close

Вход

Забыли?

вход по аккаунту

?

Tunable wideband microwave band-stop and band-pass filters using YIG/GGG-gallium arsenide layer structure

код для вставкиСкачать
UNIVERSITY OF CALIFORNIA,
IRVINE
Tunable Wideband Microwave Band-Stop and Band-Pass Filters Using
YIG/GGG-GaAs Layer Structure
DISSERTATION
submitted in partial satisfaction of the requirements for the degree of
DOCTOR OF PHILOSOPHY
in Electrical and Computer Engineering
by
Gang Qiu
Dissertation Committee:
Professor Chen Shui Tsai
Professor Guann-Pyng Li
Professor Ozdal Boyraz
2008
UMI Number: 3342926
INFORMATION TO USERS
The quality of this reproduction is dependent upon the quality of the copy
submitted. Broken or indistinct print, colored or poor quality illustrations and
photographs, print bleed-through, substandard margins, and improper
alignment can adversely affect reproduction.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if unauthorized
copyright material had to be removed, a note will indicate the deletion.
®
UMI
UMI Microform 3342926
Copyright 2009 by ProQuest LLC.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
ProQuest LLC
789 E. Eisenhower Parkway
PO Box 1346
Ann Arbor, Ml 48106-1346
© 2008 Gang Qiu
The dissertation of Gang Qiu
is approved and is acceptable in quality and form
for publication on microfilm and in digital formats:
JT(JM
J / IS'etc
Committee Chair
University of California, Irvine
2008
DEDICATION
To
My parents and my wife, Jing Chen,
Without whose support it would never have been undertaken
in
TABLE OF CONTENTS
Page
LIST OF FIGURES
viii
LIST OF TABLES
xv
ACKNOWLEDGEMENTS
xvi
CURRICULUM VITAE
xviii
ABSTRACT OF THE DISSERTATION
CHAPTER 1:
xx
INTRODUCTION
1
1.1
Introduction to Device Application
1
1.2
Microwave Interaction with Ferrimagnet
3
1.2.1
Equation of Motion of Magnetization
4
1.2.2
Polder Tensor Permeability
9
1.2.3
Ferromagnetic Resonance
13
1.2.4
Magnetic Properties of YIG/GGG Film
15
1.3
APPENDIX A l
Research Objective and Thesis Organization
17
Maxwell's Equations in MKS and CGS System of Units
18
REFERENCES
CHAPTER 2:
2.1
21
THEORETICAL MODELING AND ANALYSIS OF
YIG/GGG-GAAS LAYER STRUCTURE
27
Theoretical Modeling
27
iv
2.2
2.1.1
Modeling Description
27
2.1.2
Full-Wave Method
28
Numerical Results and Analysis
2.2.1
APPENDIX 2
FMR Absorption and Its Band-Stop
Filter Application
40
2.2.2.
Wideband FMR Frequency Tunability
42
2.2.3
Material and Geometric Parameter Effect
45
2.2.4
Phase Shifter Applications
50
Ferromagentic Resonance (FMR) Linewidth
53
55
REFERENCES
CHAPTER 3:
3.1
DEVICE SIMULATIONS OF MICROWAVE BAND-STOP
FILTER USING YIG/GGG-GAAS LAYER STRUCTURE
57
Simulation Using Equivalent Circuit Method
57
3.1.1
Calculation of Radiation Resistance
59
3.1.2
Calculation of Values of Lumped Element
65
3.1.3
Simulation of Lumped Element
Equivalent Circuit
3.2
67
Simulation using ANSOFT HFSS
69
3.2.1
Model and Parameter Assignments
69
3.2.2
Simulation Results and Discussion
73
75
REFERENCES
CHAPTER 4:
40
TUNABLE WIDEBAND MICROWAVE BAND-STOP FILTER
USING YIG/GGG-GAAS LAYER STRUCTURE
v
77
4.1
4.2
Enhanced Microwave FMR Absorption Using Microstrip
Step-Impedance Low-Pass Filter
78
4.1.1
Microstrip Step-Impedance LPF Design
79
4.1.2
AC Magnetic Field Simulation
85
4.1.3
Device Simulations
92
Experimental Results
94
4.2.1
Device Fabrication and Measurement
94
4.2.2
Device Performance of Tunable Wideband
Microwave Band-Stop Filter
4.3
100
Band-Stop Filter with Large Stop-Band Bandwidth Using
Microstrip Meander Line with Inhomogeneous Bias Magnetic
Field
105
4.3.1
Inhomogeneous Bias Magnetic Field
105
4.3.2
Microstrip Meander Line Design
108
4.3.3
Experimental Results
111
REFERENCES
CHAPTER 5:
113
TUNABLE WIDEBAND MICROWAVE BAND-PASS FILTER
USING YIG/GGG-GAAS LAYER STRUCTRUES
115
5.1
Band-Pass Filter Architecture
116
5.2
Device Simulations
117
5.2.1
Simulation Using Equivalent Circuit Method
117
5.2.2
Simulation Using ANSOFT HFSS
121
5.3
Experimental Results
124
VI
5.3.1
Band-Pass Filter with Narrow Stop-Band Bandwidth
125
5.3.2
5.4
Band-Pass Filter with Large Stop-Band Bandwidthl27
Discussions
131
5.4.1
Electronic Tunability
131
5.4.2
Power Handling Capability
135
REFERENCES
CHAPTER 6:
6.1
6.2
6.3
136
TUNABLE WIDEBAND FILTERS USING YIG/GGG-GAAS
LAYER ON RT-DUROID SUBSTRATE
138
Band-Stop Filter on RT-Duroid6010LM
138
6.1.1.
High Frequency Circuit Board Introduction
138
6.1.2
Band-Stop Filter Using 100 // m Thick YIG On
RT-Duroid6010LM
140
An X-Band Tunable Band-Pass Filter
143
6.2.1
Design of An X-Band Composite Band-Pass Filter 144
6.2.2
Experimental Results and Discussion
Future Works Outlined
156
157
REFERENCES
CHAPTER 7:
151
CONCLUSIONS
158
vn
List of Figures
Figure 1.1
Spin Magnetic Dipole Moment and Angular Momentum
for a Spinning Electron
4
Figure 1.2
Tuning of FMR Peak Absorption Frequency
15
Figure 2.1
The Multi-Layer Magnetic Structure
28
Figure 2.2
Outline of Analytical Analysis of the Multi-Layer
Magnetic Structure
Figure 2.3
29
Calculated Microwave Attenuation vs. rf Frequency
when H = 2,200 Oe
41
Figure 2.4
Calculated FMR Frequencies vs. Biased Magnetic Field
43
Figure 2.5
Calculated FMR Peak Absorption Level vs. FMR Frequency
44
Figure 2.6
Calculated Attenuation vs. Microwave Frequency
in 8 to 10 GHz
45
Figure 2.7
Effect of FMR Linewidth on Attenuation
46
Figure 2.8
Effect of GaAs Thickness on Attenuation
47
Figure 2.9
Effect of GGG Thickness on Attenuation
48
Figure 2.10
Effect of Air Layer Thickness on Attenuation
49
Figure 2.11
Effect of YIG Thickness on Attenuation
50
Figure 2.12
Calculated Propagation Constant (Real and Imaginary Parts)
at H0=2,7lOOe
Figure 2.13
51
Calculated Phase Shift at 9.66 GHz while H0 is
Changed from 2,71 QOe to 3,42O0e
Figure 3.1
Device Configuration of the Microwave Band-Stop
viii
52
Filter using YIG/GGG-GaAs Layer Structure
Figure 3.2
.
58
Lumped Element Equivalent Circuit Model of the Microwave
Band-Stop Filter
59
Figure 3.3
Cross-Section View of MSSW Excitation Geometry
61
Figure 3.4
Calculated Radiation Resistance Rm versus Wavenumber k at
t = 350^/w, d = 6.%/um, b = 256jum and if0 = 2,200Oe
Figure 3.5
The Circuit Schematics in Microwave Office Simulator
Figure 3.6
Simulated S-parameters (S21) of the Equivalent Circuit
of Figure 3.5
Figure 3.7
65
68
68
The Physical Model of The Band-Stop Filter Configuration
in HFSS Using a YIG/GGG-GaAs Layer Structure
70
Figure 3.8
Edit-material Interface of Ferrimagnetic Material in HFSS
71
Figure 3.9
Derivation Blocks of Relative Tensor Permeability [//]
Using the Four Parameters Ms , AH,
Figure 3.10
co, and H0
Simulated S-Parameter (S 2 l ) of the Microwave
Band-Stop Filter using YIG/GGG-GaAs Layer Structure
Figure 3.11
72
73
Simulated H-field Pattern on the Surface of the YIG Layer
at 8.28GHz
74
Figure 4.1
Design Outline of Step-Impedance LPF
78
Figure 4.2
Ladder Network for The Low-Pass Filter
80
Figure 4.3
A 10-Element Step-Impedance LPF
84
Figure 4.4
Simulated S-Parameters (S21 and S11) of the
10-Element Step-Impedance LPF and the 50 Q TML
Figure 4.5
Simulated AC Magnetic Field (H-Field) Distributions
at Frequency of 8.5 GHz along the 50 Q Microstrip
Figure 4.6
84
Simulated AC Magnetic Field (H-Field) Distributions
ix
87
at Frequency of 8.5 GHz along the 10-Element
Step-Impedance LPF
Figure 4.7
88
Simulated AC Magnetic Field (H-field) Intensities along
the Y-Axis Center Lines of The 10-Segment Step-Impedance
LPF and The 50 Q Microstrip
Figure 4.8
89
Simulated Power Density Distribution at Frequency of
8.5 GHz on the Surface of GaAs of the 10-Segment
Step-Impedance LPF
Figure 4.9
90
Simulated Surface Power Density Distribution along The
Cross-Section Direction (X-direction in Figure 4.8) over the
TML, the Inductive Segment and Capacitive Segment of the
Step-Impedance LPF
Figure 4.10
91
Simulated Transmission Loss (S21) and Return Loss (Sn) of
the YIG/GGG-GaAs-Based Microwave Band-Stop Filter at
FMR Frequency of 8.5 GHz using the 50 TML and the
10-Segment Stepped-Impedance LPF
Figure 4.11
93
The Flip-Chip Device Configuration of the Microwave
Band-Stop Filter using YIG/GGG-GaAs Layer Structure
94
Figure 4.12
Process Flow for Fabricating GaAs-based Microstrip Line
95
Figure 4.13
Layout of the Step-Impedance LPF with Two Mitered 90°
Bends
Figure 4.14
97
Photo of Fabricated GaAs-based Microstrip Step-Impedance
LPF with Two Mitered 90° Bends together with Two 2.4 mm
Connectors
98
Figure 4.15
Setup of the Microwave Power Measurement System
99
Figure 4.16
Setup of the Network Analyzer Measurement System
100
Figure 4.17
Measured S21 and S11 of the YIG/GGG-GaAs-Based
x
Microwave Band-Stop Filter at FMR Frequency of 8.5 GHz
Using the 50 Q. Microstrip and the 10-Element Step-Impedance
LPF
102
Figure 4.18
Measured S2i of the YIG/GGG-GaAs-Based Microwave
Band-Stop Filter using the 50 Q Microstrip and the 10-element
Step-Impedance LPF
103
Figure 4.19
Measured FMR Frequencies vs. Biased Magnetic Field
104
Figure 4.20
The Arrangement For Facilitating Non-Uniform Bias
Magnetic Fields in YIG/GGG Layer
Figure 4.21
105
Measured Magnetic Field Profiles Normalized to the
Four Values of Magnetic Field at the Center of the Gap
along the Y-Axis
Figure 4.22
107
Measured Magnetic Field Profiles Normalized to the Four
Values of Magnetic Field at the Center of the Gap along the
X-Axis
Figure 4.23
108
Layout of the Four-Segment Microstrip Meander Line using
the Same 10-Element Step-Impedance LPFs
109
Figure 4.24
Miter Bend Layout in Microwave Office
110
Figure 4.25
Simulated S21 of a Microstrip with Two Miter Bend using
Different Miter Coefficient
Figure 4.26
110
A Wideband YIG/GGG/GaAs-Based Microwave Band-Stop
Filter using Microstrip Meander-Line and Non-Uniform Bias
Magnetic Field
Figure 4.27
111
Measured S21 of the Tunable YIG/GGG-GaAs-Based
Microwave Band-Stop Filter using a Meander Line with
Four Segments of Step-Impedance LPF
Figure 5.1
Realization of the Tunable Band-Pass Filter using a Pair of
xi
112
Band-Stop Filters in Cascade
Figure 5.2
Lumped Element Equivalent Circuit of the YIG/GGGGaAs-based Band-Pass Filter
Figure 5.3
122
Simulated and Measured Transmission Losses (S21) of the
Tunable Band-Pass Filter
Figure 5.7
124
Photo of the Microwave Band-Pass Filter using Cascaded
Band-Stop Filters
Figure 5.8
121
Schematics of the Band-Pass Filter in HFSS 3-D Modeler
Simulator
Figure 5.6
119
Simulated S-parameters (S21) of the YIG/GGG-GaAs-based
Microwave Band-Pass Filter
Figure 5.5
117
Calculated Radiation Resistance ^ v e r s u s Wavenumber
k for Band-Stop Filter (a) No.l, and (b) No.2
Figure 5.4
116
125
Comparison of the Simulated and Measured S21 of a
YIG/GGG-GaAs Based Microwave Band-Pass Filter with
Narrow Stop-Band Bandwidth
Figure 5.9
126
Comparison of the Simulated and Measured S21 of a
YIG/GGG-GaAs Based Microwave Band-Pass Filter with
Large Stop-Band Bandwidth
Figure 5.10
Measured 2-D Non-Uniform Bias Magnetic Field Profile
Centered at (a) 2,750 Oe and (b) 4,150 Oe
Figure 5.11
127
128
Measured Transmission Characteristics of the Tunable
Band-Pass Filter in a Wide Frequency Range of
5.90-17.8 GHz
130
Figure 5.12
The Sketch of the Electromagnet
131
Figure 5.13
The Measured Changes of Magnetic Fields in the Air Gap
versus the DC Current in the Coils with the Air Gap Distance
xii
as a Parameter
132
Figure 5.14
The Equivalent Circuit Used to Model the Coil
134
Figure 5.15
The Simulated and Measured Transient Voltages of the
Coil when the Serial Resistors are 1.5 k Q , 270 Q and 47 Q
Figure 5.16
135
Measured Transmission Characteristics of the Band-Stop
Filter at Different Input Microwave Power Levels of
(a) l m W (b) lOmW (c) lOOmW, and (d) 500mW
Figure 6.1
The Layout (a), and the Simulated Transmission Loss (S21) (b),
of the Step-Impedance LPF on Duroid 6010LM
Figure 6.2
136
140
Measured S21 of the YIG/GGG-RT-Duroid-Based Microwave
Band-Stop Filter at FMR Frequency of 8.5 GHz Using the
100 ju m Thick YIG Sample and the 6.8 ju m Thick YIG Sample
Figure 6.3
142
A Scheme of Realizing an X-band (8 -12 GHz) Microwave
Band-Pass Filter
143
Figure 6.4
BPF Using Quarter-Wave Short-Circuited Stubs
144
Figure 6.5
The Layout of the X-Band BPF
148
Figure 6.6
Simulated Transmission Loss (S21) of the X-Band BPF
148
Figure 6.7
The X-Band BPF (a), A Step-Impedance LPF (b), and the
Composite X-Band BPF (c)
150
Figure 6.9
Simulated Transmission Loss (S21) of the Composite
X-Band BPF
Photo of Fabricated X-Band Composite BPF
150
151
Figure 6.10
Measured Transmission Loss (S21) of the Composite
Figure 6.8
X-Band BPF
152
Figure 6.11
The Simulated Sensitivity of the S21 to the Shunt Stub Lengths
Figure 6.12
The Simulated Sensitivity of the S21 to the Shunt Stub Grounding
Resistance
154
xm
153
Figure 6.13 The High-End Stop-Band Tunability of the BPF by Applying
Bias Magnetic Fields of 2,800 Oe and 2,450 Oe
Figure 6.14
The Low-End Stop-Band Tunability of the BPF by Applying
Bias Magnetic Fields of 990 Oe and 1,060 Oe
xiv
155
156
List of Tables
Table 2-1
Boundary Conditions of the Four-Layer Magnetic
Layer Structure
36
Table 2-2
Field Independent Variables and Field Conversion Variables
37
Table 4-1
Specification of the Step-Impedance LPF
79
Table 4-2
Geometry of the 10-Element Step-Impedance LPF
83
Table 5-1
Geometric Parameters and Bias Magnetic Fields Used
in the Simulation
118
Table 5-2
Values of Lumped Elements For Band-Stop Filter 1 and 2
120
Table 5-3
Measured Insertion Losses and Band-Widths of the
Band-Pass Filter of Figure 5.11
Table 5-4
130
Measured Center Magnetic Fields and Maximum Change
of Magnetic Field in the Center of the Air gap and the
Maximum Tuning Ranges of the FMR Frequencies
Table 5-5
133
The Comparison between the Simulated and Experimental
Results of Figure 5-15
134
Table 6-1
Admittance and Impedance of the BPF
146
Table 6-2
Width and Length of Stubs and Connecting Lines in Figure 6.5 147
Table 6-3
Geometric Dimensions of The X-Band Composite BPF
xv
149
ACKNOWLEDGEMENTS
First of all, I would like to express my most sincere appreciation and deepest
gratitude to my advisor, Professor Chen S. Tsai who has given me his
instructive guidance, mentoring, full support, patience and encouragement
throughout the course of my Ph.D. research. It has been a great honor to be able
to study under his guidance, and his keen dedication to science and high
standard to research have stimulated me during my whole study of Ph.D.
research and will forever benefit me in my future life.
I also like to express my gratitude to Professor G.P. Li who supported me for
my first year of research and kindly guide me in my first teaching experience in
his class. I like to thank both Professor G. P. Li and Professor Ozdal Boyraz for
serving on my dissertation committee. The time and efforts they put in
reviewing my dissertation are greatly appreciated.
I would like to thank Dr. Hui Jae Yoo, and the former graduate Boh~Shun Chiu
for their helps in the initial phase of this research. Professor Shirley C. Tsai has
also been very encouraging throughout this work. I would also like to thank my
fellow colleagues, Masatoshi M. Kobayashi, Chun-wei Chung, Yun Zhu and
xvi
Kai-Himg Chi for their helps and friendship provided in my research. I would
like to thank the rest of Professor Tsai's research group, Ning Wang, Dr. Rong
Wei Mao, Dr. Eugene Song, Shih-Kai Lin and Serhan Isikman.
Financial support provided by the UC DISCOVERY Program is gratefully
acknowledged.
xvii
CURRICULUM VITAE
Gang Qiu
2000
B.S. in Electrical Engineering, Nanjing University, China
2003
M.S in Electrical Engineering, Nanjing University, China
2003-2008
Research Assistant and Teaching Assistant, University of
California, Irvine
Ph.D. in Electrical & Computer Engineering, University of
California, Irvine
2008
FIELD OF STUDY
Magnetic Thin-Film-Based Microwave Device Application
PUBLICATIONS
Journal Papers
1.
C. S. Tsai, G. Qiu, H. Gao, L. W. Yang, G. P. Li, S. A. Nikitov, and Y. Gulyaev.
"Tunable wideband microwave band-stop and band-pass filters using
YIG/GGG-GaAs layer structures." IEEE Trans. Magn., vol.41, pp.3568-3570,
2005.
2.
G. Qiu, C. S. Tsai, M. M. Kobayashi, and B. T. Wang, "Enhanced microwave
ferromagnetic resonance absorption and bandwidth using a microstrip
meander line with step-impedance low-pass filter in a yttrium iron
garnet-gallium arsenide layer structure", /. Appl. Phys., vol.103, 2008.
3.
G. Qiu, C.S. Tsai, B. T. Wang, and Y. Zhu, "A YIG/GGG/GaAs-based
magnetically tunable wideband microwave band-pass filter using cascaded
xvm
band-stop filters", IEEE Trans. Magn., vol.44, issue 11,2008.
4. C. S. Tsai, and G. Qiu, "Wideband microwave filters using FMR tuning in
flip-chip YIG-GaAs layer structures", accepted and to be published in IEEE
Trans. Magn., vol. 45, 2009.
Conference Papers
1. C.S. Tsai, G. Qiu, H. Gao, L.W. Yang, G.P. Li, and S.A. Nikitov, "Tunable
wideband
microwave band-stop and band-pass filters
using
YIG/GGG-GaAs layer structures", IEEE International Magnetics Conference,
Nagoya, Japan, April 2005.
2. G. Qiu, M. Kobayashi, B. T. Wang, and C.S. Tsai, "Enhanced microwave
ferromagnetic resonance absorption and bandwidth using a microstrip
meander line with step-impedance low pass filter in a yttrium iron garnet gallium arsenide layer structure", 52nd Annual Conference on Magnetism and
Magnetic Materials, Paper EH-03, Nov 5-9, TAMPA, FLORIDA, 2007.
3. G. Qiu, B.T. Wang, C.S. Tsai, "A YIG/GGG/GaAs-based magnetically
tunable wideband microwave band-pass filter using cascaded band-stop
filters", IEEE International Magnetics Conference, Madrid, Spain, May 2008.
4. C. S. Tsai, and G. Qiu, "Wideband microwave filters using FMR tuning in
flip-chip YIG-GaAs layer structures", International Conference on Microwave
Magnetics, Fort Collins, Coronado, September 2008.
Oral Presentation
1. G. Qiu, M. Kobayashi, B. T. Wang, and C.S. Tsai, "Enhanced microwave
ferromagnetic resonance absorption and bandwidth using a microstrip
meander line with step-impedance low pass filter in a yttrium iron garnet gallium arsenide layer structure", Oral Presented at 52nd Annual Conference
on Magnetism and Magnetic Materials, Nov 5-9, TAMPA, FLORIDA, 2007.
xix
ABSTRACT OF THE DISSERTATION
Tunable Wideband Microwave Band-Stop and Band-Pass Filters
Using YIG/GGG-GaAs Layer Structures
by
Gang Qiu
Doctor of Philosophy in Electrical and Computer Engineering
University of California, Irvine, 2008
Professor Chen Shui, Tsai Chair
Magnetic thin-film-based microwave devices, in many applications, provide
definite advantages of low cost, small size, and, in particular, enhanced
compatibility with planar microwave circuit design such as monolithic
microwave
integrated
circuits
(MMIC).
The
ferromagnetic
resonance
(FMR)-based microwave filters have the advantages to possess the unique
capability of potential high-speed electronic tunability, using magnetic field, for
very high carrier frequency and very large bandwidth.
In this dissertation research, a full-wave method of modeling and analysis of
yttrium iron garnet (YIG)/ gadolinium gallium garnet (GGG)-gallium arsenide
xx
(GaAs) flip-chip layer structure was carried out predicting the device
application as wideband tunable microwave band-stop filter utilizing the FMR
absorptions of this magnetic layer structure in microwave frequency band.
Detail simulations were then carried out aimed at optimal device performances
of the microwave band-stop filter using YIG/GGG-GaAs layer structure. In the
experimental studies, a magnetically-tuned microwave band-stop filter using
YIG/GGG-GaAs flip-chip layer structure with wideband tunability of
stop-band center frequency and bandwidth has been accomplished using a
microstrip meander line together with non-uniform bias magnetic field. A
microwave filter with tunable FMR absorption frequency range of 5.0 to 21 GHz,
an absorption level of -35.5 dB and a corresponding 3 dB absorption bandwidth
as large as 1.70 GHz, centered at 20.3 GHz, have been demonstrated.
A magnetically-tunable wideband microwave band-pass filter with large tuning
ranges for both the center frequency (5.90 -17.80 GHz) and the bandwidth (1.27
- 2.08 GHz) in the pass-band has also been realized using a pair of cascaded
aforementioned band-stop filters. For example, the measured transmission
characteristics of the band-pass filter at center frequency of 8.28 GHz, using 2-D
non-uniform bias magnetic fields centered at 2,750 Oe and 4,150 Oe facilitated
xxi
by NdFeB permanent magnets, shows a - 3 dB bandwidth of 1.73 GHz, an
out-of-band rejection of - 33.5 dB, and an insertion loss of - 4.2 dB. A good
agreement between the simulation and experimental results for the band-pass
filter in the center frequency and the bandwidths of the pass-band and the two
guarding stop-bands has been accomplished.
xxn
Chapter 1
Introduction
1.1 Introduction to Device Applications
Microwave ferrimagnetic materials and devices have been developed and
constructed over the past five decades [1]. In contrast to ferromagnetic materials,
a ferrimagnet is a magnetic dielectric that allows an electromagnetic wave to
penetrate in the ferrimagnet, thereby permitting interactions between the rf
magnetic field in the propagating microwave and the magnetization in the
ferrimagnet. In the classical analysis within the linear regime under the smallsignal approximation, the behavior of the ferrimagnetic materials can be
described by the Polder tensor permeability. This macroscopic description of the
material property can then be incorporated in the Maxwell's equations to analyze
wave propagation properties in a ferrimagnetic medium and in a ferrimagneticloaded waveguide and transmission lines. The magnetic anistropy of a
ferrimagnetic material is induced by a dc biased magnetic field. This dc bias
magnetic field aligns the magnetic dipoles in the ferrimagnetic materials to
produce a non-zero magnetic dipole moment, and make the dipoles to precess
about the axis of the dc bias magnetic field in the preferred right-hand circularly
polarized (RHCP) manner. A microwave signal with RHCP rf magnetic field,
therefore, will interact strongly with the dipole moments, while a signal with
1
left-hand circularly polarized (LHCP) rf magnetic field will interact much less
strongly. Since the sense of the polarization changes with the direction of
microwave propagation, a microwave signal will generally propagate in a
ferrimagnet differently in different directions. This effect can be used to design
and construct directional devices such as circulators and isolators. The other
important characteristic of a ferrimagnet is that the interaction with applied
microwave signal can be tuned by adjusting the strength of the dc bias magnetic
field. This effect leads to a variety of tunable devices such as tunable resonators,
filters, and phase shifters. Accordingly, the microwave ferrimagnetic devices can
be divided into two categories based on whether directional property or
tunability property is used in the applications.
Conventional microwave ferrimagnetic devices have for long used bulk
ferrimagnetic materials with non-planar waveguide structures [1-2]. However,
for the microwave and millimeter-wave applications, there are increasing
interests in using ferrimagnetic thin-film structures because, in many cases, thinfilm structures provide definite advantages of low cost, small size, and, in
particular, enhanced compatibility with planar microwave circuit design such as
monolithic microwave integrated circuits (MMIC). Although poly crystalline
ferrimagnet are usually used in microwave directional (control) devices where a
narrow ferromagnetic resonance (FMR) linewidth is not required, single
crystalline ferrimagnet, almost always yttrium iron garnet (YIG), is necessary in
the device applications of band-pass and band-stop filters and resonators where
2
a low FMR linewidth is a must [3]. The high-quality single crystalline liquid
phase epitaxy (LPE)-grown YIG/ gadolinium gallium garnet (GGG) layers have
been commercially available for many years. More recently, there has been
increasing research activities in the ferromagnetic thin film-based [4-9], single
crystalline hexagonal ferrite thin film-based [10-14], and ferrite-ferroelectric
composite thin film-based
[15-21] microwave devices in high
frequency
application. Although the monolithic integration combining these thin films with
semiconductor in a system-on-a chip (SOC) is the ultimate goal, there are still
some severe limitations in the development of ferri- and ferro-magnetic thin
films and devices that are fully MMIC compatible, where the major problems are
the high temperature process for growing ferrite thin film [3], and the required
bulk external bias magnetic field [22]. Therefore, MMIC compatible ferrimagnetic
devices with a hybrid structure using ferrimagnet and semiconductor fabricated
separately and then combine in some device configuration is one of the key
research focuses.
1.2 Microwave Interaction with Ferrimagnet
The theoretical description of microwave interaction with ferromagnetic material
starts with the derivation of equation of motion of magnetic moment of an
electron in a dc magnetic field. The analysis is explored by introducing the
Polder tensor permeability to be able to apply Maxwell's equation in the
macroscopic level. It has been seen that, in the field of microwave magnetics,
3
researchers from physics and engineering preferred to use CGS system of units
and MKS system of units respectively. The unit conversions are easy and clear
when dealing with length, weight, or speed, but not the electrical and magnetic
field quantities in the two systems [23]. A brief review of Maxwell equation in
MKS units and CGS units is provided appendix A.
1.2.1 Equation of Motion of Magnetization
Figure 1.1 Spin Magnetic Dipole Moment and Angular Momentum for a
Spinning Electron
The magnetic properties of a material are due to the existence of magnetic
moments. The magnetic moment (m) of an electron is contributed by the orbital
4
angular momentum and spin angular momentum of an electron. There is a
Lande g factor in quantum physics used to measure the relative contributions of
the orbital momentum and the spin momentum to the total m . For most of
microwave ferrimagnetic materials, the total m is due to spin momentum only
while the Lande g factor is equal to 2. The m is, therefore, given by [24]
m
= -^S=—a
me
= -MBo-
(MKS)
(1.1)
2me
where e is the electron charge, meis the mass of the electron, and Sis the spin
angular momentum of an electron. The spin angular momentum ( S ) of an
2
electron is given by cr = ~S in equation (1.1) where Pi is the Planck's constant and
h
a is the Pauli Spin Operator [24]. The Bohr Magneton juB is then defined as
-e%l2me (in MKS units) and its value is equal to 921x\0~1A A*m2.
Since the
charge of the electron is negative, equation (1.1) is given by
m
= JLs = -2&-S = -rS
m„
(MKS)
(1.2)
ft
where the constant y is the ratio of the magnetic moment to the angular
momentum; y is called the gyromagnetic ratio or magnetogyric ratio and its
value is equal to Inx2.8xlO10rad/(secxtesla)
or 1.759xlOnra<i/(secxfes/a)
(in
MKS units). It is shown in equation (1.2) that the magnetic moment (m) of an
5
electron is proportional to its spin angular momentum ( S ) and the vector
direction of m is opposite to the vector direction of S.
We will now start to derive the Polder permeability tensor in both MKS and CGS
unit used to describe the interaction between a microwave and a ferromagnetic
material. Consider a free electron in a z-directed dc bias magnetic field as shown
in Figure 1.1. The torque (T) will be exerted on the magnetic dipole and it is
expressed by
f = m x ^ = / / 0 m x ^ (MKSunits)
f = mxW0 (CGSunits)
(1.3)
(1.4)
since torque (T) acting on a body equals to the time rate of change of the angular
momentum (S), equation (1.3) and (1.4) can be written as
— = jU0mxH0 (MKSunits)
dt
(1.5)
— -mxH0
dt
(1.6)
(CGSunits)
combing equation (1.5) or (1.6) to (1.2) gives the equation of motion of magnetic
dipole moment
dfti
—' —"
= -ju0ymxH0
(MKSunits)
(1.7)
dt
dm
= -ym x H0 (CGS units)
dt
6
(1.8)
Now assuming the bias magnetic field is only at z direction as shown in Figure 1,
i.e., H0=H0z.
The equation (1.7) and (1.8) can be decomposed into its vector
components as (1.9) and (1.10)
dm
dt
dmY —-x
dt
dm,, •y
dt
dmT —-z
dt
dmY —-x
dt
dm,, —-y
dt
dm, —-z
dt
dm
dt
-w
= -r
x
y
m„
m„
0
0
x
mx
0
y
my
0
z
m. (MKS units)
Hn
z
mz (CGS units)
Hn
(1.9)
(1.10)
The equation (1.9) and (1.10) are further developed to (1.11) and (1.12)
dm
dt
dm
= ju0ymxH0
dt
dm
=0
dt
(MKS units)
dm
- = -ymyHG
dt
dm
- = ymxH0 (CGS units)
dt
dm
=0
dt
7
(1.11)
(1.12)
The equation (1.11) and (1.12) can be re-arranged to be the following differential
equations (1.13)
d2m
2
2^- + co mx=0
dt
(MKS and CGS units)
d2m
2
dt
2^
(1.13)
+ G) Qmy=0
where co0 is called Lamor precessing frequency and its value is given by
G)Q = yjU0H0 (MKS
units)
or
co0 = yH0
(CGS
units).
The
y
2;rx2.8xl010rad/(secxfes/(3) (MKS units) or 2;rx2.8xl0 6 rad/(secx<3e) (CGS units).
As an example, at the dc bias magnetic field of 10,000 Oe, the Lamor precessing
frequency will be2;rx2.8xl0 10 rac//(sec). One solution for the equation (1.13) is as
follows
mx = A cos a>0t
my=A sin co0t
(1.14)
m=C
where A and C are arbitrary constants. The solution (1.14) shows that the x and y
components of m is right-hand circular polarized (RHCP) and z component of m
is determined by its initial value C. The magnitude of m is a constant equal to
sA2 + C2 and the precessing angle 9 (see Figure 1.1) is given by
Sin0 =
4A2+C2
8
(1.15)
is
In the absence of any damping forces, the m of the electron will precess about
H0 at the angle 9 (see Figure 1.1) indefinitely and it is called free electron
precessing. The equations (1.7) and (1.8) are the equation of motion of magnetic
moment of a free electron. Now assuming, in a real magnetic material, there are
N unbalanced electrons per unit volume. The magnetization is defined as the
total magnetic moments per unit volume as M = Nm , and the equation of
motion of magnetization is now given by
— = -V0yMxH0
dt
(MKS units)
i^L = -YM x H0 (CGS units)
dt
(1.16)
(1.17)
In the ferrimagnetic materials, most of the magnetic dipole will be aligned by H0
and reach its limit value called saturation magnetization Ms.
1.2.2 Polder Tensor Permeability
We will derive the Polder tensor permeability in this sub-section by adding a
small rf magnetic field (induced by propagating microwave) to the precessing
spinning system. Assuming H is the added rf magnetic field, the total magnetic
field is
lft=H0z + H
9
(1.18)
where under the small signal approximation, L f t r « # 0 . This field produces a
resultant total magnetization given by
(1.19)
Mt =Msz + M
Where M is the induced magnetization by H. Here we will derive the Polder
tensor permeability in MKS units. When combine equations (1.18) and (1.19) to
the equation of motion of magnetization (1.16), it gives equation (1.20)
dMt
dt
dMv
dt
dMy
= -M»r
dt
dMz
dt
y
X
dMs
dt
K
M
Hx
H
y
>
z
M2+Ms
(1.20)
H2+H0_
The equation (1.20) can be expanded to (1.21)
dM„
= -WM(H0+Hz)
+ Moy(Ms+Mz)Hy
dt
dM.y
-^^yMx{H,
+Hz)-ju0r(Ms+Mz)Hx
dt
did.
=
-MQyMxHy+^yMyHx
dt
(1.21)
Under small signal approximation, we can ignore MH product. Equation (1.21)
will be arranged as
10
dM,
= -co0My+amHy
dt
X
dlfy
(1.22)
= a)0Mx-comHx
dt
d~Mz
-n
dt
Where co0 = yjuGH0 (Lamor precessing frequency) and com = yn0Ms. The equation
(1.22) can be further rearranged as
d2M
,
dHv
2 ' + con M
+ G)ncoH„
x r = mm
dt
dt
d2M.y
+ colM,,
= -am — - + co.coH,,
0 m
y
0^y
I dt2
dt
(1.23)
J
Assume the M and H are both relates to co as elM, i.e., — = jco and —- = -co2.
dt
dt1
The equation (1.23) can be written as
(O (O H
{CO2, ~ ®2)Mx =Q""m*
0 + mx 'X +J" "mJ^nF
-*-y
JK
(coG -co)M=
J
(1.24)
-jcocomHx + co0comH
The equation (1.24) can be re-written with tensor susceptibility [%\ as
M = [x]H =
sCxx
sCxy
sCyx
Xyy
0
0
0
0 H
0
(1.25)
where the elements of [%\ are given by
y
Axx
= y
/lyy
=
G)0COm
-—-—
2
,,2
co0 — co
11
(1.26)
Xxv
X yx
J<°®m
1
6D0
(1.27)
1
-CO
To relate B and H, we have from equation (A1.5) (see Appendix Al) that
B = ju0(H + M) = \fj\H and the resultant Polder tensor permeability [//] is given by
M-
JU
JK
0
-JK
fi
0 (z axis)
0
0
(1.28)
M,_
where the elements of tensor permeability are then given by
a
M = Ml
+
Xxx) = Mo(l + Zyy) = Ml
+
^m
CO0
K
<w»„
= -JMoXxy = JMoZy, = A)
<»0
2
X
2
2
2
(1.29)
-CD
(1.30)
-<y
A material having this form of permeability is called gyrotropic, meaning that an
x (ory) component of H gives both x and y components of B, with 90° phase
difference between them.
Please note that if the direction of bias magnetic field is reversed, both H0 and
Ms will change signs, so co0 and com will both changed signs. From equation (1.28)
it shows that ju will be unchanged, but K will change sign. We summarize for
different /n w i t h respect to different bias magnetic field direction in equation
(1.31) as follows
12
w=
0
0
0
-JK
M
0
y"o
0
A>_
0"
0
M
JK
0
-J'K
//
0
0
y"
-y'* -
p
]K
If]'
M-
A,
0
0
J*
0
(-z axz's)
(x axis)
(-x axis)
/*
-JK
0 A> 0
(y axis)
JK 0
^ .
0 7'K"
' V
0
A) 0 (-y axis)
[/<]•
0 M
-JK
/"
M
(1.31)
This macroscopic Polder tensor permeability now is ready to be able to
implement in Maxwell's equation to calculate the wave propagation properties
in a ferrimagnetic media or ferrimagnet transmission lines.
1.2.3 Ferromagnetic Resonance
As introduced previously, the total electron magnetic moment or magnetization
in the ferromagnetic sample precess about the direction of the dc biased
magnetic field and its precessing frequency is determined by the strength of the
bias magnetic field. When adding an external rf transverse field, there is a strong
resonance or coupling between the magnetization in ferromagnet and the rf
transverse field when the frequency of the rf field is coincide to the precessing
frequency of the magnetization. At this moment, the energy of the rf transverse
13
field will be strongly transferred to magnetic precessing system. This phenomena
is called ferromagnetic resonance (FMR), and its corresponding peak absorption
frequency is called FMR frequency. The Lamor precession frequency is just an
ideal case of FMR frequency where a single magnetic dipole is in an infinite
ferromagnetic medium. However, it is usually the case that the ferromagnetic
sample is a finite sample with certain shape. As an example, the FMR frequency
of a magnetic thin film layer is highly affected by the shape of the sample. The
shape of the ferromagnetic sample plays an important role because the
demagnetization field is large. The effect that the amount of internal
magnetization in the ferromagnet depends on the shape of the sample is called
the demagnetization.
Kittel's equation [25] present the FMR frequency by adding the demagnetization
f a c t o r ^ , Ny and7Vz. Then the FMR frequency can be generally defined as
«o = r*J(H +(Ny-Nz)Ms)(H
+(NX-NZ)MS)
(CGSUnits)
(1.32)
For example, in a magnetic thin film layer, when the bias field is applied to the
plane of the film (e.g., x-z plane), Nx=Nz=0;
Ny=4x
, then the FMR frequency
is then given by
co0 = yJ(H)(H
+AnMs) (CGS Units)
14
(1.33)
where y and Msare the gyromagnetic ratio and saturation magnetization of the
sample. H is the internal biased magnetic field where any anisotropy of the
sample should be considered.
The tuning of the microwave FMR peak absorption frequency is clearly shown in
equation (1.32) or (1.33) and it can be depicted in Figure 1.2 where FMR peak
absorption frequency can be tuned in a wide frequency band by changing the
bias magnetic field H.
"\
3
o
Peak FMR Absorption
Frequency / ^ T u n i n g by
Magnetic Field H
>
CO
o
• /
fres(H)
Microwave Frequency
Figure 1.2 Tuning of FMR Peak Absorption Frequency
1.2.4 Magnetic Properties of YIG/GGG Film
Pure yttrium iron garnet (YIG) has cubic crystal structure with chemical formula
Y3Fe50i2. Each unit cell contains eight formula units. The basic lattice point is
15
m3m and the lattice constant is 12.376 A [26]. Pure gadolinium gallium garnet
(GGG) has the chemical formula GdsGasOn and also belongs to the cubic crystal
structure. The lattice constant of GGG substrates which are prepared by
Czochraliski crystal growth technique is 12. 383 A [22]. Single crystalline YIG thin
films are most commonly grown on lattice-matched GGG substrate by liquid
phase epitaxy (LPE) technique where a piece of polished GGG substrate was
dipped into a bath of molten flux and garnet materials, i.e., YIG, for a short time.
Typical film thickness ranges from 1 // m to 100 ju m. A 0.1 ju m transitional layer
limits the purity of submicron thin films. Severe cracking of thick YIG films
caused by the slight lattice mismatch between the epi-layer and the substrate
places an upper limit on thickness of YIG films on GGG. The best quality YIG
films are grown on [111] face GGG substrates with surface dislocation density of
1 defect/cm 2 . Single crystalline YIG thin film with its remarkable resonance
properties has attracted a great deal of research efforts. The very low intrinsic
damping of YIG film has made it an ideal vehicle for the study of fundamental
relaxation
properties,
spin-wave
excitations,
and
the
contribution
of
inhomogeneities to the linewidth. In additional to its fundamental values in
research, YIG has been found useful in many microwave applications [27]. Its gfactor of 2, narrow linewidth, and small anisotropy field make it especially
suitable for microwave-frequency applications. In many microwave devices,
such as ferromagnetic amplifier, resonance filters, harmonic generators, and
passive limiters, YIG has been widely used because of its small resonance
16
linewidth. In the room temperature, the Lande g-factor of YIG is equal to 2, the
saturation magnetization 4;rM s is near -1,700 Oe, and the Linewidth of polished
single crystalline YIG at X-band can be well below a few Oe's [27]. YIG is a
magnetic insulator where, in the room temperature, the electrical resistivity is ~
109
CI/cm.
1.3 Research Objective and Thesis Organization
Microwave tunable filters play critical roles in many microwave- and millimeterwave communication systems. For example, microwave band-stop filters are
required in many applications for suppression of the frequency parasitics,
undesired spurious bands or harmonics in microwave and millimeter-wave
devices and modules. Traditional techniques based on the use of half-wavelength
short-circuit stubs, chip capacitors or cascade rejection band filters are narrow
band in principle [28]. More recently, the planar electromagnetic band-gap (EBG)
structures have suggested some potential for wide stop-band band rejection
applications [29-30]. The FMR-based microwave filters have the advantages to
possess the unique capability of potential high-speed electronic tunability, using
magnetic field, for very high carrier frequency and very large bandwidth [31].
In this dissertation research, a magnetically-tuned microwave band-stop filter
using YIG/GGG- gallium arsenide (GaAs) flip-chip layer structure with
wideband tunability of stop-band center frequency and bandwidth has been
accomplished using a microstrip meander line together with non-uniform bias
17
magnetic field [32, 34]. A magnetically-tunable wideband microwave band-pass
filter with large tuning ranges for both the center frequency and the bandwidth
in the pass-band has also been realized using a pair of cascaded aforementioned
band-stop filters [33, 34]. The thesis consists of 6 chapters. In Chapter 2, the
theoretical modeling and analysis of YIG/GGG-GaAs layer structures are carried
out, and the calculated results predict possible device application as wideband
tunable microwave filters and phase shifters. Simulations of the microwave
band-stop filter using equivalent circuit model and finite element analysis (FEA)
method by ANSOFT High Frequency Structure Simulator (HFSS) are carried out
in Chapter 3. Chapter 4 and 5 presents the experimental study of the
magnetically-tuned wideband microwave band-stop and band-pass filters using
YIG/GGG-GaAs layer structures including device designs, fabrication, testing
and measurement results. Chapter 6 concludes the thesis with the discussion and
some future research topics.
Appendix
Al Maxwell's Equations in MKS and CGS System of Units
The four Maxwell's equations supplemented by two constitutive relations are
usually written in the form shown below. Equations (Al.l) to (A1.6) express the
Maxwell equations in MKS system of units
18
dB
~~dt
VxE =
VxH =
T
dD
J+
(Al.l)
(A1.2)
dt
V»Z) = ~Pv
(A1.3)
V»2? = 0
(A1.4)
B = /j0(H + M) = /iH
(A1.5)
D = s0E + T = sE
(A1.6)
where / = crE. The units of each field quantity are defined as
E = Electrical Field Intensity (volt/m)
D = Electrical Displacement (coulomb/ m2)
H = Magnetic Field Intensity (amp/m)
B = Magnetic Flux Density (weber/m 2 , tesla)
J = Current Density (am/m 2 )
pv = Charge Density (coulomb/m 3 )
a = Conductivity (ohms/m)
M = Magnetization (amp/m)
P = Electric Polarization (coulomb/ m2)
19
ju0 = Free Space Permeability (henrys/m)
e0 = Free Space Permittivity/Dielectric Constant (farads/m)
ju and s are the material permeability and permittivity.
Equations (A1.7) to (A1.12) express the Maxwell equations in CGS system of
units
V x ^ - I ^
c Bt
(A1.7)
vx^=i^ + i^
c
V*D = -4xpv
V»g = 0
B = H + 47TM = /JH
D = £ +4^? = f£
The units of each field quantity are defined as
E = Electrical Field Intensity (statvolts/cm)
D = Electrical Displacement (statcoulomb/ cm2)
H = Magnetic Field Intensity (oersted)
B = Magnetic Flux Density (maxwell/cm 2 , gauss)
pv = Charge Density (statcoulomb/cm 3 )
20
(AL8)
c dt
(A 1.9)
(ALIO)
(ALU)
(A1.12)
a = Conductivity (l/(statohms/cm))
M = Magnetization (oersted)
P = Electric Polarization (statcoulomb/ cm2)
Mo=
£ =1
o
ju and s are the material permeability and permittivity.
Reference
1.
J. D. Adam, L. E. Davis, G. F. Dionne, E. F. Schloemann, and S. N. Stitzer
"Ferrite devices and materials." IEEE Trans. MTT, vol.50, pp.721-737, Mar.
2002.
2.
David M. Pozar, Microwave Engineering, 3rd ed., John Wiley & Sons, Inc.,
2005.
3.
J. D. Adam, S. V. Krishnaswamy, S. H. Talisa, and K. C. Yoo., "Thin-film
ferrites for microwave and millimeter-wave applications," / Magn Magn
Mater, vol.83, pp.419-424,1990.
4.
V. S. Liau, T. Wong, W. Stacey, S. Ali, and E. Schloemann, "Tunable bandstop filter based on epitaxial Fe film on GaAs," IEEE MTT-S Dig., pp. 957960,1991.
5.
C. S. Tsai, J. Su, and C. C. Lee, "Wideband electronically tunable
microwave bandstop filters using iron film-gallium arsenide waveguide
21
structures/' IEEE Trans. Magn., vol.35, pp.3178-3180,1999.
6.
B. Kuanr, I. R. Harward, D. L. Marvin, T. Fal, R. E. Camley, D. L. Mills,
and Z. Celinski, "High-frequency signal processing using ferromagnetic
metals," IEEE Trans. Magn., vol.41, pp. 3538-3543,2005.
7.
E. Salahum, G. Tanne, P. Queffelec, M. Lefloc'h, A.-L. Adenot, and O.
Acher "Application of ferromagnetic composite in different planar tunable
microwave devices." Microwave and Optical Technology Letter, vol.30, Aug.
2001.
8.
B. Kuanr, L. Malkinski, R. E. Camley, Z. Celinski, and P. Kabos, "Iron and
permalloy based magnetic monolithic tunable microwave devices." /. Appl.
Phys., vol.97, pp.8591-8593,2003.
9.
N. Cramer, D. Lucie, R. E. Camley, and Z. Celinski. "High attenuation
tunable microwave notch filters utilizing ferromagnetic resonance." /. Appl.
Phys., vol.87, pp.6911-6913,2000.
10.
V. G. Harris, Z. Chen, Y. Chen, S. Yoon, T. Sakai, A. Gieler, A. Yang, Y. He,
K. S. Ziemer, N. X. Sun and C. Vittoria, "Ba-hexaferrite films for next
generation microwave devices" /. Appl. Phys., vol.99, 08M911,2006.
11.
Zhaohui Chen, Aria Yang, Anton Geiler, V. G. Harris, C. Vittoria, P. R.
Ohodnicki, K. Y. Goh, M. E. McHenry, Zhuhua Cai, Trevor L. Goodrich
and Katherine S. Ziemer, "Epitaxial growth of M-type Ba-hexaferrite films
on MgO (111) | | SiC (0001) with low ferromagnetic resonance linewidths,"
Appl. Phys. Lett, vol. 91,182505,2007.
22
12.
Yajie Chen, Anton L. Geiler, Taiyang Chen, Tomokazu Sakai, C. Vittoria
and V. G. Harris, "Low-loss barium ferrite quasi-single-crystals for
microwave application," /. Appl. Phys., vol.101, 09M501, 2007.
13.
Y. Chen, I. Smith, A. L. Geiler, C. Vittoria, V. Zagorodnii, Z. Celinski, and
V. G. Harris, "Realization of hexagonal barium ferrite thick films on Si
substrates using a screen printing technique," /. Phys. D: Appl. Phys., vol.
41,2008.
14.
Y. Y. Song, J. Das, Z. Wang, W. Tong, and C. E. Patton, "In-plane c-axis
oriented barium ferrite films with self-bias and low microwave loss," Appl.
Phys. Lett. Vol. 93,172503-1-3,2008.
15.
M.I. Bichurin, LA Korner and V.M. Petrov, "Theory of magnetoelectric
effects at microwave frequencies in a piezoelectric magnetostrictive
multilayer composite", Physical Review B, vol. 64, 094409, 2001.
16.
M.I. Bichurin and V.M. Petrov, "Theory of low-frequency magnetoelectric
coupling in magnetostrictive-piezoelectric bilayers", Physical Review B,
vol.68,054402,2003.
17.
S. Shastry and G. Srinivasan, "Microwave magnetoelectric effects in single
crystal bilayers of yttrium iron garnet and lead magnesium niobate-lead
titanate", Physical Review B, vol.70, 064416, 2004.
18.
Mirza I. Bichurin and Vladimir M. Petrov, "Composite magnetoelectrics:
their microwave properties", Ferroelectrics, vol.162, pp.33-35,1995.
19.
S. S. Kalarickal, D. Menard, J. Das, C. E. Patton, X. Zhang, L. C. Sengupta,
23
and S. Sengupta, J., "Static and high frequency magnetic and dielectric
properties of ferrite-ferroelectric composite materials," /. Appl. Phys.
Vol.100,084905-1-9,2006.
20.
S. D. Yoon, C. Vittoria, Y. N. Srivastava, A. Widom, and V. G. Harris,
"Magnetoelectric effects in composite of nanogranular Fe/Ti02-d films,"
Appl. Phys. Lett, vol.92, 042508, 2008.
21.
Carl Pettiford, Saumitro Dasgupta, Jin Lou, Soack D. Yoon and N. X. Sun
"Bias field effects on the microwave frequency behavior of a PZT/YIG
magnetoelectric Mayer", IEEE Trans Magn., vol.43,3343,2007.
22.
H. L. Glass, "Ferrite films for microwave and millimeter-wave devices,"
Proceeding of IEEE, vol.76, pp.151-158,1988.
23.
Carmine Vittoria, Microwave Properties of Magnetic Films, World Scientific
Inc., 1993.
24.
Richard L. Liboff, Introductory Quantum Mechanics, 4th ed., Addison
Wesley Inc., 2002.
25.
C. Kittel, Introduction to Solid State Physics, 7th ed., John Wiley & Sons, Inc.,
1996.
26.
Gerhard Winkler, Magnetic Garnet, Vieweg Tract in Pure and Applied
Physics, Friedr. Vieweg & Sohn Verlagsgesellschaft mbh, Braunschweig,
1981.
27.
Wilhelm H. Von Aulock, Handbook of Microwave Ferrite Materials, Academic
Press, New York and London, 1965.
24
28.
F. Martin, F. Falcone, J. Bonache, R. Marques, and
M. Sorolla,
"Miniaturized coplanar waveguide stop band filters based on multiple
tuned split ring resonators." IEEE Microwave and Wireless Components
Letters, vol.13, pp.511-513, 2003.
29.
V. Radisic, Y. X. Qian, and T. Itoh. "Broad-band power amplifier using
dielectric photonic bandgap structure." IEEE Microwave and Guided Wave
Letters, vol.8, pp.13-14,1998.
30.
F. Falcone, T. Lopetegi, M. Irisarri, M. A. G. Laso, M. J. Erro, and M.
Sorollaet. "Compact photonic bandgap microstrip structures." Microwave
and Optical Technology Letters, vol.23, pp.233-236,1999.
31.
C. S. Tsai, G. Qiu, H. Gao, L. W. Yang, G. P. Li, S. A. Nikitov, and Y.
Gulyaev. "Tunable wideband microwave band-stop and band-pass filters
using YIG/GGG-GaAs layer structures." IEEE Trans. Magn., vol.41,
pp.3568-3570,2005.
32.
G. Qiu, C. S. Tsai, M. M. Kobayashi, and B. T. Wang, "Enhanced
microwave ferromagnetic resonance absorption and bandwidth using a
microstrip meander line with step-impedance low-pass filter in a yttrium
iron garnet-gallium arsenide layer structure", /. Appl. Fhys., vol.103, 2008.
33.
Gang Qiu, Chen S. Tsail, Bert S. T. Wang, and Yun Zhu, "A
YIG/GGG/GaAs-Based
Magnetically Tunable Wideband
Microwave
Band-Pass Filter Using Cascaded Band-Stop Filters", IEEE Trans. Magn.,
vol.44, issue 11, 2008.
25
34.
C. S. Tsai, and G. Qiu, "Wideband microwave filters using FMR tuning in
flip-chip YIG-GaAs layer structures", accepted and to be published in
IEEE Trans. Magn., 2009.
26
Chapter 2
Theoretical Modeling and Analysis of YIG/GGG-GaAs
Layer Structure
In this chapter, the theoretical modeling and analysis of YIG/GGG-GaAs flipchip layer structure is carried out. A four-layer model and full-wave method are
used to calculate the wave propagation property of the magnetic layer structure
and the results show clearly maximum microwave energy absorptions at FMR
frequency and the wideband FMR absorption frequency tunability when tuning
the bias magnetic field. The theoretical results predict a potential device
application as wideband tunable microwave band-stop filter utilizing the FMR
absorption features of this magnetic layer structure in microwave frequency
band. A tunable phase shifter in microwave frequency band, as another device
application, is also discussed in this chapter.
2.1 Theoretical Modeling
2.1.1 Model Description
The magnetic layer structure used in this theoretical study is shown in Figure 2.1.
The analytical modeling and analysis method used in this chapter is based on a
two-layer (magnetic/dielectric) model in [1]. In Figure 2.1, the magnetic layer
structure consists of a YIG/GGG layer and a GaAs layer with thickness of d\,
|<i2|-|Jl| and |J4| - |J3|, respectively. A thin air layer with thickness of |c/3| in
27
between is used to model the effect of the air gap due to the existence of the
microstrip line in the experimental arrangement. The boundary between YIG
film and air gap is set at y - 0 as shown in Figure 2.1. Both the internal bias
magnetic field H0z and microwave propagation are in the z direction. The
microwave is designated to propagate along z direction with propagation
constant^. Because of the finite boundary on y direction, there is propagation
constant k as well, but kx = 0 due to infinite dimension on the x direction. The
propagation constant k2, for a given frequency of co, will be carried out to
characterize the wave propagating properties along the magnetic layer structure.
1
d2
d1
0
-d3
-d4
Figure 2.1 the Multi-Layer Magnetic Structure
2.1.2 Full-Wave Method
The method of theoretical analysis is outlined in Figure 2.2.
28
for a given co,
A(j)
findkztomake\M\-0
real(kz) Phase
imag(kz) Attenuation
t
y
PEC
Ex,Ez=0aty = d2,-d4
d2
InYIG, Hx =
Y,A(j)emyeJk-z
EX,EZ,HX, Hz continuous
dl
0
k
-[01
Wl
aty = Q,dl,-d3
HzHyExEyEz~A(j)(j
Total16 B.C.
Same for GaAs, GGG, Air,
••
-d3
GaAs
-d4 • • -
PEC
= lto4),
Total 16 unkown indepentent variables.
t
plug in
Maxwell Two CurlEqs.
Vx£ =
VX#:
k=0 and
\_ffi_
-cdt
\8D
for a given kz and a
tensor[n\
jggk
Vx(-Vxg) = -—
£
C
^
OU
[Q]
= [0]
when \Q\ = 0,
there are four k solutions
c dt
Figure 2.2 Outline of Analytical Analysis of the Multi-Layer Magnetic Structure
We will start with Maxwell's two curl equations to develop a relation involving
the magnetic field component H, then k is determined by a given kz and
frequency co. Each k gives an electromagnetic mode allowed in the layer and
the superposition of all the modes with independent variables or coefficients
represents the field in the layer. The analysis is carried out in the YIG layer first
and the similar analysis is carried out for the remaining dielectric layers (GGG,
GaAs, and air layer). Once all the field components are represented by their
corresponding independent variables, i.e., four independent variables for each
layer and the total are 16 independent variables, the boundary condition (B.C.)
29
will be used to write a matrix equation MV=0, where M is 16x16 B.C. matrix and
V is the vector of the sixteen independent variables. There is only nontrivial
solution if the determinant of M is equal to zero. Given a frequency co, we find
kz to make determinant of M is zero.
The CGS system of units is used in this section for the derivation. Starting from
Maxwell's two curl equations and the two constitutive relations in (2.1) to (2.4)
Vx£ = - I f
(2.1)
c dt
VxJ? = I ^
(2.2)
c at
B = H + 4TTM = JUH
(2.3)
D = E + 4xP = sE
(2.4)
We obtain
Vx(^-VxH) = --^pL
s
c
dt
In this derivation, the wave propagating is assumed in a form of Ae
(2.5)
j(kxx+ky+kzz-cot)
d
., d
., d
.,
, d2
and, therefore, — = jkxx — = jky — = jkzz and -^-j
= -co2 . Expanding left hand
2
dx
dy
8z
dt
side, we have
30
Vx(-Vxtf) = x :(-kykxHy-kAH,+KH*+kM
s
+y -(-KkH
-kxkHx
k2H+k2Hy)
+
(2.6)
-kykzHy+k2xHz+k2yHz)
+ z ~(-KKHx
Note that kx=0 due to infinite dimension on the x direction. Equation (2.6) turns
to
1
Vx(-VxH) = x (k2Hx+k2Hx)
£
2
+y -(-kzkyHz+k Hy)
(2.7)
-(-kykzHy+k2yHz)
+z
where e is the dielectric constant of the corresponding layer.
The right hand side of equation (2.5) is expanded when plug in the tensor
permeability [ju], we now consider the ferromagnetic material and [ju] is given as
follows [2].
"1 + 4 % ,
[//] = [/] + 4 4 * ] =
4
^ZyX
0
2
(yH0 + jcoa)
A„;
4%, °"
1 + ^Zyy
0
2
- co
. .
4n J
- co
(yH0 + jcoa) - co
0
= -jjUT
0
yMsco
——2
T
(yH0 + jcoa) - co
YMSQ>
(yH0 + jcoa)
A
0
1
0
7>r
0
//,
0
0
1
31
0
0
1
(2.8)
Where y and a axe the gyromagnetic ratio and the Gilbert damping factor,
respectively. The damping factor a is related to the ferromagnetic resonance
AHv
linewidth AH and frequency co as cx =
— [3] (see Appendix A2). Expanding the
2co
right hand side of equation (2.5), we have
i a2 (juH)
c2 dt2
—— JC
2
2
CO
(0
-^Hx^+—HyMT
2
2
CO
+y
CO
„
2-HXMr+ — HyA
c
c
(2.9)
CO
+z
2 a,
Equate (2.7) and (2.9), we have this following matrix equation [£)][#] = 0,
W>
s
s
H
.[iTco
J
c
H
£
KK
0
The equation
KK \ v']
fh°>
y
Hz
CO
~0~
= 0
0
(2.10)
s
(2.10) has nontrivial
solution when the |£?| = 0 , that
is
Ak* + Bk2+C = 0, where
A=
2 2
EC
B=
CO
EC
J(MI+MI2-VT2)—Tl-(1
2„4
C=
2M>
EC*
, ,k4 „ 2
>
2 2
EC
+
EC
M)
(2.11)
^
+-r(#r -M )
Therefore, given kz and co, there exist four solutions for k which corresponds to
32
four different electromagnetic modes allowed, k is given as
i
-B±(B2-4AC)2
:+
2A
MO ;=i to 4
(2.12)
Now the /f is readily to be written as linear superposition of the four modes with
different k . H now to be written as
^=XaO'Moy*' (0 v^
(2.13)
j=i
where
X ( 0 2 . K2
-+£
a(i) =
ju^2
S
2^
f
.•Mr®
2
V
C
C
J,
^(0 2
k2
£•
S
m-
W>
2V
K(i)2
• MTco
Km
(2.14)
co
2
J
The electrical field E can be represented in terms of Hby the Maxwell's curl
•
1„
rr
1 QE
.
,
,
equation—V x H =
, or equivalently
s
c 8t
33
c
£
MkzHx-kxHz) =
(2.15)
C
£
l(kxHy-kyHx)
=
£
£
C
JSLEXk-*^,)--^
C
£
C
Now the E can be represent in terms of A(i) as follows
E
* =—
£C0 j=\
L
Z\(kM^-kyd)m)A(i)eJk^e^
k
eJ
y(i)y'eiK:
(2.16)
£CO~~?
Now all E(Exx,E y,Ezz)
and H(Hxx,H
y,Hzz)aie
written in terms of the four
independent variables A(i)\.
=lto4
The
above
derivations
H(Hxx,Hyy,Hzz)
are
focused
on
calculating E(Exx,E y,Ezz)
and
in the ferromagnetic material. Now the similar analysis is to be
carried out in the dielectric materials, i.e., GaAs, GGG and air layer. Since the
permeability in dielectrics is simply represented by ju = I , so the matrix
equation[g][i/] = 0 for dielectric material is (note that kx = 0)
K K2
£
£
0
0
a?2
0
0
c2
k2
co2
KK
£
C2
£
KK
£
34
"o"
Hy
0
0
y
K co2
£
X"
C2
Hz_
(2.17)
We can determine the ky value by a given kz and co from the top left element of
[Q] and lower right 2x2 elements of [Q], respectively. Both of them are turned
out to be same mathematic condition as follows
K2
k.
+^
CO
=0
r
£
(2.18)
C
Therefore, k can be computed as
2
= ± Uco -k.
K
i
Y2
(2.19)
The block diagonal character of the [Q] means that we can not express H and
H2 in terms of Hx. They are expressed separately as follows.
Hy=jrC(i)eJk>(i)yeJk>z
(2.20)
Hz=fdS(i)C(i)e^'(i)yeJk-z
r=l
where
r
S(i) =
e
£
,2 A
CD
C
Kky(i)K
Finally the E can be represent in terms of B(i) and C(i) as follows
35
(2.21)
E*=—i[(*. -^o)^(o)c(/)^(°v^;
SCO _ .
kzB(i)ejkAi)yeJKz
E =—-Y
(2.22)
scott
Ez=-^-±-ky(i)B(i)eJkAi)ye^
£0)
=1
The derivations above are applicable for the three different dielectric materials
including GGG, GaAs and air. The differences are the material parameters and
its k 's and, therefore, its corresponding independent variables. Now we should
combine all E and //fields in dielectrics (in GaAs, GGG, and air layer) and
ferromagnetic material (YIG) to the B.C.. The boundary conditions are
summarized in Table 2-1. The notations of the field independent variables
(e.g.,^(/),5(/)...) and field conversion factors (e.g.,a(/),/?(z)...) for each material
is summarized in Table 2-2.
Table 2-1 Boundary Conditions of the Four-Layer Magnetic Layer Structure
y -axis Position
y = d2
y = d\
Boundary Conditions (B.C.)
=
^xGGG
J-f
n
y=o
— M
^xYlG
^xAlR
**xAIR
y = -d4
n
=
=
=
"'
=
• f-f
^zAIR
zYIG »
~ -"zAIR'
=
^zGaAs
HxGaAs,nzAIR
=
n
~ ^ zAIR »
^xAIR'^zYlG
^xGaAs'
^zYIG'
—M
xYIG > " zGGG
~ ^xAIR •> &ZY1G
^xGaAs
36
' ^zGGG
^xYIG •> ^iGGG
xGGG
**xYIG
y = -c/3
u
^xGGG
^ ' ^zGaAs
'
—tlzGaAs,
=
^'
Table 2-2 Field Independent Variables and Field Conversion Variables
Material
GGG
Independent Variable
Field Conversion Factor
*(0L to2 ;C(0L o2
YIG
^•)L o 4
Air
^0L to2 ;£(0|, lto2
F
(OL 2 ;G(o|, lto2
*(0L, 2
«(0|,=1/o4;A(0Llto4
tfOL*
GaAs
<PWLo2
There are total 16 B.C., and, according to those B.C., the following equations are
given
At y = dl
ExGGG ~ 0
t [(*, - KGGG OW)) c ( * y W i ) V*< Z '= 0
e
GGGG)
EzGGG
i=l
=
(2.23a)
^
ZU^'V^'V^o
£
GGG<^
«'=1
At y - d\
^xGGG
~
^xYIG
Z [(*. - W (0^(0) C(/y w ° V^ ^
£
GGGC0
>'=1
t[(K^)-kyY1G(i)m)meJkyY,Gii)ye^
SYJQCO , = I
^zGGG
=
^zYIG
k
J ,GOG(')y
^kyGCG(i)B(i)ejk^a)y
e
8
GGG®
ikz:
»=1
Jk,no(')y
EWOAO**"8^
SYJQCO
ajkzz
i=\
rr
" " xr/G
TJ
- " *GGG
JkyBc(')yik^
i=i
" zGGG
i=i
=
HzYIG
(2.23b)
1=1
1=1
37
At y = 0
^xAIR
~
^xYlG
t[(kz-kyA!R(i)m)meJKA'R(i)yeJk>°
£
6)
AIR
<=1
X[(^«(0-V/ G 0')A0)^(0e 7VG<0 ^ Az
YIG
^zAIR
»=1
~
^zYlG
fiyAIR^iy
SWO^'V^e
£
AIR0)
JKZ
i=l
YKvomav^e
Jkyna(')yoJKz
£yjGG)
^zAIR
,=1
~
™zYIG
Y,0(i)E(i)eJk^{i)yeJKz =
Y^p^Aiiy^'e^
(2.23c)
At y = - J 3
^xAIR
^xGaAs
-kyA1R(i)m)E{i)eJk^(i)ye^]
t[(K
e
AIRCO
i=\
E[(*,-WO*o)^i> w 'V
S
GaAs(D
-^z^ffl
=
i=l
^zGaAs
X^OPOVv<^
jk,Amii)y
sATD
a>
AIR™
Jkzz
i=l
JkyGa.4s(')y
jkzZ
% ^ < ^ i=l
**xAIR
=
tlxGoAs
2
2>o>
JkyAmOv
Jkzz
2
_ V
J=l
"z/lffi
{t)y
JKz
i=l
=
**• zGaAs
^(/)£(/y
(=1
k
=£*•(»>J7{r\J y<*«*
Vs(0
V
M
(2.23d)
= XP(OG(0^
(=1
38
WO)
V
V
y = -d* \
^xGaAs
~
C
Y(7/~
£
GaAsCO
EzGaAs
"
/-
d\m(i'\\G(i'\rikyaaA'{ji)yJk'z' = 0
(2.23e)
(=1
=
^
- ^ t W O ^ W O V ' ' =o
Now equations (2.23 a-e) are used to write a matrix equation MV=0, where M is
B.C. matrix and V is the vector of the sixteen independent variables.
A(l)'
A(2)
A(3)
A(4)
B(l)
B(2)
OT,
1,1
OT
1,2
™1,16
w21
w,2,2
"h,l6
C(l)
C(2)
DO)
™16,1
™16,2
™16,16
= 0
D{2)
E{\)
E(2)
F(l)
F(2)
G(l)
G(2)
(2.24)
Equation (2.24) has nontrivial solution when the determinant of M is equal to
zero. For a given frequency co, Mutter's method was applied to find kz which
makes the determinant of M to be zero. The calculated k, is the wave
39
propagating constant containing the information regarding the attenuation and
phase. The results are analyzed in detail in the next section.
2.2 Numerical Results and Analysis
2.2.1 FMR Absorption and Its Band-Stop Filter Application
We re-write equation (1.32) here as (2.25)
*>o = rJ(HMernal+(Ny
-Nz)Ms)(Hinternal+(Nx-Nz)Ms)
(CGS Units)
(2.25)
In the magnetic layer structure depicted in Figure 2.1, when the bias field is
applied to the plane of the film (x-z plane), Nx=Nz=0;
Ny=4n: , then the FMR
frequency is
*>0 = / M - — Win*™, +**K) (CGS Unite)
(2.26)
The FMR theory predicts that there will be a strong resonance at microwave
frequency in the ferromagnetic layer structure described in Figure 2.1. Now we
will calculate the wave propagation attenuation based on the full-wave method
described in previous section to examine the FMR absorption in the layer
structure in a wide microwave frequency regime. In this calculation, the material
and geometric parameters used are in consistent with experimental arrangement,
therefore, the thickness of GaAs substrate and YIG film are 350 jum and 6.8 jum,
respectively. A 1.0 fim air layer is used to model the effect of the air gap due to
the existence of the 1.0 jum thick microstrip line. The GGG substrate used to
40
epitaxial-grown YIG sample is ~ 350 jum. The AH and Ms of YIG sample are 1 Oe
and l,160Oe , respectively, same as the material properties used in the
experiments. The dielectric constant
besGGG =14.7 and £GaAs=l\.l,
of GGG and GaAs are set to
respectively. As an example, a 2,200Oe field is
applied to +z direction. The propagation distance along z direction was fixed at
0.57 cm for all the calculation in this chapter which is ready to be compared with
experimental arrangement. The calculated microwave attenuation vs. rf
frequency in the frequency of 8.0 to 8.5 GHz is shown in Figure 2.3.
-i
-10 \00 -20
C
o
1
"iU
-30
I
-40
r
i
•
r
~ O.O
GaAs =350un
Z-distance =0.
H. t
•4=
03
1
= 2,200
internal
'
-50
FMR frequency = 8.2708 GHz
-60
8.0
J
8.1
I
.
8.2
I
8.3
.
L
8.4
Frequency (GHz)
Figure 2.3 Calculated Microwave Attenuation vs. rf Frequency when
H = 2,200 Oe
41
8.5
Figure 2.3 shows clearly a maximum microwave power absorption at frequency
of 8.2708 GHz. As a comparison, the predicted FMR frequency by equation (2.26)
is 8.2645 GHz which are essentially the same to the peak absorption frequency
shown in Figure 2.3. From the device application point of view, Figure 2.3
demonstrates a clear band-stop filtering function at microwave frequency regime,
and, throughout this dissertation, the wideband tunable microwave band-stop
and band-pass filters to be discussed are all based on this basic FMR absorption
mechanism in this magnetic layer structures.
2.2.2 Wideband FMR Frequency Tunability
By plug in different values of the bias magnetic fields, the calculations show that
the frequencies of the maximum microwave power absorption associated with
this magnetic layer structure were changed in a wide frequency band. The
comparison between the calculated microwave power absorption frequency (0 to
~ 25 GHz) and the predicted FMR frequency by equation (2.26) vs. the bias
magnetic field (0 to 8000Oe) is shown in Figure 2.4, while we see an excellent
agreement between the calculated microwave peak absorption frequencies and
the FMR frequency theory. Clearly, wideband tunability of FMR absorption
frequency is shown in Figure 2.4.
42
-1000
0
1000 2000
3000
4000
5000
6000
7000
8000 9000
Internal Bias Magnetic Field (Oe)
Figure 2.4 Calculated FMR Frequencies vs. Biased Magnetic Field
From the application point of view, the maximum microwave power absorption
level at FMR frequency is crucial when it is used as a microwave band-stop filter.
Therefore, the FMR peak absorption level vs. FMR frequencies is calculated and
shown in Figure 2.5. Clearly, Figure 2.4 and 2.5 combined predict a potential
device application as a tunable microwave band-stop filter with large tuning
range of peak absorption frequency with large peak absorption levels.
43
1
30
CD
cz
1
I
—-1
1
'
1
•
40
45
1
1
1
1
1
1
-
•
\
•50 -
-
X -V.
X
•55
-
^•-^
^•^
•60 -
•
i
•65
1
YIG = 6.8um
GGG = 350um
Air= 1.0um
GaAs =350um
z-distance=0.57cm •
35
o
03
CD
Q_
1
•
o
CO
<
1—
"
1
6
•
l
1
8
10
.
1
I
12
14
.
I
.
16
I
.
18
20
FMR Frequency (GHz)
Figure 2.5 Calculated FMR Peak Absorption Level vs. FMR Frequency
As a typical example, the calculated attenuation vs. microwave frequency in a
frequency range of 8 to 10 GHz is shown in Figure 2.6, where the bias magnetic
fields used are from 2,200 Oe to 2,700 Oe.
44
-"
n
T
"
r~
'"" T
'
1
"
1
'
1
'
1
"^
'
i
'
1
1
'
'
'
1
'
"\
^
-10
'
-
'
r
-20 _
_
*
CQ
3 ^ -30 c
•2 -40
*
-
^"-V
II
CO
13
0
H—»
<
-
y
1
i
i
i l l
0U
li
II
u
I
„ nnn „
-60 ~YIG = 6.8um 2,300 Oe 2' 400 Oe 2,500 Oe
1 :
2,200 Oe
2,600 Oe 2,700 Oe
-
• GGG = 350um
Air^LOum
-70 ~ GaAs =350um distance =0.57cm
_«n
8.0
i
8.2
.
i
8.4
.
i
8.6
.
i
.
8.8
i
.
9.0
i
•
9.2
I
9.4
i
I
9.6
.
I
.
9.8
10.0
Frequency (GHz)
Figure 2.6 Calculated Attenuation vs. Microwave Frequency in 8 to 10 GHz
2.2.3 Material and Geometric Parameters Effect
The microwave power absorption predicted in this magnetic layer structure is
utilizing the strong coupling, at FMR frequencies, between the rf microwave field
and the precessing magnetization in the magnetic layer. As with any resonance
system, the effect of losses must be considered in its frequency response. The
major parameter in the measurement of the loss in FMR system is the FMR
linewidth (AH). Appendix A2 gives a brief introduction of FMR linewidth and
its association with magnetic damping factor of the ferromagnet. AH is generally
used to characterize the contribution of intrinsic loss mechanism and to
45
determine the role of magnetic inhomogeneities as well [5].
-10
CQ
c
o
-20
•+=
-30
I
-40
CD
13
H. t
= 2,200 Oe
internal
DeltaH=0.8Oe
DeltaH=1 Oe
DeltaH=2 Oe
DeltaH=4 0e
uaAs =JbiJum
Ustance =0.57c
-50
-60
8.0
8.1
8.2
8.3
8.4
8.5
Frequency (GHz)
Figure 2.7 Effect of FMR Linewidth on Attenuation
Figure 2.7 shows the effect of FMR linewidth ( AH = 0.8,1, 2, 4 Oe ) on the
microwave attenuation at 8.2708GHz when H = 2,200Oe. As shown in Figure 2.7,
the lower AH corresponds to higher FMR peak absorption level and a narrower
FMR absorption bandwidth, holding all other parameters constant.
The effects of dielectric layer thickness and ferromagnetic layer thickness on the
microwave attenuation are also calculated. The thickness of the dielectric layers
has a significant impact on the calculated attenuations. As shown in Figure 2.8, a
46
thickness of 150 urn GaAs layer provides much higher attenuation and slightly
wider absorption bandwidth than others, holding all other parameters constant.
The same effect happened on the GGG. As shown in Figure 2.9, a thickness of
150 um GGG layer also provides much higher attenuation and slightly wideband
absorption bandwidth than others, holding all other parameters constant. The
effects of thickness of GGG and GaAs are almost identical because they are
nearly symmetric in the magnetic layer structure.
10
0
= 2,200 Oe
te
-10 h H,internal
^-v -20
DO
/stance
w
-30 h GaAs Thickness t4
C
—14
= 450 um
o
14 = 350 um
"ro -40
t4 = 200 um
ZJ
t4 = 150 um
c
_?> -50
-60 h
-70 h
8.0
8.1
8.2
8.3
8.4
Frequency (GHz)
Figure 2.8 Effect of GaAs Thickness on Attenuation
47
8.5
10
jgg|SS4SSaSS«£8SiffiSS!Sili«SS!aSfe
-10
H.,
internal
= 2,200 Oe
'/L? -
'
GaAs =350um
Air- I.Oum
-20
c
o
-30
=5 -40
C
5
-50
o.oum
GGG Thickness t2
t2 = 450 urn
t2 - 350 urn
t2 = 200 urn
t2 = 150 urn
-60
-70
8.0
8.1
8.2
8.3
8.4
8.5
Frequency (GHz)
Figure 2.9 Effect of GGG Thickness on Attenuation
The air layer is used to model the thin air gap due to the existence of microstrip
transmission line. It has a typical value of a few microns. As shown in Figure 2.10,
the thickness of air layer has little effect on the propagation attenuation as
expected.
48
-10 \- H. ,
internal
00
YIG = 6.8um
GGG = 350um
GaAs =350um
^-distance =0.5
= 2,200 Oe
'
-20
c
o
•^3 - 3 0
CD
C
£ j -40
<
-50
-60
8.0
Air Thickness t3
-t3 = 0um
-t3= 1 urn
t3 = 1.5 urn
-t3 = 2um
8.1
8.2
8.3
8.4
8.5
Frequency (GHz)
Figure 2.10 Effect of Air Layer Thickness on Attenuation
The thickness of the YIG has a significant impact on the calculated attenuations.
Unlike metallic thin film where increasing the thickness beyond skin depth has
little effect on attenuation, the conductivity of magnetic insulator (i.e., YIG) is
very low and the wave can penetrate and propagate inside the medium. As
shown in Figure 2.11, for example, a thickness of 20.8 urn YIG layer provides
much higher attenuation and much wider absorption bandwidth than a
thickness of 6.8 um cases, holding all other parameters constant.
49
-10 f- H
1
= 2,200 Oe
internal
'
GO -20
c
g
-30
13
C -40
CD
-50
5G = 35Gum
ir= 1.0urn
iAs =35
YIG Thickness t1
—
tl = 2.8 urn
11 = 6.8 urn
t1 = 8.8 urn
t1 = 15.8 urn
t1 =20.8 urn
-60
8.0
8.1
8.2
8.3
8.4
8.5
Frequency (GHz)
Figure 2.11 Effect of YIG Thickness on Attenuation
2.2.4 Phase Shifter Application
Phase shifters find applications in test and measurement systems, but the most
important use is in phased array antenna systems. In general, the change of the
effective permeability under the bias magnetic field of single crystalline ferrite
materials is more sensitive than the polycrystalline form. Therefore, in recent
years, the microwave phase shifters based on single crystalline ferri- or ferromagnetic thin film structures have been actively studied [6-8].
50
3*
CO
-i—>
C/)
c
o
O
c
o
CD
O)
CD
s_
Q.
O
u.
0_
9.50
9.55
9.60
9.65
9.70
9.75
9.80
9.85
9.90
9.95
10.00
Frequency (GHz)
Figure 2.12 Calculated Propagation Constant (Real and Imaginary Parts)
at
H0=2,7\0Oe
The YIG/GGG-GaAs layer structure discussed in this chapter has possible device
application as tunable phase shifters. Figure 2.12 shows the calculated
propagation constant (both real and imaginary part) in 9.5 to 10 GHz while the
bias magnetic field is 2,710 Oe. The wave is very dispersive (see Figure 2.12 real
part ofkz) near the resonance. In the phase shifter application, in principle, the
operating frequency is near the FMR frequency for maximum change of the
phase with small bias magnetic field variation, and, in the meantime, the
attenuation due to the change of the phase should remain low. In other words,
51
the operating frequency of the phase shifter should be near the FMR frequency
which gives maximal dynamic range of the phase change and the minimum
attenuation variations. For example, the possible operating frequency band for
the phase shifter application of the magnetic layer structure when bias magnetic
field is 2,710 Oe is indicated in Figure 2.12 (see the frequency range between blue
lines).
As an example, Figure 2.13 shows the calculated phase shifts at the operating
frequency of 9.66 GHz with the bias magnetic field tuned from 2,710 Oe to 3,420
Oe, while the attenuation loss variation is within 0.3 dB.
500
400
0
300
D)
CD
CD 2 0 0
CO
CD
Q_
100
0
9.50
J
I
9.55
1
I
9.60
1
I
I
9.65
I
9.70
1
I
9.75
1
I
9.80
1
I
9.85
I
I
9.90
I
I
9.95
L
10.00
Frequency (GHz)
Figure 2.13 Calculated Phase Shift at 9.66 GHz while H0 is changed from
2,71OOeto3,42O0e
52
As a conclusion, the calculated wave propagation property of the YIG/GGGGaAs layer structure shown clearly maximum microwave power absorptions at
FMR frequency and the wideband FMR absorption frequency tunability when
tuning the bias magnetic field. The theoretical results predict a potential device
application as a tunable microwave band-stop filter with large tuning range of
peak absorption frequency with large peak absorption levels.
Appendix
A2 Ferromagnetic Resonance (FMR) Linewidth
Laudau and Lifshitz introduced the equation of motion of magnetization with
damping effect originally.
— =W M x / / - n M x —
dt
\M\
dt
(MKSunit)
(A2.1)
where:
M: magnetization {A I m)
H: bias magnetic field {A I m)
y: gyromagnetic ratio, In x 2.8 xlO10 (rad /(sec* tesla))(MKS)
/J0 : free space permeability
a: damping coefficient
We can begin with this lossy equation of motion of magnetization to derive the
lossy tensor susceptibility \%\, and thus tensor permeability [//], or loss can be
accounted for by making the resonant frequency complex co0 <- a>0 + jaco.
53
When we plug the complex resonant frequency co0 + jam into equation (1.26) and
(1.27) in chapter 1, the complex tensor susceptibility [j] can be given as:
stxx
sCxx
J si xx
[AXF
s^xy
J /Cxy
/ A r\ r)\
where
\jol -6>2(l + a 2 )] + 4<z>2<y2a2
[<y2-<y2] + 4a>lco2a2
acoa>m\a>Q+G)2(l + a2)\
aa>a>m\a)Q+G)2(l + a2)\
=
Xxx =
2
^— =
—2
^42.3(6)
2
2
2
2 2 2
2
2
[&>0 - <» (1 + a )] + 4o) a) a \col - a> ] + 4&>0Wa
(a « 1 , 1 + a 2
2 1+ 2
2
2
2
a*»mM-» ( a )l
coo)m\o) -co (l + a )]
Xxy =
^
[<y02-a>2(l + a 2 )]
=
2
=
^
2
+ 4c?0Wa
l^o^a
=
2
2
2
2 2
[(y0 -cj (l + a )] +46> ft> a
2
^
-42.3(c)
2 2
+ 4cv G) a
2_^a
=
2
=
2
[<»02-<y2]
2
A 2 m
2
2 2 2
[<» -<» ] +4<» o a
The damping coefficient a is related to the linewidth (AH) of the susceptibility
curve near the resonance. The linewidth is defined as the width of the curve of
Z^ vs. H0 where zlx has decreased to half of its peak value.
The imaginary part zL w^ g ° t o maximal when co - co0 which is:
acoa>m\(D2 + co2(l + a2)\
y
=
!=
[rt-m2]
=L
+ 4co2co2a2
Assuming when*; = co02, x„ = - £ , m a x / so
54
i+«2=i
—s
~>
y
„
=
co
__2L_
2™
acocom a>l2 + a>2
1
2
2
2
[co 02-co ] + 4 f i 4 © V
ffl.
-X-
2
««
=> <902 = coy[\ + 2a «<y(l + a )
=> Aft>0 = 2(<»02 - <0O)« 2©(1 + a ) - 2<y = 2 a »
. TT A<»n 2aco
=>AH-—=
ju0y
MoT
AHMnV
CM
or a =
2®
(A2.5)
Reference
1.
R. J. Astalos and R. E. Camley, "Theory of a high frequency magnetic
tunable filter and phase shifter", /. Appl. Phys., vol.83, pp.3744-3749, April
1998.
2.
Carmine Vittoria, Microwave Properties of Magnetic Films, World Scientific
Inc., 1993.
3.
David M. Pozar, Microwave Engineering, 3rd ed., John Wiley & Sons, Inc.,
2005.
4.
C. Kittel, Introduction to Solid State Physics, 7th ed., John Wiley & Sons, Inc.,
1996.
5.
B. Heinrich and J. F. Cochran, "Ultrathin metallic magnetic film", Adv.
Phys., vol.42, pp.523-549,1993.
6.
H. How, P. Shi, L. C. Kempel, K. D. Trott, and C. Vittoria. "Single-crystal
YIG phase shifter using composite stripline structure at X band." /. Appl.
Phys, vol.87, pp.4966-4968,2000.
7.
E. Salahum, G. Tanne, P. Queffelec, M. Lefloc'h, A. L. Adenot, and O.
55
Acher "Application of ferromagnetic composite in different planar tunable
microwave devices." Microwave and Optical Technology Letter, vol.30, Aug.
2001.
8.
Bijoy Kuanr, L. Malkinski, R. E. Camley, Z. Celinski and P. Kabos; " Iron
and permalloy based magnetic monolithic tunable microwave devices." /.
Appl. Phys, vol.97, pp.8591-8593,2003.
56
Chapter 3
Device Simulations of Microwave Band-Stop Filter
using YIG/GGG-GaAs Layer Structure
The theoretical analysis of YIG/GGG-GaAs layer structure in Chapter 2 predicts
the device application as a tunable wideband microwave band-stop filter. In this
chapter, simulations aimed at device performance of the microwave band-stop
filter using YIG/GGG-GaAs layer structure are carried out. A lumped element
equivalent circuit method of the band-stop filter is presented first in this chapter.
The advantage of a circuit model of the band-stop filter is the easy incorporation
with commercial circuit simulator, and, therefore, an electronic subsystem, e.g.,
an oscillator, utilizing the band-stop filter (resonator) can be further simulated
with a reliable equivalent circuit model. The simulations of finite element
analysis (FEA) using ANSOFT High Frequency Structure Simulator (HFSS) is also
discussed in this chapter. HFSS utilize 3-D full-wave FEA to conduct simulations
for two-port parameter (S, Y, Z) extraction, and its capability of simulating em
field distribution assist designs and optimizations of microstrip transmission line
(transducer) in this YIG/GGG-GaAs-based microwave band-stop filter.
3.1 Simulations using Equivalent Circuit Method
The basic device configuration of a tunable microwave band-stop filter using
YIG/GGG-GaAs layer structure is shown in Figure 3.1. A YIG/GGG layer is laid
57
directly upon the GaAs-based microstrip line in a flip-chip configuration. An
external bias magnetic field H0 is supplied along the z direction. The incoming
microwave propagating along the microstrip is coupled into the flipped
YIG/GGG layer and maximum coupling and, thus, the peak absorption of the
microwave occurs when its carrier frequency coincides with the FMR frequency.
YIG/GGG
Layer
X
Microwave
Ouput
GaAs
Substrate
round
Plane
Transmission
Line
Microwave
input
Figure 3.1 Device Configuration of the Microwave Band-Stop Filter using
YIG/GGG-GaAs Layer Structure
A theoretical modeling and analysis of this layer structure has been carried out in
detail in Chapter 2. In this section, the simulation of the YIG/GGG-GaAs based
microwave band-stop filter using a lumped element equivalent circuit model is
presented [1]. As we stated before, once a circuit model of the microwave bandstop filter is available, it can be easily incorporated with commercial circuit
58
simulator, e.g., Advanced Design System (ADS) or Microwave Office by Applied
Wave Research, Inc, and, furthermore, an electronic subsystem utilizing the bandstop filter (resonator) circuit model can be simulated. The simulation of the
microwave band-stop will be presented by: (1) the calculation of the radiation
resistance Rm of a YIG/GGG film in flip-chip coupling configuration, (2) FMR
frequency knowledge and experimental data [2], and (3) the simulation of a
lumped element equivalent circuit of the microwave band-stop filter using
Microwave Office. The resulting lumped element equivalent circuit model [1] is
shown in Figure 3.2.
l:n
Zo
|
CZI
n:l
1
C
Vin(V)
j I
L
Zo
R
Figure 3.2 Lumped Element Equivalent Circuit Model of the Microwave BandStop Filter
3.1.1 Calculation of the Radiation Resistance
As we studied in Chapter 1, when a ferrimagnet is bias by a large externally
magnetic field, the ferrimagnet become magnetically saturated to produce a
59
saturation magnetization. Each individual magnetic dipole in the ferrimagnet
will precess in a resonant frequency, e.g., Lamor precessing frequency. Due to
the dipole-dipole coupling and quantum mechanical exchange coupling, the
collective interactions among neighboring magnetic dipole moments produce a
continuum spectrum of precessing modes or spin waves at frequency bands near
the resonant frequency. Exchange-free spin wave spectrums obtained under the
magnetostatic approximation are known as magnetostatic wave (MSW) [3-6]. In
essence,
MSW
are
relatively
slow-propagating,
dispersive,
magnetically
dominated electromagnetic (em) waves which exist in biased ferrites at
microwave frequencies. It is well studied that three magnetostatic wave (MSW)
modes can exist in a ferromagnetic layer depending on the orientation of the bias
magnetic field relative to the ferromagnetic film and the propagating microwave
direction [3-6]. These modes are magnetostatic surface wave
(MSSWs);
magnetostatic forward volume wave (MSFVWs); and magnetostatic backward
volume waves (MSBVWs) [3-6]. In the microwave band-stop filter configuration
shown in Figure 3.2, the external bias magnetic filed H0 is applied in the z
direction in the plane of the YIG/GGG film and along the direction of the
microwave propagation, and, therefore, MSSWs are to be excited in this
configuration with propagation direction along the ±y axis [4].
60
GGG
Microstrip
YIG
d 1
dn
b
Substrate
/////////
I IA
Ground
Figure 3.3 Cross-Section View of MSSW Excitation Geometry
A theoretical analysis is developed in [4] for excitation of MSSWs with microstrip
transmission line in flip-chip configuration as shown in Figure 3.3. Energy
carried away in MSSWs propagating perpendicular to the microstrip (in ±y
direction) is related to electromagnetic energy propagating along the microstrip
line (in z direction) by an equivalent radiation resistance Rm. Here we will use
the formulism developed in [4]. The Rm of the excited MSSWs with YIG/GGG
film flip-chip coupling configuration is given by the expression.
(3.1)
Where A+ and A_ are the Rm associated with MSSW propagation along ±y
directions, respectively. A+ and A_ are given as
61
A± = u^coR,
sin(M 0 /2) 2
bkjl
2
1 - 4£07 exp(-2£0/) - exp(-4£0/)
[2k0d{(ul2s + lf -Mn}]~ x[2
[l + exp(-2£00]
x {{uns +1) sinh(^0J) + ux x cosh(&0<i) }2 + (uus + 2w, xk0d) {(ul2s+1)2 - u2n}
(3.2a)
- {ul2s[(ul2s+1)2 - Wj2 ] - 2w2j} cosh(2k0d) - w, x (u22 - 1 - u\x) sinh(2^0c/)]
where
i?t0 = (Wj j - w^s -1) exp(-£0 d) tanh(k0t) I AkQ (un-u12s + tanh(k0t))
Ak0=l + un(tf d)(l-tanh
k0t)[un -(uns-tanhk0t)
2 -i-l
]
(3.2b)
(3.2c)
The t, d and b axe defined in Figure 3.3 of the cross-sectional view of the
excitation geometry. un and un are diagonal and off-diagonal components of the
permeability tensor, respectively. s = ±\ represents the MSSWs propagating
directions of ±y direction in Figure 3.3. a and the propagation constant k0 are
related by dispersive equation of MSSWs in this configuration and will be
calculated shortly.
The formulism of co-k relation of excited MSSWs in the YIG/Dielectric layer is
well developed in [5-6]. The relative permeability tensor uris given again as
follows. The permeability tensor used here is in CGS units.
ux
-iu2
0
iu2
ux
0
where
Q = o)/a)M,
aH=coclcoM
62
0
0
1
(3.3)
o)-27ixf
is the wave angular frequency, coc = 2zr xyH0 is the gyromagnetic
angular frequency (y = 2.SMHz/Oe is the gyromagnetic ratio, and the H0is the
internal biased magnetic field), a>M = 2n x yAnMs ( AnMs is the saturation
magnetization = l,760Oe). The dispersive equation for MSSWs written in terms
of Q and Q.H is given by [5]
ei\k]d
1
l + (fls + Q g ) [ l + tanh(-|fc|0]
2(Qs + Q„) + l l-(Qs-Q„)[l-tarJi(-|&|0]
(3.4)
The problem is now to find the value of k which, for a given frequency of / ,
satisfies the implicit dispersive equation (3.4). This is a root-finding problem
requiring an initial guess at the value range of the root. In our case, the
wavenumber k ranges over 10 <k<l05cm'1 . The range of / is the frequency
range of excited MSSWs at ±y direction under this device configuration
determined by the YIG intrinsic properties (e.g., Ms) and external bias magnetic
field (H0). The lower frequency limit of the excited MSSWs is given as [5-6]
-|l/2
/,=rt4*M,)
£
(3.5)
- -(—£- + 1)
°>M
®M
For the cases of dIt —» 0 (it is the usual case that the thickness of ferromagnet is
much thinner than the dielectric substrate), the upper frequency limit of the
excited MSSWs is given as [5-6]
f2=r(4xMs)(^
+b
®M
2
63
(3.6)
If we further expand equation (3.5) by plug in 6)c=2jrx yH0 and coM = In x y4nMs,
equation (3.5) turns to
-11/2
= yJ(H0)(H0+4xMs)
/=K4*M,)
(3.7)
Now it is very interesting that the equation (3.7) is identical to equation (2.26) in
Chapter 2. This relation is important and it is the bridge to understand the
relation between the FMR absorption theory and the excited MSSWs in the
ferromagnetic sample. Equation (2.26) is the FMR frequency derived from FMR
theory with demagnetization effect (sample shape) considered. Equation (3.5) is
the characteristic surface mode of a ferromagnetic sample magnetized in its
plane obtained in the magnetostatic limit [6]. This relation states that the energy
dissipated by the interaction between rf transverse magnetic field of propagating
microwave and precessing magnetization of ferromagnet is transferred to the
MSSWs propagating perpendicular to the microwave propagation, where the
sample is magnetized in the plane of ferromagnet and also along the microwave
propagation
direction.
Energy
carried
away
in MSSWs is related
to
electromagnetic energy propagating along the microstrip line by an equivalent
radiation resistance Rm.
Radiation resistance Rm now can be readily calculated based on equation (3.1),
(3.2) and (3.4). The parameters used in this Rm versus k diagram are consistent
64
with experimental arrangements as t-35Qfj,m , d = 6.8jum , b = 256/jm and
H0 = 2,200Oe. The calculated Rm versus k diagram is
300
i—'—r
i—•—r
250
i—•—r
t=350um
d=6.8um
b=256um
H=2,200Oe
3> 200 CD 150
O
C
CD
•*—•
CO 100
'co
CD
a:
c
50
o
"-1—<
03
T3
CD
0
Q^
0
50
100
_L
150
J_
200
_L
250
J_
300
JL
350
400
_L
450
500
Propagation Constant (k) (cm"1)
Figure 3.4 Calculated Radiation Resistance Rm versus Wavenumber
kd&t = 350jum, d = 6.Sjum, b-256/im andH0 = 2,200Oe.
Figure 3.4 will be used to calculate the values of lumped elements in the next
subsection.
3.1.2 Calculation of Values of Lumped Elements
65
Figure 3.4 shows the Rm dependence of propagation constant k of MSSWs. In the
device configuration with a constant bias magnetic field, different modes of
MSSWs can be excited and propagate along the ±y direction. For lumped
elements of equivalent circuit model, a dominant mode can be determined by the
resonant property of MSSWs in the rectangle YIG sample. If ly,lz are the planar
dimensions of the YIG sample in (y,z)
I YITT
wavenumber will be k = knm = | ( — ) 2 + (
V
plane (see Figure 3.1), the resonance
TTITT
y
) 2 [7], and the wavenumber of the
*
main mode (n =l,m =1) is ku = n l(—)2 +(—)2 . In our simulations, the geometric
parameters of YIG sample are also consistent with experimental arrangements as
ly = 2.8mm and lz -9mm , therefore, the dominant mode is t u «12cm"' and the
corresponding Rm is 12Q/cm.
In the equivalent circuit model shown in Figure 3.2, the lumped element R , L
and C are derived as R = Rm x/ , L = R/(yx AH) (y is the gyromagnetic ratio and
Miis
the linewidth of the YIG film), and C = l/(o^xL)(o)r
=2xxfr,
fr is the
FMR frequency predicted in equation (2.26)). Values of the lumped element are
now
given
as:
R = RJy =336ohm
,
L = R/(yAH) = 191.05nH
,
and
C = \l co2rL - 0.0019425pF, where linewidth AH is assumed to be a constant value
1 Oe . The Vin and the Z0 (see Figure 3.2) is the microwave signal and
66
characteristic impedance of the microstrip line, respectively. Two transformers
are used by defining the turns ratio n , a value representing the connection with
external circuit which can be estimated and by fitting experimental data [8]. n
can be given as n = I—=$— , where (X = -^J— , Z0 = 50ohm (characteristic
impedance of the microstrip transducer). The external quality factor Qext is a
parameter counting for the microstrip as a coupling structure, and it can be
defined as Qext =
\
u0coMVK
tm=\um
[3] ( V = lyl2d and K = \n[(b + tm+2dQ)/(b + tm)]/4d0
is the thickness of the microstrip line). The resulting turns ratio is
n « 2.5023.
3.1.3 Simulation of Lumped Element Equivalent Circuit
We use Microwave Office to simulate the lumped element equivalent circuit. The
circuit schematics are shown in Figure 3.5 and the simulated S-parameter (S21) is
shown in Figure 3.6. It is shown in Figure 3.6 that the microwave band-stop filter
has the stop-band peak absorption at frequency of 8.27 GHz with absorption
level of more than -30 dB. The results are consistent with experimental data to be
presented in next chapter. The equivalent circuit method will further be
implemented in the calculation of microwave band-pass filter in Chapter 4.
67
SRLC
ID=RLC1
R=3.36 Ohm
L=191.1 nH
C=0.001943pF
XFMR
ID=XF1
N=2.502
PORT
P=1
Z=50 Ohm
XFMR
ID=XF2
N=2.502
PORT
P=2
Z=50 Ohm
1 2
nl:l
Figure 3.5 The Circuit Schematics in Microwave Office Simulator
u
—l
| — •• • i
-\
t=350um
d=6.8um
b=256um
H=2,200Oe
11
il
11
-15
S
CO
_
u
"
-
11
IfII
t r -20
CD
<D
•
I1
CO
-i—>
• — i
\\ 1f
-5
2,
^—v
—
H
„„
•
25
-
E "
CD
s_
fi -30
-
•
-
CO
-35
8,27 GHz
i
.An
8.0
8.1
8.2
8.3
8.4
.
8.5
8.6
8.7
8.8
8.9
9.0
Frequency (GHz)
Figure 3.6 Simulated S-parameters (S21) of the Equivalent Circuit of Figure 3.5
68
3.2 Simulation using ANSOFTHFSS
3.2.1 Model and Parameter Assignments
ANSOFT Corporation's High Frequency Structure Simulator (HFSS) is an
industry standard high-performance
full-wave
electromagnetic
(em) field
simulator for arbitrary 3D volumetric passive device modeling. HFSS utilizes the
3D full-wave Finite Element Method (FEM) to conduct simulations for two-port
parameter (S, Y, Z) extraction, and it is also capable of generating visualizations
of em field patterns. The HFSS simulation in this section for the microwave bandstop filter using YIG/GGG-GaAs layer structure is to simulate the microwave
transmission characteristics (S-parameters) of the band-stop filter and the
pertinent high frequency field (E-field and H-field) distributions in the multilayer structure. The simulation is particular useful when the electrical transducer
(e.g., microstrip and step-impedance low-pass filter) are specifically designed for
optimized device performances. One example is that the simulated H-field
concentration on the inductive-elements of the designed step-impedance low
pass filter, in contrast to a 50 Q microstrip, enhances the coupling of the
microwave magnetic field into flipped YIG/GGG layer and, thus, increases the
microwave power absorptions at the FMR frequencies (this part will be detailed
in Chapter 4)
The major procedures in the HFSS simulation of the microwave band-stop filter
using YIG/GGG-GaAs layer structure is building up a physical model,
69
characterizing all associated materials including the ferromagnetic layer, adding
solution setup, running the adaptive solver and generating plots.
Radiation boundaries are at
faces of cubic except the
bottom one
YIG/GGG Layer
Waveport 1
mi
Microstrip
BiasH
;•
X
V
id/
Waveport 2
GaAs Substrate
\
Perfect E plan at
bottom of substrate
Figure 3.7 The Physical Model of The Band-Stop Filter Configuration in HFSS
Using a YIG/GGG-GaAs Layer Structure
The physical model was built as shown in Figure 3.7. The GaAs substrate, the
silver microstrip, the YIG layer and the GGG layer are, respectively (in X Y Z
axis),
10 4 X10 4 X350/WJ 3
,
104x256xl//w3
,
9000 x 6256 x6.8/W
,
and
9000 x 6256 x350//m3 . The material parameters for GaAs and silver are given in
the material library of HFSS. The GGG was assigned as a perfect dielectric
material with relative permittivity 14.7 (the same as YIG layer). The direction of
the microwave propagation was assigned from waveport 1 to waveport 2. The
70
direction of the internal magnetic field, H0, was assigned in the same direction as
microwave propagation shown in Figure 3.7. The bottom of the GaAs substrate
was assigned as a perfect electrical, E, plane which serves as the signal ground
plane.
The parametric input data for the ferromagnetic YIG layer is the key step in this
simulation. Figure 3.8 shows the edit-material box of ferrite materials in HFSS in
which eight material parameters are shown. The relative permeability, magnetic
loss tangent, magnetic saturation, Lande G factor, and Delta H (AH) are the five
material parameters associated with the tensor permeability, [//], of the YIG layer.
The five materials parameters together with co (frequency) and H0 (internal bias
magnetic field) are used in HFSS to characterize a magnetic material.
NOTS
j Tp
Value i
Unta
State 14.?
f
IRdative Permeability
Simple
1
i
]8ylk Conductivity
Simple
0,01
I
{Dielectric Loss Tangent
Simple
0
"t IMagnetic Loss Tangent
Simple
0
I j Magnetic Saturation
Simple^
1760 _ Jaawt
'
ItLandeGFactor^_
iilDeftaH.- .
... . . .
^ J j p l e ^ J ^ ._
Simple,, ! _
Sitmsni/m
v _._
-i
. _j
. Q e _ . ... J
Figure 3.8 Edit-material Interface of Ferrimagnetic Material in HFSS
For most microwave ferrite materials, Lande G factor has a value in the range
from 1.99 to 2.01 and it is safely to assign it as 2.00. The magnetic saturation, Ms ,
71
and AH, together with frequency, co, and internal bias magnetic field, H0, are
sufficient to assign the components in [ju]. Figure 3.9 shows the formulas that
HFSS used to compute the [ju] from the four parameters (Ms , AH,
co, and
H0). This formulism is indeed agreed with the formulism discussed in Appendix
A2. The actual assignment for the YIG layer in which the Ms =1,760 Oe and
AH =1 Oe. The H0 was assigned to be 175070 A/m or 2,200 Oe in this simulation.
The relative permeability and the magnetic loss tangent were assigned to be 1
and 0 in this simulation.
«>|}W
& =
n
Uh
-JK
}K
jU
o
. ( w ' - f . ' 2 ) + M0<i>„,ar<r
„2-«i»2)" + 4 a ^ V
Mod),,, Ifti;I
u =
A n — A,t,t
0
JAxx
<|J X»
+ «>:(1 + a2))
(ftij - <U2) + 4a'|cri>2rt2
A'jry ~ XXy "•" jXxy
«%>,„(<«^-4> 2 {l + < r ) )
Xxif
0
0
((Wjj-a)2)
1
+ 4<<>Ju>2rt2
2(,)cni!,„in2<v
A'ttf
*~
(<ti^ - a) 2 )
+ 4a>2l<i>2<l2
tl
10
Y = 2 JI X2.8X10 rad;nHz/Tesla
«o = ,«o}'Ho
Aff/V
26>
Ho: Internal magnetic field
Ms: Saturation magnetization
to = 2 JI X applied ac signal frequency
A H : Linewidth of the susceptibility curve
near the resonance
Figure 3.9 Derivation Blocks of Relative Tensor Permeability [ju] Using the
Four Parameters Ms , AH,
72
co, and
H0.
3.2.2 Simulation Results and Discussions
Figure 3.10 shows the simulated S-parameter (S 2l ) of the microwave band-stop
filter in the frequency range of 8.0 - 9.0 GHz. The simulated S2l shows that the
microwave band-stop filter has the stop-band peak absorption at frequency of
8.28 GHz with absorption level of more than -30 dB. The FMR frequency of this
band-stop filter occurred at 8.28 GHz agrees with the FMR frequency given in
equation (2.26) and also consistent with the simulated FMR frequency in Figure
3.6.
ctjo-
4M»-
8.4©
Ff«q |6HteJ
Figure 3.10 Simulated S-Parameter (S 2l ) of the Microwave Band-Stop Filter
using YIG/GGG-GaAs Layer Structure
73
Figure 3.11 Simulated H-field Pattern on the Surface of the YIG Layer at 8.28GHz
The em field pattern is also studied in this simulation where Figure 3.11 shows
the magnetic field (H-field) pattern on the surface of the YIG layer (contact
surface to GaAs substrate) at the FMR frequency of 8.28 GHz. The major features
in the Figure 3.11 are that the H-field pattern demonstrated a clear wave pattern
which is propagates in the y-direction on the surface of the YIG layer (see Figure
3.11). These findings agree with the theoretical treatment in [9].
The
magnetostatic surface waves (MSSW) was excited based on this configuration
74
and it is propagating on the surface the YIG layer in the direction of H0 x n,
where n is the outwardly directed surface normal [9]. In this simulation, H0xn
represent the xx(-z) = y direction shown in Figure 3.7 (-z is the surface normal
of the surface contact to GaAs substrate). Both the simulated 521 and the H-field
pattern agree with the expected results [9].
The HFSS simulations will further be implemented in the design of optimized
transmission line in microwave band-stop filter in Chapter 4, and simulations of
microwave band-pass filter in Chapter 5.
Reference
1.
G. Bartolucci, R. Marcelli, "A generalized lumped element modeling of
magnetostatic wave resonators", /. Appl. Phys., vol.87, pp.6905-6907,2000.
2.
C. S. Tsai, and Jun Su, "A wideband electronically tunable magnetostatic
wave notch filter in yttrium iron garnet-gallium arsenide material
structure", Appl. Phys. Lett, vol.74, pp.2079-2080,1999.
3.
W. S. Ishak, "Magnetostatic wave technology: a review," Pro. IEEE., vol.76,
pp.171-187,1988.
4.
A.K, Ganguly and D.C. Webb, "Microstrip excitation of magnetostatic
surface waves: theory and experiment", IEEE Trans, on MTT, vol.23, no.12,
pp.998-1006,1975.
5.
W. L. Bongianni, "Magnetostatic Propagation in a Dielectric Layered
Structure", /. Appl. Phys., vol.43, pp.2541-2548,1972.
75
6.
R. W. Damon and J. R. Eshbach, " Magnetostatic modes of a ferromagnet
slab", /. Phys. Chem. Solids, vol. 19, pp.308-320,1961.
7.
R. Marcelli, M. Rossi, P. De Gasperis, and Jun Su, "Magnetostatic wave
single and multiple stage resonators", IEEE Trans, on Magn., vol.32, no.5,
pp.4156-4161,1996.
8.
J. Helszajn, YIG Resonators and Filters, Wiley, New York, pp.115,1985.
9.
J. D. Adam and J.H. Collins, "Microwave magnetostatic delay devices
based on epitaxial yttrium iron garnet", Proceedings of IEEE, vol.64, no.5,
1976.
76
Chapter 4
Tunable Wideband Microwave Band-Stop Filter Using
YIG/GGG-GaAs Layer Structure
The theoretical analysis of YIG/GGG-GaAs layer structure and device
simulations of microwave band-stop filter using YIG/GGG-GaAs layer structure
have been studied in Chapter 2 and 3. In this Chapter, the experimental study of
tunable wideband microwave band-stop filter using YIG/GGG-GaAs layer
structure is carried out in detail. Enhanced microwave FMR absorptions in
YIG/GGG-GaAs layer structures using a microstrip step-impedance low-pass
filter (LPF) are presented first. The field simulations of the step-impedance LPF
show clearly that, in contrast to a 50 Q. microstrip, the ac magnetic fields of the
propagating microwaves are heavily concentrated in its inductive elements.
Stronger local ac magnetic fields at each inductive element of the step-impedance
LPF facilitate enhanced coupling into the magnetic over-layer and, thus,
significantly increase the microwave power absorptions at the FMR frequencies.
The measured transmission loss (S21) and return loss (Sn) of -25.0 dB and -8.7 dB
using the microstrip step-impedance LPF, at FMR frequency of 8.5 GHz, show a
much higher level of microwave FMR absorption in the YIG/GGG-GaAs layer
structure as compared to a 50 Q. microstrip with the measured S21 and Sn of -20.8
dB and -5.8 dB. The microwave transmission characteristics (S21) of the bandstop filter in a large base band of 2.0 - 20.0 GHz, using both the step-impedance
77
LPF and the 50 Q microstrip, were also measured and compared. The
simultaneous enhancement of FMR absorption level and widening of absorption
bandwidth has been accomplished in a microwave band-stop filter that utilizes a
microstrip meander-line with step-impedance LPFs inserted in a non-uniform
bias magnetic field. A microwave filter with tunable FMR absorption frequency
range of 5.0 to 21 GHz, an absorption level of -35.5 dB and a corresponding 3 dB
absorption bandwidth as large as 1.70 GHz, centered at 20.3 GHz, have been
demonstrated.
4.1 Enhanced Microwave FMR Absorption Using Microstrip Step-Impedance
Low-Pass Filter
In this section, the design and simulations of the step-impedance LPF including
the simulated ac magnetic fields (H-field) of the propagating microwaves in the
two types of transmission lines and the overall device simulation are presented.
Filter Specification
I
Low-Pass Filter Prototype
I
Conversion of Impedance
and Frequency
I
Implementation by
Microstrip
Figure 4.1 Design Outline of Step-Impedance LPF
78
4.1.1 Microstrip Step-Impedance LPF Design
The design procedures of the microstrip step-impedance LPF is outline in Figure
4.1. We start with the filter specification to design the prototype low pass filter.
The design specification of the low pass filter is listed in Table 4-1.
Table 4-1 Specification of the Step-Impedance LPF
Filter Response
Substrate
Metal Material
Cut-off
„
Frequency
Band-Reject
_
Frequency
Off-band
...
..
Attenuation
„ ^ .,
Materials
_,. .
Thickness
35 GHz
45 GHz
20 dB
GaAs
350 urn
Ag
,
Impedance
T
50 ohm
The insertion loss method is employed to characterize the filter response for the
low-pass filter design [1-2]. The insertion loss, or power loss ratio (PLR), is
defined as the ratio of the power available from the source to the power
delivered to the load. In our specific application, a minimal insertion loss over
the passband is important because the designed step-impedance LPF is used as a
transmission line to guide the microwaves in the magnetic layer structures. A
binomial or Butterworth response is used to characterize the filter design which
provides the flattest possible passband region for a given filter complexity. For
the low-pass filter with Butterworth response, PLR is specified by [1-2]:
\2N
f
^,=1 +
CO
\<°cj
79
(4.1)
where a and coc are the microwave frequency and the cutoff
frequency,
respectively, and N is the order of the low-pass filter. The passband of the lowpass filter extends from co = 0 to co = coc where the PLR is - 3 dB, and the
attenuation increases monotonically as the frequency increases beyond the cutoff
frequency. The ladder circuit that provides the power loss characteristics of this
filter type with shunt capacitors (C i , i = \to 5) and series inductors (L t , i = 1 to 5) is
shown in Figure 4.2.
Figure 4.2 Ladder Network for The Low-Pass Filter
The element values of the ladder circuit, normalized with respect to the source
impedance and the cutoff frequency, can be calculated as [1-2]:
gk =2 sin
2k-l
2N
"\
•n
k = l,2,...,N
(4.2)
where gk are the normalized element values of the shunt capacitors and the
series inductors. The order of the low pass filter N is determined by the filter
response of design specification, specifically TV = 10 in our design in order to
achieve more than 20 dB off-band attenuation at 45 GHz band-reject frequency
80
with 30 GHz cut-off frequency. The actual values of the capacitors and inductors
can be readily computed from the normalized element values using the source
impedance and the frequency transformations [1-2].
(4.3a)
Ct = T & - * = l,3,5,7,9
Z
0®c
Lk=-^t
k = 2,4,6,8,10
(4.3b)
where Z0 is the load impedance of the ladder circuit.
The microstrip implementation of shunt capacitors and series inductors is
realized using alternating segments of low and high characteristic impedance
lines (or low-Z and high-Z lines). A short microstrip with high characteristic
impedance can be approximate as a serial inductor, and a short microstrip with
low characteristic impedance can be approximate as a shunt capacitor [1-2],
specifically, in our filter design, high-Z of 75 Q a n d low-Z of 30 Q were used.
The characteristic impedance of the microstrip is determined by the ratio of the
width of microstrip, W, to the thickness of the substrate, d. One of the wellW
established experience formulas for calculating the — ratio is given by [2]
d
W_
d
%eAd
e2A-2
2d
B - 1 - ln(25 -1) + ^-^-Qn(B -1) + 0.39 - — )
71
£„
2s„
where
81
— <2
d
W_< 2
d
(4.4a)
6
°V
2
^+1
*'
(4.4b)
and Z is the desired characteristic impedance of the microstrip, i.e., 75 fi and 30
Q in our design for serial inductors and shunt capacitors. From equation (4.4a-b),
the widths of the 50£2 , 75Q and 30Q microstrip are calculated to be
256jum ,&0jum and 670jum respectively based on the 350jum thick GaAs substrate.
The length of each segment are calculated by
Z
r
_ gk
bk^LL
k,capacitor
r> y
lr — \
l
a
^ 7 Q
' J ' ^' ' '
(4.5)
h,inductor=^
* = 2,4,6,8,10
Where gk are prototype element values for serial inductors and shunt capacitors,
ZL and ZH are low and high characteristic impedance of the microstrip, i.e.,
30 Q and 75 Q. respectively, Z0 = 50 Q is the characteristics impedance of the
load system.
In I—
The effective propagation constant J3e is given by j5e =—•s]se ,
K
where Xc is the wavelength at the cutoff frequency and the effectively
permittivity se is given by
s=——2 + —2
,
V
82
f^l
W
(4.6)
With the above equations, the microstrip implementation of the 10-element, i.e.,
five capacitor and five inductor, step-impedance LPF is shown in Figure 4.3.
Note that the 256 jum wide line serves as a 50 Q line, and the 670 fj,m and 80 jum
wide lines are the low and high characteristic impedance lines of 30 Q and 75 Q ,
corresponding to the shunt capacitors and the series inductors, respectively. The
width, W, and length, L, of each element of the 10-element step-impedance LPF
indicated in Figure 4.3 are listed in Table 4-2. The thickness of the metal, t, was
chosen to be 1.0 jum for the experimental consideration.
Table 4-2 Geometry of the 10-Element Step-Impedance LPF
Cj
C2
C3
C4
C5
Vf(jum)
670
670
670
670
670
L(jum)
84
221
232
232
190
A
W (jum)
80
80
80
80
80
L (jum)
486
635
659
624
278
83
256 urn
670 urn
WM
Jr
8 0 urn
Figure 4.3A 10-Element Step-Impedance LPF
Frequency (GHz)
Figure 4.4 Simulated S-Parameters (S21 and Sn) of the 10-Element StepImpedance LPF and the 50 QTML
The simulated S-parameters (S2land Sn) of the step-impedance LPF and the 50
84
Q. microstrip transmission line (TML) using Microwave Office is shown in Figure
4.4. The simulated S21 and Sn greater than -0.3 dB and less than -16.0 dB,
respectively, up to 30 GHz shows that the 10-segment stepped-impedance LPF
can be efficiently act as a TML over a large span of base band frequency.
4.1.2 AC Magnetic Field Simulations
In this section, the ac magnetic field components of the propagating microwave
in the YIG/GGG-GaAs layer structure are simulated using ANSOFT
HFSS.
Utilization of such step-impedance LPF in lieu of a 50 Q microstrip for
enhancement of the FMR power absorption in the layer structure has been
clearly demonstrated by the simulated ac magnetic field (H-field) components of
the propagating microwaves along the two types of transmission lines. Figure 4.5
and Figure 4.6 are, respectively, the simulated magnitude of ac magnetic fields
(H-field) on the surface of the GaAs substrate at 8.5 GHz along the 10-element
step-impedance LPF and the 50 Q microstrip. Figure 4.6 clearly shows that the
ac magnetic fields of the propagating microwaves are heavily concentrated in
each inductive element (note that the narrow microstrip segments are the high
characteristic impedance lines corresponding to the series inductors). Specifically,
the H-field intensity in the inductive line segments is seen to be greater than 70
A/m in contrast to a much lower H-field intensity of 30 A/m along the 50 n
microstrip (see Figure 4.5 and 4.6). The heavily concentrated magnetic fields in
each inductive element are more clearly shown in Figure 4.7 where the simulated
85
ac magnetic field intensities along the center lines of the step-impedance LPF and
the 50 Q microstrip were extracted. The five peak and notch regions in Figure
4.7 correspond to the H-field intensities in the five inductive and capacitive
elements of the LPF, respectively, and they show clearly that much stronger local
H-fields exist at each inductive line segment.
86
H-Field [A/m]
I
5.5000e+001
5.1563e+001
4.8125e+001
4.4688e+001
4.1250e+001
3.7813e+001
3.4375e+001
3.0938e+001
2.7500e+001
2.4063e+001
2.0625e+001
1.7188e+001
1.3750e+001
1.0313e+001
6.8750e+000
3.4375e+000
O.OOOOe+000
30 A/m
I
y
i
X
Center Line
Figure 4.5 Simulated AC Magnetic Field (H-Field) Distributions at Frequency of
8.5 GHz along the 50 Q Microstrip
87
H-Field [A/m]
I
8.0000e+001
7.5000e+001
7.0000e+001
6.5000e+001
6.0000e+001
5.5000e+001
5.0000e+001
4.5000e+001
4.0000e+001
3.5000e+001
3.0000e+001
2.5000e+001
2.0000e+001
1.5000e+001
1.0000e+001
5.0000e+000
O.OOOOe+000
= 70 A/m
y
A
X
Center Line
Figure 4.6 Simulated AC Magnetic Field (H-Field) Distributions at Frequency of
8.5 GHz along the 10-Element Step-Impedance LPF
88
E
c
o
(0
2
Y-Axis Distance [mm]
Figure 4.7 Simulated AC Magnetic Field (H-field) Intensities along the Y-Axis
Center Lines of The 10-Segment Step-Impedance LPF and The 50 Q. Microstrip
The surface power density distribution on GaAs substrate by computing the
power density as ExH
is also simulated over the 10-element step-impedance
LPF and shown in Figure 4.8. As shown in Figure 4.8, the surface power density
is also much higher concentrated in the inductive segment than the capacitive
segment. A comparison between the surface power density on GaAs substrate
along the cross-section direction (X-direction in Figure 4.8) at 8.5 GHz over the
step-impedance LPF and 50 Q microstrip are plotted in Figure 4.9.
89
Power (W/m2)
Density
5.0000e+005
4.6875e+005
4.3750e+005
4.0625e+005
3.7500e+005
3.4375e+005
3.1250e+005
2.8125e+005
2.5000e+005
2.1875e+005
1.8750e+005
1.5625e+005
1.2500e+005
9.3750e+004
6.2500e+004
3.1250e+004
0.0000e+000
:-S:#
INDUCTIVE
CAPACITIVE
y
X
Figure 4.8 Simulated Power Density Distribution at Frequency of 8.5 GHz on the
Surface of GaAs of the 10-Segment Step-Impedance LPF
90
50
50
45
-45
LPF:INDUCTIVE
ELEMENT
\l
E
40
s.>
35
u
^*
+J
"55
c
0)
-40
-35
30
-30
TML
25
-25
0)
20
-20
5
o
a.
15
Q
a>
o
10
t(0
3
5
</5
-15
I LPF:CAPACITIVE
\
ELEMENT
-10
-5
0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0
1.0
Distance along the Cross Section [mm]
Figure 4.9 Simulated Surface Power Density Distribution along The CrossSection Direction (X-direction in Figure 4.8) over the TML, the Inductive Segment
and Capacitive Segment of the Step-Impedance LPF
A final note on the above field and power simulations is that the input power
used in HFSS is normalized to 1 W for all the simulations. From above
simulation results, the much stronger ac magnetic fields at each inductive line
segment of the LPF will facilitate stronger coupling into the magnetic over-layer
during the microwaves propagation, and, thus, enhance the interaction between
the ac magnetic fields of the microwaves and the precessing magnetic dipoles in
91
the magnetic layer. Enhanced FMR power absorption, therefore, will occur if the
frequency of the propagating microwaves coincides with the FMR frequency of
the magnetic layer.
4.1.3 Device Simulations
The HFSS is used again for the overall device performance simulation. The
physical model is same as the model shown in Figure 3.7 except for different
geometry. The GaAs substrate, the YIG layer and the GGG layer are, respectively
(in X Y Z axis) 10 4 xl0 4 x350//w 3 ,9000x6256x6.8//w 3 and 9000 x 6256 x350//m3 .
The 50Q microstrip line are 256jum wide and the geometry of the 10-elment
step-impedance LPF are in Table 4-2. The material parameters for GaAs and
silver are given in the material library of HFSS. The GGG was assigned as a
perfect dielectric material with relative permittivity 14.7 (the same as YIG layer).
The direction of the internal magnetic field, HQ =2,3OO0e, was assigned in the
same direction as microwave propagation. The bottom of the GaAs substrate was
assigned as a perfect electrical, E, plane which serves as the signal ground plane.
The assignment of the material property of YIG is the same as Section 3.2. The
simulated transmission loss (S21) and return loss (Sn) of the YIG/GGG-GaAsbased band-stop filter at FMR frequency of 8.5 GHz using the 50 Q microstrip
and that using the step-impedance LPF are shown in Figure 4.10. The S21 and Sn
of -30.0 dB and -6.0 dB, respectively, using the microstrip step-impedance LPF
clearly show a significantly higher level of microwave power absorption in the
92
magnetic layer structure as compared to the 50 Q microstrip with the simulated
S21 and Sn of —22 dB and -5.0 dB, respectively. The large tunable range of FMR
frequency and the corresponding S21 and Sn parameters measured have verified
the simulation results and will be shown in Section 4.3.
Stepped-lmpedance LPF
ko
Stepped-lmpedance LPF
-40
-i
8.0
1
8.1
1
1
8.2
1
1
8.3
1
1
8.4
1
1
8.5
1
1
8.6
1
1
8.7
1
1
8.8
1
1
8.9
•40
r>
9.0
Frequency (GHz)
Figure 4.10 Simulated Transmission Loss (S21) and Return Loss (Sn) of the
YIG/GGG-GaAs-Based Microwave Band-Stop Filter at FMR Frequency of 8.5
GHz using the 50 TML and the 10-Segment Stepped-lmpedance LPF
93
4.2 Experimental Results
4.2.1 Device Fabrication and Measurements
The basic flip-chip device configuration of the microwave band-stop filter using
YIG/GGG-GaAs layer structure is shown in Figure 4.11 where the 10 element
step-impedance LPF was used as the microstrip transmission line.
The single-crystalline YIG sample was furnished by Shin-Etsu Chemical Co.,
Japan. The YIG film is grown on lattice-matched GGG sample on [111] face by
liquid phase epitaxy (LPE) technique. The thickness of the YIG sample is 6.8 fim.
The measured 4?rMs and AH are 1,760 Oe and 1 Oe at 9.2 GHz, respectively,
according to the data sheet provided.
YIG/GGG Layer
Step-impedance
Low-Puss Filter
Microwave
Output
Microwave
Input
GaAs
Substrate
Ground Plane
Figure 4.11 The Flip-Chip Device Configuration of the Microwave Band-Stop
Filter using YIG/GGG-GaAs Layer Structure
94
The metallization/photolithography/etching process is used to fabricate the
GaAs-based microstrip line, i.e., the step-impedance LPF and 50 Q TML, as
shown in Figure 4.12. A 1.0//m silver is deposited onto GaAs using e-beam
evaporation deposition technique. The process started with the photo-resist
spinning coating of Shipley 1827® at a thickness of 2.7 jum . Iron masks are
produced in a separate procedure and aligned to the substrate in a Karl Suss
Aligner. Near-UV exposure defines resolutions with ~4 um. The exposed sample
then is developed in Microposit 319®. The electrode patterns are hard baked at
95° C for 30 min. A chemical etching is followed to remove silver. The chemical
enchant is a room temperature 1:1:10 dilution of NH4OH, H2O2 and DI- H2O
solutions. The final step is an acetone bath to strip the photo-resist.
Near UV light
UUUUIU
Mask
PR
Substrate Preparation
Metalization
Photo-Resist (PR) Spin
Mask Align and Exposure
I
PR Strip
Chemical Etching
Develop PR and Bake
Figure 4.12 Process Flow for Fabricating GaAs-based Microstrip Line
95
Once the YIG/GGG sample and the GaAs-based microstrip line are ready, the
flip-chip technique is used to assembly the YIG/GGG sample to the microstrip
line. Although flip chip components are predominantly in semiconductor
devices, passive components, e.g., filters and MEM devices, can also be used in
flip chip assembly.
In the device packaging, the GaAs-based microstrip line was bonded to an
aluminum holder using Transene® silver-based surface mount adhesive. The 2.4
mm connectors are used to connect the microstrip to the coaxial cable. The 2.4
mm connectors are designed to be operated up to 50 GHz. The microstrip/stepimpedance LPF is designed with right-angle bends for easy supply of bias
magnetic field to be same as the microwave propagation direction. The
optimized bend design will be discussed in Section 4.3. The layout of the stepimpedance LPF with two mitered 90° bends is shown in Figure 4.13. The photo
of the actual fabricated device including the 2.4 mm connected is shown in
Figure 4.14.
96
Figure 4.13 Layout of the Step-Impedance LPF with Two Mitered 90° Bends
The fabricated device then was inserted into the external bias magnetic field
facilitated by a pair of neodymium (Nd 2 Fe 14 B) permanent magnets (0.75" in
diameter and 0.5" in thickness). The magnetic field intensities in the center of the
YIG/GGG sample were varied by tuning the gap, d, between the permanent
magnet pair (see Figure 4.19). The non-uniformity of the biased magnetic field
provide by this arrangement will be discussed in detailed in Section 4.3.
97
Figure 4.14 Photo of Fabricated GaAs-based Microstrip Step-Impedance LPF
with Two Mitered 90° Bends together with Two 2.4 mm Connectors
Two measurement systems are used in this device measurement as shown in
Figure 4.15 and Figure 4.16. The microwave power measurement system has a
Signal Generator (HP83630B 0-26.5GHz) to send microwave to the DUT through
a directional coupler (HP 87301E) where the coupled power from the directional
coupler is the reference power that is captured by a power sensor (HP 8487D)
and fed into one channel o f the power meter (Agilent E4419A). The output of the
directional coupler will be sent to DUT and the output of DUT enters the other
directional coupler and fed to the other channel of the power meter. The
98
microwave power consumption by the DUT can be obtained by comparing the
two power input to the power meter (see Figure 4.15).
HP 83630B
Signal Gen
GPIB
HP S7301E
Coupler
HP 87301E
Coupler
IOUT
Signal
DUT
Agilent 4419A
Power Meter
GPIB
—j
5Qohm " |
-10dBl
10dBl
(Probe
HP 8487D
power Sensor
HP 8487D
Power Sensor
CH_B
CH A
BELL 620
Gaussmeter
GPIB
Work Station
Figure 4.15 Setup of the Microwave Power Measurement System
The network analyzer measurement system consists of the 8510C Network
Analyzer, the 8517B S-parameter Test Set, and the 83621A Signal Generator (up
to 20GHz). The network analyzer system is a standard instrument
measurement
the
microwave
transmission
characteristics
to
(S-parameters)
including the magnitude and phase information.
For both of the system, the bias magnetic field intensity was measured by
BELL620 Gaussmeter. The BELL620 Gaussmeter is a precision magnetic flux
measuring instrument, featuring high stability with Hall Effect magnetic field
probes. Measurement range extends from 1 mG per scale division to 30 kG full
scale.
99
HP 8510C
Network Analyzer
GPIB
HP 83621A
Signal Gen
,GPIB
OUT
HP 8514B
Test Set
GPIB
Port 1
Port 2
w
W
DUT
f
4
^
1 Probe
^
^
1
1
1
S
M
%.
1
%
BELL 620
Gaussmeter
IN
GPIB
Work Station
Figure 4.16 Setup of the Network Analyzer Measurement System
4.2.2 Device Performance of Tunable Wideband Microwave Band-Stop Filter
In the experiments, the YIG film used is 6.8 jum in thickness with dimension of
2.8x9.0mm2 in the X and Y directions (see Figure 4.11). The 256 //w wide 50 Q
microstrip and the 10-element step-impedance LPF (see Figure 4.13) presented in
Section 4.1 were used to compare the microwave power absorptions at the FMR
frequencies. The bias magnetic field (HQ) supplied by a pair of NdFeB permanent
magnets was set in the same direction as the microwave propagation. The
100
transmission characteristics were then measured using HP 8510C Network
Analyzer (see Figure 4.16).
The measured transmission loss (S21) and return loss (Sn) of the YIG/GGGGaAs-based band-stop filter at FMR frequency of 8.5 GHz using the 50 Q
microstrip and that using the step-impedance LPF are presented in Figure 4.17.
Bias magnetic field of 2,100Oe was applied to set the FMR frequency at 8.5 GHz
[3-4]. Note that the measured FMR absorption frequency of 8.5 GHz in Figure
4.17 is identical to the simulated carrier frequency in Figure 4.10. The S21 and Sn
of -25.0 dB and -8.7 dB, respectively, using the microstrip step-impedance LPF
clearly show a significantly higher level of microwave power absorption in the
magnetic layer structure as compared to the 50 Q microstrip with the measured
S21 and Sn of -20.8 dB and -5.8 dB, respectively.
As we studied in Chapter 2 and Chapter 3, the peak FMR absorption frequency
of the band-stop filter can be tuned in a wide frequency band by varying the bias
magnetic fields [3-4]. The microwave transmission characteristics of the bandstop filter in the frequency range of 2.0-20.0 GHz using the two types of
transmission lines were also measured and compared in Figure 4.18. Clearly,
enhanced peak FMR absorptions in the YIG/GGG-GaAs flip-chip layer structure
were accomplished in a base band as large as 2.0 to 20.0 GHz using the stepimpedance LPF.
101
Step-Impedance LPF
(/)
iw
-25
-25
-30
I- -30
Step-Impedance LPF
-35
6.5
7.0
7.5
8.0
8.5
9.0
-35
9.5 10.0 10.5
Frequency (GHz)
Figure 4.17 Measured S21 and Sn of the YIG/GGG-GaAs-Based Microwave BandStop Filter at FMR Frequency of 8.5 GHz Using the 50 Q Microstrip and the 10Element Step-Impedance LPF.
102
-10
ST
*~L -20
CM
1020 Oe
1440 Oe
O)
-
t
2100 Oe
•30
t
/
/
N
f
2670 Oe
k
«
50 Ohm Microstrip
. 3250 Oe J
r P
'
-40
8
10
f
3850 Oe I
Step-Impedance LPF
6
-30
4gQg Q 6 5 3 0 0 Oe
12
14
16
18
-40
20
Frequency (GHz)
Figure 4.18 Measured S21 of the YIG/GGG-GaAs-Based Microwave Band-Stop
Filter using the 50 Q Microstrip and the 10-element Step-Impedance LPF
The magnetic field (H0) dependence of the FMR frequency (fr) is given by
equation (4.7) [3-4] and also be verified in the measurement.
MH0) = y[(H0
2
+Han)(H0+Han+4xMs)J
(4.7)
In equation (4.7), AnMs (1,76O0e) and Han are, respectively, the saturation
magnetization and the anisotropy field of the YIG film. The value of the Hm of
103
YIG sample can be determined by fitting the experimental results to the equation.
Figure 4.19 shows a good agreement between the FMR theory in equation (4.7)
and measured FMR frequency when Han is fitted to be 100 Oe.
1000 2000 3000 4000 5000 6000 7000
20 •
N
fM=r>IW0+Ha)(H0+Ha+4xM,)
20
y = 2.SMHz/Oe,Ha=100Oe
AnM =1150 Gauss
X
o
15
~15-l
o
C
O
I- 10
£
O
•
i
•
i
•
i
•
i
\- 5
Calculated
Measured
«
•
i
•
1000 2000 3000 4000 5000 6000 7000
External Bias Magnetic Field (Oe)
Figure 4.19 Measured FMR Frequencies vs. Biased Magnetic Field
104
4.3 Band-Stop Filter with Large Stop-Band Bandwidth Using Microstrip
Meander Line with Inhomogeneous Bias Magnetic Field
4.3.1 Inhomogeneous Bias Magnetic Field
Microwave band-stop filters with desirable device performances, i.e. wideband
frequency selectivity with high peak absorption level and large absorption
bandwidth, were discussed in this section using a four-segment microstrip
meander-line constructed by the same 10-element step-impedance LPFs together
with a 2-D non-uniform bias magnetic field [4-5].
tMmnn'
Microwave
Output
Figure 4.20 The Arrangement For Facilitating Non-Uniform Bias Magnetic Fields
in YIG/GGG Layer
105
The non-uniform bias magnetic field in the YIG/GGG layer was facilitated by the
a pair of NdFeB permanent magnets as shown in Figure 4.20, and the intensity of
the non-uniform bias magnetic field distribution desired was set by adjusting
the separation of the gap, d, in between. The non-uniform field distributions are
clearly shown in the measured magnetic field profiles normalized to the four
values of magnetic field at the center of the gap along the Y-axis and X-axis in
Figure 4.21 and 4.22, respectively. Figure 5.10 (a) and 5.10 (b) show the measured
2-D non-uniform bias magnetic fields in the 8.0 x8.0mm2 YIG/GGG sample (see
Figure 4.20), centered at 2,750 Oe and 4,150 Oe, respectively, in which the field
non-uniformity is clearly shown. Since the FMR frequency for peak absorption
depends on the bias magnetic field, the different bias magnetic fields at the
separate locations of the four segments of the meander-line would result in a
large widening of the peak absorption bandwidth.
106
160*
150140-
A
d=18.0mm H=3,700 Oe
d=28.5mm, H=1,940 Oe
d=35.0mm, H=1,325 0 e
d=42.0mm, H=990 Oe
A
• v
A
• •
• /
v
•
<
130-
A
•
«
4
A
•
V
A
AV
*
^ •
A
4 •
4
A
\ A
* ';,
120-
*A
^
* V A
A ,
•^••^
110-
#
#
•
•«
*
<
V
* ^ AA
« <
''«
v
.
V* «
**••<«
A
NS&
•
Center . ^
*>J&k
T
^P^*
^ 4 ^
10090-2
^#
j •
% •
A
A
•
•*
A
0
2
4
6
8
10 12 14 16 18
Position along Y-axis (mm)
ure 4.21 Measured Magnetic Field Profiles Normalized to the Four Values of
Magnetic Field at the Center of the Gap along the Y-Axis
107
6^
] _
ive Magi tic ield to the Cen
3
100-
^^^•*^l^.
95< ^
V
90-
A v •
%
A.*? •
^*
V •
>
-4
85" *
80°.
75-
A
A
*
*
-,
^
•
•
<
A
A
A
A
70-
A
A
652
"
1 '
0
1
2
i
d=18.0mm H=3,700 Oe
d=28.5mm, H=1,940Oe
d=35.0mm, H=1,325 0e
d=42.0mm, H=990 Oe
i
4
i
i
i
6
i
8
i
i
i
i
4
•
\
v
W
«
A
A
1?
O
'v
A
±
v
CD
r-
<9
v£\
»V . A
A
LL
*-*
«S
Center
»
&
V
•
\ \
A
\
i
i
i
i
i
10 12 14 16 18
Position along x-axis (mm)
Figure 4.22 Measured Magnetic Field Profiles Normalized to the Four Values of
Magnetic Field at the Center of the Gap along the X-Axis
4.3.2 Microstrip Meander Line Design
In order to fully utilize the non-uniformity of the 2-D bias magnetic field, a multisegment microstrip meander line was designed and implemented in the
experiments. The same 10-element step-impedance LPFs were used to construct
a four-segment microstrip meander-line shown in Figure 4.23.
108
2.0mm
2.0mm
Figure 4.23 Layout of the Four-Segment Microstrip Meander Line using the Same
10-Element Step-Impedance LPFs
One of the key designs of a meander line is the mitered 90° bends that fold each
microstrip line side by side. These bend segments are actually a microstrip
discontinuity that can introduce parasitic reactance [6]. In order to minimize the
parasitic effect, simulation was carried out using Microwave Office to look for the
optimal design. Microwave Office introduces a new parameter called the Miter
Coefficient (MC) to distinguish different miter bends [7]. The definition of the
miter bend segment is shown in Figure 4.24 where the MC is defined as
M =d
109
(4.8)
Clearly, M can only have a value between 1 > M > 0.
I
"Is
JL.
W i - ^ l 4^W^I
Figure 4.24 Miter Bend Layout in Microwave Office
0.0
-0.2
M = 0.8: Lowest Overall Loss
CQ
T3
-0.4 A
s_
0
CD
E
2
-0.6 J
M
M
M
M
M
M
= 0.0
= 0.2
= 0.5
= 0.7
= 0.8
= 0.9
CO
Q_
W
-0.8 4
-1.0
8
12
Frequency (GHz)
Figure 4.25 Simulated S21 of a Microstrip with Two Miter Bend using
Miter Coefficient
110
Microwave Office was used again to simulate the transmission loss (S21) of a
microstrip line with two miter bend using different MCs. Figure 4.25 shows
clearly M=0.8 corresponds to the lowest loss transmission, and the corresponding
Wx and a of the miter are 204.8 jum and 651.7 fitn, respectively, when the
W = 256 //m.
4.3.2 Experimental Results
Figure 4.26 shows the device configuration of the YIG/GGG-GaAs-based
microwave band-stop filter with wideband tunability of stop-band center
frequency and bandwidth utilizing a four-segment microstrip meander-line with
2-D non-uniform bias magnetic fields.
Ground Plane
^ j l • ''\\ H^M^'^^W
v^
Substrate
Figure 4.26 A Wideband YIG/GGG/GaAs-Based Microwave Band-Stop Filter
using Microstrip Meander-Line and Non-Uniform Bias Magnetic Field
111
QQ
•a
w
w •
O
c
o
"55
£
(A
C
re
1)940 O
-45
J
i
i j 7 5 0 Oe3.700 O e 4 ' 8 5 0
L
8
0 e
1.70GHz J
t
6,100 Oe
L _ I
10
12
14
16
i_
18 20 22 24
Frequency (GHz)
Figure 4.27 Measured S2i of the Tunable YIG/GGG-GaAs-Based Microwave
Band-Stop Filter using a Meander Line with Four Segments of Step-Impedance
LPF
The measured transmission loss (S21) of the tunable band-stop filter just
described is shown in Figure 4.27. The experimental data demonstrated a large
tunable absorption frequency range of 5 to 21 GHz and an absorption level of 35.5 dB together with a corresponding 3 dB absorption-bandwidth as large as
112
1.70 GHz at 20.3 GHz. Clearly, the desirable capability of the band-stop filter for
wideband frequency selectivity with high peak absorption level and large
absorption bandwidth has been accomplished.
Reference
1.
G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, ImpedanceMatching Networks, and Coupling Structures, Artech House, Dedham, Mass.,
1980.
2.
David M. Pozar, Microwave Engineering, 3rd ed., John Wiley & Sons, Inc.,
2005.
3.
C. S. Tsai, G. Qiu, H. Gao, L. W. Yang, G. P. Li, S. A. Nikitov, and Y.
Gulyaev, "Tunable wideband microwave band-stop and band-pass filters
using YIG/GGG-GaAs layer structures." IEEE Trans. Magn., vol.41,
pp.3568-3570, 2005.
4.
G. Qiu, C. S. Tsai, M. M. Kobayashi, and B. T. Wang, "Enhanced
microwave ferromagnetic resonance absorption and bandwidth using a
microstrip meander line with step-impedance low-pass filter in a yttrium
iron garnet-gallium arsenide layer structure", /. Appl. Phys., vol.103, 2008.
5.
C. S. Tsai, and G. Qiu, "Wideband microwave filters using FMR tuning in
flip-chip YIG-GaAs layer structures", accepted and to be published in
IEEE Trans. Magn., 2009.
6.
B. C. Wadell, Transmission Line Design Handbook. Artech House, 1991.
113
7.
Advanced Wave Research, Microwave Office User's Manual.
114
Chapter 5
Tunable Wideband Microwave Band-Pass Filter Using
YIG/GGG-GaAs Layer Structure
Chapter 4 discussed in detail the experimental study of the tunable wideband
microwave band-stop filter using YIG/GGG-GaAs layer structure. In this
Chapter, the microwave band-pass filter using YIG/GGG-GaAs layer structure
with large tuning ranges for the center frequency (5.90 - 17.80 GHz) and the
bandwidth (1.27 - 2.08 GHz) in the pass-band using a pair of aforementioned
microwave band-stop filters in cascade is presented. The design and simulation
of the band-pass filter were carried out using equivalent circuit method and
ANSOFT HFSS, specifically the simulation that incorporates multi-segment
microstrip meander-lines and 2-D non-uniform bias magnetic fields was carried
out using ANSOFT HFSS. The measured transmission characteristics of the bandpass filter at center frequency of 8.28 GHz, using 2-D non-uniform bias magnetic
fields centered at 2,750 Oe and 4,150 Oe facilitated by NdFeB permanent magnets,
shows a - 3 dB bandwidth of 1.73 GHz, an out-of-band rejection of - 33.5 dB, and
an insertion loss of - 4.2 dB. A good agreement between the simulation and
experimental results for the band-pass filter in the center frequency and the
bandwidths of the pass-band and the two guarding stop-bands has been
accomplished.
115
5.1 Band-Pass Filter Architecture
B i a s ?VWe7
Microwave
Input
Hoz(jlo2>Hoi)
Microwave
Output
Band-Stop
Band-Stop
Filter No.1
+*A Filter No.2
sie Pass-band
freq
freq
High-«»nc8 Stop-band
-end! Stos-bana
•f
:lr(t3Qi
J i n
1
Figure 5.1 Realization of the Tunable Band-Pass Filter using a Pair of Band-Stop
Filters in Cascade
As discussed in Chapter 4, the YIG/GGG-GaAs-based microwave band-stop
filter with wideband tunability of stop-band center frequency and bandwidth
has demonstrated a large tuning range in peak absorption frequency of 5.0 to
21.0 GHz and an absorption level of - 35.5 dB together with a corresponding 3 dB
bandwidth as large as 1.70 GHz (see Figure 4.26) [1]. It is clear that by using a
pair of such band-stop filters in cascade (Figure 5.1) in which different nonuniform bias magnetic fields (H02 > H0l) are applied, a band-pass filter with large
tuning ranges for both the center frequency and the bandwidth in the pass-band
116
can be realized by properly programming the low-end and the high-end values
of the bias magnetic fields (Hmand H02) [2-3]. Figure 5.1 shows the scheme of
realizing the tunable band-pass filter using a pair of band-stop filter in cascade.
5.2 Device Simulations
5.2.1 Simulation Using Equivalent Circuit Method
YIG Band-stop Filter
No.2
YIG Band-stop Filter
No.1
Figure 5.2 Lumped Element Equivalent Circuit of the YIG/GGG-GaAs-based
Band-Pass Filter
As we presented in Chapter 3, the equivalent circuit method was used to
simulate the band-stop filter, and the same method is implemented here in this
chapter to simulate the device performance of the band-pass filter. Figure 5.2
shows the lumped element equivalent circuit of the YIG/GGG-GaAs-based
microwave band-pass filter. Please note that, in this equivalent circuit method,
117
the microstrip line for each band-stop filter (no.l and no.2) is the 50
Q transmission line.
The Vin and the Z0 (Z0 =50iQ) are, respectively, the input microwave and the
characteristic impedance of the transmission line. The formulism used to
calculate the values of the lumped elements, namely, Ri, R2, Li, L2, Ci, C2 and the
returns ratio ni and m, are derived in Chapter 3. The geometric parameters and
the applied bias magnetic fields which are used to in this simulation for the
band-stop filter no.l and no. 2 are listed in the Table 5-1. Please note that those
parameters are the same as our experimental arrangement, and the simulation
results will be compared with the experimental data shown in Section 5.3. The
calculated radiation resistance Rm versus wavenumber k for the band-stop filter
no.l and no.2 are shown in Figure 5.3 (a) and (b) respectively.
Table 5-1: Geometric Parameters and Bias Magnetic Fields Used in the
Simulation
YIG Band-stop Filter 1
t
d
"
350 um
6.8 um
"~""
YIG Band-stop Filter 2
350 um
6.8 um
b
256 um
256 um
H
1,300 Oe
2,050 Oe
118
•
"P
i
i
i
i
180
1
'
1
i
• -,
i
i
,
i
i
i
O
>
*
~
160
t=350um
d=6.8um
b=256um
H =1,300 Oe
"O 140
'>—^
Q : S 120
8 100
c 80
B
CO
0
K.
c
'_
_
.
-
60
40
O
«
T3
CO
Q:
20
^
^
g
^
^
^
^
0
-90
.
i
c
•
i
i
100
150
200
•
50
.
i
I
250
300
.
I
.
I
350
.
I
400
.
5C
450
1
Propagation Constant (k) (cm )
(a)
•
i
'
I
i
i
•
i
•
1
i
l
i
1
i
l
i
^ - . 250
E
.o
"p
£
•
200
£
° ^ 150
0
O
c
CD
-*i 100
w
"to
CD
*
50
C
.
\
i
t=350um
d=6.8um
b=256um
H=2,030 Oe
\
I
\
- I
\
i
-
g
*^—i
CO
"•5
CO
CC
o
• _i_ i
50
100
i
i
150
200
.
i
250
•
i
300
i
i
350
i
i
400
i
i
450
i
500
Propagation Constant (k) (cm1)
(b)
Figure 5.3 Calculated Radiation Resistance Rm versus Wavenumber k for
Band-Stop Filter (a) No.l, and (b) No.2
119
Two identical YIG samples are used both in experiments and in simulations
where / = 2.%mm and lz =9mm (ly,lzxe the planar dimensions of the YIG sample
in (y,z) plane (see Figure 3.3). Therefore, the wavenumber of the main mode
(n=l, m=l) of the MSSWs is approximately equal to klA& 12crrT1 and the
corresponding radiation resistance Rm I cm and other values of lumped elements
are listed in Table 5-2 as follows:
Table 5-2 Values of Lumped Elements For Band-Stop Filter 1 and 2
YIG Band-stop Filter 1
YIG Band-stop Filter 2
Rm/cm
12
14.5
R(ohm)
3.36
4.06
L(nH)
382.11
461.71
C(pF)
1.9287E-3
0.82617E-3
n
5.4
7.0
Microwave Office is used again to simulate the lumped element equivalent circuit
whose parameters are given in Table 5-2. The simulated S-parameter (S21) plot
directly from Microwave Office is shown in Figure 5.4. These simulated results
have been compared to the experimental results in Figure 5.7 in Section 5.3. As
we can see in Figure 5.7, a good agreement between the experimental results and
the simulation results has been achieved.
120
Graph 1
u
I
-10
I
-20
lil-
^DB(IS[2,1]|)
-30 ;
YIG_1
I
i
j
-40
2
4
6
8
Frequency (GHz)
10
12
Figure 5.4 Simulated S-parameters (S21) of the YIG/GGG-GaAs-based Microwave
Band-Pass Filter
5.2.1 Simulation Using ANSOFT HFSS
The simulation of the band-pass filter that incorporates four-segment microstrip
meander-lines and 2-D non-uniform bias magnetic fields have been carried out
using ANSOFT HFSS in this section. The HFSS can simulate the exact design of
your device including the multi-segment microstrip line. More importantly, we
incorporate two-dimension non-uniformity of the bias magnetic field into
simulation, specifically, the non-uniform bias magnetic field with sixteen (4x4)
121
discrete values that was taken from measurement data are implemented into the
simulation. The results showed a good agreement between the simulation and
experimental results for the band-pass filter in the center frequency and the
bandwidths of the pass-band and the two guarding stop-bands.
Figure 5.5 Schematics of the Band-Pass Filter in HFSS 3-D Modeler Simulator
A physical model of a band-pass filter with exact design of the two four-segment
microstrip meander-lines, the YIG/GGG layer and the GaAs substrate were first
built as shown in Figure 5.5. In this simulation, we keep the two four-segment
microstrip meander-line structure exactly the same as design, but the trace
distance between the two band-stop filter are not exactly the same as the
122
experiments. The main reason here is that the longer distance of the trace
between the two band-stop filters will result in a much large side of device, and
consequently, a much longer simulation time. The effects of the trace difference
between the simulation and real measurements will only be the small differences
of the transmission loss (S21) which has been neglected here in the simulation.
The material property of the YIG sample has been assigned where the Linewidth
AH = 1.0 Oe, the Lande G Factor = 2, the Saturation Magnetization AnMs = 1,760
Oe, and the relative permittivity sr = 14.7.
For the 2-D non-uniform bias magnetic field, we directly implemented the
experimental data into the simulations, namely, we used 16 discrete values (4x4)
from the measured 2-D non-uniform bias magnetic field data. The measured
non-uniform bias magnetic fields centered at 2,750 Oe and 4,150 Oe will be
shown shortly in next section in Figure 5.8.
With all aforementioned assignments ready, the microwave transmission loss
(S21) of the band-pass filter are simulated and the results is shown Figure 5.6. As
you will see shortly in Figure 5.8, a good agreement between the experiment
results and the simulation results has been achieved for the band-pass filter in
the center frequency and the bandwidths of the pass-band and the two guarding
stop-bands.
123
"i—•—r
s S f f l *^ra^«aa3s&vj^ 3 .- a s ( a ,
CO
•D
ex
tn
H-4,22<3Hz
t
w=2,75p..Oa.
(centered)
11
H
12
13
w01 *4 T 150Oe
(centered)
15
14
16
17
Frequency (GHz)
Figure 5.6 Simulated and Measured Transmission Losses (S21) of the Tunable
Band-Pass Filter
5.3 Experimental Results
In the band-pass filter experiments, two band-stop filters are cascaded externally
through coaxial cable to realize this band-pass filter. A photo of the real device is
shown in Figure 5.7.
124
Figure 5.7 Photo of the Microwave Band-Pass Filter using Cascaded Band-Stop
Filters
5.3.1 Band-Pass Filter with Narrow Stop-Band Bandwidth
In the experiments, without incorporating the multi-segment microstrip line
where each of the band-stop filter only contain single-segment 50 Q microstrip
line, a pair of identical YIG/GGG samples 2.8 x 9.0mm2 (same as simulation in
Section 5.2.1) was placed in separate bias magnetic fields supplied by two pair of
permanent magnets (see Figure 4.20 for the bias magnetic field arrangement) for
125
band-stop no.l and no.2. For the bias magnetic fields of 1,300 Oe and 2,050 Oe,
the measured transmission characteristics of the band-pass filter (black circle in
Figure 5.8) at the passband center frequency of 7.1 GHz shows a 3 dB bandwidth
of 1,450 MHz, out-of-band rejection of 33dB, and an insertion loss of 1.5 dB.
Clearly, good agreement between the experimental results and the simulation
results (red dot in Figure 5.8, same as Figure 5.4) has been achieved.
Insertion Loss= -1.5dB
BW(-3dB)=1450 MHz
Shape Factor 1.56 (30dB/3dB)
-h
(M
"*«Ham*.
-1(H
PI
00
S -20
CM
CO
c -30
o
"55
w
g -40w
c
w
o
a
m
is
Measurec
Simulatec
t
O
O
o
o
i± -50 J
-60
&
o
O
o
sn
o
CO
T
3
T"
1
1
4
6
7
CM
1
8
r
9
10
11
12
Frequency (GHz)
Figure 5.8 Comparison of the Simulated and Measured S21 of a YIG/GGG-GaAs
Based Microwave Band-Pass Filter with Narrow Stop-Band Bandwidth
126
5.3.2 Band-Pass Filter with Large Stop-Band Bandwidth
The microwave band-stop filter with wideband tunability of stop-band center
frequency and bandwidth utilizing the four-segment microstrip meander-line is
used to construct the band-pass filter with large stop-band bandwidth. The
experimental arrangement for facilitating the 2-D non-uniform bias magnetic
field was shown in Figure 4.20.
10
Central Frequency=12.28 GHz
BW(-3dB)=1.73GHz
Insertion Loss =-4.2 dB
Measured
Simulated
••""IITI'I"*
— 1.22 GHz
-40
Hn =2,750 Oe
01
H 0 ,=4,150Oe
(centered)
'
(centered)
10
11
12
13
14
15
16
17
Frequency (GHz)
Figure 5.9 Comparison of the Simulated and Measured S21 of a YIG/GGG-GaAs
Based Microwave Band-Pass Filter with Large Stop-Band Bandwidth
127
Measured Non-uniform Magnetic Field
3100
3000
2900
2600
2700
2600
(a)
Measured Non-uniform Magnetic Field
Figure 5.10 Measured 2-D Non-Uniform Bias Magnetic Field Profile Centered at
(a) 2,750 Oe and (b) 4,150 Oe
128
In the experiments, two YIG/GGG samples each with the dimension of
8.0mmx8.0mmx6.8//m in X, Y and Z-directions (see Figure 5.5) were used. The
measured transmission characteristics (see circle line in Figure 5.9) at the center
frequency of 12.28 GHz shows a - 3dB bandwidth as large as 1.73 GHz, an out-ofband rejection of - 33.5 dB, and an insertion loss of - 4.2 dB. As clearly shown in
Figure 5.9, a good agreement between the experiment results and the simulation
results has been achieved for the band-pass filter in the center frequency and the
band widths of the pass-band and the two guarding stop-bands. The large stopband at each end of the pass-band was realized by the two band-stop filters in
which the non-uniform bias magnetic fields were centered at 2,750 Oe (H0,) and
4,150 Oe (H02). The highly non-uniformity of the bias magnetic fields centered at
2,750 Oe (Hm) and 4,150 Oe (H02) are measured and shown in Figure 5.10 (a) and
(b), respectively.
Large tuning ranges in the pass-band center frequency (5.90-17.80 GHz) and the
bandwidth (1.27-2.08GHz) of the band-pass filter were also measured and shown
in Figure 5.11. Note that the measured S21 lower than the low-end stop-band and
higher than the high-end stop-band are not plotted in the figure, i.e. only the two
stop-bands and the pass-band are plotted. The measured pass-band bandwidths
and insertion losses are listed in Table 5-3.
129
8
10
12
14
16
18
20
Frequency (GHz)
Figure 5.11 Measured Transmission Characteristics of the Tunable Band-Pass
Filter in a Wide Frequency Range of 5.90-17.8 GHz
TABLE 5-3 Measured Insertion Losses and Band-Widths of the Band-Pass Filter
of Figure 5.11
Pass-Band Center
5.90
9.00
12.28
17.80
BW@-3dB (MHz)
1,270
1,300
1,730
2,080
Insertion Loss (dB)
-3.1
3.9
-4.2
-6.6
130
5.4 Discussions
5.4.1 Electronic Tunability
Air Gap (d)
Solenoids
NdFeB Permanent
Magnets
NdFeB Permanent
Magnets
Steel Yoke
Figure 5.12 The Sketch of the Electromagnet
The magnetic circuit that incorporates inductive coils for high-speed electronic
control of bias magnetic field within the YIG/GGG sample and, thus, the peak
FMR absorption frequency will be discussed in this section [3]. Figure 5.12 shows
the components of the magnetic circuit that were used to facilitate electronic
tuning of the band-stop and band-pass filter. Each of the disk-shape NdFeB
permanent magnet has the dimensions of 0.5" in thickness and 0.75" in diameter.
The electric wire used for the solenoids is of the size of 28 a.w.g. and the number
131
of turns in each coil is 820. The pair of solenoids was wrapped around the NdFeB
permanent magnets to facilitate electronic tuning of the magnetic field in the air
gap. The measured changes of magnetic fields in the air gap versus the DC
currents in the coils, with the air gap distance as a parameter, are shown in
Figure 5.13.
CD
O
CD
Air Gap Distances
• 11.0mm
A 17.1mm
500• 24.1mm
^ 30.6mm
•
600-
•
•
•
O 400"0
c:
•
•
CO
CO
o
200-
o
•
•
C/5
0
CD 100C
CO
x:
A
H
•
A
A
A
•
+
9
•
0
•
•
^
•
9
9
1* *
0- A
I
A
A
9
0
0.0
•
A
•
300-
•
A
•
i
0.1
i
|
0.2
.
|
0.3
i
i
i
i
i
i
i
i
i
i
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
DC Current (Amp)
Figure 5.13 The Measured Changes of Magnetic Fields in the Air Gap versus the
DC Current in the Coils with the Air Gap Distance as a Parameter
Table 5-4 lists the measured magnetic fields and maximum in the center of air
gap at four discrete air gaps of 11,17.1, 24.1, and 30.6 mm, and its corresponding
maximum tuning ranges of the FMR frequencies. Using different combinations of
132
the air gap and the current in the coils, a tuning range as large as 5.5-18.8 GHz
for the FMR absorption frequencies was realized.
TABLE 5-4 Measured Center Magnetic Fields and Maximum Change of
Magnetic Field in the Center of the Air gap and the Maximum Tuning Ranges of
the FMR Frequencies
Air Gap(mm)
~"
Center Magnetic Field (Oe)
Change of H @ DC
11.0
17.1
241
30.6
5,200
3,250
2,000
1,425
+ 590
±470
±325
±245
15.4-18.8
10.2-12.9
7.0-9.0
5.5-7.0
Current= ±1.2 Amp
Maximum Tuning Range (GHz)
It is of interest to determine the time it would take to tune electronically the dc
magnetic field, and thus the tuning speed of the FMR absorption frequency. The
electrical parameters of the coils were measured by using Agilent 4294A
impedance analyzer. The measured values of the inductance, capacitance, and
resistance are 12.2 mH, 165.5 pF, and 20 Q (from 40Hz to 100 kHz), respectively,
as shown in Figure 5.14 where the major electrical parameters are the inductance
and the resistance by the coil together with a very small parasitic capacitance. In
the experiments, a step-function voltage (0-2Vpp) from a function generator was
used to drive the coil to measure the transient voltages of the coils. A serial
resistance is used to control the response time (time constant) of the circuit. The
OrCAD Pspice is used to simulate the circuit and the results are used to compare
133
with experimental results in Figure 5.15. The measured response time was found
to be in good agreement with the calculated values based on the measured
inductance, capacitance, and resistance of the coil.
The comparisons of the
response times and static voltages between the simulated results and measured
results are shown in Table 5-5. It is clearly shown in Table 5-5 that the higher
series resistor will result in a faster response (small time-constant) and lower
static voltage, and therefore, the lower static-state current.
J
prrrs
R
\Mr
*
Figure 5-14 The Equivalent Circuit Used to Model the Coil
Table 5-5 The Comparison between the Simulated and Experimental Results of
Figure 5-15
Simulation
Experiments
Series Resistor
Response Time
(//s)
Static Voltage
(mV)
47
270
1,500
47
270
160
43.3
9.4
209
69.5
1,500
12
360
118
30
360
120
70
134
2.2
m Measured 1.5K ohm
— Simulated 1.5K ohm
2.0
1.8
>
CO
1.6
o
o
1.4
.c
-*-»
c
o
1.2
CD
0
D)
CD
,4—1
o
>
A
—
Measured 270 ohm
Simulated 270 ohm
•
Measured 47 ohm
Simulated 47 ohm
1.0
0.8
0.6
0.4
0.2
0.0
T — • — i — • — i — • — i — • — i — ' — i — ' — i — ' — i — ' — i —
0
50
100
150
200
250
300
350
r
~
400
450
500
Times(us)
Figure 5-15 The Simulated and Measured Transient Voltages of the Coil when
the Serial Resistors are 1.5 k Q , 270Q. and 47 Q
5.4.2 Power Handling Capability
The power handling capability of the band-stop and band-pass filter are also
interested and measured in a wide frequency range [3]. A typical measurement
results is shown in Figure 5-16 where the microwave transmission characteristics
(S21) of the band-stop filter using one segment microstrip SILPF were measured
at different microwave power input levels in the range of 1 - 500 mW. The
measurement data (see Figure 5-16) shows no obvious changes at the four
discrete microwave power input levels (lmW, 10mW, 100mW, and 500mW) in
135
the important quantities of FMR frequencies, power absorption levels, and FMR
absorption spectrums.
o
-5
-10
-15
CQ
860 Oe
1,325 Oe
S -20
S
OJ -25
1,940 Oe
-30 K
Input Power = 1 m W
-35
-40.
3
4
1,940 Oe
2,750 Oe
Input Power = 10 m W
•
5 6 7 8 9 10 11 12 13
Frequency (GHz)
(a)
3
0
1
8
1X
T
°
-10
2,750 Oe
•
5„ 6 7 8 9 10 11 12 13
Frequency (GHz)
4
3 -20
-30
tff-25
5
A?
°
I y
Y P
1,940 Oe
-35 Input Power = 500 mW
-35 .Input Power = 100 mW
4
Q
0
-30
2,750 Oe
3
\Y
860 Oe t
W
1,325 Oe |
S-20
860 Oe '
V
1,325 Oe t
1,940 Oe
yj -25
•
^-15 .
-15
2
-
-5
-10
-40.
•
0
-5
^
-
|
6 7 8 9 10 11 12 13 -402
Frequency (GHz)
(c)
3
4
t
2,750 Oe
5 6 7 8 9 10 11 12 13
Frequency (GHz)
(d)
Figure 5-16. Measured Transmission Characteristics of the Band-Stop Filter at
Different Input Microwave Power Levels of (a) l m W (b) lOmW (c) lOOmW, and
(d) 500mW
Reference
1.
G. Qiu, C. S. Tsai, M. M. Kobayashi, and B. T. Wang, "Enhanced
microwave ferromagnetic resonance absorption and bandwidth using a
microstrip meander line with step-impedance low-pass filter in a yttrium
136
iron garnet-gallium arsenide layer structure", /. Appl. Phys., vol.103,2008.
2.
Gang Qiu, Chen S. Tsail, Bert S. T. Wang, and Yun Zhu, "A
YIG/GGG/GaAs-Based Magnetically Tunable Wideband Microwave
Band-Pass Filter Using Cascaded Band-Stop Filters", IEEE Trans. Magn.,
vol.44, issue 11, 2008.
3.
C. S. Tsai, and G. Qiu, "Wideband microwave filters using FMR tuning in
flip-chip YIG-GaAs layer structures", accepted and to be published in
IEEE Trans. Magn., 2009.
137
Chapter 6
Tunable Wideband Filters using YIG/GGG Layer on RTDuroid Substrates
Chapter 2 to 5 presented theoretical and experimental studies of FMR-based
tunable wideband microwave band-stop and band-pass filters using YIG/GGGGaAs layer structure. In this Chapter, the filter counterparts using YIG/GGG
layer on RT-Duroid substrate are presented. The band-stop filtering using
YIG/GGG layer with a YIG film thickness of 100 ju m on RT-Duroid 6010LM
substrate is demonstrated first showing a much wider FMR absorption
bandwidth and a higher absorption level compared to the results obtained with
YIG thickness of 6.8 jum. A scheme for realizing an X-band microwave bandpass filter with tunable center frequency and pass-band bandwidth using
YIG/GGG layer on Duroid 6010LM is discussed. A composite X-band (8-12GHz)
band-pass filter (BPF) which employs a quarter-wave short-circuited stubs-based
X-band BPF and a 9-element step-impedance LPF as the transmission line is
proposed, designed and simulated. Finally, the experimental results and some
future works outlined.
6.1 Band-Stop Filter on RT-Duroid 6010LM
6.1.1 High-Frequency Circuit Board Materials
138
The market of RF/microwave circuit board has greatly evolved over the past
several decades from military applications using waveguides to commercial
applications using low-cost substrates. The conventional circuit board materials
such as FR-4 were developed as a way of supporting conductors to replace cable
connections as a means for conducting electrical current. The combination of
metal conductor and supporting material had the primary purpose of providing
a reliable connection between any two points. This approach came about as a
way of reducing the cost and size of electrical circuits. The requirements for these
conventional materials were simplicity, good adhesion of the conductor to the
substrate material, substrate material to be rigid and low cost. However, the
board material at high frequency, e.g., higher than 500MHz, is much more than
just a support for the conductor; it also forms part of the circuit by dictating the
length, width and spacing of the traces as well as the way in which the resulting
circuit function. It is important to understand that at RF /microwave frequency,
a signal trace becomes an element by itself with distributed resistance,
capacitance, and inductance. At such high frequencies, the dimensions of the
circuit play a vital role in its function. Changing dimensions of the traces and
spaces with better utilization of the board can drastically improve the
performance. In general, high-frequency applications require circuit board
materials with many special properties and electrical characteristics that are not
critical for DC but are essential for high frequency analog circuitry and high
speed digital circuitry. When selecting circuit board materials for RF/ microwave
139
applications, proper control of the dielectric constant, low dissipation factor or
loss tangent, and thicknesses of the substrate is particularly important.
Rogers Corporation, Advanced Circuit Materials Division has an extensive selection
of high frequency laminates for many types of applications that include linear
power amplifiers and antennas for cellular and PCS base stations, phased array
antennas, radar systems and high performance wireless components. Potential
application of RT-Duroid circuit board materials for linear power amplifier using
photonic band gap structure [1-2], and planar microwave circulator applications
[3] have been demonstrated.
6.1.2 Band-Stop Filter using 100 ju m Thick YIG on Duroid 6010LM
-10
QQ
•o
5.70 mm
s -30
-40
-50
-60
5
10
15
20
25
30
35
40
45
50
Frequency (GHz)
(a)
(b)
Figure 6.1 The Layout (a), and the Simulated Transmission Loss (S21) (b), of the
Step-Impedance LPF on Duroid 6010LM
140
In this section, a band-stop filter using the same basic device configuration of
Figure 4.11 but with the 350//m GaAs substrate replaced by the Duroid 601OLM
substrate is presented. The RT-Duroid 6010LM substrate has the desirable
features of high and stable dielectric constant of 10.5 for circuit size reduction,
low loss (loss tangent of 0.0023) for operation at X-band, and well-controlled
thickness of 254 ju m. The layout and the simulated transmission loss (S21) of the
9-element step-impedance LPF on Duroid 601 OLM substrate are shown in Figure
6.1 (a) and (b), respectively. Note that the design methodology has been
presented in Chapter 4.
In the measurements, the YIG films used are 6.8 jum and 100 jum in thickness
with dimension of 6.0x8.0mm2 in the X and Y directions (see Figure 4.11 for
device coordinates). Two band-stop filters, one with 6.8 jum thick YIG sample
and the other with 100 jum thick YIG sample, were used in the experiments to
compare the microwave power absorptions at the FMR frequencies. The bias
magnetic field (H0) supplied by a pair of NdFeB permanent magnets was set in
the same direction as the microwave propagation. The transmission losses (S21)
were then measured using the power meter measurement system (see Figure
4.15 for the measurement system). The measured S21 of the two band-stop filters
shows that a much wider FMR absorption bandwidth and greater absorption
level occurred when using the 100 / / m thick YIG sample as compared to that
141
using the 6.8 ju m thick YIG sample. These experimental findings are indeed in
line with the theoretical prediction presented in Chapter 2.
•>
1
'
1
'
1
'
1
'
1
'
1
'
1
'
1
'
1
r
Frequency (GHz)
Figure 6.2 Measured S21 of the YIG/GGG-RT-Duroid-Based Microwave BandStop Filter at FMR Frequency of 8.5 GHz Using the 100 ju m Thick YIG Sample
and the 6.8 ju m Thick YIG Sample
For example, the measured S21 of the two band-stop filters at the FMR frequency
of 8.5 GHz are shown in Figure 6.2. The bias magnetic field of 2,100Oe was
applied to set the FMR frequency at 8.5 GHz. The measured S21 of -35.5 dB using
the 100 ju m thick YIG sample clearly shows a significantly greater level of
142
microwave power absorption as compared to that using the 6.8 ju m thick YIG
sample with the measured S21 of -20.0 dB. A much wider FMR absorption
bandwidth is also seen in Figure 6.2.
6.2 An X-Band Tunable Band-Pass Filter
8 GHz
Microwave
Input
GHz
y
I 12 GHz
-/
/
Band-Stop Filter ".TV Band-Stop Filter
#1
#2
fre
Tunable X-Band BPF
S21
Microwave
Output
GHz
12 GHz
fre
Figure 6.3 A Scheme of Realizing an X-band (8 -12 GHz) Microwave Band-Pass
Filter
A scheme for realizing an X-band (8-12 GHz) microwave band-pass filter (BPF)
with tunable center frequency and pass-band bandwidth using YIG/GGGDuroid 6010LM is shown in Figure 6.3. The basic idea of the BPF using cascaded
band-stop filters is the same as that shown in Figure 5.1 of Chapter 5 except that
the X-band BPFs were used here to replace the step-impedance LPFs in the
band-stop filter #1 and #2. A microwave BPF with the pass-band of 8 to 12 GHz
was designed first as transmission line structure for band-stop filters #1 and #2.
143
As shown in Figure 6.3, an X-band BPF with tunable center frequency and passband bandwidth can be realized by simultaneously tuning the low-end and highend stop-bands and varying the bias magnetic fields of the band-stop filters #1
and #2, respectively.
6.2.1 Design of an X-Band Composite Band-Pass Filter
Figure 6.4 BPF Using Quarter-Wave Short-Circuited Stubs
Shunt quarter-wave short-circuited stubs were used to design and construct the
X-band BPF (see Figure 6.4). In this configuration, the filter is comprised of shunt
short-circuited stubs (shown as ln in Figure 6.4) that are Xg / 4 long with
connecting lines (shown as ln_ln in Figure 6.4) that are also X / 4 long, where A
is the guided wavelength in the medium of propagation at the mid-band
frequency
of
the
BPF. This
shunt
quarter-wave
short-circuited
stubs
configuration has the unique advantages that can combine with step-impedance
LPF to form a compact composite BPF [4].
This BPF was designed by using Chebyshev (or equal ripple referred to in the
literature) LPF as its prototype filter which has a sharp cut off response and then
144
transformed to the band-pass response to form a BPF [5]. In the prototype filter
design, four stubs (n=4) and pass-band ripple lower than 0.1 dB were specified.
The corresponding prototype element values are listed as follows [5]. The four
shunt quarter-wave short-circuited stubs were subsequently inserted into the
four inductive elements of the step-impedance LPF.
gi=1.1088; g2=1.3061; #=1.7703; g4=0.8180; g5=1.3554; go=l
Note that for a given filter degree n, the stub BPF characteristics will depend on
the characteristic admittances of the stub lines denoted by Yi (i = 1 to n) and the
characteristic admittances of the connecting lines denoted by Yy+i (i = 1 to n - 1).
The normalized Yi (i = 1 to n) and Yy+i (i = 1 to n - 1) are determined using
equations (6.1).
4,2
Am
Yo
Mt t++1
T
t
'
/%!
=
4-l,„
=
j fel&,-H
h
8og
Vg;g/+1
for i = 2 to n - 2
fo
-=Ito«-1
VUTi \~~T-l
Yi =goYJ( l~^)gilm()+
YolNui-
-y-
Yn = Y0[ g„gn+i -gogi -r Jtanl? + F 0 ^«-i,« - ~ ? J ^
'0
WUWiw^-^|
Y
"';,!+1
i,H-i = Y0[ — p — J
fcl-2B,-.
for / = 1 to n - 1
(6.1)
145
f
where 9 = —
2
a02
j
, o)2 =\2GH2,Q\
=%GHz,G)0 =\OGHz, gi is the prototype
element values, and h is a dimensionless constant that can be set to 2. The
resulting normalized Yi (i = 1 to n ) , Yy+i (i = 1 to n - 1) and the corresponding
impedances transformed Zi (i = 1 to n) and Zy+i (i = 1 to n - 1) are listed in Table
6-1.
Table 6-1 Admittance and Impedance of the BPF
Admittance(Y)
Yo
Yi
Y12
Y2
Y23
Y3
Y 34
Y4
Impedance (Z)
1
2.0103
1.303
3.9295
1.4584
4.117
1.0123
2.1977
Z0
50
Zi
Z12
24.8719
38.3729
12.7243
34.2841
12.1447
49.3924
22.7510
z2
Z23
Z3
Z34
z4
The width (W) of each stub in the BPF was computed using Equation (6.2) (a-d)
[51.
's.+0
60
V
^
J
s-\
f
*r"
V
+-e+lr l 0.23 +
0.11
,Wld<2
W _ SxeA W_
<2
d ~ e1A-2' d
5=
W low = dx7T
(B-l)-hi(2B-l)
60TT 2
+
(6.2a)
"r J
,Wld>2
0.61
e-l
l n ( 5 - l ) + 0.392e„
(6.2b)
(6.2c)
W
,^->2(6.2d)
d
where Z. are the impedances in Table 6-1, £,.= 10.5 is the relative dielectric
constant of Duroid 6010LM substrate, and d - 254jum is the substrate thickness.
146
The length (L - Ag / 4 ) of each stub in the BPF was computed using equation (6.3)
(a-b),
>L __h
4
75
(mm)
f(GHz)^e
4 ^
£•+1
£.„ = -
£ - 1f
-a*
1+
V u J
•+ -
w4 +
a = lH
10
(6.3a)
In
uJ
v52y
4
w +0.432
49
+ 18.7
- -In 1 + 18.1
(6.3b)
V
/
f
s 0.053
6 = 0.564 e - 0 . 9 ^
v ^+3
Finally, the dimensions of the width (W) and length (L) of each stub and the
connecting line of the BPF are listed in Table 6-2. The layout of the X-band BPF
thus designed is shown in Figure 6.5. The designed BPF was then simulated
using AWR Microwave Office Simulator. The simulated transmission loss (S21) is
shown in Figure 6.6.
Table 6-2: Width and Length of Shunt Stubs and Connecting Lines in Figure 6.5
Width (W)(um)
231.6
Wo
Wi
762.8
383.4
W12
1837.4
w2
463.4
W23
1944.1
w3
237.5
W34
865.6
w
Length (L)(um)
3157
Lo
Li
2972.6
3085.4
L12
2828.2
U
3055.5
L23
2819.7
3153.8
L34
2951.1
u
u
4
147
wo
Figure 6.5 The Layout of the X-Band BPF
1
0
^ ^ ^ M « *•
8.0GHz A
pa
M ^ ^ l
'
r
T
" 1'"
^ A 12.4 GHz
1
-10
CD
-d
O)
+•>
1
%
-20
-30
\
M
-40
f
-50
-fin
\
¥
2
,
^k
1
1
1
4
6
8
.X
10
12
14
16
18
Frequency (GHz)
Figure 6.6 Simulated Transmission Loss (S21) of the X-Band BPF
148
Subsequently, the designed X-band BPF (see Figure 6.7 (a)) was combined with a
step-impedance LPF (see Figure 6.7(b)) to realize a composite X-band BPF
(Figure 6.7 (c)) having compact structure and used as the transmission structure
for the cascaded band-stop filters #1 and #2. In this design, the four shunt stubs
in Figure 6.7 (a) were inserted into the four inductive elements ( 4 0 ' = 1,2,3,4) in
Figure 6.7(b)) of the step-impedance LPF, and the length of each stubs
(Ll,L2,L3,L4)
and length of each inductive elements (LH,L12,L13,L14) are tuned
to form the desired frequency responses. The width of each shunt stub and that
of the capacitor and inductor in the step-impedance LPF were keep constant. The
width of each shunt capacitor and serial inductor are 757.1 ju m and 153.1 ju m,
respectively, as shown in Figure 6.7 (b). AWR Microwave Office Simulator was
used for the tuning and optimization in the simulation. The dimensions of the
composite X-band BPF are listed in Table 6-3. The simulated S21 of the X-band
composite BPF are shown in Figure 6.8.
Table 6-3: Geometric Dimensions of The X-Band Composite BPF
Wl
W2
W3
W4
LI
L2
L3
L4
762.8 jum
1837.4//m
1944.1//m
865.6//m
3106 ju m
3439//m
3424 jum
3176 jum
Lcl
Lc2
Lc3
Lc4
Lc5
Lll
L12
L13
L14
149
111.5 /urn
492 jum
642.3 jum
492 jum
111.5 /jm
957.3 jum
1997 /um
2199.3 jum
1190.6 /um
(c)
Figure 6.7 The X-Band BPF (a), The Step-Impedance LPF (b), and the Composite
X-Band BPF (c)
T—•—r
1
7.9 GHz
'
12.2GHz
1
r
A
-\ -10
-20 \-
Figure 6.8 Simulated Transmission Loss (S21) of the Composite X-Band BPF
150
6.2.2 Experimental Results and Discussion
The designed X-band composite BPF was fabricated
using the same
photolithograph process as described in Chapter 4. A photo of the device
fabricated is shown in Figure 6.9. The transmission characteristics of the
composite BPF is measured using the Power Meter Measurement System (see
Figure 4.15 for the measurement system) and the measured S21 is shown in
Figure 6.10.
>•_«.
<*-:
Figure 6.9 Photo of Fabricated X-Band Composite BPF
151
— • — i — ' — i — ' — i — ' •
-5
-10
-15
i
'
i —>—r"'
i
6.5 GHz
"
J
•
i
•
i
•
i
i
l
i
1
i
10.5 G H z
•
„ ^ * ^ ^
-
-20
£T -25
Afc
-35
U -
-40
-45
i
-50
3
4
5
6
7
I
8
9
10
11
12
,
I
13
1
1
14
1
1
15
1
16
Frequency(GHz)
Figure 6.10 Measured Transmission Loss (S21) of the Composite X-Band BPF
Two major discrepancies between the measured and simulated transmission
characteristics are identified. First, the measured pass-band of 6.5 -10.5 GHz is
seen to shift towards the low frequency region as compared to the simulated
pass-band of 8-12 GHz shown in Figure 6.8. This pass-band frequency shift is
attributable to the stub length inaccuracy during the experimentation. In the
experiments, four holes at the end of each shunt stub (see Figure 6.9) were drilled
manually and filled with Transene® silver-based surface mount adhesive. As a
result, it is difficult to accurately control the length of each stub. As a verification,
the sensitivity of the S21 to the shunt stub lengths was simulated and shown in
152
Figure 6.11.
It is clearly seen that the pass-band frequency shifts greatly towards
the high- or low- frequency end when the lengths of the stubs are deviated from
their ideal values by 1,000 ju m.
T — ' — i — ' — i — ' — i — ' — i — ' — i — ' — i — « — r
2
4
6
8
10
12
14
16
18
Frequency (GHz)
Figure 6.11 The Simulated Sensitivity of the S21 to the Lengths of Shunt Stubs
The second discrepancy between the measurement and simulation result is that
the measured insertion loss of ~-7dB is much higher than the simulation results.
This higher insertion loss in the pass-band is attributable to the imperfect
grounding of the shunt stubs. The measured average resistance of each shunt
stub to ground is about 1.0 ohm. The sensitivity of S21 to the shunt stub
grounding resistance was simulated and shown in Figure 6.12. It is seen that, the
153
insertion loss in the pass-band increases by more than 6dB as the shunt stub
grounding resistance increases from 0 to 1.6 Q..
5
0
1
1
1
1
1
1
1
1
Ground Resistance 0.6Ohm
r
1
'
1
r -
Perfect Ground
-5
-10
-15
T5
C/5
-20
-25
-30
-35
-40
-45
18
Freuqency (GHz)
Figure 6.12 The Simulated Sensitivity of the S21 to the Shunt Stub Grounding
Resistance
Encouraged by the preliminary results presented above, the same X-band
composite BPF was used to demonstrate its low- and high-end tunability. In the
experiments, the YIG films used were 100 pirn in thickness with dimension of
6.0x8.0WOT2 in the X and Y directions (see Figure 4.11). The bias magnetic field
was again supplied by a pair of NdFeB permanent magnets in the same direction
as the microwave propagation. Again, the S21 was then measured using the
154
Power Meter Measurement System. As illustrated in Figure 6.3, the pass-band
bandwidth of the BPF can be changed by tuning the bandwidth of the low- and
high-end stop-bands. The measured high-end and low-end stop-band tunability
of the BPF by applying the bias magnetic fields of 2,800 Oe and 2,450 Oe, and 990
Oe and 1,060 Oe, respectively, are shown in Figure 6.13 and 6.14. Figure 6.13 and
6.14 clearly show that both the low- and high-end stop-bands could be shifted
downward or upward by applying appropriate external bias magnetic fields.
CO
7
8
9
10
11
12
13
14
15
16
Frequency(GHz)
Figure 6.13 The High-End Stop-Band Tunability of the BPF by Applying Bias
Magnetic Fields of 2,800 Oe and 2,450 Oe
155
0
-i—|—i—|—i—[—i—|—i—|—i—|-
1
•<—i—'—r
i
'
i
Original
-5
-10
PQ
73
CD
.45 L_i
I
i_l
i L
7
8
9
10
11
12
13
14
15
16
Frequency(GHz)
Figure 6.14 The Low-End Stop-Band Tunability of the BPF by Applying Bias
Magnetic Fields of 990 Oe and 1,060 Oe
6.3 Future Works Outlined
As discussed in the previous section, realization of the composite X-band BPF
with desired center frequency and pass-band bandwidth together with greatly
reduced insertion loss was one of the objectives of this research. For this purpose,
the approach involving accurate control of the shunt stub lengths and the
minimization of the grounding resistances need to pursued
156
Following realization of the X-band composite BPF just described, the meandertyped BPF can be realized by using two or more such composite BPFs and then
incorporated in the band-stop filters to simultaneously enhance the FMR peak
absorptions levels and broaden the absorption bandwidths. Finally, a pair of
band-stop filters each with the meander-type BPF can be cascaded as shown in
6.3 to realize the proposed X-band tunable band-pass filters.
Reference
1.
V. Radisic, Y. X. Qian, and T. Itoh. "Broad-band power amplifier using
dielectric photonic band-gap structure", IEEE Microwave and Guided Wave
Letters, vol.8, pp.13-14,1998.
2.
Maite Irisarri, Miguel A. G. Laso, Maria J. Erro, and Mario Sorolla.
"Compact photonic band-gap microstrip structures", Microwave and Optical
Technology Letters, vol.23, pp.233-236,1999.
3.
S. D. Yoon, Jianwei Wang, Nian Sun, C. Vittoria and V. G. Harris, "Ferritecoupled line circulator simulations for application at X-band frequency,"
IEEE Trans. Magn., vol. 43, pp.2639,2007.
4.
C. Hsu, F. Hsu, and J. Kuo, "Microstrip bandpass filters for ultrawideband (UWB) wireless communications," in IEEE MTT-S Int. Dig., pp.
679-682, June 2005.
5.
G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance
Matching Networks, and Coupling Structures, Artech House, Dedham, 1980.
157
Chapter 7
Conclusions
Wideband communication and radar systems require high-speed electronicallytunable wideband microwave band-stop and band-pass filters. FMR-based
microwave devices possess the unique capability of high-speed electronic
tunability, using magnetic field, for very high carrier frequency and very large
bandwidth. Various types of FMR-based
microwave filters
using
bulk
ferrimagnetic yttrium iron garnet (YIG) materials have long been constructed
and utilized in system applications. In recent years, tunable FMR absorption in
YIG thin film structures has also been investigated for broadband microwave
device applications. Although the monolithic integration combining magnetic
thin film structure with semiconductor substrate in a system-on-a chip (SOC) is
the one of the most important goal of magnetoelectronics, there are currently still
some severe limitations in the development of ferri- and ferro-magnetic thin
films and devices that are fully MMIC compatible. Therefore, MMIC compatible
ferrimagnetic
semiconductor
devices
with
fabricated
a
hybrid
separately
structure
using
ferrimagnet
and then combine in some
and
device
configuration is one of the current research directions.
In this dissertation research, the FMR-based microwave band-stop filter and
band-pass filter using YIG/GGG-GaAs layer structure have been throughout
studied. A full-wave method of modeling and analysis of the YIG/GGG-GaAs
158
flip-chip layer structure was first carried out for the device application as
wideband tunable microwave band-stop filter utilizing the FMR absorptions of
this magnetic layer structure in microwave frequency band. Detail simulations
were then carried out aimed at optimal device performances of the microwave
band-stop filter using YIG/GGG-GaAs layer structure. In the experimental
studies, a magnetically-tuned microwave band-stop filter using YIG/GGGgallium arsenide (GaAs) flip-chip layer structure with wideband tunability of
stop-band center frequency and bandwidth has been accomplished using a
microstrip meander line together with non-uniform bias magnetic field. A
magnetically-tunable wideband microwave band-pass filter with large tuning
ranges for both the center frequency and the bandwidth in the pass-band has
also been realized using a pair of cascaded aforementioned band-stop filters.
The filters application using the same YIG/GGG layer on high frequency circuit
board materials, i.e., RT-Duroid 6010LM, has also been studied
and
demonstrated in this thesis, and the results shows promising filter application on
those high frequency laminate materials.
Both of the band-stop and band-pass filters studied in this thesis, when fully
developed, should find applications in frequency-hopping wideband microwave
communication and signal processing systems.
159
Документ
Категория
Без категории
Просмотров
0
Размер файла
2 695 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа