in Figure 5.15, with the two compact coupled lines with meandered slots, shown in
Figure 5.18.
- 105 -
14
Frequency (GHz)
12
10
fU 3dB
L1=2.95mm, g4=1mm
L1=2.95mm, g4=2mm
L1=2.25mm, g4=1mm
L1=2.25mm, g4=2mm
8
6
4
fL 3dB
2
0
0.2
0.3
0.4
0.5
0.6
W3
Figure 5.19. Lower and upper 3-dB cut-off frequencies of the two modified coupled lines shown
in Fig. 5.
5.2.3
Simulation and Measurement Results
The geometric parameters of the proposed UWB bandpass filter, shown in Figure
5.11, is optimized to take into account the combination effects of the slow wave CPW in
the middle section and the compact coupled lines on the sides. The optimized UWB
bandpass filter is fabricated using a LPKF Protomat C60 system, is 11 mm long (without
the feed lines), and is shown in Figure 5.20. As can be seen in Figure 5.20, the proposed
UWB bandpass filter is approximately 40% shorter than the conventional
UWB
bandpass filter shown in Figure 5.12. The dimensions of the proposed UWB bandpass
filter are summarized in Table 5.4.
- 106 -
Figure 5.20. Photograph of the fabricated UWB bandpass filter and a penny
Table 5.4. Dimensions of the miniaturized UWB bandpass filter shown in Figure 5.20.
S
2mm
FW1
0.2mm
g4
1.5mm
G
0.9mm
FW2
0.2mm
w1
0.4mm
Wg
5mm
FL3
1.1mm
w2
0.2mm
L1
2.95mm
g1
0.15mm
w3
0.2mm
L2
5.1mm
g2
0.5mm
S1
0.2mm
g3
0.5mm
The simulated and measured insertion and return loss of the proposed UWB filter
are shown and compared in Figure 5.21. As can be seen in Figure 5.21, the proposed
UWB filter has realized the UWB passband requirement specified by FCC (3.1GHz 10.6GHz), and the measurement results are similar to the simulation results. Within the
passband the insertion loss is less than 1dB, and return loss is below -10 dB over the
entire passband. The simulated group velocity varies in a range of 0.15ns to 0.39ns, and
- 107 -
0
S11 and S21 (dB)
-10
-20
-30
S11, simulated
S21, simulated
S11, measured
S21, measured
-40
-50
2
4
6
8
10
12
Frequency (GHz)
Figure 5.21. Simulated and measured insertion and return loss of the UWB bandpass filter.
1.0
Group Delay (ns)
0.5
0.0
-0.5
Measurement
Simulation
-1.0
-1.5
2
4
6
8
10
Frequency (GHz)
Figure 5.22. Simulated and measured group delay of UWB bandpass filter.
- 108 -
12
the maximum variation in the group velocity in the UWB passband is about 0.24ns. The
measured group velocity is in the range of 0.21ns to 0.40ns since it includes the feed lines
and SMA connectors. Thus, the proposed filter has a very good linearity of signal transfer
compared to the conventional CPW design [33], whose group velocity variation is in a
range of 0.25ns to 0.58ns with maximum variation of 0.33ns.
5.3
Summary
In this chapter, two compact filters, CPW EBG structure and UWB bandpass filter,
are presented and studied. Miniaturization of these two filters is realized by using slow
wave structures and/or meandered coupled lines. Both CPW EBG structure and UWB
bandpass filter on CPW reduce their size approximately by 40% while maintaining filters?
performances including low insertion loss and small group delay variation.
- 109 -
CHAPTER 6
MINIATURIZED ANNULAR RING SLOT ANTENNAS
Recently, several types of annular slot antennas for achieving dual or multiple
bands or wide band have been studied [41-45]. However, these antennas have large
dimensions and thus are not suitable for wireless communication systems of small handheld devices. Only a few compact designs for annular slot antennas have been studied in
the literature [46-48]. The size of the antennas in [46-48] is reduced using a couple of
design methodologies such as capacitive loading [46], artificial dielectric lens [47], and
triangular slot with a protruded tuning stub [48].
In this chapter, two compact designs for single- and dual-band CPW-fed annular
ring slot antennas are presented and studied. These antennas are smaller in size and easier
in fabrication than the previous designs in [46-48]. The reduction in size is achieved by
utilizing the inner area of the ring to form meandered-slot sections.
In the following sections, geometrical characteristics of both single- and dualband antennas are investigated, and their performance is evaluated by simulations and
measurements of return loss, far-field radiation patterns, and gains.
- 110 -
6.1
Ring Slot Antenna
The ring slot resonator was first proposed by Kawano and Tomimuro [9] for
measuring the dispersion characteristic of slotline. The ring slot structure is the
mechanical dual of the microstrip ring resonator as shown in Figure 6.1. The microstrip
ring is a microstrip segment bent to form a loop where the ring slot is slotline segment
bent to form a loop. Analysis of ring slot antenna can be found in [50]. To use the
structure as an antenna, the first order mode is excited as shown in Figure 6.2, and the
corresponding impedance seen by the voltage source will be real at the resonant
frequency.
A first order estimate of the resonant frequency can be derived from the
transmission line equivalent circuit of the ring slot. Since the structure is symmetrical, a
magnetic wall can be loaded across the ring as shown in Figure 6.3(a). This operation
yields the equivalent transmission line equivalent circuit as shown in Figure 6.3(b). At
the resonant frequency of the first order mode, the two lines are each half wavelength
long electrically. Knowledge of the mechanical length and the velocity factor allows the
calculation of resonance to within 10% to 15 % of the true frequency [50]. The smaller
the relative gap g/rav, the better the estimate will be. Using the standard spherical
coordinates point (R, ? and ?) at which the fields are measured, the far-field equations of
electric fields are
e jk0 r j n e jn? ?
? E0 ? k sin ? ? ??
2 ?
r
Eq. 6.1
e jk0 r j n ?1e jn?
cos ? ?? E? e ? k sin ? ? ??
2
r
Eq. 6.2
E? ? r , ? , ? ? ? ? k0
E? ? r , ? , ? ? ? ? k0
- 111 -
Figure 6.1. Comparison of (a) microstrip ring and (b) slot ring structures.
+
V
Figure 6.2. A slot ling antenna with a sinusoidal electric field distribution at the first resonance.
- 112 -
where ?? ? ???? ?? and their linear combination of Hankel-transformed estimates are
used
E? o ? k0 sin ? ? ? E?? ? ? ? k0 sin ? ? ? E?? ? ? ? k0 sin ? ?
Eq.6.3
E? e ? k0 sin ? ? ? E?? ? ? ? k0 sin ? ? ? E?? ? ? ? k0 sin ? ?
Eq. 6.4
where the (n▒1)-th order Hankel transform is given by
ro
E? ? ? ? ?? ? ? ? J n ?1 ?? r ? dr
ri
Eq. 6.5
where Jn(?r) is the n-th order Bessel function of the first kind, ? is the Hankel-transform
variable, and ri and ro are the inner and outer ring radii, respectively. These integrals can
be evaluated analytically using tables. At the center of the ring, r=0, n is the order of
rsonance being analyzed. In the case of interest, n=1 and ?= ?0=the resonant frequency.
For the infinite thickness of the dielectric substrate, the preceding equations must be
modified for the better accuracy. The input impedance (Zin) at the feed point shown in
Figure 6.3(a) can be calculated by
? ? r ?2 ?
?ln ? 0 ? ?
? ? ri ? ??
Z in ? ?
P
Eq. 6.6
where P is the power given by
P?
??
sphere
1
2
2
E? ? E?
Z fs
where Zfs is the intrinsic impedance of free space.
- 113 -
2
ds
Eq. 6.7
(a)
(b)
Figure 6.3. Transmission line equivalent circuit of slot-ring antenna. (a) With magnetic wall
across slot ring. (b) Resulting transmission equivalent circuit.
(a)
(b)
(c)
Figure 6.4. Three possible feed configurations for the slot ring resonator: (a) microstrip coupling,
(b) slotline coupling, and (c) CPW coupling.
Coupling between the external feed line and slot-ring can be classified into three
types: microstrip coupling, CPW coupling, and slot-line coupling. Figure 6.4 shows three
possible coupling schemes. Microstrip coupling that utilizes the microstrip to slot-line
transition is a capacitive coupling. The lengths of input microstrip coupling stubs shown
- 114 -
in Figure 6.4(a) can be adjusted to optimize the loaded-Q values. However, less coupling
may affect the coupling efficiency and cause higher insertion loss. The trade-off between
the loaded-Q and coupling loss depends on the applications. The slotline ring coupled to
a slotline feed is an inductively coupled ring resonator. The metal gap between the
slotline ring and the external slotline feeds is used to couple magnetic field energy.
Therefore, the maximum electric field points of this resonator are opposite to those of the
capacitively coupled slotline ring resonator. Hence slotline fed slot-ring is the dual of the
microstrip fed slot-ring. The CPW-coupled slot-line ring resonator using CPW to slot-line
transition is also a capacitively coupled ring resonator. The CPW coupling is formed by a
small coupling gap between the external CPW feed lines and the slotline ring. The
loaded-Q value and insertion loss are dependent on the gap size. This type of slotline ring
resonator is truly planar and also allows easy series and shunt device mounting. In this
study, CPW coupling is used to feed signal to a slot-ring antenna. In the next section, a
single-band meandered annular ring slot antenna is presented and discussed.
6.2 Single-Band Meandered Annular Ring Slot Antenna
6.2.1
Design
Figure 6.5 shows the geometry of the proposed CPW-fed meandered annular ring
slot antenna printed on a substrate with relative permittivity of ?r and a thickness of h. As
shown in the Figure 6.5, the proposed antenna consists of a conventional annular ring of
radius R and additional meandered slots with its length parameter FL. The slot width of S
is fixed for both the annular ring slot and meandered slots. The angle between two
- 115 -
a
Figure 6.5. Geometries of the antenna designed in this study.
neighboring meandered slots is ?. The ground plane is extended 5mm from the edge of
the annular ring slot. The proposed antenna is fed by a 50 ? coplanar waveguide feed line
which has a center strip width of W and gap spacing of G.
The CPW feed line has a tuning stub of length t and is a distance g1 away from the
conducting strip in the center of the antenna. This tuning stub is used for matching of the
antenna. By controlling two geometrical parameters, the length (t) of the tuning stub and
the gap (g1) between the tuning stub and the conducting strip, impedance matching of the
antenna is obtained.
- 116 -
Test antennas are fabricated on a FR-4 substrate with relative permittivity of 4.4
and a thickness of 1.5mm (59mil). The proposed antenna with a radius of R=8mm is
simulated for different meandered slot length parameter FL from 0mm to 4mm using
Ansoft HFSS. For each meandered slot length parameter (FL), the tuning stub length (t)
and the gap (g1) between the tuning stub and the center conducting strip is optimized for
impedance matching. The geometries of the five designed antennas (Antenna 1 ? 5) are
summarized in Table 1.
Table 6.1. Dimensions of the five test antennas.
R
S
FL
?
t
g1
Antenna 1
8mm
0.6mm
0mm
-
4mm
0.4mm
Antenna 2
8mm
0.6mm
1mm
45░
4mm
0.2mm
Antenna 3
8mm
0.6mm
2mm
45░
4mm
0.1mm
Antenna 4
8mm
0.6mm
3mm
45░
3mm
0.5mm
Antenna 5
8mm
0.6mm
4mm
45░
4mm
0.1mm
Antenna 6
11.9mm
0.6mm
0mm
-
6mm
0.8mm
Note: W=3mm and G=0.4mm for all designs
6.2.2
Simulation and Measurement Results
The five designed antennas are fabricated on FR4 epoxy substrate using a LPKF
milling machine and are measured using an Anritsu network analyzer. The five test
antennas fabricated are shown in Figure 6.6.
- 117 -
Figure 6.6. Photograph of the fabricated test antennas (Antenna 1 ~ 5)
6.2.3
Return Loss
Figure 6.7 shows the measured return loss of the fabricated antennas. As shown in
Figure 6.7, the resonance frequency of the proposed antennas decreased from 4.27GHz to
2.82GHz due to increase in the total slot length by the meandered slots as the meandered
slot length parameter (FL) increases. The resonant frequency of the proposed antenna can
be decreased further by increasing the length of the meandered slots, but it is limited due
to the confined area of the inner conducting strip for a given radius (R). Moreover, the
proposed antenna tunes the resonant frequency maintaining the total size of the antenna
unlike a conventional annular ring slot antenna which requires change in the radius of the
ring slot.
6.2.4
Size Reduction
A conventional annular ring slot antenna (Antenna 6) which has the same
resonant frequency as the proposed antenna with R=8mm and FL=4mm (Antenna 5) is
designed and fabricated to compare their sizes. The conventional annular ring slot
- 118 -
0
Return Loss (dB)
-10
-20
FL=0mm
FL=4mm
-30
-40
Ant.1 (FL=0mm)
Ant.2 (FL=1mm)
Ant.3 (FL=2mm)
Ant.4 (FL=3mm)
Ant.5 (FL=4mm)
1
2
?f= 1.45 GHz
3
4
5
6
Frequency (GHz)
Figure 6.7. The measured return loss of the meandered annular ring slot antennas with different
meandered slot lengths.
antenna with R=11.9mm has the same resonant frequency with the targeted meandered
annular slot antenna. The conventional annular ring slot antenna and targeted meandered
annular ring slot antenna fabricated are shown in Figure 6.8, and their measured return
loss is plotted in Figure 6.9. Even though there is a slight difference between the resonant
frequency due to fabrication error by the milling machine, the measured return loss of the
two antennas is almost similar as shown in Figure 6.9. In contrast, the meandered annular
ring slot antenna is about 55% smaller than the conventional antenna when excluding the
ground plane. Even including the ground plane, the meandered annular ring slot antenna
is approximately 44% smaller than the conventional one.
- 119 -
Figure 6.8. Photograph of the fabricated antenna 5 (right) and 6 (left).
0
Return Loss (dB)
-10
-20
-30
Antenna 1 (R=8mm, FL=0mm)
Antenna 5 (R=8mm, FL=4mm)
Anteann 6 (R=11.9mm, FL=0mm)
-40
2
3
4
Frequency (GHz)
Figure 6.9. Measured return loss of the antenna 5 and 6.
- 120 -
5
90 (+y)
90 (+y)
-10
-10
-20
-20
0(+x)
180
270
0 (+z)
180
co-pol
cross-pol
x-y plane
270
y-z plane
(a)
90
90
180
0
180
0
270
270
(b)
Figure 6.10. Measured x-y plane (H-plane) and y-z plane (E-plane) radiation patterns for
Antenna 5 and 6. (a) Antenna 5 (f=2.82GHz) and (b) Antenna 6 (f=2.79GHz).
6.2.5
Far-Field Radiation Patterns
The far-field radiation patterns of the meandered annular ring slot antenna
(Antenna 5) and conventional annular ring slot antenna (Antenna 6) in both the x-y and
- 121 -
y-z planes were measured at their resonant frequency (2.82GHz and 2.79GHz
respectively) and are shown in Figure 6.10. As shown in Figure 6.10, the meandered
annular ring slot antenna has omnidirectional radiation patterns which are similar to the
conventional antenna. The cross-polarization level of the meandered annular ring slot
antenna is higher than conventional antenna because of the meandered slot in the center
strip.
The measured gain of the meandered ring slot antenna (Antenna 5) is 0.97dBi,
and the conventional antenna is 2.35dBi (Antenna 6). Decrease in the gain of the
meandered annular ring slot antenna is due to several reasons. First, meandering the ring
slot increase energy stored in the antenna and thus results in reduction in radiation
efficiency. Second, the physical size of the meandered ring slot antenna is smaller than
the conventional ring slot antenna.
6.3 Dual-Band Annular Ring Slot Antenna using Meandered Slots
In this section, a dual-band annular ring slot antenna that consists of a meandered
ring slot and a regular circular ring slot is presented and studied. To reduce the size of the
antenna, the inner slot of a conventional dual-band annular ring slot antenna is replaced
with the meandered ring slot discussed in the previous section. Incorporating the
meandered ring slot reduces the size by approximately 40% and enables easy tuning of
the resonant frequency created by the inner meandered ring slot.
- 122 -
Figure 6.11. Geometry of the proposed dual-band CPW-fed annular ring slot antenna with
meandered slot.
6.3.1
Design
Figure 6.11 shows the geometry of the proposed dual-band annular ring slot
antenna printed on a substrate with relative dielectric constant of ?r and a thickness of h.
As shown in Figure 6.11, the proposed antenna consists of two concentric ring slots with
radii of R1 and R2, respectively and is fed by a coplanar waveguide with signal strip width
of S and gap width of G. Unlike the conventional dual-band annular ring slot antenna in
[47], the inner slot of the proposed antenna is meandered to increase its total slot length.
The total length of the meandered inner slot is controlled by two geometrical parameters:
a length parameter FL and an angle ? between two neighboring meandered slots. The
- 123 -
Table 6.2. Geometric parameters of the test antennas and their frequency characteristics
FL
(mm)
T
(mm)
G1
(mm)
G2
(mm)
Reference
0
5
0.5
Antenna 1
0.5
5
Antenna 2
1.0
Antenna 3
Resonant frequency
Physical length
f1
(GHz)
f2
(GHz)
Outer slot
(mm)
Inner slot
(mm)
1.0
3.62
4.23
52.28
40.82
0.5
1.0
3.64
4.09
52.28
47.82
5
0.2
1.0
3.57
3.76
52.28
54.82
1.5
5
0.5
1.0
3.60
3.60
52.28
61.82
Antenna 4
2.0
5
0.5
1.0
3.52
3.34
52.28
68.82
Antenna 5
3.0
5
0.15
1.0
3.46
2.92
52.28
82.82
Antenna 6
4.0
5
0.2
1.0
3.46
2.68
52.28
96.82
R1=9.1mm, R2=8.0mm, S1=0.6mm, S2=0.6mm, ?=45░,S=3mm, G=0.4mm
coplanar waveguide used as a feeding structure is designed to have 50 ohm characteristic
impedance for measurement. The ground plane is extended 5mm from the edge of the
outer ring slot. The CPW feed line has a tuning stub of length t and is a distance g1 away
from the conducting strip in the center of the antenna. The ring conductor strip between
two ring slots is a distance g2 away from the CPW feed line. The proposed antenna is
matched to the source by adjusting three geometrical parameters (t, g1, and g2).
Test antennas are fabricated on FR-4 substrate with relative permittivity of 4.4
and thickness of 1.5mm (59mil). The radii R1 and R2 of the inner and outer ring slots are
fixed at 9.1mm and 8mm respectively, and the slot width S is 0.6mm. The total length of
the outer slot is approximately 52mm excluding the slot length due to the stub in the
CPW feed line, and the total length of the inner slot varies from 43mm to 68mm by
adjusting the length (FL) of the additional meandered slots. In this study, the length
- 124 -
Figure 6.12. Picture of the test antenna 6 fabricated on FR4 epoxy material.
parameter FL of the additional meandered slots for the inner ring slot varies from 0.5mm
to 4mm.
6.3.2
Simulation and Measurement Results
6.3.2.1
Fabrication of Test Antennas
Several test antennas with different values of FL are designed using Ansoft HFSS
to investigate the effects of the meandered inner slot. For each value of FL, the tuning
stub length (t), the gap (g1) between the tuning stub and the center strip, and gap (g2)
between the tuning stub and the circular conductor are optimized for impedance matching.
- 125 -
The geometries of one reference antenna (FL=0mm) and six test antennas (Antenna 1-6)
are summarized in Table 6.2
The test antennas were fabricated using a mechanical milling machine (LPKF
C30) and are measured using an Anritsu network analyzer. One of the fabricated test
antennas, Antenna 6, is shown in Figure 6.12.
6.3.2.2
Return Losses
The measured return loss of the test antennas are shown in Figure 6.13. As shown
in Figure 6.13, the first two resonant frequencies of the reference antenna are located at
f1=3.62GHz and f2=4.23GHz which are determined by the lengths of the outer and inner
ring slots respectively. As the meandered slot length parameter (FL) increases, the
resonant frequency f2, created by the inner meandered ring slot, shifts to a lower
frequency from 4.23GHz to 2.63GHz, while the resonant frequency f1, created by the test
antenna outer slot, remains nearly constant.
Variation of the first two resonant frequencies of the test antennas for different
values of FL is presented in Figure 6.14. As the value of FL increases from 0mm to 4mm,
the ratio of the first two resonant frequencies decrease from 1.17 to 0.77 due to an
increase
- 126 -
0
-10
-10
Return Loss (dB)
Return Loss (dB)
0
-20
f1
f2
fr1
-30
fr2
-40
-50
2.0
2.5
3.0
3.5
Frequency (GHz)
4.0
-50
2.0
4.5
f1
-30
-40
Reference (FL=0.0mm)
Antenna 1 (FL=0.5mm)
f2
-20
fr1
Reference (FL=0.0mm)
Antenna 2 (FL=1.0mm)
2.5
3.0
3.5
Frequency (GHz)
(a)
Return Loss (dB)
Return Loss (dB)
-10
Wide Band
f1
-20
-30
fr1
2.5
f2
3.0
3.5
Frequency (GHz)
-30
fr2
4.0
-50
2.0
4.5
f2
-20
-40
Reference (FL=0.0mm)
Antenna 3 (FL=1.5mm)
Wide Band
f1 fr1
2.5
3.0
3.5
Frequency (GHz)
-10
-10
f1
fr1
-30
-50
2.0
Return Loss (dB)
Return Loss (dB)
0
f2
fr2
4.5
f1
-20
f2
-30
fr1
fr2
-40
Reference (FL=0.0mm)
Antenna 5 (FL=3.0mm)
2.5
4.0
(d)
0
-20
fr2
Reference (FL=0.0mm)
Antenna 4 (FL=2.0mm)
(c)
-40
4.5
0
-10
-50
2.0
4.0
(b)
0
-40
fr2
Reference (FL=0.0mm)
Antenna 6 (FL=4.0mm)
3.0
3.5
Frequency (GHz)
4.0
4.5
-50
2.0
(e)
2.5
3.0
3.5
Frequency (GHz)
(f)
Figure 6.13. Measured return losses of the reference antenna and test antennas.
- 127 -
4.0
4.5
4.5
1.5
f2
3.5
1.0
f1
f2/f1
f2 / f1
Frequency (GHz)
4.0
3.0
2.5
0
1
2
3
4
0.5
FL (mm)
Figure 6.14. The first two resonant frequencies and its frequency ratio for different values of FL.
in the total length of the meandered inner slot. In conventional dual-band annular ring
slot antennas [47], the frequency ratio of the two resonant frequencies f1 and f2 is greater
than one due to the conducting strip between the inner and outer slots. In this case, it is
difficult to merge two operating bands.
The frequency ratio of the two resonant frequencies of the proposed dual-band
annular ring slot antenna can be easily controlled due to the meandered inner slot. As a
result, the ratio is generally less than one as shown in Figure 6.14. When adjusting the
frequency ratio to approximately nearly one, the two operating bands of the antenna are
merged and thus produce one wide operating band as shown in Figure 6.13 (c) and (d).
Moreover, meandering the inner slot of the dual-band annular ring slot antenna
enables size reduction in the total area of the dual-band ring slot antenna. For example,
- 128 -
the total area of the test antenna 6 excluding the ground plane is 40% smaller than the
conventional dual-band annular ring slot antenna which has the same resonant
frequencies. The conventional dual-band annular ring slot antenna has an outer slot radius
of 12mm while the test antenna 6 radius is 9.1mm.
6.3.2.3
Far-Field Radiation Patterns
The far-field radiations of the test antenna 6 with FL=4mm were measured for
two principal planes (x-y plane and x-z plane) in an anechoic chamber and are plotted in
Figure 6.15. As shown in Figure 6.15, the test antenna 6 radiates like an electrically small
dipole antennas for f1=3.55GHz and f2=2.76GHz, but the radiation patterns in the two
principal planes for the resonant frequencies are in opposite fashion due to the meandered
inner slot. For the resonant frequency f2=2.76GHz, the cross-polarization level is higher
than the conventional circular ring slot antenna due to change of direction of magnetic
current in the meandering the inner slot. The measured antenna gain of the test antenna 6
is 3.80dBi and 5.79dBi at f1=3.55GHz and f2=.276GHz respectively.
z
?= 0
x
?= 0
-y 270
90 y
90 x
-x 270
x-y plane
f1=3.65GHz
x-z plane
180
180
-x
-z
- 129 -
0
0
270
270
90
90
180
180
(a)
0
0
270
270
90
180
180
0
270
90
0
90
270
180
90
180
(b)
Figure 6.15. Measured radiation patterns of (a) the reference antenna (FL=0mm) and (b) antenna
6 (FL=4mm). The x-y plane is H-plane, and the y-z plane is E-plane.
- 130 -
6.4 Summary
In this chapter, two compact designs for single-band ring slot antenna and dualband ring slot antenna which are fed by a coplanar waveguide feed line with a tuning stub
are presented and experimentally studied. The experimental results demonstrate that the
size can be significantly reduced by introducing meandered slots to the conventional
annular ring slot and the resonant frequency can be adjusted without change in total area
size.
- 131 -
CHAPTER 7
CONCLUSION AND FUTURE WORK
This thesis has presents several design techniques for miniaturized passive
RF/microwave circuits such as interconnects, filters, and antennas. It has successfully
demonstrated the usefulness of the design techniques with simulations and measurements.
It has also introduced lumped element circuit models of an electromagnetic bandgap
(EBG) structure to analyze the EBG structure from a viewpoint of electric circuits.
Lumped element circuit models were developed to characterize the stopband
response of the EBG structures. The lumped element circuit models developed
significantly reduce analysis time compared to full-wave simulations while providing
accurate results, which were verified by simulation and measurement results.
Slow wave coplanar waveguides (CPWs) are used to control the effective
dielectric constant by adjusting geometrical parameters, to control the speed of
electromagnetic waves, and to reduce the size of passive circuits. Design guidelines for
slow wave CPWs on high resistivity silicon wafer were established, and these design
guide lines help a circuit designer to utilize the slow wave CPW in other applications.
- 132 -
The slow wave structure developed was incorporated in the short slot of 90░ CPW
circular bend and successfully suppressed the excitation of slot-line mode without wirebonds or air-bridges by equalizing the electrical length of the inner and outer slots of the
90░ circular bend, which reduces the fabrication cost. Another approach, fast-wave
method, was also developed to equalize the electrical length of the slots and to suppress
the excitation of slot-line mode. To match the electrical length, dielectric material of the
longer slot was removed using deep trenching process.
Slow wave approach for filter designs demonstrated on a high resistivity silicon
wafer and on FR4 epoxy material achieved approximately 40% reduction in length
compared with conventional filters. Two stopband filters of EBG type, which have high
impedance sections of different geometry, achieved 37.5% or 45.4% reduction in length
respectively compared with conventional ones. A miniaturized UWB bandpass filter was
also designed using slow wave CPWs and couples lines with meandered slots and
reduced its size by 40% compared to a conventional UWB filter designed based on CPW
MMR structure. Improvement in performance was also demonstrated with a decrease in
group delay.
The work on ring slot antennas demonstrated that the size of single- and dualband annular ring slot antennas can be significantly reduced by meandering the slot. It
was also shown that the meander ring slot antenna can control its resonant frequency by
adjusting the geometry of the antenna without increase in the total surface area.
- 133 -
7.1
Future Work
The slow- and fast-wave design approaches for right angled CPW bend structures
were successfully demonstrated on a high resistivity silicon wafer using standard
microelectronic fabrication process. Thus, it is also needed to demonstrate these wirebond free techniques on printed circuit board (PCB) that which has coarse accuracy in
fabrication because frequency response of effective dielectric constant of slow wave
CPWs depends on their size. Another natural question for wire-bond free techniques in
right-angled CPW bend structures is how to remove wire-bonds needed at 3 and 4 port
CPW circuits (i.e. T-junctions or CPW crosses). The slow wave approach can help
resolve this, but it may need another approach because there is different mechanisms that
create higher-order modes.
The meandered annular ring slot antenna achieved significant reduction in the
surface area in compared to a conventional ring slot antenna. The resonant frequency of
the meandered ring slot antenna is controlled by adjusting additional meandered slot
without change in the total surface area. The next step in the meandered ring slot antenna
is to develop a tunable antenna using varactors which control its resonant frequency
electrically.
The final step in this work is to implement a complete system, which consists of
active components, interconnects, filters and antennas, using design approaches discussed
in this work for the passive RF components. The EBG structure would be used to reduce
coupling between components of the system, and wire-bond free techniques would
- 134 -
reduce fabrication cost. Miniaturized filters and antennas would significantly shrink the
total size of the system.
- 135 -
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- 139-
APPENDIX A
Modeling
A.1
Dispersion Diagram
Dispersion diagrams of electromagnetic bandgap (EBG) structures are obtained
using the full-wave analysis tool, Ansoft?s HFSS 9.1. This section describes the solution
setup techniques of the HFSS to get the dispersion diagrams of EBG structures.
A.1.1
Optimetrics and Eigenmode Solver
The eigenmode solver in HFSS 9.1 enables direction calculation of the permitted
resonance frequencies for a unit cell structure. Computation can be performed over the
entire range of field relationship between linked boundary condition (LBC) pairs by using
Optimetrics. The Optimetrics interface automates the process of altering parametrically
the phase relationship of LBC pair?s to match each value in a table of desired
configuration setups and executing each resultant solution.
- 140 -
A.1.2
3D Model
Rogers
RO3010
vacuum
Rogers
RO3010
vacuum
vacuum
UNIT CELL
mm
1.15
12.5mm
EBG material
Figure A.1. Metallo-dielectric EBG structure and its unit cell. The metal plates place on the top
and bottom of the dielectric material.
The unit cell of the metallo-dielectric EBG structure is shown in Figure A.1.1
with dimension. The unit cell consists of a substrate of 12.5mm wide, 11.66mm long, and
1.15mm thick and three cylindrical holes arranged in triangle. The radius of the hole is
3mm. The top and bottom of the substrate are metal plates.
A.1.3
Material Setup
The material of each 3D object must be assigned in the setup materials category.
The cylindrical air holes and the substrate are set to the default values in the material. The
vacuum is used instead of air. The parameters of each material are shown in Table A.1.
Table A.1. Material parameters
Relative
permittivity
Relative
permeability
Bulk
conductivity
Dielectric
loss tangent
Magnetic
loss tangent
Vacuum
1
1
0
0
0
RO3010
10.2
1
0
0.0035
0
- 141 -
A.1.4
Boundaries/Sources Setup
The master and slave boundaries are assigned to the side faces of the substrate
with phase relationship (Figure A.2). The variables for the parametric analysis are the
phase relationship between each opposing pair of linked boundaries. By varying the
phase between the boundaries the permissible eigensolutions for each phase relationship
are calculated. Both the top and bottom conductors are selected as rectangular plane and
assigned perfect E (Figure A.3). The perfect E boundaries do not make a big simulation
difference compared with a finite conductivity of copper (5.8e7 S/m).
(a)
(b)
(c)
Figure A.2. Linked boundary condition and phase relationship fro HFSS eigensolution analysis.
(a) Phase relation between master and slave boundary conditions. (b) Master 1 and Slave 1. (c)
Master 2 and Slave 2.
Figure A.3. Perfect E boundaries are assigned to the top and bottom face of the substrate.
- 142 -
A.1.5
Solution Setup
To calculate the resonances of a structure the eigenmode solver is selected as a
solution type, and the details of the solution setup are shown in Figure A.4. The minimum
resonance frequency is 0.1GHz, and number of modes that we are interested in is 3. The
eigenmode solver will find the first three resonance frequencies.
Figure A.4. Solution setup for calculating resonance frequencies of the EBG structure.
Figure A.5. Setup sweep analysis of Optimetrics.
- 143 -
To find the resonance frequency with different phase relationship, Optimetric
setup is shown as shown in Figure A.5. The parametric setup shown in Figure A.5 is for a
plot of possible solution frequencies in the ? to X direction. For this direction, the phase
between the first pair of LBCs is held at zero and the phase between the second pair is
varied from 0? to 180?.
A.1.6
Dispersion Diagrams in x and y directions
For a plot of possible solutions frequencies in x direction, the phase between the
first pair of LBCs is held constant at zero (Phase 1) and the phase between the second
pair is varied from 0? to 180? (Phase 2). For solution frequencies in y direction, the phase
between the second pair of walls is held zero (Phase 2) while the phase between the first
pair is incremented from 0? to 180? (Phase 1). The results of this analysis are shown in
Figure A.6. The horizontal axis of each graph represents the changing phase variable, and
is analogous to having the wave vector plotted in a true dispersion diagram. The bandgap
in x direction is approximately 4.69GHz to 6.2GHz, and the bandgap in y direction is
approximately 5.5GHz to 6.56GHz.
- 144 -
12
10
Frequency (GHz)
8
6
4
2
0
mode 1
mode 2
mode 3
0
20
40
60
80
100
Phase (Deg)
120
140
160
180
(a)
12
10
Frequency (GHz)
8
6
4
2
0
mode 1
mode 2
mode 3
0
20
40
60
80
100
Phase (Deg)
120
140
160
180
(b)
Figure A.6. The dispersion diagrams of the EBG structure shown in Figure A.1 about x an y
directions. (a) x-direction. (b) y-direction.
- 145 -
APPENDIX B
FABRICATION
Fabrication of all designs in this thesis is described in this section. All test circuits
are fabricated using either printed circuit board (PCB) techniques or stand
microelectronic fabrication techniques. All fabrication on on-wafer circuits was done at
the Nanofabrication Center (NFC) at the University of Minnesota, Twin Cities.
B.1
Parallel Plate EBG Structure
The parallel plat EBG structures shown in Figure 2.10 are fabricated on Rogers
RO 3010 laminate with dielectric constant of 10.2 and thickness of 1.15mm using printed
circuit board (PCB) techniques. The first step of the fabrication is to draw layouts of topside and bottom-side of the EBG structure and to convert them to the board plotter files.
AutoCAD 98LT is used for layout, and CircuitCam 4.0 is used to convert the layout files.
The next step is milling and drilling processes. These processes are done with the LPKF
ProtoMat C60 milling machine shown in Figure B.1 . The air holes are made from the
bottom side using drill bits, and the feed lines are formed from the top-side using milling
- 146 -
bits. The final step of the fabrication is assembly. The conductive copper tape with
conductive adhesive provided from 3M is attached on the both top- and bottom-sides. To
minimize the effect of air bubbles between the substrate and the copper tape the assembly
is put under sufficient pressure. Figure B.2 shows how to attach the copper tape on the
substrate.
Figure B.1. LPKF ProtoMat C60 milling machine.
- 147 -
Figure B.2. Assembly of the parallel plate EBG structure.
B.2
Fabrication Recipe #1
This recipe is used to fabricate slow wave CPWs, right angled CPW bend
structures with slow wave compensation and CPW EBG structures.
- Number of Mask: 1
- Wafer Side: Front
1. Solvent clean wafer
(a) Soak 1 minute in acetone
(b) Soak 1 minute in isopropyl alcohol
(c) Soak 1 minute in methanol
- 148 -
(d) Rinse in DI water and air-dry with N2 gun
2. Deposit seed layers using the AJA sputter or the CHA evaporator
(a) Ti (400┼) / Au (1500┼) / Ti (400┼)
3. Photolithography
(a) Prebake on 115░C hotplate for 1 min
(b) Vapor prime HMDS (1min)
(c) Spin Shipley 1045 photoresist on the wafer at 500rpm for 15 sec, then
4500rpm for 40 sec (3.5?m)
(d) Soft bake the photoresist on 105░C for 1 min
(e) Hard contact align (MA6/BA6 aligner) and expose 15 sec
(f) Develop in Shipley MF351:DI 1:5 for 1min 30 sec
(g) Rinse in rinse tank for 1 min and air dry with N2
4. Measure resist thickness using Dektek
5. Electroplate the Au to 3?m thick
(a) Heat bath to 70░C
(b) Calculate the current to obtain a density of 2mA/cm2
(c) Set current to calculated value
(d) Electroplate about 30 min for 3?m of gold
(e) Rinse in rinse tank and air dray with N2
6. Measure the thickness of plated gold using Dektek
7. Remove the photoresist using acetone
8. Remove the seed layers
- 149 -
(a) Remove Ti seed layer with 1:10 HF:DI for 3 sec
(b) Rinse in rinse tank
(c) Remove Au seed layer with GE6 for 20 sec
(d) Rinse in rinse tank
(e) Remove Ti seed layer with 1:10 HF:DI for 3 sec
(f) Rinse in rinse tank and air dry with N2
B.3
Fabrication Recipe #2
This recipe is used to fabricate right angled CPW bend structures with fast wave
compensation.
- Number of Mask: 2
- Wafer Side: Front
1. Solvent clean wafer
(a) Soak 1 minute in acetone
(b) Soak 1 minute in isopropyl alcohol
(c) Soak 1 minute in methanol
(d) Rinse in DI water and air-dry with N2 gun
2. Deposit seed layers using the AJA sputter or the CHA evaporator
(a) Ti (400┼) / Au (1500┼) / Ti (400┼)
3. Photolithography
(a) Prebake on 115░C hotplate for 1 min
- 150 -
(b) Vapor prime HMDS (1min)
(c) Spin Shipley 1045 photoresist on the wafer at 500rpm for 15 sec, then
4500rpm for 40 sec (3.5?m)
(d) Soft bake the photoresist on 105░C for 1 min
(e) Hard contact align (MA6/BA6 aligner) and expose 15 sec
(f) Develop in Shipley MF351:DI 1:5 for 1min 30 sec
(g) Rinse in rinse tank for 1 min and air dry with N2
4. Measure resist thickness using Dektek
5. Electroplate the Au to 3?m thick
(a) Heat bath to 70░C
(b) Calculate the current to obtain a density of 2mA/cm2
(c) Set current to calculated value (20mA)
(d) Electroplate about 30 min for 3?m of gold
(e) Rinse in rinse tank and air dray with N2
6. Measure the thickness of plated gold using Dektek
7. Remove the photoresist using acetone
8. Remove the seed layers
(a) Remove Ti seed layer with 1:10 HF:DI for 3 sec
(b) Rinse in rinse tank
(c) Remove Au seed layer with GE6 for 20 sec
(d) Rinse in rinse tank
(e) Remove Ti seed layer with 1:10 HF:DI for 3 sec
- 151 -
(f) Rinse in rinse tank and air dry with N2
9. Photolithgoraphy
(a) Prebake on 115░C hotplate for 1 min
(b) Spin Shipley 1813 photoresist on the wafer frontside at 2500rpm for
30 sec (1.3?m)
(c) Soft bake the photoresist on 105░C for 1 min
(d) Hard contact align (MA6/BA6 aligner) and expose 6 sec
(e) Develop in Shipley MF351:DI 1:5 for 30 sec
(f) Rinse in rinse tank for 1 min and air dry with N2
10. Deep Trenching
(a) Deep trench etch the wafer for 18 min 40 sec (targeting depth: 55?m)
(b) Remove the photoresist using acetone
(c) Rinse in DI water and air dry with N2
(d) Dry on 115░C hotplate for 1min
- 152 -
APPENDIX C
TEST AND MEASUREMENT
C.1
Measurement Apparatus
All circuits fabricated on silicon wafers are measured using a HP8510C automatic
network analyzer (ANA) connected on Cascade Microtech/Alessi RF1 microwave onwafer probe station with Cascade GSG250 probes (250?m pitch, ground-signal-ground,
air coplanar waveguide) as shown in Figure C.1. The wafer is placed on the vacuum
chuck, and the probes are connected via 2.4mm coaxial cable to the ANA. The network
analyzer processes the S-parameter data, and the data is transferred to the computer by
the software WinCal. Two calibration techniques used are the LRM and the NIST?s
MultiCal TRL (Through-Reflect-Line) de-embedding calibration depending on the
circuits. Calibration standards are designed on each wafer as required. The LRM
calibration technique, which moves the reference plane to the tip of the probes, uses an
ISS calibration chip.
- 153 -
HP8510C
2.4mm cable
Microscope
DUT
Cascade probe Grounded chuck
Probe station
Figure C.1. HP 8510C network analyzer with Cascade MicroTech probe station used for on-wafer
devices.
Circuits fabricated on printed circuit boards such as FR4, RO3010, RO6010 using
a milling machine, LPKF C60, are measured an Anritsu 37369D network analyzer or
HP3510C network analyzer. All circuits are measured through SMA connectors mounted
on the circuits except the parallel plate EBG waveguides. The parallel plate EBG
waveguide is measured using a microstrip test fixture shown in Figure C.2. Standard one
port or full two port calibrations are performed with the Anritsu K-calibration kit (Model
3652) for antennas and filters. The TRL calibrations are performed with Inter-Continental
Microwave calibration kit (ICM TRL-303B), shown in Figure C.3, for the parallel plate
EBG waveguide.
- 154 -
Figure C.2. EBG waveguide placed in the microstrip fixture.
Figure C.3. Inter-Continental Microwave calibration kit.
- 155 -
C.2
TRL Calibration
The Thru-Reflect-Line (TRL) calibration technique is used to move the reference
planes at the inputs to the devices and to remove the effects of the feed lines, cables, and
probes. The TRL calibration is performed using the calibration standards fabricated on
the same silicon wafer on which the devices are located. The calibration standards used in
this thesis consists of three delay lines that cover the band of interest from 1GHz to
50GHz, an open and/or a short, and a thru line. In this work, the open standard is used as
the reflect standard.
Figure C.4 shows the TRL calibration standards used. The through line is 1400um,
and the reference plane is located at the middle of the through-line. Each delay line
includes feedline of length, 700um, at each port. The delay line must cover the desired
bandwidth where relative phase (?l) is constrained between 45░ and 135░. The function of
sin(?l) of each delay line is plotted to determine the bandwidth of each line at Figure C.5.
As can be seen in Figure C.5, three delay lines of L1=900um, L2=2500um, and L3=700
covers the frequency band from 0.2GHz to 50GHz. These calibration standards designed
are used for CPW EBG structures, slow wave CPWs, and right angled CPW bend
structures with slow- or fast-wave methods.
- 156 -
Figure C.4. TRL calibration standards for on-wafer circuits.
?
?
Figure C.5. The sinusoidal response of three delay line. y ? sin ? ldelay lines 1,2,3 .
- 157 -
C.3
Antenna Measurement
C.3.1
Far-field Radiation Pattern
Once the resonant frequencies of the antennas are measured, far-field radiation
patterns are taken to characterize the operational performance of each antenna. These
measurements are obtained using the indoor anechoic test chamber at the University of
Minnesota. The test set-up is shown in Figure C.6. The Anritsu 37369D network analyzer
is connected to the turn-table on which the antenna under test sets. The computer in the
system is used to control the turn-table and to take data from Anritsu network analyzer
with the measurement software DAMs Model 5000. The LNA, which is designed to work
up to 18GHz with average gain of approximately 38dB, is used to amplify the receive
signal from the AUT.
For the far-field radiation pattern measurements, the anechoic chamber is
arranged such that the source remains stationary as the antenna under test (AUT) rotates
on the turn table. Principal far-field radiation patterns consist of collinear polarization
(co-pol) and cross polarization (cross-pol) plots, which are broken into either E-plane or
H-plane cuts. The polarization of the radiation pattern measurement, either collinear or
cross, is defined by the polarization of the source antenna. The source antennas used are
standard rectangular aperture horn antennas. Thus, to obtain an E-plane co-polarization
radiation patterns, the electric fields of both antennas must aligned parallel (collinear) and
then the turn-table must rotate 360 degrees along the E-plane of the antennas. E-plane
cross-pol is obtained by rotating the transmit antenna 90 degrees such that the E-field
- 158 -
align anti-parallel, and then scanning the turn-table. Likewise, H-plane co-pol is
measured when the H-field
(a)
(b)
Figure C.6. Antenna test set-up. (a) Configuration of the anechoic chamber system and (b) AUT
mounted on the turn-table which is connected a LNA.
- 159 -
align parallel. H-plane cross-pol is measure when the H-fields align anti-parallel. Figure
C.7 illustrates the required antenna alignments to obtain the desired polarization
measurement.
Photo illustrates
(a) H-plane co-pol: H fields of antennas
??
E
are
???
H
??
E
aligned parallel.
(b) H-plane cross-pol: rotate source
antenna
by 90░. H-fileds are aligned antiparallel
Photo illustrates
???
H
(a) E-plane cross-pol: E-fields of
??
E
??
E
antennas
are aligned anti-parallel.
(b) E-plane co-pol: rotate source antennas
by 90░. E-fields are aligned parallel
Figure C.7. Alignment of the AUT and source to obtain desired polarization measurements.
C.3.2
Gain Measurement
The gain of the antenna is measured by the comparison method using standard
gain antenna whose gain and reflection coefficient are known accurately. The power
- 160 -
received by the standard gain antenna and the test antenna are measured, respectively,
under the same condition as shown in Figure C.8. Eq. C.1 and Eq. C.2 describes how the
gain of an antenna is determined using the comparison method.
Figure C.8. Comparison method (gain transfer technique) for gain measurement using a standard
gain antenna.
GT
?
?G
?
P ?1 ? ? ?
PT 1 ? ? S
2
2
S
Eq. C.1
S
T
?P
GT ? dB ? ? GS ? dB ? ? 10 log10 ? t
? Ps
? 1 ? ?T
?
?
10
log
?
10 ?
? 1? ?
?
S
?
?
?
2
?
?
2
? 1 ? ?T
? GS ? dB ? ? Pt (dB) ? Ps (dB ) ? 10 log10 ?
? 1? ?
S
?
?
?
2
?
?
2
Eq. C.2
where GT is the gain of the test antenna, GS is the gain of the standard gain antenna, PT is
the power received by the test antenna, PS is the power received by the standard gain
antenna, ?T is the reflection coefficient of the test antenna, and ?S is the reflection
coefficient of the standard gain antenna.
- 161 -
ass filter in
this study. The proposed filter is composed of a slow wave CPW for a low-impedance
section in the middle of the design and a pair of coupled line structures with meandered
slots for two high-impedance sections at the input and output sides of the design. By
- 96 -
Figure 5.12 Conventional UWB bandpass filter designed based on coplanar waveguides.
using the slow wave CPW and meandered slots, the filter?s length is approximately 0.56
?g at the center of UWB passband and thus is about 40% shorter than the conventional
UWB filters in [33-34]. As a result, the group delay effects are reduced due to shorter
length of the UWB filter.
5.2.2.1
Conventional UWB Bandpass Filter of CPW Type
Figure 5.12 shows the geometry of the conventional UWB bandpass filter on
CPW which consists of an open-ended CPW multiple mode resonator (MMR) and two
edge coupled lines. This MMR has one low-impedance section in middle and two high
impedance sections in two sides. The high impedance sections are edge-coupled with the
signal line whose ground planes are widened as shown in Figure 5.12. To get a UWB
passband, the first three resonant modes are allocated near the lower-end, center, and
- 97 -
high-end of the targeted UWB frequencies, and the quarter-wave edge coupled line excite
two additional poles below and above the UWB's center or 6.85GHz.
Figure 5.13(a) depicts the open-ended CPW stepped impedance MMR. It is
composed of three distinctive sections, one low-impedance section in the middle and two
identical high-impedance sections insides. Figure 5.13(b) is its equivalent transmission
line network model, in which the two CPW step discontinuities are ignored since their
effects in fact rarely affect the UWB bandpass filter behavior. This CPW MMR aims to
make effective use of its lowest multiple resonant modes for wideband filter design. This
MMR resonator is very similar to SIR [40] in geometry and equilvalent topology, but it
should be emphasized here that the so-called SIR only uses the lowest or dominant
resonant mode in the design of narrow band filters with widened upper stopband.
The input admittance (Yin) at the left open-end, looking into the right side, as
indicated in Figure 5.13(b).
Yin ? jY2 ?
2 ? K tan ?1 ? tan ? 2 ?? K ? tan ?1 tan ? 2 ?
K ?1 ? tan 2 ?1 ??1 ? tan 2 ? 2 ? ? 2 ?1 ? K 2 ? tan ?1 tan ? 2
Eq. 5.2
where K=Y1/Y2 is the admittance ratio of two dissimilar sections in this MMR. At the
resonance, Yin=0 is valid. From Eq. 5.2, a set of algebraic equations are established to
solve all the resonant to solve all the resonant frequencies, including the three lowest
ones of interest, i.e. f1, f2, and f3. In this conventional design, electrical lengths of these
two sections are selected as ?1? ?2= ? such that the three separate closed-form equations
- 98 -
(a)
(b)
Figure 5.13. (a) Geometry and (b) equivalent circuit network of the open-ended CPW multiplemode resonator (MMR).
are deduced to individually determine f1, f2, and f3. As can been in Eq. 5.3-Eq. 5.5, the
lower and higher frequencies, f1 and f3, are mainly controlled by K, while the center f2
relies on the selected actual lengths of the three sections in this MMR.
? ? f1 ? ? tan ?1 K
? ? f2 ? ?
Eq. 5.3
?
Eq. 5.4
2
? ? f3 ? ? ? ? tan ?1 K
Eq. 5.5
- 99 -
(a)
(b)
Figure 5.14. (a) Geometry and (b) equivalent circuit model of an edge-coupled line.
Figure 5.14(a) describes the geometry of an edge-coupled line with enlarged
ground-to-ground distance which is a frequency distributed CPW element over 110%
UWB passband. The equivalent circuit model of this edge coupled line is shown in
Figure 5.14(b). The circuit model consists of a J-inverter network with susceptance (J) in
the middle part and two feed lines in the two end-sides as in Figure 5.14(b). The middle
J-network, in relation to the coupling section with finger shape, is represented by a
frequency-dependent J-inverter susceptance (J) and two equal electrical lengths (?1 and
?2). The J-susceptance as well as two electrical lengths are derived in terms of the three
independent parameters of an Y-matrix, B11, B12=B21, and B22.
- 100 -
B12 cos ?2
J
??
cos ?1 ? B11 cos ?1
Y1Y2
tan ??1 ? ?
tan ??2 ? ?
2 ? B11 ? B22 B ?
1 ? B222 ? B112 ? B
2
Eq. 5.7
2
Eq. 5.8
2 ? B22 ? B11 B ?
1 ? B112 ? B222 ? B
Eq. 5.6
where B11=B11/Y1, B22=B22/Y2, B12=B12/?(Y1Y2), and |B|2=B11B22-B122.
The conventional UWB bandpass filter shown in Figure 5.12 is constructed by
combining the open-ended CPW resonator in the middle and an edge coupled CPW at the
two ends. To achieve the specified UWB passband, the three sections of this MMR are
arranged to be approximately, half-, and quarter-wave length, i.e., ?g2/4, ?g1/2, and ?g2/4,
respectively.
5.2.2.2
Modified Open-Ended MMR
The modified MMR replaces the regular 50? CPW for the low impedance section
of the conventional MMR, shown in Figure 5.13(a), with a 50 ? slow wave CPW as
shown in Figure 5.15. This slow wave CPW, used as a low-impedance section, is
designed based on a regular 50? CPW with signal line width of 2mm, gap width of
0.9mm, and ground width of 5mm on Rogers?s Duroid RO3010 (?r=10.2) with thickness
of 1.27mm (50mils). To increase the effective dielectric constant of the slow wave CPW
- 101 -
Figure 5.15. Schematic and geometric parameters of the modified open-ended multiple mode
resonator (MMR) using the slow wave structure (w4=0.8mm, g5=0.2mm).
and to maintain its characteristic impedance, the inductance and capacitance per unit
length are increased for the same ratio as describe in the Chapter 3.
Figure 5.16(b) compares the slow wave factor of the designed 50? CPW
compared to the reference straight CPW which consists of a signal line of 2mm, gap of
0.9mm, and ground planes of 5mm. The length of unit cell of the designed slow wave
CPW 0.7mm. The finger-shaped pattern on the ground plane is 0.2mm x 1.1mm, and the
finger-shaped patterns on the signal line is 0.2mm x 0.9mm. The dimensions of the slow
wave CPW is summarized in Table 5.3. As shown in Figure 5.16, the slow wave factor of
the designed 50? slow wave CPW is in a range from 4.4 to 5 which is approximately
double of the regular CPW fabricated on the same substrate. Therefore, the low
impedance section of the CPW MMR can be reduced in size by approximately 50%. The
estimated length of the slow wave CPW, located in the middle section, is about 4.9mm
(0.5 ?g at 6.86GHz).
- 102 -
Table 5.3. Dimensions of the slow wave CPW used in the middle of the CPW MMR. The
geometrical parameters are described in Figure 5.11. Unit of all values is millimeters.
S
G
Wg
S1
FW1
FW2
FL3
g2
g3
2
0.9
5
0.1
0.2
0.2
1.1
0.5
0.5
6
Slow wave CPW (Part A in Fig. 1)
CPW
5
??k
4
3
2
1
2
4
6
8
10
12
Frequency (GHz)
Figure 5.16. (a) Geometry of a slow wave CPW and (b) slow wave factor of the reference CPW
and slow wave CPW developed.
The three resonant frequencies of the modified open-ended slow wave CPW
MMR shown in Figure 5.17 are controlled by two parameters, the admittance ratio of two
dissimilar sections and the length of three sections, like the conventional open-ended
stepped impedance MMR. To analyze its frequency characteristics, the modified MMR is
simulated for different dimensions. The simulation results are summarized in Figure 5.17.
As the length (L1= L2) of three sections is increased, all three resonant frequencies
decrease as expected. For fixed value of L1 and L2, the second and third frequencies
- 103 -
12
f3
f1, f2, and f3 (GHz)
10
8
f2
6
f1
4
2
0
g4=0.9mm
g4=2mm
g4=3mm
4.0
4.5
5.0
5.5
L1=L2 (mm)
Figure 5.17.The first three resonant frequencies of the modified open-ended slow wave MMR
for different geometric sizes. The electrical length of the middle section is about double of that
of the side sections even though the physical length of both sections is the same.
decrease as the slot width (g4) increases. For UWB filtering performance, three resonant
frequencies have to be placed between the lower and upper end of the UWB passband,
and thus L1=L2=5.1 mm, and g4=1.5 mm are chosen from Figure 5.17.
5.2.2.3
Compact Coupled Line
Figure 5.18 shows a compact coupled line with meandered slots to be used for the
high impedance section. The physical length of the conventional ╝ ?g coupled line is
reduced by meandering the slot of the coupled line. This modified coupled line is
simulated for different dimensions to obtain at least 110% UWB passband. The
relationship between the geometric parameters and upper and lower 3dB cut-off
- 104 -
Figure 5.18. Schematic of two modified interdigitated coupled lines with meandered slots for
different lengths based on part B in Fig. 1 (S=2mm, G=0.9mm, Wg=5mm, FL1=FL2=0.65mm-w3,
w1=0.4mm, w2=0.2mm, g1=0.15mm). (a) Design 1: L1=2.95mm and (b) Design 2: L1=2.25mm.
frequencies are summarized in Figure 5.19. As the slot length is reduced by increasing
the value of w3, both upper and lower cut-off frequencies increase. The upper cut-off
frequencies are more sensitive on both the total slot length and the physical length of the
coupled line than the lower cut-off frequencies. However, both cut-off frequencies barely
change with g4. From the simulation results, L1=2.95mm and w3=0.2mm are chosen.
Finally, a new compact CPW-fed UWB filter shown in Figure 5.11 is constructed by
combining the modified open-ended slow-wave CPW stepped impedance MMR, shown
in Figure 5.15, with the two compact coupled lines with meandered slots, shown in
Figure 5.18.
- 105 -
14
Frequency (GHz)
12
10
fU 3dB
L1=2.95mm, g4=1mm
L1=2.95mm, g4=2mm
L1=2.25mm, g4=1mm
L1=2.25mm, g4=2mm
8
6
4
fL 3dB
2
0
0.2
0.3
0.4
0.5
0.6
W3
Figure 5.19. Lower and upper 3-dB cut-off frequencies of the two modified coupled lines shown
in Fig. 5.
5.2.3
Simulation and Measurement Results
The geometric parameters of the proposed UWB bandpass filter, shown in Figure
5.11, is optimized to take into account the combination effects of the slow wave CPW in
the middle section and the compact coupled lines on the sides. The optimized UWB
bandpass filter is fabricated using a LPKF Protomat C60 system, is 11 mm long (without
the feed lines), and is shown in Figure 5.20. As can be seen in Figure 5.20, the proposed
UWB bandpass filter is approximately 40% shorter than the conventional
UWB
bandpass filter shown in Figure 5.12. The dimensions of the proposed UWB bandpass
filter are summarized in Table 5.4.
- 106 -
Figure 5.20. Photograph of the fabricated UWB bandpass filter and a penny
Table 5.4. Dimensions of the miniaturized UWB bandpass filter shown in Figure 5.20.
S
2mm
FW1
0.2mm
g4
1.5mm
G
0.9mm
FW2
0.2mm
w1
0.4mm
Wg
5mm
FL3
1.1mm
w2
0.2mm
L1
2.95mm
g1
0.15mm
w3
0.2mm
L2
5.1mm
g2
0.5mm
S1
0.2mm
g3
0.5mm
The simulated and measured insertion and return loss of the proposed UWB filter
are shown and compared in Figure 5.21. As can be seen in Figure 5.21, the proposed
UWB filter has realized the UWB passband requirement specified by FCC (3.1GHz 10.6GHz), and the measurement results are similar to the simulation results. Within the
passband the insertion loss is less than 1dB, and return loss is below -10 dB over the
entire passband. The simulated group velocity varies in a range of 0.15ns to 0.39ns, and
- 107 -
0
S11 and S21 (dB)
-10
-20
-30
S11, simulated
S21, simulated
S11, measured
S21, measured
-40
-50
2
4
6
8
10
12
Frequency (GHz)
Figure 5.21. Simulated and measured insertion and return loss of the UWB bandpass filter.
1.0
Group Delay (ns)
0.5
0.0
-0.5
Measurement
Simulation
-1.0
-1.5
2
4
6
8
10
Frequency (GHz)
Figure 5.22. Simulated and measured group delay of UWB bandpass filter.
- 108 -
12
the maximum variation in the group velocity in the UWB passband is about 0.24ns. The
measured group velocity is in the range of 0.21ns to 0.40ns since it includes the feed lines
and SMA connectors. Thus, the proposed filter has a very good linearity of signal transfer
compared to the conventional CPW design [33], whose group velocity variation is in a
range of 0.25ns to 0.58ns with maximum variation of 0.33ns.
5.3
Summary
In this chapter, two compact filters, CPW EBG structure and UWB bandpass filter,
are presented and studied. Miniaturization of these two filters is realized by using slow
wave structures and/or meandered coupled lines. Both CPW EBG structure and UWB
bandpass filter on CPW reduce their size approximately by 40% while maintaining filters?
performances including low insertion loss and small group delay variation.
- 109 -
CHAPTER 6
MINIATURIZED ANNULAR RING SLOT ANTENNAS
Recently, several types of annular slot antennas for achieving dual or multiple
bands or wide band have been studied [41-45]. However, these antennas have large
dimensions and thus are not suitable for wireless communication systems of small handheld devices. Only a few compact designs for annular slot antennas have been studied in
the literature [46-48]. The size of the antennas in [46-48] is reduced using a couple of
design methodologies such as capacitive loading [46], artificial dielectric lens [47], and
triangular slot with a protruded tuning stub [48].
In this chapter, two compact designs for single- and dual-band CPW-fed annular
ring slot antennas are presented and studied. These antennas are smaller in size and easier
in fabrication than the previous designs in [46-48]. The reduction in size is achieved by
utilizing the inner area of the ring to form meandered-slot sections.
In the following sections, geometrical characteristics of both single- and dualband antennas are investigated, and their performance is evaluated by simulations and
measurements of return loss, far-field radiation patterns, and gains.
- 110 -
6.1
Ring Slot Antenna
The ring slot resonator was first proposed by Kawano and Tomimuro [9] for
measuring the dispersion characteristic of slotline. The ring slot structure is the
mechanical dual of the microstrip ring resonator as shown in Figure 6.1. The microstrip
ring is a microstrip segment bent to form a loop where the ring slot is slotline segment
bent to form a loop. Analysis of ring slot antenna can be found in [50]. To use the
structure as an antenna, the first order mode is excited as shown in Figure 6.2, and the
corresponding impedance seen by the voltage source will be real at the resonant
frequency.
A first order estimate of the resonant frequency can be derived from the
transmission line equivalent circuit of the ring slot. Since the structure is symmetrical, a
magnetic wall can be loaded across the ring as shown in Figure 6.3(a). This operation
yields the equivalent transmission line equivalent circuit as shown in Figure 6.3(b). At
the resonant frequency of the first order mode, the two lines are each half wavelength
long electrically. Knowledge of the mechanical length and the velocity factor allows the
calculation of resonance to within 10% to 15 % of the true frequency [50]. The smaller
the relative gap g/rav, the better the estimate will be. Using the standard spherical
coordinates point (R, ? and ?) at which the fields are measured, the far-field equations of
electric fields are
e jk0 r j n e jn? ?
? E0 ? k sin ? ? ??
2 ?
r
Eq. 6.1
e jk0 r j n ?1e jn?
cos ? ?? E? e ? k sin ? ? ??
2
r
Eq. 6.2
E? ? r , ? , ? ? ? ? k0
E? ? r , ? , ? ? ? ? k0
- 111 -
Figure 6.1. Comparison of (a) microstrip ring and (b) slot ring structures.
+
V
Figure 6.2. A slot ling antenna with a sinusoidal electric field distribution at the first resonance.
- 112 -
where ?? ? ???? ?? and their linear combination of Hankel-transformed estimates are
used
E? o ? k0 sin ? ? ? E?? ? ? ? k0 sin ? ? ? E?? ? ? ? k0 sin ? ?
Eq.6.3
E? e ? k0 sin ? ? ? E?? ? ? ? k0 sin ? ? ? E?? ? ? ? k0 sin ? ?
Eq. 6.4
where the (n▒1)-th order Hankel transform is given by
ro
E? ? ? ? ?? ? ? ? J n ?1 ?? r ? dr
ri
Eq. 6.5
where Jn(?r) is the n-th order Bessel function of the first kind, ? is the Hankel-transform
variable, and ri and ro are the inner and outer ring radii, respectively. These integrals can
be evaluated analytically using tables. At the center of the ring, r=0, n is the order of
rsonance being analyzed. In the case of interest, n=1 and ?= ?0=the resonant frequency.
For the infinite thickness of the dielectric substrate, the preceding equations must be
modified for the better accuracy. The input impedance (Zin) at the feed point shown in
Figure 6.3(a) can be calculated by
? ? r ?2 ?
?ln ? 0 ? ?
? ? ri ? ??
Z in ? ?
P
Eq. 6.6
where P is the power given by
P?
??
sphere
1
2
2
E? ? E?
Z fs
where Zfs is the intrinsic impedance of free space.
- 113 -
2
ds
Eq. 6.7
(a)
(b)
Figure 6.3. Transmission line equivalent circuit of slot-ring antenna. (a) With magnetic wall
across slot ring. (b) Resulting transmission equivalent circuit.
(a)
(b)
(c)
Figure 6.4. Three possible feed configurations for the slot ring resonator: (a) microstrip coupling,
(b) slotline coupling, and (c) CPW coupling.
Coupling between the external feed line and slot-ring can be classified into three
types: microstrip coupling, CPW coupling, and slot-line coupling. Figure 6.4 shows three
possible coupling schemes. Microstrip coupling that utilizes the microstrip to slot-line
transition is a capacitive coupling. The lengths of input microstrip coupling stubs shown
- 114 -
in Figure 6.4(a) can be adjusted to optimize the loaded-Q values. However, less coupling
may affect the coupling efficiency and cause higher insertion loss. The trade-off between
the loaded-Q and coupling loss depends on the applications. The slotline ring coupled to
a slotline feed is an inductively coupled ring resonator. The metal gap between the
slotline ring and the external slotline feeds is used to couple magnetic field energy.
Therefore, the maximum electric field points of this resonator are opposite to those of the
capacitively coupled slotline ring resonator. Hence slotline fed slot-ring is the dual of the
microstrip fed slot-ring. The CPW-coupled slot-line ring resonator using CPW to slot-line
transition is also a capacitively coupled ring resonator. The CPW coupling is formed by a
small coupling gap between the external CPW feed lines and the slotline ring. The
loaded-Q value and insertion loss are dependent on the gap size. This type of slotline ring
resonator is truly planar and also allows easy series and shunt device mounting. In this
study, CPW coupling is used to feed signal to a slot-ring antenna. In the next section, a
single-band meandered annular ring slot antenna is presented and discussed.
6.2 Single-Band Meandered Annular Ring Slot Antenna
6.2.1
Design
Figure 6.5 shows the geometry of the proposed CPW-fed meandered annular ring
slot antenna printed on a substrate with relative permittivity of ?r and a thickness of h. As
shown in the Figure 6.5, the proposed antenna consists of a conventional annular ring of
radius R and additional meandered slots with its length parameter FL. The slot width of S
is fixed for both the annular ring slot and meandered slots. The angle between two
- 115 -
a
Figure 6.5. Geometries of the antenna designed in this study.
neighboring meandered slots is ?. The ground plane is extended 5mm from the edge of
the annular ring slot. The proposed antenna is fed by a 50 ? coplanar waveguide feed line
which has a center strip width of W and gap spacing of G.
The CPW feed line has a tuning stub of length t and is a distance g1 away from the
conducting strip in the center of the antenna. This tuning stub is used for matching of the
antenna. By controlling two geometrical parameters, the length (t) of the tuning stub and
the gap (g1) between the tuning stub and the conducting strip, impedance matching of the
antenna is obtained.
- 116 -
Test antennas are fabricated on a FR-4 substrate with relative permittivity of 4.4
and a thickness of 1.5mm (59mil). The proposed antenna with a radius of R=8mm is
simulated for different meandered slot length parameter FL from 0mm to 4mm using
Ansoft HFSS. For each meandered slot length parameter (FL), the tuning stub length (t)
and the gap (g1) between the tuning stub and the center conducting strip is optimized for
impedance matching. The geometries of the five designed antennas (Antenna 1 ? 5) are
summarized in Table 1.
Table 6.1. Dimensions of the five test antennas.
R
S
FL
?
t
g1
Antenna 1
8mm
0.6mm
0mm
-
4mm
0.4mm
Antenna 2
8mm
0.6mm
1mm
45░
4mm
0.2mm
Antenna 3
8mm
0.6mm
2mm
45░
4mm
0.1mm
Antenna 4
8mm
0.6mm
3mm
45░
3mm
0.5mm
Antenna 5
8mm
0.6mm
4mm
45░
4mm
0.1mm
Antenna 6
11.9mm
0.6mm
0mm
-
6mm
0.8mm
Note: W=3mm and G=0.4mm for all designs
6.2.2
Simulation and Measurement Results
The five designed antennas are fabricated on FR4 epoxy substrate using a LPKF
milling machine and are measured using an Anritsu network analyzer. The five test
antennas fabricated are shown in Figure 6.6.
- 117 -
Figure 6.6. Photograph of the fabricated test antennas (Antenna 1 ~ 5)
6.2.3
Return Loss
Figure 6.7 shows the measured return loss of the fabricated antennas. As shown in
Figure 6.7, the resonance frequency of the proposed antennas decreased from 4.27GHz to
2.82GHz due to increase in the total slot length by the meandered slots as the meandered
slot length parameter (FL) increases. The resonant frequency of the proposed antenna can
be decreased further by increasing the length of the meandered slots, but it is limited due
to the confined area of the inner conducting strip for a given radius (R). Moreover, the
proposed antenna tunes the resonant frequency maintaining the total size of the antenna
unlike a conventional annular ring slot antenna which requires change in the radius of the
ring slot.
6.2.4
Size Reduction
A conventional annular ring slot antenna (Antenna 6) which has the same
resonant frequency as the proposed antenna with R=8mm and FL=4mm (Antenna 5) is
designed and fabricated to compare their sizes. The conventional annular ring slot
- 118 -
0
Return Loss (dB)
-10
-20
FL=0mm
FL=4mm
-30
-40
Ant.1 (FL=0mm)
Ant.2 (FL=1mm)
Ant.3 (FL=2mm)
Ant.4 (FL=3mm)
Ant.5 (FL=4mm)
1
2
?f= 1.45 GHz
3
4
5
6
Frequency (GHz)
Figure 6.7. The measured return loss of the meandered annular ring slot antennas with different
meandered slot lengths.
antenna with R=11.9mm has the same resonant frequency with the targeted meandered
annular slot antenna. The conventional annular ring slot antenna and targeted meandered
annular ring slot antenna fabricated are shown in Figure 6.8, and their measured return
loss is plotted in Figure 6.9. Even though there is a slight difference between the resonant
frequency due to fabrication error by the milling machine, the measured return loss of the
two antennas is almost similar as shown in Figure 6.9. In contrast, the meandered annular
ring slot antenna is about 55% smaller than the conventional antenna when excluding the
ground plane. Even including the ground plane, the meandered annular ring slot antenna
is approximately 44% smaller than the conventional one.
- 119 -
Figure 6.8. Photograph of the fabricated antenna 5 (right) and 6 (left).
0
Return Loss (dB)
-10
-20
-30
Antenna 1 (R=8mm, FL=0mm)
Antenna 5 (R=8mm, FL=4mm)
Anteann 6 (R=11.9mm, FL=0mm)
-40
2
3
4
Frequency (GHz)
Figure 6.9. Measured return loss of the antenna 5 and 6.
- 120 -
5
90 (+y)
90 (+y)
-10
-10
-20
-20
0(+x)
180
270
0 (+z)
180
co-pol
cross-pol
x-y plane
270
y-z plane
(a)
90
90
180
0
180
0
270
270
(b)
Figure 6.10. Measured x-y plane (H-plane) and y-z plane (E-plane) radiation patterns for
Antenna 5 and 6. (a) Antenna 5 (f=2.82GHz) and (b) Antenna 6 (f=2.79GHz).
6.2.5
Far-Field Radiation Patterns
The far-field radiation patterns of the meandered annular ring slot antenna
(Antenna 5) and conventional annular ring slot antenna (Antenna 6) in both the x-y and
- 121 -
y-z planes were measured at their resonant frequency (2.82GHz and 2.79GHz
respectively) and are shown in Figure 6.10. As shown in Figure 6.10, the meandered
annular ring slot antenna has omnidirectional radiation patterns which are similar to the
conventional antenna. The cross-polarization level of the meandered annular ring slot
antenna is higher than conventional antenna because of the meandered slot in the center
strip.
The measured gain of the meandered ring slot antenna (Antenna 5) is 0.97dBi,
and the conventional antenna is 2.35dBi (Antenna 6). Decrease in the gain of the
meandered annular ring slot antenna is due to several reasons. First, meandering the ring
slot increase energy stored in the antenna and thus results in reduction in radiation
efficiency. Second, the physical size of the meandered ring slot antenna is smaller than
the conventional ring slot antenna.
6.3 Dual-Band Annular Ring Slot Antenna using Meandered Slots
In this section, a dual-band annular ring slot antenna that consists of a meandered
ring slot and a regular circular ring slot is presented and studied. To reduce the size of the
antenna, the inner slot of a conventional dual-band annular ring slot antenna is replaced
with the meandered ring slot discussed in the previous section. Incorporating the
meandered ring slot reduces the size by approximately 40% and enables easy tuning of
the resonant frequency created by the inner meandered ring slot.
- 122 -
Figure 6.11. Geometry of the proposed dual-band CPW-fed annular ring slot antenna with
meandered slot.
6.3.1
Design
Figure 6.11 shows the geometry of the proposed dual-band annular ring slot
antenna printed on a substrate with relative dielectric constant of ?r and a thickness of h.
As shown in Figure 6.11, the proposed antenna consists of two concentric ring slots with
radii of R1 and R2, respectively and is fed by a coplanar waveguide with signal strip width
of S and gap width of G. Unlike the conventional dual-band annular ring slot antenna in
[47], the inner slot of the proposed antenna is meandered to increase its total slot length.
The total length of the meandered inner slot is controlled by two geometrical parameters:
a length parameter FL and an angle ? between two neighboring meandered slots. The
- 123 -
Table 6.2. Geometric parameters of the test antennas and their frequency characteristics
FL
(mm)
T
(mm)
G1
(mm)
G2
(mm)
Reference
0
5
0.5
Antenna 1
0.5
5
Antenna 2
1.0
Antenna 3
Resonant frequency
Physical length
f1
(GHz)
f2
(GHz)
Outer slot
(mm)
Inner slot
(mm)
1.0
3.62
4.23
52.28
40.82
0.5
1.0
3.64
4.09
52.28
47.82
5
0.2
1.0
3.57
3.76
52.28
54.82
1.5
5
0.5
1.0
3.60
3.60
52.28
61.82
Antenna 4
2.0
5
0.5
1.0
3.52
3.34
52.28
68.82
Antenna 5
3.0
5
0.15
1.0
3.46
2.92
52.28
82.82
Antenna 6
4.0
5
0.2
1.0
3.46
2.68
52.28
96.82
R1=9.1mm, R2=8.0mm, S1=0.6mm, S2=0.6mm, ?=45░,S=3mm, G=0.4mm
coplanar waveguide used as a feeding structure is designed to have 50 ohm characteristic
impedance for measurement. The ground plane is extended 5mm from the edge of the
outer ring slot. The CPW feed line has a tuning stub of length t and is a distance g1 away
from the conducting strip in the center of the antenna. The ring conductor strip between
two ring slots is a distance g2 away from the CPW feed line. The proposed antenna is
matched to the source by adjusting three geometrical parameters (t, g1, and g2).
Test antennas are fabricated on FR-4 substrate with relative permittivity of 4.4
and thickness of 1.5mm (59mil). The radii R1 and R2 of the inner and outer ring slots are
fixed at 9.1mm and 8mm respectively, and the slot width S is 0.6mm. The total length of
the outer slot is approximately 52mm excluding the slot length due to the stub in the
CPW feed line, and the total length of the inner slot varies from 43mm to 68mm by
adjusting the length (FL) of the additional meandered slots. In this study, the length
- 124 -
Figure 6.12. Picture of the test antenna 6 fabricated on FR4 epoxy material.
parameter FL of the additional meandered slots for the inner ring slot varies from 0.5mm
to 4mm.
6.3.2
Simulation and Measurement Results
6.3.2.1
Fabrication of Test Antennas
Several test antennas with different values of FL are designed using Ansoft HFSS
to investigate the effects of the meandered inner slot. For each value of FL, the tuning
stub length (t), the gap (g1) between the tuning stub and the center strip, and gap (g2)
between the tuning stub and the circular conductor are optimized for impedance matching.
- 125 -
The geometries of one reference antenna (FL=0mm) and six test antennas (Antenna 1-6)
are summarized in Table 6.2
The test antennas were fabricated using a mechanical milling machine (LPKF
C30) and are measured using an Anritsu network analyzer. One of the fabricated test
antennas, Antenna 6, is shown in Figure 6.12.
6.3.2.2
Return Losses
The measured return loss of the test antennas are shown in Figure 6.13. As shown
in Figure 6.13, the first two resonant frequencies of the reference antenna are located at
f1=3.62GHz and f2=4.23GHz which are determined by the lengths of the outer and inner
ring slots respectively. As the meandered slot length parameter (FL) increases, the
resonant frequency f2, created by the inner meandered ring slot, shifts to a lower
frequency from 4.23GHz to 2.63GHz, while the resonant frequency f1, created by the test
antenna outer slot, remains nearly constant.
Variation of the first two resonant frequencies of the test antennas for different
values of FL is presented in Figure 6.14. As the value of FL increases from 0mm to 4mm,
the ratio of the first two resonant frequencies decrease from 1.17 to 0.77 due to an
increase
- 126 -
0
-10
-10
Return Loss (dB)
Return Loss (dB)
0
-20
f1
f2
fr1
-30
fr2
-40
-50
2.0
2.5
3.0
3.5
Frequency (GHz)
4.0
-50
2.0
4.5
f1
-30
-40
Reference (FL=0.0mm)
Antenna 1 (FL=0.5mm)
f2
-20
fr1
Reference (FL=0.0mm)
Antenna 2 (FL=1.0mm)
2.5
3.0
3.5
Frequency (GHz)
(a)
Return Loss (dB)
Return Loss (dB)
-10
Wide Band
f1
-20
-30
fr1
2.5
f2
3.0
3.5
Frequency (GHz)
-30
fr2
4.0
-50
2.0
4.5
f2
-20
-40
Reference (FL=0.0mm)
Antenna 3 (FL=1.5mm)
Wide Band
f1 fr1
2.5
3.0
3.5
Frequency (GHz)
-10
-10
f1
fr1
-30
-50
2.0
Return Loss (dB)
Return Loss (dB)
0
f2
fr2
4.5
f1
-20
f2
-30
fr1
fr2
-40
Reference (FL=0.0mm)
Antenna 5 (FL=3.0mm)
2.5
4.0
(d)
0
-20
fr2
Reference (FL=0.0mm)
Antenna 4 (FL=2.0mm)
(c)
-40
4.5
0
-10
-50
2.0
4.0
(b)
0
-40
fr2
Reference (FL=0.0mm)
Antenna 6 (FL=4.0mm)
3.0
3.5
Frequency (GHz)
4.0
4.5
-50
2.0
(e)
2.5
3.0
3.5
Frequency (GHz)
(f)
Figure 6.13. Measured return losses of the reference antenna and test antennas.
- 127 -
4.0
4.5
4.5
1.5
f2
3.5
1.0
f1
f2/f1
f2 / f1
Frequency (GHz)
4.0
3.0
2.5
0
1
2
3
4
0.5
FL (mm)
Figure 6.14. The first two resonant frequencies and its frequency ratio for different values of FL.
in the total length of the meandered inner slot. In conventional dual-band annular ring
slot antennas [47], the frequency ratio of the two resonant frequencies f1 and f2 is greater
than one due to the conducting strip between the inner and outer slots. In this case, it is
difficult to merge two operating bands.
The frequency ratio of the two resonant frequencies of the proposed dual-band
annular ring slot antenna can be easily controlled due to the meandered inner slot. As a
result, the ratio is generally less than one as shown in Figure 6.14. When adjusting the
frequency ratio to approximately nearly one, the two operating bands of the antenna are
merged and thus produce one wide operating band as shown in Figure 6.13 (c) and (d).
Moreover, meandering the inner slot of the dual-band annular ring slot antenna
enables size reduction in the total area of the dual-band ring slot antenna. For example,
- 128 -
the total area of the test antenna 6 excluding the ground plane is 40% smaller than the
conventional dual-band annular ring slot antenna which has the same resonant
frequencies. The conventional dual-band annular ring slot antenna has an outer slot radius
of 12mm while the test antenna 6 radius is 9.1mm.
6.3.2.3
Far-Field Radiation Patterns
The far-field radiations of the test antenna 6 with FL=4mm were measured for
two principal planes (x-y plane and x-z plane) in an anechoic chamber and are plotted in
Figure 6.15. As shown in Figure 6.15, the test antenna 6 radiates like an electrically small
dipole antennas for f1=3.55GHz and f2=2.76GHz, but the radiation patterns in the two
principal planes for the resonant frequencies are in opposite fashion due to the meandered
inner slot. For the resonant frequency f2=2.76GHz, the cross-polarization level is higher
than the conventional circular ring slot antenna due to change of direction of magnetic
current in the meandering the inner slot. The measured antenna gain of the test antenna 6
is 3.80dBi and 5.79dBi at f1=3.55GHz and f2=.276GHz respectively.
z
?= 0
x
?= 0
-y 270
90 y
90 x
-x 270
x-y plane
f1=3.65GHz
x-z plane
180
180
-x
-z
- 129 -
0
0
270
270
90
90
180
180
(a)
0
0
270
270
90
180
180
0
270
90
0
90
270
180
90
180
(b)
Figure 6.15. Measured radiation patterns of (a) the reference antenna (FL=0mm) and (b) antenna
6 (FL=4mm). The x-y plane is H-plane, and the y-z plane is E-plane.
- 130 -
6.4 Summary
In this chapter, two compact designs for single-band ring slot antenna and dualband ring slot antenna which are fed by a coplanar waveguide feed line with a tuning stub
are presented and experimentally studied. The experimental results demonstrate that the
size can be significantly reduced by introducing meandered slots to the conventional
annular ring slot and the resonant frequency can be adjusted without change in total area
size.
- 131 -
CHAPTER 7
CONCLUSION AND FUTURE WORK
This thesis has presents several design techniques for miniaturized passive
RF/microwave circuits such as interconnects, filters, and antennas. It has successfully
demonstrated the usefulness of the design techniques with simulations and measurements.
It has also introduced lumped element circuit models of an electromagnetic bandgap
(EBG) structure to analyze the EBG structure from a viewpoint of electric circuits.
Lumped element circuit models were developed to characterize the stopband
response of the EBG structures. The lumped element circuit models developed
significantly reduce analysis time compared to full-wave simulations while providing
accurate results, which were verified by simulation and measurement results.
Slow wave coplanar waveguides (CPWs) are used to control the effective
dielectric constant by adjusting geometrical parameters, to control the speed of
electromagnetic waves, and to reduce the size of passive circuits. Design guidelines for
slow wave CPWs on high resistivity silicon wafer were established, and these design
guide lines help a circuit designer to utilize the slow wave CPW in other applications.
- 132 -
The slow wave structure developed was incorporated in the short slot of 90░ CPW
circular bend and successfully suppressed the excitation of slot-line mode without wirebonds or air-bridges by equalizing the electrical length of the inner and outer slots of the
90░ circular bend, which reduces the fabrication cost. Another approach, fast-wave
method, was also developed to equalize the electrical length of the slots and to suppress
the excitation of slot-line mode. To match the electrical length, dielectric material of the
longer slot was removed using deep trenching process.
Slow wave approach for filter designs demonstrated on a high resistivity silicon
wafer and on FR4 epoxy material achieved approximately 40% reduction in length
compared with conventional filters. Two stopband filters of EBG type, which have high
impedance sections of different geometry, achieved 37.5% or 45.4% reduction in length
respectively compared with conventional ones. A miniaturized UWB bandpass filter was
also designed using slow wave CPWs and couples lines with meandered slots and
reduced its size by 40% compared to a conventional UWB filter designed based on CPW
MMR structure. Improvement in performance was also demonstrated with a decrease in
group delay.
The work on ring slot antennas demonstrated that the size of single- and dualband annular ring slot antennas can be significantly reduced by meandering the slot. It
was also shown that the meander ring slot antenna can control its resonant frequency by
adjusting the geometry of the antenna without increase in the total surface area.
- 133 -
7.1
Future Work
The slow- and fast-wave design approaches for right angled CPW bend structures
were successfully demonstrated on a high resistivity silicon wafer using standard
microelectronic fabrication process. Thus, it is also needed to demonstrate these wirebond free techniques on printed circuit board (PCB) that which has coarse accuracy in
fabrication because frequency response of effective dielectric constant of slow wave
CPWs depends on their size. Another natural question for wire-bond free techniques in
right-angled CPW bend structures is how to remove wire-bonds needed at 3 and 4 port
CPW circuits (i.e. T-junctions or CPW crosses). The slow wave approach can help
resolve this, but it may need another approach because there is different mechanisms that
create higher-order modes.
The meandered annular ring slot antenna achieved significant reduction in the
surface area in compared to a conventional ring slot antenna. The resonant frequency of
the meandered ring slot antenna is controlled by adjusting additional meandered slot
without change in the total surface area. The next step in the meandered ring slot antenna
is to develop a tunable antenna using varactors which control its resonant frequency
electrically.
The final step in this work is to implement a complete system, which consists of
active components, interconnects, filters and antennas, using design approaches discussed
in this work for the passive RF components. The EBG structure would be used to reduce
coupling between components of the system, and wire-bond free techniques would
- 134 -
reduce fabrication cost. Miniaturized filters and antennas would significantly shrink the
total size of the system.
- 135 -
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- 139-
APPENDIX A
Modeling
A.1
Dispersion Diagram
Dispersion diagrams of electromagnetic bandgap (EBG) structures are obtained
using the full-wave analysis tool, Ansoft?s HFSS 9.1. This section describes the solution
setup techniques of the HFSS to get the dispersion diagrams of EBG structures.
A.1.1
Optimetrics and Eigenmode Solver
The eigenmode solver in HFSS 9.1 enables direction calculation of the permitted
resonance frequencies for a unit cell structure. Computation can be performed over the
entire range of field relationship between linked boundary condition (LBC) pairs by using
Optimetrics. The Optimetrics interface automates the process of altering parametrically
the phase relationship of LBC pair?s to match each value in a table of desired
configuration setups and executing each resultant solution.
- 140 -
A.1.2
3D Model
Rogers
RO3010
vacuum
Rogers
RO3010
vacuum
vacuum
UNIT CELL
mm
1.15
12.5mm
EBG material
Figure A.1. Metallo-dielectric EBG structure and its unit cell. The metal plates place on the top
and bottom of the dielectric material.
The unit cell of the metallo-dielectric EBG structure is shown in Figure A.1.1
with dimension. The unit cell consists of a substrate of 12.5mm wide, 11.66mm long, and
1.15mm thick and three cylindrical holes arranged in triangle. The radius of the hole is
3mm. The top and bottom of the substrate are metal plates.
A.1.3
Material Setup
The material of each 3D object must be assigned in the setup materials category.
The cylindrical air holes and the substrate are set to the default values in the material. The
vacuum is used instead of air. The parameters of each material are shown in Table A.1.
Table A.1. Material parameters
Relative
permittivity
Relative
permeability
Bulk
conductivity
Dielectric
loss tangent
Magnetic
loss tangent
Vacuum
1
1
0
0
0
RO3010
10.2
1
0
0.0035
0
- 141 -
A.1.4
Boundaries/Sources Setup
The master and slave boundaries are assigned to the side faces of the substrate
with phase relationship (Figure A.2). The variables for the parametric analysis are the
phase relationship between each opposing pair of linked boundaries. By varying the
phase between the boundaries the permissible eigensolutions for each phase relationship
are calculated. Both the top and bottom conductors are selected as rectangular plane and
assigned perfect E (Figure A.3). The perfect E boundaries do not make a big simulation
difference compared with a finite conductivity of copper (5.8e7 S/m).
(a)
(b)
(c)
Figure A.2. Linked boundary condition and phase relationship fro HFSS eigensolution analysis.
(a) Phase relation between master and slave boundary conditions. (b) Master 1 and Slave 1. (c)
Master 2 and Slave 2.
Figure A.3. Perfect E boundaries are assigned to the top and bottom face of the substrate.
- 142 -
A.1.5
Solution Setup
To calculate the resonances of a structure the eigenmode solver is selected as a
solution type, and the details of the solution setup are shown in Figure A.4. The minimum
resonance frequency is 0.1GHz, and number of modes that we are interested in is 3. The
eigenmode solver will find the first three resonance frequencies.
Figure A.4. Solution setup for calculating resonance frequencies of the EBG structure.
Figure A.5. Setup sweep analysis of Optimetrics.
- 143 -
To find the resonance frequency with different phase relationship, Optimetric
setup is shown as shown in Figure A.5. The parametric setup shown in Figure A.5 is for a
plot of possible solution frequencies in the ? to X direction. For this direction, the phase
between the first pair of LBCs is held at zero and the phase between the second pair is
varied from 0? to 180?.
A.1.6
Dispersion Diagrams in x and y directions
For a plot of possible solutions frequencies in x direction, the phase between the
first pair of LBCs is held constant at zero (Phase 1) and the phase between the second
pair is varied from 0? to 180? (Phase 2). For solution frequencies in y direction, the phase
between the second pair of walls is held zero (Phase 2) while the phase between the first
pair is incremented from 0? to 180? (Phase 1). The results of this analysis are shown in
Figure A.6. The horizontal axis of each graph represents the changing phase variable, and
is analogous to having the wave vector plotted in a true dispersion diagram. The bandgap
in x direction is approximately 4.69GHz to 6.2GHz, and the bandgap in y direction is
approximately 5.5GHz to 6.56GHz.
- 144 -
12
10
Frequency (GHz)
8
6
4
2
0
mode 1
mode 2
mode 3
0
20
40
60
80
100
Phase (Deg)
120
140
160
180
(a)
12
10
Frequency (GHz)
8
6
4
2
0
mode 1
mode 2
mode 3
0
20
40
60
80
100
Phase (Deg)
120
140
160
180
(b)
Figure A.6. The dispersion diagrams of the EBG structure shown in Figure A.1 about x an y
directions. (a) x-direction. (b) y-direction.
- 145 -
APPENDIX B
FABRICATION
Fabrication of all designs in this thesis is described in this section. All test circuits
are fabricated using either printed circuit board (PCB) techniques or stand
microelectronic fabrication techniques. All fabrication on on-wafer circuits was done at
the Nanofabrication Center (NFC) at the University of Minnesota, Twin Cities.
B.1
Parallel Plate EBG Structure
The parallel plat EBG structures shown in Figure 2.10 are fabricated on Rogers
RO 3010 laminate with dielectric constant of 10.2 and thickness of 1.15mm using printed
circuit board (PCB) techniques. The first step of the fabrication is to draw layouts of topside and bottom-side of the EBG structure and to convert them to the board plotter files.
AutoCAD 98LT is used for layout, and CircuitCam 4.0 is used to convert the layout files.
The next step is milling and drilling processes. These processes are done with the LPKF
ProtoMat C60 milling machine shown in Figure B.1 . The air holes are made from the
bottom side using drill bits, and the feed lines are formed from the top-side using milling
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bits. The final step of the fabrication is assembly. The conductive copper tape with
conductive adhesive provided from 3M is attached on the both top- and bottom-sides. To
minimize the effect of air bubbles between the substrate and the copper tape the assembly
is put under sufficient pressure. Figure B.2 shows how to attach the copper tape on the
substrate.
Figure B.1. LPKF ProtoMat C60 milling machine.
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Figure B.2. Assembly of the parallel plate EBG structure.
B.2
Fabrication Recipe #1
This recipe is used to fabricate slow wave CPWs, right angled CPW bend
structures with slow wave compensation and CPW EBG structures.
- Number of Mask: 1
- Wafer Side: Front
1. Solvent clean wafer
(a) Soak 1 minute in acetone
(b) Soak 1 minute in isopropyl alcohol
(c) Soak 1 minute in methanol
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(d) Rinse in DI water and air-dry with N2 gun
2. Deposit seed layers using the AJA sputter or the CHA e
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