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Wideband Tunable Microwave Filters and Phase Shifters Using Magnetic YIG/GGG Layer Structure

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UNIVERSITY OF CALIFORNIA,
IRVINE
Wideband Tunable Microwave Filters and Phase Shifters Using Magnetic
YIG/GGG Layer Structure
DISSERTATION
submitted in partial satisfaction of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
in Electrical and Computer Engineering
by
Yun Zhu
Dissertation Committee:
Chancellor’s Professor Chen Shui Tsai, Chair
Professor Guann-Pyng Li
Professor Michael M Green
2013
UMI Number: 3589471
All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent upon the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed,
a note will indicate the deletion.
UMI 3589471
Published by ProQuest LLC (2013). Copyright in the Dissertation held by the Author.
Microform Edition © ProQuest LLC.
All rights reserved. This work is protected against
unauthorized copying under Title 17, United States Code
ProQuest LLC.
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, MI 48106 - 1346
c 2013 Yun Zhu
DEDICATION
To my parents Huabiao Zhu and Qiaolan Ye
for their sacrifices and unconditional love
ii
TABLE OF CONTENTS
Page
LIST OF FIGURES
iv
LIST OF TABLES
v
ACKNOWLEDGMENTS
vi
CURRICULUM VITAE
vii
ABSTRACT OF THE DISSERTATION
x
1 Introduction
1.1 Tunable Microwave Filters and Phase Shifters
and Realizations . . . . . . . . . . . . . . . . .
1.1.1 Tunable Microwave Filters . . . . . . . .
1.1.2 Tunable Microwave Phase Shifter . . . .
1.2 Dissertation Motivation and Organization . . .
1
Applications
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
2 Ferromagnetic Resonance and Magnetostatic Waves
YIG/GGG Layer Structure
2.1 Equation of Motion of Magnetization [155] . . . . . . . . . .
2.2 Polder Permeability Tensor [155] . . . . . . . . . . . . . . .
2.3 Ferromagnetic Resonance (FMR) [155] . . . . . . . . . . . .
2.4 Magnetostatic Waves (MSWs) . . . . . . . . . . . . . . . . .
2.4.1 Walker’s Equation . . . . . . . . . . . . . . . . . . .
3 FMR Based Tunable Microwave Filters and Phase Shifter
iii
1
1
8
10
in
.
.
.
.
.
12
13
17
22
28
31
35
3.1
3.2
3.3
3.4
3.5
Tunable Band-Pass Filter Using Cascaded Band-Stop Filters
on GaAs Substrate . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Device Architecture and Working Principle . . . . . . .
3.1.2 Design and Simulation . . . . . . . . . . . . . . . . . .
3.1.3 Fabrication and Experimental Results . . . . . . . . . .
A Tunable X-band Band-Pass Filter Module . . . . . . . . . .
3.2.1 Device Architecture and Working Principle . . . . . . .
3.2.2 Design and Simulation . . . . . . . . . . . . . . . . . .
3.2.3 Experimental Results and Discussion . . . . . . . . . .
A Composite Tunable X-band BPF Module . . . . . . . . . .
3.3.1 Device Architecture and Working Principle . . . . . .
3.3.2 Design and Verification . . . . . . . . . . . . . . . . . .
3.3.3 Experimental Results and Discussion . . . . . . . . . .
A Varactor and FMR-Tuned BPF Module . . . . . . . . . . .
3.4.1 Device Architecture and Working Principle . . . . . .
3.4.2 Design and Simulation . . . . . . . . . . . . . . . . . .
3.4.3 Experimental Results and Discussion . . . . . . . . . .
A Magnetically- and Electrically- Tunable Microwave Phase
Shifter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Device Architecture . . . . . . . . . . . . . . . . . . . .
3.5.2 Experimental Results . . . . . . . . . . . . . . . . . . .
36
36
38
41
44
44
46
51
55
57
58
63
69
70
72
76
85
85
87
4 Propagation Characteristics in 1-D and 2-D Magnonic
Crystals: Verification and Applications
96
4.1 MSWs in a Non-structured YIG Thin Film . . . . . . . . . . . 97
4.2 Propagation Characteristics of MSVWs in 1-D Magnonic Crystal with Normal Incidence . . . . . . . . . . . . . . . . . . . . 101
4.2.1 Band Structures Calculation and Verification . . . . . . 101
4.3 Propagation Characteristics of MSVWs in 1-D MC with Oblique
Incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.3.1 Bandgaps Calculation and Verification . . . . . . . . . 112
4.3.2 A. MSFVWs, Incident Angle θ = 0◦ , 14◦ , and 25◦ ; Bias
magnetic field H0 =1650Oe . . . . . . . . . . . . . . . . 114
4.3.3 B. MSBVWs, Incident Angle θ = 0◦ , 14◦ , and 25◦ ; Bias
magnetic field H0 = 1,385 Oe . . . . . . . . . . . . . . . 117
iv
4.4
4.5
Propagation Characteristics of MSVWs in 2-D Magnonic Crystal121
4.4.1 Bandgaps Calculation and Verification . . . . . . . . . 121
Magnonic Crystal Based Tunable Microwave Filters and Phase
Shifter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.5.1 MC-Based Tunable Microwave Filter . . . . . . . . . . 133
4.5.2 MC-Based Tunable Phase Shifter . . . . . . . . . . . . 134
4.5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 136
5 Conclusion
141
Bibliography
143
v
LIST OF FIGURES
Page
2.1
2.2
2.3
2.4
2.5
2.6
2.7
3.1
3.2
3.3
3.4
3.5
Spin magnetic dipole moment and angular momentum for a
spinning electron. . . . . . . . . . . . . . . . . . . . . . . . . . 17
(a).Tuning of ferromagnetic resonance (FMR) peak absorption
frequency by bias magnetic field. (b).Wideband YIG/GGG/GaAsbased microwave BSF using microstrip meander-line and nonuniform bias magnetic field. . . . . . . . . . . . . . . . . . . . . . 25
(a). The configuration and measured magnetic field profile for
facilitating a 2-D non-uniform bias magnetic field,(b). Measured transmission characteristics of a tunable YIG/GGG GaAsbased band-stop filter. . . . . . . . . . . . . . . . . . . . . . . 27
Comparison of calculated and measured peak absorption frequencies versus bias magnetic fields. . . . . . . . . . . . . . . . 29
The motion of precession for a magnetic moment described by
the Landau-Lifshitz equation. . . . . . . . . . . . . . . . . . . 30
The precession passing down in the ferromagnetic material to
form the magnetostatic/spin wave. . . . . . . . . . . . . . . . 31
The relative directions of propagation constant k and steady
magnetization M0 of three types of magnetostatic waves, and
n0 is a unit vector normal to the plane. . . . . . . . . . . . . . 32
A wideband YIG/GGG/GaAs-based microwave BSF using microstrip meander-line and non-uniform bias magnetic field. . .
Realization of the tunable BPF using a pair of BSFs in cascade.
A ten-element step impedance low-pass filter (SILPF). . . . .
Schematics of the BPF in HFSS 3-D modeler simulator. . . .
Preliminary discrete module of a wideband tunable BPF using
a pair of BSFs in cascade. . . . . . . . . . . . . . . . . . . . .
vi
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38
39
40
42
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
Measured and simulated transmission characteristics of the
tunable BPF. . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a) An YIG/GGG-RT/Duroid-based tunable X-band BPF module consisting of an 8-12 GHz passive BPF and a pair of tunable BSFs.(b)Realization of the tunable X-band BPF module
using an 8-12 GHz passive BPF and a pair of tunable BSFs.
The stop-bands of the two BSFs superimpose upon the 8-12
GHz passband of the passive BPF and facilitate tuning of the
passband toward (a) the high end, (b) the low end, and (c) the
center. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a) Layout of the passive BPF; (b)Simulated and measured
transmission characteristics (S21 ) of the passive BPF. . . . . .
The schematic of the tunable X-band Band-pass Filter module.
Tuning of the passband of the BPF module toward (a) the high
end, till 11.2 GHz, (b) the low end, with full passband (7.811.8 GHz) tuning realized, and (c) the center, with passband
narrowed to 9.6-10.0 GHz. . . . . . . . . . . . . . . . . . . . .
(a) The design of composite-BPF (iii) by combing four opencircuited stubs of an X-band BPF (i) with the four inductive
elements of a SILPF (ii) which can function as a BPF and a
tunable BSF simultaneously. (b). A compact tunable BPF
module using a pair of composite-BPFs connected in cascade.
Superposition of the two stop-bands from composite-BPF No.1
and No.2 connected in cascade upon their 8-12 GHz passbands
and facilitate tuning of the passband toward (a) the high end,
(b) the low end, and (c) the center. . . . . . . . . . . . . . .
(a) to (b). By specifying WL and d2 , the X-band BPFs opencircuited stubs can be embedded into a SILPF to preserve the
band-pass function. (c). Layout of the composite-BPF. . . . .
(a).The measured S21 (dB) shows a passband from 7.9-12.2
GHz, 1.6 dB insertion loss, and a peak absorption at 10.25
GHz with 2,690 Oe field applied. (b). Peak absorption comparison among three different structures. . . . . . . . . . . . .
vii
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45
48
51
54
56
58
60
62
3.15 The simulated (in blue) result shows good agreement with
the measured (in red) transmission characteristics of the tunable BPF module consisting of cascaded composite-BPFs in
RT/Duroid substrate. It also shows a sharper frequency response than that of the single composite-BPF (in black). . . .
3.16 The schematic of the RT/Duroid-based X-band BPF module.
3.17 Tuning of the passband of the BPF module toward (a). the
high-end, till 11.8 GHz; (b). the low-end, with full passband
tuning realized, and (c). the center, with a narrow passband
centered at 9.9 GHz. . . . . . . . . . . . . . . . . . . . . . . .
3.18 The architecture of the newly realized BPF module using a
pair of FMR-tuned BSFs and a varactor-tuned X-band passive
composite-BPF. . . . . . . . . . . . . . . . . . . . . . . . . .
3.19 The layout of the X-band passive composite-BPF with a symmetrical structure. . . . . . . . . . . . . . . . . . . . . . . . .
3.20 (a). Architecture of the radial stub, (b). A microstrip RF
choke using a pair of radial stubs in cascade is capable of providing a wider stopband. . . . . . . . . . . . . . . . . . . . . .
3.21 Simulated performance of the microstrip RF choke. . . . . . .
3.22 The varactor and FMR-tuned BPF module. . . . . . . . . . .
3.23 (a).By increasing the reverse bias voltages applied to the varactors from 2 to 22 V, the 3 dB passband was continuously
tuned from 7.7-12.4 GHz to 11.4-17.5 GHz. (b).The corresponding 3 dB BW were enlarged from 4.7 GHz to 6.1 GHz
indicating a frequency span of 9.8 GHz, namely from 7.7-17.5
GHz.(c).The series resistance of the varactors degrades the
transmission characteristics. . . . . . . . . . . . . . . . . . . .
3.24 Arrangement for producing nonuniform bias magnetic fields in
YIG/GGG layer. . . . . . . . . . . . . . . . . . . . . . . . . .
3.25 Tuning and narrowing of the passband of the new BPF module
toward: (a). the high-end; (b). the low-end, and (c). any
frequency region within the maximum frequency coverage of a
span 9.8 GHz. . . . . . . . . . . . . . . . . . . . . . . . . . . .
viii
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65
67
71
73
75
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77
79
81
84
3.26 (a) The architecture of the newly realized magnetically- and
electrically- tuned composite phase shifter, (b).Geometry of a
microstrip transmission line with a YIG/GGG film laid on a
GaAs/Duroid substrate. . . . . . . . . . . . . . . . . . . . . .
3.27 (a).Calculated propagation loss and (b) phase shift at 9.66
GHz by tuning the bias magnetic field from 2,610 to 3,320 Oe.
3.28 Measured (a). S21 phase shift in degree, and (b). S21 and S11
magnitudes with magnetic fields tuned from 2,610 to 3,320 Oe
in the frequency range of 9.50 to 9.70 GHz. . . . . . . . . . . .
3.29 The measured (a) phase shift in degree, and (b) S21 (dB) of
an electrically- tuned phase shifter by increasing the reversed
bias voltage from 6V to 18V. . . . . . . . . . . . . . . . . . . .
3.30 (a) Measured phase shift versus magnetic field, (b) the corresponding insertion loss variation. . . . . . . . . . . . . . . . .
3.31 Total phase shifts achieved by combined magnetic and electric
tunings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1
4.2
4.3
4.4
4.5
4.6
4.7
MSWs excited in a non-structured YIG/GGG thin film of a
(a) square, and (b) parallelogram shape. . . . . . . . . . . . .
The simulation and experimental comparisons of MSWs in a
rectangular YIG/GGG sample. . . . . . . . . . . . . . . . . .
The comparison of the MSBVWs excited in a non-structured
rectangular and a parallelogram YIG thin film with (a). simulated, (b) experimental results. . . . . . . . . . . . . . . . . .
Unit cell in a 1-D MC. d1 and d2 are the thicknesses of nonetched and etched magnetic layer, respectively. a1 and a2 are
the widths of non-etched and etched layers, and the lattice
constant a = a1 + a2 . . . . . . . . . . . . . . . . . . . . . . . .
Band structure of a 1-D magnonic crystal for MSFVW with
parameters of Ms = 140 G, H0 = 1850 Oe, n = 2, d1 = 10 μm,
d2 = 5 μm, a1 = 5 μm, and a2 = 5 μm. . . . . . . . . . . . . .
(a). The 3-D model of the 1-D MC sample; (b). the SEM
image of the 1-D MC structure. . . . . . . . . . . . . . . . . .
Experimental setup for (a) MSFVWs, and (b) MSBVWs excitation and bandgap tunability test. . . . . . . . . . . . . . . .
ix
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88
90
92
93
94
98
99
100
101
102
103
105
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
The band structure calculated by our approach with the geometry and material parameters presented in [124]. . . . . . .
(a) Measured spectrum of MSBVW in a MC with the following
parameters: Ms = 140 G, H0 ≈ 1650 Oe, d1 = 100 μm,
d2 ≈ 80 μm, a1 ≈ 85 μm, and a2 ≈ 75 μm. (b) Calculated
band structure of MSBVW in the 1-D MC with the following
parameters: Ms = 140 G, H0 = 1650 Oe, n = 2, d1 = 100 μm,
d2 = 80 μm, a1 = 85 μm, and a2 = 75 μm. . . . . . . . . . . .
The experimental and theoretical results of MSFVW propagating in 1-D MC with bias magnetic field, H0 , of 1350 Oe. . .
Measured bandgaps under different magnetic fields of (a). MSFVW, bandgaps marked as A-C and (b). MSBVWs, bandgaps
marked as D-G. . . . . . . . . . . . . . . . . . . . . . . . . . .
Oblique incidence of MSVWs upon a 1-D MC, when k is the
wave number of the MSVWs and θ is the incident angle. . . .
2-D band structure of the MSFVWs in a 1-D MC. The range
of incident angle θ is from -45◦ to 45◦ . The dimensions of the
unit cell are a1 = 50 μm, a2 = 50 μm, a = 100 μm , d1 =
100 μm, and d2 = 80 μm as shown in Fig. 4.4. The saturation
magnetization 4πMs is 1760 G. The bias magnetic field is 1975
Oe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-D band structure of the MSBVWs in a 1-D MC. The range
of incident angle θ is from -45◦ to 45◦ . The dimensions of the
unit cell, the saturation magnetization, and the bias magnetic
field are given in the caption of Fig. 4.13. . . . . . . . . . . . .
Variation of bandgaps with the incident angle:(a) MSFVWs,(b)
MSBVWs. The mid-gap frequency of the bandgap increases
as the incident angle increases, while the width of the bandgap
decreases as the incident angle increases. . . . . . . . . . . . .
(a) The unit cell of a 1-D MC with periodic variation in layer
thickness. a1 and a2 , and d1 and d2 are, respectively, the width
and the thickness of unetched and etched parts of the YIG film.
(b) Geometry of a 1-D MC and microstrip transducers. . . . .
x
106
107
109
110
113
114
115
116
117
4.17 Experimental and calculated results of the MSFVWs propagating in a 1-D MC with incident angle (a), (b):θ = 0◦ ; (c),
(d):θ = 14◦ ; (e), (f):θ = 25◦ under a bias magnetic field of
1,650 Oe. (a) Experimental Resutls,θ = 0◦ ; (b) Calculated
Results θ = 0◦ ; (c) Experimental Resutls,θ = 14◦ ; (d) Calculated Results θ = 14◦ ; (e) Experimental Resutls,θ = 25◦ ;
(f)Calculated Results θ = 25◦ . . . . . . . . . . . . . . . . . . .
4.18 Experimental and calculated results of the MSBVWs propagating in a 1-D MC with incident angle (a), (b):θ = 0◦ ; (c),
(d):θ = 14◦ ; (e), (f):θ = 25◦ under a bias magnetic field of
1,385 Oe. (a) Experimental Resutls,θ = 0◦ ; (b) Calculated
Results θ = 0◦ ; (c) Experimental Resutls,θ = 14◦ ; (d) Calculated Results θ = 14◦ ; (e) Experimental Resutls,θ = 25◦ ;
(f)Calculated Results θ = 25◦ . . . . . . . . . . . . . . . . . . .
4.19 (a) Geometry and reduced first Brillouin zone in 2-D MCs of
square lattice . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.20 Calculated band structures of MSVWs in a 2-D MC at H0 =
1650 Oe, MS = 1750 Gauss, and the geometric parameters:a
= 200 μm, R = 0.32a, and d1 = 100μm, and the corresponding
wave numbers:Γ: kx = 0, ky = 0; X: kx = 0.5(2π/a) = 157.08
cm−1 ,ky = 0; M : kx = ky =0.5(2π/a) = 157.08 cm−1 : (a) MSFVWs, d2 = 55μm, (b) MSFVWs, d2 = 35μm, (c) MSBVWs,
d2 = 55μm, (d) MSBVWs, d2 = 35μm. . . . . . . . . . . . . .
4.21 Calculated bandgaps versus the incidence angle of the MSVWs:
(a) For the MSFVWs in a 2-D MC. Dark area shows that the
bandgap exists at all incidence angles; (b) For the MSBVWs
in a 2-D MC. Dark area shows that the bandgap exists at all
incidence angles; and (c) For the MSFVWs in a 1-D MC. The
dark area shows a limited range of incidence angle. . . . . . .
4.22 The optical image of the 2-D MC sample with square lattice
(a) and the setup for experiments (b). . . . . . . . . . . . . . .
4.23 Comparison between experimental results and calculated results of MSFVWs at three H0 : 3,000, 3,125, and 3,250 Oe.
The passband and bandgaps could be adjusted by tuning the
H0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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120
122
123
125
126
128
4.24 Calculated band structures of the MSFVWs at three H0 : 3,000,
3,125, and 3,250 Oe. . . . . . . . . . . . . . . . . . . . . . . .
4.25 Comparison between measured and calculated results of the
MSBVWs at three values of H0 : 1,160, 1,375, and 1,600 Oe.
The passband and bandgaps were tuned by varying the H0 . . .
4.26 Calculated band structures for MSBVWs at three values of
H0 : 1,160, 1,375, and 1,600 Oe. . . . . . . . . . . . . . . . . .
4.27 Relative direction of incident MSBVWs and the 2-D MC. The
incidence angle of the MSBVWs (θ) was varied by rotating the
sample around the Z-axis. . . . . . . . . . . . . . . . . . . . .
4.28 Insertion loss measurement of MSBVWs in the 2-D MC sample
at the incidence angles of 0◦ , 10◦ , 20◦ , and 30◦ , and H0 =1,600
Oe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.29 Excitation of MSBVWs to function as a tunable BPF with a
BSF embedded in (a) 1-D MC with 1,180, 1,200 and 1,250 Oe
applied, and (b) 2-D MC with 1,250 Oe, 1,265 Oe and 1,280
Oe applied, respectively. . . . . . . . . . . . . . . . . . . . . .
4.30 The measured (a) S21 (dB) and (b) the corresponding phase
shift in a 1-D MC with a field of 1,180 and 1,200 Oe applied. .
4.31 The measured (a) S21 (dB) and (b) the corresponding phase
shift in a 1-D MC with a field of 1,200 and 1,250 Oe applied. .
4.32 Measured differential phase shift in the (a). left passband and
(b)right passband of the bandgap with fields 1,250, 1,265 and
1,280 Oe applied on a 2-D MC structure. . . . . . . . . . . . .
xii
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130
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132
133
135
138
139
140
LIST OF TABLES
Page
3.1
3.2
3.3
3.4
3.5
3.6
3.7
The Dimensions of the ten-element SILPF. . . . . .
Simulation Parameters of the YIG Film . . . . . . .
Width and Length of 8-12 GHz Passive BPF . . . .
The Measured Tunability of X-band BPF Module .
The Dimensions of The Composite-BPF(Unit: μm)
Comparison Between Two X-Band BPF Modules .
The Dimension of the Composite BPF . . . . . . .
4.1
Comparison of the first two bandgap frequencies between experimental and theoretical results with bias magnetic field H0
of 1,650 Oe. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of the first two bandgap frequencies between experimental and theoretical results with bias magnetic field H0
of 1,350 Oe. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison between measured MSFVWs and MSBVWs in a
1-D MC with analytically calculated Results. UNIT:[GHz] . .
Calculated and Measured MSFVWS Bandgaps Comparison . .
Calculated and Measured MSBVWS Bandgaps Comparison . .
Comparison of mid-gap frequency and bandgap width at Γ-X
and M -Γ between experimental results and calculated results
for MSFVWs. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of Mid-gap frequency and bandgap width at Γ-X
and M -Γ between experimental results and calculated results
for MSFVWs. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mid-gap Frequencies of the Bandgaps of MSBVWs versus the
Incidence Angle . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2
4.3
4.4
4.5
4.6
4.7
4.8
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ACKNOWLEDGMENTS
I would like first to express my deepest and most sincere appreciations to my
research advisor, Chancellor’s Professor Chen S. Tsai. It has been a great
honor for me to have been accepted into his research group, thrived under
his able supervision and complete my Ph.D. study at UCI. Professor Tsai’s
high standard, perseverance, modesty, loyalty, and genuine concerns for his
group members as well as the students overall set a great example for me to
follow. His guidance provided the shining light that helped me go through
smoothly the adventurous journey as a Ph.D. student. His knowledge and
experience are vast; I’ve been lucky to have had all the privileges to look
to him for advice. I wouldn’t have gotten this far without Professor Tsai’s
constant guidance, support, and encouragement. I also want to express my
sincere gratitude to Professor Shirley C. Tsai for her kindness and neverending encouragement and enlightenment throughout my Ph.D study at UCI.
I would like to thank Professor G. P. Li and Professor Michael Green for
serving on my dissertation committee. The time and efforts they spent in
reviewing my dissertation are greatly appreciated.
I’m thankful for the assistance of Dr. Gang Qiu, a former member of Professor
Tsai’s research group and currently a Senior Engineer at Broadcom, during
the initial phase of my research. I also thank the current fellow members,
Dr. Rongwei Mao and Kai-hung Chi, for the stimulating discussions and
contributions they provided as well as Shih-Kai Lin, Ning Wang, Eric Chien
and James Maduzia for helpful discussions and friendship.
I especially thank my parents, Huabiao Zhu and Qiaolan Ye, for their numerous sacrifices and unconditional love. I owe them everything and wish that
I could show them how much love and respect I have for them. It is also a
pleasure to thank my sister, Xia Zhu, for all her advice and love. Finally,
I want to thank Mrs. Kimberly Burrows-Egan and Dr. John Robert Egan,
MD, for their kindness and friendship.
Financial supports provided by UC DISCOVERY Program and Shih-Lin
Electric Corp., USA. are gratefully acknowledged.
xiv
CURRICULUM VITAE
Yun Zhu
EDUCATION
Ph.D.in Electrical and Computer Eng.
University of California, Irvine
M.S. in Mech. and Elec. Engineering
Xiamen University
2013
Irvine, California
2007
Xiamen, P.R.China
FIELD OF STUDY
Magnetic Thin-Film-Based Microwave Device Application
JOURNAL PUBLICATIONS RESULTS FROM DISSERTATION
RESEARCH
1. Gang Qiu, Chen. S. Tsai, B.S. T. Wang, and Yun Zhu. A YIG/GGG/GaAsBased Magnetically Tunable Wideband Microwave Band-Pass Filter Using Cascaded Band-Stop Filters. IEEE Transactions on Magnetics,
44(11):3123-3126, 2008.
2. Yun Zhu, Gang Qiu, Kai H. Chi, B. S. T Wang, and Chen S. Tsai. A
Tunable X-Band Band-Pass Filter Module Using YIG/GGG Layer on
RT/Duroid Substrate. IEEE Transactions on Magnetics, 45(10):41954198, 2009.
3. Yun Zhu, Gang Qiu, Kai H. Chi, B. S. T Wang, and Chen S. Tsai.
A Compact XBand Tunable Bandpass Filter Module Using a Pair of
Microstrip Composite Bandpass Filters in Cascade. IEEE Transactions
on Magnetics, 46(6):1424- 1427, 2010.
4. Yun Zhu, R. W. Mao, and C. S. Tsai. A Varactor and FMR-Tuned
Wideband Band-Pass Filter Module With Versatile Frequency Tunabilxv
ity. IEEE Trans. on Magnetics,47(2):284-288, 2011(Invited Paper).
5. Kai H. Chi, Yun Zhu, Rong W. Mao, James P. Dolas, and Chen S. Tsai.
An approach for analysis of magnetostatic volume waves in magnonic
crystals. Journal of Applied Physics, 109(7):07D320, March 2011.
6. Kai H. Chi, Yun Zhu, Rong W. Mao, S. A. Nikitov, Y. V. Gulyaev,
and Chen S. Tsai. Propagation Characteristics of Magnetostatic Volume
Waves in One- Dimensional Magnonic Crystals with Oblique Incidence.
IEEE Transactions on Magnetics, 47(9):3708-3711, 2011.
7. Yun Zhu, Gang Qiu, and Chen S. Tsai. A magnetically- and electricallytunable microwave phase shifter using yttrium iron garnet/gadolinium
gallium garnet thin film. Journal of Applied Physics, 111(7):07A502,
2012.
8. Kai H. Chi, Yun Zhu, and Chen S. Tsai. Two-Dimensional Magnonic
Crystal With Periodic Thickness Variation in YIG Layer for Magnetostatic Volume Wave Propagation. IEEE Transactions on Magnetics,49(3):10001004,2013.
CONFERENCE PUBLICATIONS
1. Yun Zhu, Gang Qiu, Kai Chi, B. Wang and Chen S. Tsai. A tunable
X-band band-pass filter using YIGGGG layer on RT-Duroid substrate.
FE-03, IEEE International Magnetics Conference 2009 (INTERMAG
2009), Sacramento, CA, May 4-8, 2009.
2. Yun Zhu, Gang Qiu, Kai H. Chi, B. Wang and Chen.S. Tsai. A
Compact X-band Tunable Band-Pass Filter Module Using A Pair of
Microstrip Composite Band-Pass Filters in Cascade. FX-05,11th Joint
MMM-Intermag Conference, Washington DC, Jan.18-22, 2010.
xvi
3. Chen S. Tsai, and Yun Zhu. Microwave X-band Band-pass Filter
Module Using Ferromagnetic Resonance Tuning on YIG/GGG-Duroid
Layer Structure. A1-2, International Conference on Microwave Magnetics (ICMM), Northeastern University in Boston, MA, June 1-4, 2010.
4. Kai-Hung Chi, Yun Zhu, and Chen S. Tsai. Propagation Characteristics of Magnetostatic Forward Volume Waves in One-Dimensional YIG
Magnonic Crystals. FD-01, IEEE International Magnetics Conference
2011 (INTERMAG 2011), Taipei, Taiwan, Apr. 25-29, 2011.
5. Gang Qiu, Yun Zhu and Chen. S. Tsai. A Magnetically-Tuned Microwave Phase Shifter Using YIG/GGG-GaAs Flip-Chip Structure, BH11, 56nd Conference on Magnetism and Magnetic Materials, Scottsdale,
AZ, Oct.30- Nov.3, 2011.
ORAL PRESENTATION
1. Yun Zhu, Gang Qiu, Kai Chi, B. Wang and Chen S. Tsai. A tunable
X-band band-pass filter using YIGGGG layer on RT-Duroid substrate.
FE-03, IEEE International Magnetics Conference 2009 (INTERMAG
2009), Sacramento, CA United States, May 4-8, 2009.
2. Gang Qiu, Yun Zhu and Chen. S. Tsai. A Magnetically-Tuned Microwave Phase Shifter Using YIG/GGG-GaAs Flip-Chip Structure, BH11, 56nd Conference on Magnetism and Magnetic Materials, Scottsdale,
AZ, Oct.30- Nov.3, 2011.
HONORS AND AWARDS
Phi Tau Phi Scholarship Western American Chapter
xvii
2012
ABSTRACT OF THE DISSERTATION
Wideband Tunable Microwave Filters and Phase Shifters Using Magnetic
YIG/GGG Layer Structure
By
Yun Zhu
Doctor of Philosophy in Electrical and Computer Engineering
University of California, Irvine, 2013
Chancellor’s Professor Chen Shui Tsai, Chair
Wideband tunable microwave filters and phase shifters are essential devices
for a variety of applications in both civilian and military communications
and signal processing systems. Such devices realized by magnetic tuning
technique are attractive because of their unique features such as high carrier
frequency, high selectivity, multi-octave tuning range capability, spurious-free
response, and inherent compatibility with other planar microwave circuits.
In this dissertation research, ferromagnetic resonance (FMR)- and magnetostatic volume waves (MSVWs)- tuning techniques were employed for realization of such high-performance devices in yttrium iron garnet/gadolinium
gallium garnet (YIG/GGG) layer structure. By placing a YIG/GGG thin
film upon a microstrip meander-line structure and applying a non-uniform
bias magnetic field, a FMR-tuned band-stop filter (BSF) with enhanced absorption level and enlarged stop bandwidth (BW) was accomplished. Usxviii
ing the same basic device architecture and technique, the following three
magnetically-tuned wideband band-pass filter (BPF) modules were devised
and constructed: 1. incorporation of cascaded BSF pairs, 2. incorporation
of an X-band passive BPF and two tunable BSFs, and 3. incorporation of
a pair of X-band composite-BPFs. An advanced BPF module with versatile frequency tunability facilitated using the combination of electric-tuning
with varactor and magnetic-tuning based on FMR was also realized. The
combined tuning technique was also employed to develop a new tunable microwave phase shifter capable of providing a large phase shift at a moderate
insertion loss variation.
MSVWs-tuned microwave filters and phase shifters using a one-dimensional
(1-D) and two-dimensional (2-D) magnonic crystals (MCs) in YIG/GGG thin
films were subsequently explored. Both the 1-D MC consisting of periodic
channels and the 2-D MC consisting of periodic holes in square lattices were
prepared by wet etching technique. The calculated bandgaps associated with
the MSVWs in the 1-D and 2-D MCs were verified experimentally. The
magnetically-tuned bandgaps created in the 1-D and 2-D MCs were shown to
function as tunable BSFs. Furthermore, the large phase shifts associated with
the left and right flat passbands of the bandgap was verified experimentally.
Compared with the FMR-tuned BSF and the phase shifter, the MSWs-tuned
counterparts have demonstrated a much smaller 3 dB BW and, thus, better
frequency selectivity and a much larger phase tuning rate, respectively.
xix
Chapter 1
Introduction
1.1
Tunable Microwave Filters and Phase Shifters Applications and Realizations
1.1.1
Tunable Microwave Filters
Tunable microwave filters are essential in many civil, military, and long distance (satellite or terrestrial) communications and signal processing systems
[1–8]. The design and development of the microwave filters has experienced
three major periods: the invention of the radar application in WWII, the
satellite communications in the late 1960s, and the cellular radio communications in the early 1980s [6, 8]. In military applications, the tunable wideband
band-pass filter (BPF) is a crucial component in the electronic countermeasures (ECM) system and its associated electronic support measures (ESM)
1
system [6]. The ESM system detects and classifies incoming radar signals
while the ECM system provides appropriate countermeasures such as jamming. The emergence of the satellite communications industry created the
demands for low-mass narrow-band low-loss filters with strict specifications
on amplitude selectivity and phase linearity [7]. For example, the intermediate frequency (IF) BPF in the satellite system is designed to remove the
unwanted frequency components amplified by the low noise amplifier (LNA)
following reception from antenna, and allows only the desired frequency components to pass through to the high power amplifier. Tunable microwave filter
is also a key component for both base-stations and handsets in cellular radio
systems. For instance, in the 2nd generation time division multiple access
(TDMA) system, such as global system for mobile communications (GSM),
the receiver filter is designed to protect the LNA and the down-converter
mixer from being overdriven by external signals, which may occur if two
mobiles are being operated simultaneously while in close proximity [8].
There are four main types of tunable filters, namely, mechanically tunable,
electrically tunable, magnetically tunable, and combined electrically and magnetically tunable filters. The mechanically tunable filters still draw considerable attention due to their large power handling capability and low insertion
loss, while their applications are largely restricted by their low tuning speed
[9]. The electrical tuning technique is characterized by a superior tuning
speed over a wide frequency range, compact structure and light weight, which
2
were actively explored in recent years [5, 9]. Active switching and tuning elements such as semiconductor PIN and varactor diodes, RF MEMS, or other
functional material-based components including ferroelectric varactors are integrated with passive filtering structures to realize the electrical tuning functions [5, 9]. In general, the electrically-tuned filters could be classified as RF
MEMS tunable filters [10–16]; tunable band-stop filters [17–20]; piezoelctric
transducer (PET)-tunable filters [21–23]; tunable combline BPFs [24–28];
reconfigurable/tunable dual-mode filters [29–32]; tunable high-temperature
superconductor (HTS) filters [33–35]; tunable dual-band filters [36], and reconfigurable ultra-wideband (UWB) filters [37, 38] etc. However, the main
disadvantages of the electrically-tuned filters arise from their low selectivity,
low stopband isolation, and low power handling capability [9]. The tunable
filters based on the third or magnetic-tuning technique possesses attractive
features such as very high carrier frequency, high selectivity, multi-octave tuning range capability, spurious-free response, and inherent compatibility with
planar microwave circuitry such as MMIC [39–44]. Typical magneticallytunable filters include ferromagnetic resonance (FMR)-[45–57] and magnetostatic waves (MSWs)-tuned filters [58–64]. The early FMR-tuned filters
mainly use spherical low-loss ferrites, e.g. yttrium, lithium or barium ferrites. The disadvantage of such earlier filters is their bulky structure, which
is difficult to be integrated with other planar microwave subsystems. Planar thin films, such as YIG , Iron, BaM films were thereafter widely used to
3
construct tunable filters [50–57, 65–69]. Magnetically-tuned magnetostatic
waves (MSWs) devices have been developed as an extension of surface acoustic wave (SAW) components at microwave frequencies [58]. The SAW-based
devices such as filters, resonators, and correlators can be realized with extremely high performances of low insertion loss, large bandwidths (BWs),
and large dynamic range in the UHF frequency [58]. By using ferromagnetic
thin films, MSWs filters and subsystems are capable of providing instantaneous BWs of up to 1 GHz at operating frequencies in the microwave bands
[58]. The MSWs filters are attractive because of their low propagation losses,
high comparability with hybrid circuits and MMICs, compact structure, and
large tunability. By setting the direction of the dc bias magnetic field, three
propagation waves, namely, magnetostatic surface waves (MSSWs), magnetostatic forward volume waves (MSFVWs), and magnetostatic backward volume waves (MSBVWs) can be excited. The microwave energy is coupled
to magnetostatic modes by means of microstrip transducers, e.g. meander
lines [70], interdigital transducers [71], gratings [70], microstrip lines [72],
unidirectional transducers [73], and other MSWs transducer models [74–76].
Short- and open-circuited microstrip transducers of a width as narrow as 10
μm are commonly used for realization of wideband MSWs devices, while the
meander lines and gratings are used to design the narrowband devices. The
MSWs terminations were also studied to suppress those unwanted reflected
waves [77–79]. One of the effective methods employed is to cut the edge
4
of YIG film at an angle (= 90◦ ) relative to the wave propagation direction
[80]. The BW of MSWs filters is determined by the thickness of the YIG
film and the propagation loss of the MSWs is proportional to the linewidth
of the YIG film, which is typically around 20∼30 dB. Finally, the tunable
microwave filters that combine both electrical- and magnetic- tuning techniques were also studied and reported. One of such widely explored tuning
methods is based on magnetoelectric effects (ME), which is defined as the
dielectric polarization response of a material to an applied magnetic field,
or an induced change in magnetization upon the application of an external electric field [81–83]. The ME multiferroic that consists of a composite
of ferromagnetic and ferroelectric materials enables the desired coupling between magnetization and electrical polarization through mechanical stresses
[84]. The electric field to magnetic field conversion is accomplished in a
two-step process: piezoelectric effect induced mechanical deformation and
magnetostriction induced magnetic fields [85]. Specifically, by applying a
voltage upon the piezoelectric-ferromagnetic composite bilayer structure, the
→
−
piezoelectric strain subjected to the electrostatic field E is transmitted to
the ferromagnetic layer and produces an anisotropy field, which is used to
tune and control the FMR frequency or the frequency of the MSW propagating in the ferromagnetic material [86]. The tunable microwave filters
that utilize ME interaction with FMR bilayer ferrite-ferroelectric composite
such as YIG/lead zirconate titanate (PZT), YIG/lead-magnesium-niobate5
lead-titanate (PMN-PT), nickel ferrite/PZT and lithium ferrite/PZT were
reported [87–93]. Lyashenko et al. reported ME interaction with MSWs by
applying stress on the YIG thin film [94, 95]. The resultant anisotropy in the
YIG thin film was capable of tuning the frequency of the MSWs by ± 25%
along its center frequency of 2-3 GHz [94, 95]. In summary, the coupling of
the electrical tuning with the magnetic tuning techniques in ME multiferroic
facilitates additional degree of freedom in frequency tuning, which further
enhances frequency and BW tunability.
By creating periodic variations in geometrical structure and/or material property of magnetic materials, a new and exciting research field called magnonic
crystals (MC) was actively studied in recent years [96–106]. MC attracts
a great deal of attention worldwide because it possesses the capability of
controlling the generation and propagation of information-carrying magnetostatic waves (MSWs) in the microwave frequency ranges analogous to the
control of light in photonic crystals (PC) in the optical frequency range. The
physical principle of the MC is based on the propagation and attenuation
of dipole-exchange spin waves or magnetostatic waves in periodic magnetic
structures. However, in contrast to the optical bands in the conventional PCs
[107, 108], the bandgaps of the MCs can be tuned by bias magnetic fields,
and thus tunable microwave devices such as delay line and filters could be envisioned and constructed. Typically, there are three major types of periodic
structures in constructing the MCs: periodic structure of different magnetic
6
materials [109–114], periodic dots or antidots [99, 115–120], and periodic magnetic film geometries [97, 98, 104, 121–125]. Other types of MC, e.g. using
periodic variation of bias magnetic fields was also reported [126]. Up to now,
research efforts on MCs are still concentrated on design, analysis, and verification of the bandgap and propagation characteristics. Various analytical
approaches have been employed for studying the propagation characteristics
of the MSWs in one-dimensional (1-D) [109, 110, 115, 117, 119, 122, 123], twodimensional (2-D) [98, 112, 116, 120] and three-dimensional (3-D) [114] MCs.
For example, the Kronig-Penny model was applied to Landau-Liftshitz equation to analyze the periodic structures of MCs that consist of ferromagnetic
materials with varying saturation magnetizations [96, 97, 111]. Plane-wave
expansion method was applied to Landau-Liftshitz equation to analyze 2-D
and 3-D MCs that are composed of various types of ferromagnetic materials
[113, 114], and the same method was also applied to Walker’s equation to analyze the periodic structures of magnetic and non-magnetic layers [118]. In
addition, Walker’s equation [104–106] as well as the transmission-line model
[121, 124, 127, 128] were also used to analyze 1-D/2-D MCs with periodic
variation in thickness of the magnetic layer. The applications of MCs on
logic gates, waveguides, sensors, and other microwave devices were explored
and reported [129–133]. Other device applications, e.g. tunable phase shifters
are currently being explored in Professor Chen S. Tsai’s group at UCI.
7
1.1.2
Tunable Microwave Phase Shifter
Tunable microwave phase shifter is another important device for both commercial and defense applications. For example, in the phased-array radar
system, it consists of hundreds to thousands of radiating elements each connected with a phase shifter to control the phase of the incoming or scanning
signal. In the collision-avoidance radar system, in order to detect and identify
obstacles and extrusions in front of the moving vehicles, steering radar of a
precise phase control is required to provide the steerable radiations [64]. In
the global position system (GPS), the receiver antennas need to follow and
track the object positions continuously, which necessitates a radiation nulls
along certain spatial directions for transmitter/receiver to warrant secure and
covert communications. Tunable phase shifter can also find its applications
in target searching/tracking radars for surveillance, satellite communication
systems, and TV program broadcasting antennas [64].
In general, phase shifter can be classified into the following three types: Reciprocal vs. Nonreciprocal, Driven vs. Latching, and Analog vs. Digital
[64]. Among various tuning techniques, both electrical and magnetic tuning
techniques have been actively studied in recent years. The electrically-tuned
phase shifters are usually facilitated by employing the frequency agile elements such as varactor, PIN diode, to achieve a high-speed tuning capability
[134–139]. The magnetic tuning is realized by varying the dc magnetic field
8
applied on the ferrite materials, e.g. YIG, BaM [140–143]. However, the magnetic field involved is usually generated by a solenoid wrapped with copper
wires on the yoke. Therefore, the large power consumption and the resulting heat dissipation are the two major concerns. Besides, the tuning speed
achievable is low and the devices are difficult to be miniaturized. To overcome such shortcomings an alternative tuning scheme using ME interaction
which combined electrical and magnetic tuning techniques was employed to
build new types of tunable phase shifters [144–147]. The phase shifters referred to above demonstrated an overall phase shift range from 18◦ /cm to
52◦ /cm. In order to realize a phase shifter capable of larger phase shift, a
new type of electric-varactor and magnetic-FMR-tuned phase shifter was devised and developed under this dissertation research [148]. In contrast to the
hybrid tuned phase shifters that utilized either ferroelectric/ferromagnetic
bilayer structures [144–147] or MSWs [145, 146], the composite phase shifter
reported in [148] has demonstrated significantly larger phase shift, namely,
260◦ /cm, smaller drive voltage, and small insertion loss variation over a wide
range of operating frequency. Finally, tunable phase shifter using the 1-D
and 2-D MCs are also being explored in Professor Chen S. Tsai’s group at
UCI.
9
1.2
Dissertation Motivation and Organization
In this dissertation research, tunable wideband microwave filters and phase
shifters using magnetic YIG/GGG thin film layer structures were devised
and studied. FMR- and MSVWs- based tuning techniques were employed
for realization of such devices. The YIG/GGG thin films grown using liquid
phase epitaxial (LPE) technique that have a linewidth of 1.0 Oe, saturation
magnetization of 1,760 Oe, and a thickness of 6.8 and 100 μm used for the
research were furnished by ShinEtsu Chemical Co., of Japan.
The dissertation consists of 5 chapters. Following Chapter 1, the Introduction, Chapter 2 provides an overview on the fundamentals of FMR and MSWs
theories. The equation of motion of magnetization and associated Polder
permeability tensor are first derived. The derivation on FMR frequency and
its experimental verification are then presented. Finally, an introduction on
MSWs and Walker’s equation is provided.
In Chapter 3, FMR-based wideband tunable microwave filters and phase
shifter are presented. Three magnetically-tuned wideband BPF modules,
namely, 1). incorporation of cascaded BSF pairs, 2). incorporation of an
X-band passive BPF and two tunable BSFs, and 3). incorporation of a pair
of X-band composite-BPFs, are detailed first. Then, an advanced BPF module with versatile frequency tunability facilitated by using the combination
10
of electric-tuning with varactor and magnetic-tuning based on FMR is introduced. Finally, utilization of the combined tuning technique for development
of a new tunable microwave phase shifter capable of providing a large phase
shift at a moderate insertion loss variation is presented.
In Chapter 4,the MSVWs-tuned microwave filters and phase shifters realized
using 1-D and 2-D MCs in YIG/GGG layer structures are presented.
Finally, a conclusion for the dissertation research is given in Chapter 5.
11
Chapter 2
Ferromagnetic Resonance and
Magnetostatic Waves in YIG/GGG
Layer Structure
Magnetic excitations in solids at microwave frequencies have been a subject
of continuing study, which began with the pioneering theory of spin waves
reported by Holstein and Primakoff [149], the discovery of FMR by Griffiths
[150], Kittel’s linear response theory for FMR [151], and Walker’s study on
magnetostatic modes [152]. A special class of magnetic excitations include
the uniform mode ferromagnetic resonance (FMR) and long wavelength propagating magnetostatic waves (MSWs) [153, 154]. The theoretical study on
both FMR and MSWs starts with the derivation of the magnetization equation of motion of an electron under a dc bias magnetic field presented in the
12
following section [155].
2.1
Equation of Motion of Magnetization [155]
The magnetic properties of a material arise from the existence of the magnetic
dipole moments, which originate mainly from electron spins [155]. In general,
the overall magnetic moments in most solids are negligible because electron
spins occur in pairs with opposite signs. In a magnetic material, however, the
electron spins are unpaired and oriented in random directions to generate a
−
small net magnetic moments. The magnetic moment (→
m) is contributed by
the orbital angular momentum and spin angular momentum of an electron.
The Lande factor, g, in quantum physics is used to measure the relative con−
tributions of the orbital momentum and the spin momentum to the total →
m.
−
For most microwave ferrite materials, the total →
m is due to spin momentum
only with Lande factor g=2 in a good approximation [155]. By applying an
external dc magnetic field, the dipole moments can be aligned in the same
direction and thus the overall magnetic moment is greatly increased. The
−
total magnetic moment (→
m) is given in Eg. 2.1
qs
→
−
m=
,
me
(2.1)
where q is the electron charge, s is the spin angular momentum and me is the
13
electron mass. The spin angular momentum s is in the opposite direction to
the spin magnetic dipole moment as shown in Fig. 2.1. The ratio of the spin
magnetic moment to the spin angular moment is called the gyromagnetic
ratio γ and its value is equal to 2π × 2.8 × 1010 rad/(sec × tesla). When a
−
→
dc bias magnetic field H0 is applied, a torque will be extered on the magnetic
dipole in Eq. 2.2
−
→
→
−
−
→
−
−
s × H0 .
T =→
m × B0 = −μ0 γ →
(2.2)
The rate of change of spin angular moment is equal to the torque that acts
on the system in Eq. 2.3
−
−
→
d→
m
−
= −μ0 γ →
m × H0 ,
dt
(2.3)
which is the equation of the motion for the magnetic dipole moment [155].
Applying the unit vector operation, Eq. 2.4 and Eq. 2.5 are obtained.
⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
dmx
dt
= −μ0 γmy H0 ,
dmy
dt
= −μ0 γmx H0 ,
dmz
dt
= 0.
14
(2.4)
⎧
⎪
⎨
⎪
⎩
d2 mx
dt2
d2 my
dt2
+ ω02 mx = 0,
+
ω02 my
(2.5)
= 0,
where ω0 in Eq. 2.6 is called the Larmor, or precession frequency. As an example, setting the dc bias magnetic field of 10,000 Oe, the Larmor precessing
frequency will be 2π × 2.8 × 10
10
rad/sec.
ω0 = μ0 γH0 .
(2.6)
One solution to Eq. 2.5 is as follows (Eq. 2.7)
⎧
⎪
⎪
mx = Acosω0 t,
⎪
⎪
⎨
my = Asinω0 t,
⎪
⎪
⎪
⎪
⎩ m = C,
z
(2.7)
where A and C are arbitrary constants. The solution in Eq. 2.7 shows that
−
the x and y components of →
m is right-hand circularly polarized (RHCP), and
−
the z component of →
m is determined by its initial value C. The magnitude
−
of →
m is a constant which is equal to Eq. 2.8
−
|→
m|2 = A2 + C 2 .
15
(2.8)
And the precession angle θ as shown in Fig. 2.1 is given in Eq. 2.9
sinθ = √
A
.
A2 + C 2
(2.9)
−
−
The projection of →
m on the xy plane in Eq. 2.7 showed that →
m traces a
−
circular path in this plane. In the absence of any damping forces, the →
m of
−
→
the electron will precess about H0 at the angle θ shown in Fig. 2.1 indefinitely and it is called free electron precessing [155]. Assume that there are N
unbalanced electron spins (magnetic dipoles) per unit volume, therefore, the
total magnetization is in Eq. 2.10
−
→
−
M = N→
m,
(2.10)
and the equation of motion becomes Eq. 2.11
−
→
−
→ −
→
dM
= −μ0 γ M × H0 ,
dt
(2.11)
→
−
−
→
where H is the internal applied field, and M is the total magnetization.
−
→
−
→
As H0 increases, more magnetic dipole moments will align with H0 until
−
→
all are aligned, and M reaches an upper limit. The material is thus called
magnetically saturated, and Ms is called saturation magnetization [155].
16
Figure 2.1: Spin magnetic dipole moment and angular momentum for a spinning electron.
2.2
Polder Permeability Tensor [155]
→
−
Application of a small rf magnetic field H signal to a magnetically saturated
−
→
ferrite material will force the precession of the dipole moments around H0 (z)
axis at the frequency of the rf field ω, based on which the Polder tensor
permeability is derived.
−
→
−
→
The total magnetic field Ht and the corresponding total magnetization Mt in
the magnetic material are expressed by Eq. 2.12 and Eq. 2.13, respectively.
17
−
→
→
−
−
Ht = H0 →
z + H,
(2.12)
−
→
−
→
−
z + M.
Mt = Ms →
(2.13)
Substituting Eq. 2.12 and Eq. 2.13 into Eq. 2.11, Eq. 2.14 is obtained, and it
is then readily expanded into Eq. 2.15
⎡
→
−
−
→
−
x →
y
z
⎢
−
→
⎢
d Mt
= −μ0 γ ⎢
⎢ M x My Mz + Ms
dt
⎣
Hx Hy Hz + H0
⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
⎤
⎥
⎥
⎥,
⎥
⎦
dMx
dt
= −μ0 γMy (H0 + Hz ) + μ0 γ(Ms + Mz )Hy ,
dMy
dt
= μ0 γMx (H0 + Hz ) − μ0 γ(Ms + Mz )Hx ,
dMz
dt
= −μ0 γMx Hy + μ0 γMy Hx .
(2.14)
(2.15)
−
→ →
−
−
→
→
−
Under small signal approximation, | H | H0 , we have |M || H | |M |H0
−
→ →
−
−→
and |M || H | |Ms |H, and the M H product term can be ignored. Eq. 2.15
is rearranged into Eq. 2.16,
18
⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
dMx
dt
= −ω0 My + ωm Hy ,
dMy
dt
= ω0 Mx − ωm Hx ,
dMz
dt
= 0,
(2.16)
where ω0 = μ0 γH0 and ωm = μ0 γMs . Eq. 2.16 can be further rearranged into
Eq. 2.17
⎧
⎪
⎨
⎪
⎩
d 2 Mx
dt2
d 2 My
dt2
+ ω02 Mx = ωm
+
ω02 My
=
dHy
dt
+ ω0 ωm Hx ,
x
−ωm dH
dt
(2.17)
+ ω0 ωm Hy .
→
−
−
→
→
−
Now, the applied H and the resulting M and H all take the time-harmonic
dependence factor ejωt , and Eq. 2.17 is thus rearranged into the following
phasor equations:
⎧
⎪
⎨ (ω 2 − ω 2 )Mx = ω0 ωm Hx + jωωm Hy ,
0
⎪
⎩ (ω02 − ω 2 )My = −jωωm Hx + ω0 ωm Hy .
(2.18)
Eq. 2.18 can be further re-written into matrix form with tensor susceptibility
[χ] in Eq. 2.19:
19
⎡
⎤
⎢ χxx χxy 0 ⎥
⎥→
−
→
→
− ⎢
⎥−
M = [χ] H = ⎢
χ
0
χ
⎢ yx yy
⎥ H,
⎣
⎦
0
0 0
(2.19)
where the elements of [χ] are given in Eq. 2.20
⎧
⎪
⎨ χxx = χyy =
ω0 ωm
,
ω02 −ω 2
⎪
⎩ χxy = −χyx =
(2.20)
jωωm
.
ω02 −ω 2
→
−
→
−
Note that the magnetic flux density B is related to H by Eq. 2.21:
−
→ →
−
→
−
→
−
B = μ0 (M + H ) = [μ] H ,
(2.21)
where the tensor permeability [μ] is given as follows [155]:
⎤
⎡
⎢ μ jk 0 ⎥
⎥ →
⎢
⎥ (−
[μ] = μ0 ([U ] + [χ]) = ⎢
−jk
μ
0
⎥ z axis),
⎢
⎦
⎣
0
0 μ0
(2.22)
where [U] is a unit tensor.
The elements of the permeability tensor are given in Eq. 2.23 and Eq. 2.24
[155]
20
μ = μ0 (1 + χxx ) = μ0 (1 + χyy ) = μ0 (1 +
k = μ0
ω0 ωm
),
ω02 − ω 2
ωωm
.
ω02 − ω 2
(2.23)
(2.24)
−
−
Accordingly, if the direction of the bias magnetic field is rotated to →
x or →
y
axis, the corresponding permeability tensor will be
⎡
⎤
0 ⎥
⎢ μ0 0
⎢
⎥ →
⎥ (−
[μ] = ⎢
0
μ
jk
⎢
⎥ x axis),
⎣
⎦
0 −jk μ
(2.25)
and,
⎤
⎡
⎢ μ 0 −jk ⎥
⎥ →
⎢
⎥ −
[μ] = ⎢
⎢ 0 μ0 0 ⎥ ( y axis).
⎦
⎣
jk 0
μ
(2.26)
The derived Polder tensor permeability as shown above can now be incorporated in the Maxwell’s Equations to analyze the wave propagation characteristics in a ferromagnetic media or transmission lines.
21
2.3
Ferromagnetic Resonance (FMR) [155]
As presented in Section 2.2, the total electron magnetic moment or magnetization in the ferrite material precesses along the direction of the dc bias
magnetic field and its precessing frequency is determined by the strength of
the bias magnetic field [154, 155]. When an external microwave rf transverse field is applied, a strong coupling between the magnetization and the
transverse field or resonance takes place when the frequency of the transverse
field is identical to the precessional frequency [156, 157]. Consequently, the
energy of the microwave transverse field is strongly coupled to the magnetic
precessing system and this phenomenon is called ferromangetic resonance
(FMR), and its corresponding peak absorption frequency is called FMR frequency [154, 158]. The Larmor Precession frequency is simply an ideal case of
FMR frequency when a single magnetic dipole is in an infinite ferromagnetic
material [158, 159].
Derivation of the FMR equation is now detailed below.
Applying an external field which is normal to a thin film plate, the relationship between the externally applied fields and the internal magnetic bias
fields is shown in (Eq. 2.27)
−
→
→
−
−
→
H = Ha − N M ,
22
(2.27)
→
−
−
→
where H is the internal filed, Ha is the external applied field and N = Nx , Ny
and Nz is the demagnetization factor for that direction of the external field.
For a z-biased ferrite with transverse rf fields, Eq. 2.27 reduces to Eq. 2.28
⎧
⎪
⎪
Hx = Hxa − Nx Mx ,
⎪
⎪
⎨
Hy = Hya − Ny My ,
⎪
⎪
⎪
⎪
⎩ H =H −N M ,
z
a
z s
(2.28)
where Hxa , Hya are the external rf field applied to the ferrite, and Ha is the
external dc bias field. From Eq. 2.19, the following relationships between the
internal transverse rf fields and the magnetization hold:
⎧
⎪
⎨ Mx = χxx Hx + χxy Hy ,
⎪
⎩ My = χyx Hx + χyy Hy .
(2.29)
Combining Eq. 2.28 and Eq. 2.29 to eliminate Hx and Hy , the following
equations are obtained:
⎧
⎪
⎨ Mx = χxx Hxa + χxy Hya − χxx Nx Mx − χxy Ny My ,
⎪
⎩ My = χyx Hxa + χyy Hya − χyx Nx Mx − χyy Ny My ,
and the solutions for Mx and My are obtained as follows:
23
(2.30)
⎧
⎪
⎨ Mx =
χxx (1+χyy Ny )−χxy χyx Ny
Hxa
D
⎪
⎩ My =
χyx
D Hxa
+
+
χxy
D Hya ,
(2.31)
χyy (1+χxx Nx )−χyx χxy Nx
Hya ,
D
where
D = (1 + χxx Nx )(1 + χyy Ny ) − χyx χxy Nx Ny .
(2.32)
For a finite-sized ferromagnetic medium the resonance occurs when D = 0 (
Eq. 2.32) at the frequency ωr =ω=ω0 as shown in Eq. 2.33
ωγ = ω = (ω0 + ωm Nx )(ω0 + ωm Ny ).
(2.33)
The frequency ω0 is called the frequency of the uniform mode, in which all
of the magnetic dipole moments precess together in phase with the same
amplitude [154].
Since ωγ =μ0 γH0 = μ0 γ(Ha −Nz Ms ), and ωm =μ0 γMs , Eq. 2.33 can be written
in terms of the applied bias field and saturation magnetization as follows:
ωγ = μ0 γ [Ha + (Nx − Nz )Ms ][Ha + (Ny − Nz )Ms ].
(2.34)
By applying the bias field in the direction perpendicular to the plane of a
24
Microwave Output
Peak FMR Absorption
Frequency f res Tuning by
Bias Magnetic Field H 0
Band-Stop Filtering with Large Bandwidth
and High Absorption Using Meander Line
and Non-uniform Magnetic Field
f res (H0)
f
Microwave Frequency
(a)
(b)
Figure 2.2: (a).Tuning of ferromagnetic resonance (FMR) peak absorption frequency by
bias magnetic field. (b).Wideband YIG/GGG/GaAs-based microwave BSF using microstrip
meander-line and nonuniform bias magnetic field.
25
magnetic thin film layer, namely, the X-Y plane, the conditions, Nx =Ny =0
and Nz =4π are valid, and the expression for the ferromagnetic resonance
frequency is simplified as follows:
ω0 = γ
(H)(H + 4πMs ),
(2.35)
where γ and Ms are the gyromagnetic ratio and saturation magnetization
of the sample, respectively. H is the internal bias magnetic field where
anisotropy field of the sample should be included. Specifically, the FMR
for the YIG/GGG thin film is given by Eq. 2.36,
ω0 = γ
(H0 + Han )(H0 + Han + 4πMs ),
(2.36)
where H0 is the applied field, Han =100 Oe is the anisotropy of the YIG
thin film, and the saturation magnetization 4πMs is around 1,760 Oe. For
example, by applying an H0 of 2,000 Oe, the peak FMR absorption frequency
ω0 is 7.97 GHz. Tuning of FMR peak absorption frequency by a bias magnetic
field is depicted in Fig. 2.2(a). It is to be noted that the stop bandwidth
and peak absorption could be further enhanced by applying a non-uniform
magnetic field. This technical feature was utilized in realization of tunable
wideband band-stop and band-pass filters to be presented in Chapter 3.
26
0.75"
Nd-Fe-B
Magnet
0.5"
YIG/GGG
Sample
d
Device
Microwave
Input
H0
\
]
Microwave
Output
Nd-Fe-B
Magnet
[
,URQ<RNH
Relative Magnetic Field to the Center (%) Relative Magnetic Field to the Center (%)
,URQ<RNH
170
d=18.0mm H=3,700 Oe
d=28.5mm, H=1,940 Oe
d=35.0mm, H=1,325 Oe
d=42.0mm, H=990 Oe
160
150
140
130
120
Center
110
100
90
-2
0
2
4
6
8
10 12 14 16 18
Position along Y-axis (mm)
100
95
Center
90
85
80
d=18.0mm H=3,700 Oe
d=28.5mm, H=1,940 Oe
d=35.0mm, H=1,325 Oe
d=42.0mm, H=990 Oe
75
70
65
-2
0
2
4
6
8
10 12 14 16 18
Position along x-axis (mm)
Com
mpany Logo
(a)
2
4
6
8
10
12
14
16
18
0
0
-10
-10
S21 (dB)
20
880Oe
1020Oe
-20
-20
1180Oe
1440Oe
1550Oe
1775Oe
2100Oe
2330Oe 2850Oe
2670Oe 3250Oe
3500Oe
-30
3850Oe
4050Oe
-40
2
4
6
8
10
12
14
-30
4600Oe
5300Oe
16
18
-40
20
Frequency (GHz)
(b)
Figure 2.3: (a). The configuration and measured magnetic field profile for facilitating a
2-D non-uniform bias magnetic field,(b). Measured transmission characteristics of a tunable
YIG/GGG GaAs-based band-stop filter.
27
Experimental verification was carried out by placing a YIG thin film of 6.8
μm thick upon a four-segment stepped-impedance low pass filter (SILPF)
meander line structure fabricated on a 350 μm thick GaAs substrate as shown
in Fig. 2.2(b). By tuning the nonuniform bias magnetic fields from 880 Oe
to 5,300 Oe as shown in Fig. 2.3(a), scanning of the FMR peak absorption
frequencies is clearly demonstrated in Fig. 2.3(b). The comparison between
the measured peak absorption frequencies and the calculated results using
Eq. 2.36 is shown in Fig. 2.4 with an excellent agreement clearly seen. In
addition, the four-layer model together with full-wave method was used to
calculate the wave propagation characteristics in the YIG/GGG-GaAs layer
structure and the microwave energy absorption around the FMR frequency
as well as frequency tunability [160].
2.4
Magnetostatic Waves (MSWs)
The theory of magnetostatic modes for spheroidal specimens was first reported by L. R. Walker, which was discovered from FMR experiments, and
such modes are often called Walker Modes [152, 161]. Röschmann and Dötsch
published a practical review on Walker modes for spheres [162]. The theory
of magnetostatic modes excited in flat and unbounded ferromagnetic thin
films was first studied and reported by Damon and Eshbach, which served
as numerous the foundations for numerous experimental studies of magnetic
28
Figure 2.4: Comparison of calculated and measured peak absorption frequencies versus bias
magnetic fields.
excitations in thin film and slabs of ferrite materials as well as device applications for microwave signal processing [163]. Later, Storey et al further
extended this work to provide quantitative results for films of finite dimensions [164, 165].
−
→
For a single magnetic moment M , its motion can be described by the LandauLifshitz equation with a damping term as follows:
λ ∂M
M × M × Hef f .
= −γ M × Hef f −
∂t
Ms
29
(2.37)
Figure 2.5: The motion of precession for a magnetic moment described by the LandauLifshitz equation.
The motion of precession described by Eq.2.37 is depicted in Fig.2.5. In
Eq.2.37, Ms is the saturation magnetization of the ferromagnetic material,
Hef f is the effective magnetic field, λ is the damping constant, and γ is the
−
→
gyromagnetic ratio. As shown in Fig.2.5, the magnetic moment M precesses
around the effective magnetic field. When one of the magnetic moments in
the ferromagnetic material is perturbed, it would interact with its neighboring magnetic moment and passes down the perturbation as shown in Fig.2.6.
From the top view, it is like a sine wave propagating in a certain direction,
and this is so-called spin wave (SW). The SWs can be divided into two categories, non-exchange magnetostatic waves and exchange spin waves. They are
both magnetostatic and spin waves, and the main difference between them
are whether the exchange interaction is been taken into consideration. In this
study, due to the long characteristic wavelengths involved the exchange interaction is neglected, and thus only the non-exchange magnetostatic waves are
considered. The MSWs are generally separated into two categories, magne-
30
tostatic volume waves (MSVWs) and magnetostatic surface waves (MSSWs).
There are two types of MSVWs, magnetostatic forward volume waves (MSFVWs) and magnetostatic backward volume waves (MSBVWs). The relative directions of bias magnetic field and propagation constant for these three
MSWs in shown in Fig.2.7.
Figure 2.6: The precession passing down in the ferromagnetic material to form the magnetostatic/spin wave.
2.4.1
Walker’s Equation
Since the propagation constant k for the MSWs is much larger than the
propagation constant k0 = ω/c in the free space, the following magnetostatic
approximations [166] can be applied to analyze its dispersion relation:
∇ × h = 0,
31
(2.38)
z
M0
k
y
d
x
0 n0 .
(a) In FVMSW, k ⊥ M
z
k
M0
y
d
x
0 ⊥ n0 .
(b) In BVMSW, k M
z
k
y
M0
d
x
0 ⊥ n0 .
(c) In MSSW, k ⊥ M
Figure 2.7: The relative directions of propagation constant k and steady magnetization M0
of three types of magnetostatic waves, and n0 is a unit vector normal to the plane.
32
∇ · μ̃h = 0,
(2.39)
where
⎤
⎡
⎢ μ iμa 0 ⎥
⎥
⎢
⎥,
μ̃ = ⎢
μ
0
−iμ
a
⎥
⎢
⎦
⎣
0
0 1
μ=
ωH (ωH + ωM ) − ω 2
,
2 − ω2
ωH
μa =
(2.40)
ωωM
.
− ω2
2
ωH
(2.41)
The magnetostatic potential ψ is introduced so that
h = ∇ψ.
(2.42)
Combining Eq.2.42 with Eq.2.38 and Eq.2.39 results in
∇ · (μ̃∇ψ) = 0,
(2.43)
which is the so-called generalized Walker’s equation [166].
By setting up a coordinate system in which the z-axis is normal to the bound-
33
ary surface, the boundary conditions for ψ are as follows:
⎧
⎪
⎪
⎪
⎪
⎨
∂ψ1
∂x
=
∂ψ2
∂x ,
∂ψ1
∂y
=
∂ψ2
∂y ,
⎪
⎪
⎪
⎪
⎩ (μ̃ ∇ψ ) = (μ̃ ∇ψ ) ,
1
1 z
2
2 z
(2.44)
where the subscripts 1 and 2 stand for the two media involved. From Eq.2.43
and μ̃ in Eq.2.40, the following so-called Walker’s equation is obtained:
∂ 2ψ ∂ 2ψ
+ 2
μ
∂x2
∂y
∂ 2ψ
+ 2 = 0.
∂z
(2.45)
The solutions for Eq.2.45 are commonly referred to as magnetostatic modes
in homogeneous media [167].
The Walker’s equation is then employed to analyze the propagation characteristics of MSWs in one-dimensional (1-D) and two-dimensional(2-D) magnonic
crystals (MCs) at normal and oblique incidence, respectively, which was reported in Ref.[104–106]. The validities of the derived theoretical approaches
were verified experimentally and presented in Chapter 4.
34
Chapter 3
FMR Based Tunable Microwave
Filters and Phase Shifter
In Chapter 2, equation of motion of magnetization and the associated Polder
permeability tensor were first introduced. Then, the fundamental FMR theories was described and relevant equations derived. The calculated FMR
absorption frequencies were thereafter compared with the experimental results with an excellent agreement. It is to be stressed that the FMR absorption frequency is magnetically tunable by adjusting a bias magnetic field
applied on a ferromagnetic layer such as an YIG/GGG film, based on which
four magnetically-tuned band-pass filter (BPF) modules were devised and
reported in this Chapter.
In Section 3.1, a tunable BPF of large tuning range using cascaded bandstop filters (BSF) on GaAs substrate [52] is first presented. A tunable X35
band BPF module consisting of an X-band (8-12 GHz) passive BPF and two
tunable BSFs with large tunability realized using inexpensive RT/Duroid
substrate [54] is then presented in Section 3.2. In section 3.3, a compact
X-band tunable BPF module which employs a pair of passive microstrip
composite-BPFs in cascade aimed at further reduction of the device size and
the insertion loss [56] is detailed. An advanced BPF module with versatile
frequency tunability facilitated using the combination of an electric varactor
and magnetic FMR tunings [57] is presented in Section 3.4. Finally, Section
3.5 presents application of the combined tuning technique for construction of
a tunable microwave composite phase shifter [148].
3.1
Tunable Band-Pass Filter Using Cascaded BandStop Filters on GaAs Substrate
3.1.1
Device Architecture and Working Principle
Fig. 3.1 shows the basic device configuration of an yttrium iron garnet/gadolinium
gallium garnet-gallium arsenide (YIG/GGG-GaAs) based tunable microwave
band-stop filter (BSF) reported for the first time [51, 53]. A YIG/GGG layer
is laid upon the GaAs-based microstrip line. An incoming microwave is coupled into the YIG/GGG layer, and the peak absorption of the microwave
power occurs when its frequency coincides with the FMR frequency of the
36
Figure 3.1: A wideband YIG/GGG/GaAs-based microwave BSF using microstrip meanderline and non-uniform bias magnetic field.
YIG/GGG layer. The external bias magnetic field (H0 ) dependence of the
FMR frequency (fr ) is given previously by Eq. 2.36 and is reproduced below:
fr (H0 ) = γ
(Han + H0 )(Han + H0 + 4πMs ),
(3.1)
where γ, 4πMs and Han are, respectively, the gyromagnetic ratio, the saturation magnetization and the anisotropy field of the YIG film. Microwave
BSF with large tuning ranges in stop-band center frequency and BW using a
microstrip meander-line together with non-uniform bias magnetic fields has
also been demonstrated [53].
It is clear that by using a pair of such BSFs in cascade (Fig. 3.2) in which
different non-uniform bias magnetic fields (H02 > H01 ) are applied, a BPF
37
with even larger tuning ranges for both the center frequency and the BW in
the pass-band can be realized by properly programming the low-end and the
high-end values of the bias magnetic fields (H02 and H01 ).
Figure 3.2: Realization of the tunable BPF using a pair of BSFs in cascade.
3.1.2
Design and Simulation
A. The BPF using Cascaded BSFs
The YIG/GGG-GaAs-based microwave BSFs aimed at wideband tunability
in both stop-band center frequency and BW was first designed utilizing a foursegment microstrip meander-line. The non-uniform distribution of the bias
magnetic fields applied over the four-segment meander-line resulted in a large
widening of the resultant stop-band BW [53]. Note that the meander-line,
which consists of four identical ten-element step-impedance low-pass filters
38
Figure 3.3: A ten-element step impedance low-pass filter (SILPF).
Table 3.1: The Dimensions of the ten-element SILPF.
W (μm)
L(μm)
C1
670
84
C2
670
221
C3
670
232
C4
670
232
C5
670
190
L1
80
486
L2
80
635
L3
80
659
L4
80
624
L5
80
678
(SILPFs) (see Fig. 3.3) in lieu of the 50 Ω microstrip, enhances the FMR
absorption level and the absorption BW [53]. Such multi-segment meanderline and non-uniform bias magnetic field based BSF 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 BW as large as 1.70
GHz [53]. The ten-element SILPF shown in Fig. 3.3 consists of the 256 μm
wide line as the 50 Ω line at the two terminals, and the 670 μm and 80 μm
wide lines as the low (30 Ω) and high (75 Ω) characteristic impedance lines,
corresponding to the shunt capacitors (Cs )and the series inductors (Ls ), respectively [53]. The finalized dimensions of the ten-element SILPF are shown
in Table. 3.1.
39
B. HFSS Simulations
The Ansoft HFSS software was used in the design and simulation of the
aforementioned BPF that incorporates four-segment microstrip meander-lines
and 2-D non-uniform bias magnetic fields. The resulting BPF depicted in
Fig. 3.4 was then simulated using HFSS. The parameters of the YIG sample
used in the simulation are listed in Table 3.2. Note that the 2-D non-uniform
bias magnetic fields used in this simulation was taken from measurement data,
where the non-uniform bias magnetic fields are applied on the BSF No.1 and
No.2, respectively [52, 53]. The simulated transmission characteristics of the
BPF is then compared with the experimental result shown in Fig. 3.6.
Figure 3.4: Schematics of the BPF in HFSS 3-D modeler simulator.
40
Table 3.2: Simulation Parameters of the YIG Film
ΔH(Oe)
1.0
3.1.3
4πMs (Oe)
1,760
Lande G Factor
2.0
εr
14.7
Dimension (X×Y×Z)
(8.0mm × 8.0mm × 6.8 μm)
Fabrication and Experimental Results
In the experimental study, a 1.0 μm thick silver layer was first deposited on
a 350 μm thick GaAs wafer. The microstrip meander-line with four identical SILPFs was then fabricated on the GaAs substrate using standard photolithography techniques. A YIG/GGG sample with the dimensions of 8.0mm
× 8.0mm × 6.8 μm (in X, Y and Z-directions) was laid upon the GaAs-based
microstrip meander-line. A pair of Nd-Fe-B permanent magnets (0.75” in diameter and 0.5” in thickness) were attached to an iron yoke to complete the
magnetic circuit as shown in Fig. 3.5. The magnetic field intensities in the
center of the YIG/GGG sample were varied by tuning the gap, d , between
the permanent magnet pair. Since, d , was comparable to the diameter of
the magnets in the arrangement the magnetic field distributions along the Xand Y- direction should be highly nonuniform [52, 53].
The transmission characteristics of the BPF fabricated was measured over
a large tuning range for the center frequency, namely, 5.90 to 17.80 GHz.
For example, the measured transmission characteristics (see circle line in
Fig. 3.6) at the center frequency of 12.28 GHz shows a -3 dB BW as large
as 1.73 GHz, an out-of-band rejection of - 33.5 dB, and an insertion loss of -
41
Figure 3.5: Preliminary discrete module of a wideband tunable BPF using a pair of BSFs in
cascade.
4.2 dB. Note that the insertion loss in the passband can be greatly reduced
using an optimized microstrip meander-line. The large stop-band at each
end of the pass-band was realized by the two BSFs in which the non-uniform
bias magnetic fields were centered at 2,750 Oe (H01 ) and 4,150 Oe (H02 ). A
good agreement between the experiment results and the simulation results
(see solid line in red in Fig. 3.6) has been achieved in the center frequency
and the BWs of the passband and the two guarding stopbands.
In conclusion, a wideband BPF with tunable center frequency of 5.90 to 17.80
GHz and corresponding BW of 1.27 to 2.08 GHz as well as large absorption
42
Figure 3.6: Measured and simulated transmission characteristics of the tunable BPF.
BW and moderate power absorption level in the two guarding stop-bands
has been realized using a pair of BSFs in cascade. By optimized design
such magnetically-tunable microwave BPFs with even larger tuning ranges
in both the center frequency and the BW as well as lower insertion losses can
be realized.
43
3.2
A Tunable X-band Band-Pass Filter Module
In Section 3.1, a tunable BPF of large tuning range using cascaded BSFs was
presented [52]. Note that its large tunability was accomplished by adjusting
the external magnetic fields applied on the YIG thin film placed on two
separate meander-line structured BSFs(See Fig. 3.5). In order to accomplish
reduction in device size, lowering material cost, and simplifying integration
with other components and subsystems, a tunable X-band BPF module using
YIG/GGG layer on RT/Duroid substrate was realized [54] and presented in
the following Sections.
3.2.1
Device Architecture and Working Principle
Fig. 3.7(a) shows the basic configuration of the RT/Duroid-based tunable
X-band BPF module which consists of an 8-12 GHz passive BPF and a pair
of tunable BSFs in cascade. Such non-semiconductor substrate-based filter
module possesses advantages of lower material cost, in comparison to those
fabricated on the semiconductor substrate such as GaAs, and potential for
integration into a variety of other RF components and subsystems [52, 55].
The passive BPF utilizes four half-wave open-circuited stubs fabricated on a
254 μm thick RT/Duroid substrate to provide a passband of 8-12 GHz. Each
of the tunable BSFs incorporates three identical segments of nine-element
44
(a)
(b)
Figure 3.7: (a) An YIG/GGG-RT/Duroid-based tunable X-band BPF module consisting of
an 8-12 GHz passive BPF and a pair of tunable BSFs.(b)Realization of the tunable X-band
BPF module using an 8-12 GHz passive BPF and a pair of tunable BSFs. The stop-bands
of the two BSFs superimpose upon the 8-12 GHz passband of the passive BPF and facilitate
tuning of the passband toward (a) the high end, (b) the low end, and (c) the center.
45
SILPFs fabricated on the substrate upon which the YIG/GGG layer is laid.
An incoming microwave is coupled into the YIG/GGG layer and the peak
absorption of the microwave power occurs when its frequency coincides with
the FMR frequency of the YIG/GGG layer. The FMR frequency varies with
an external bias magnetic field H0 in accordance with Eq. 3.1. The capability
of multi-element SILPF over a 50 Ω microstrip for significant enhancement
in FMR peak absorption level with the flip-chip YIG/GGG layer structure
was demonstrated recently [52, 53, 55].The nonuniform bias magnetic field
along the Y-axis over the three-segment meander-line would result in a large
widening of the stop-band BW. Accordingly, the passband of the BPF module
can be tuned toward its high end, center and low end (see Fig. 3.7(b))via
simultaneous tuning of the stopbands of the two BSFs.
3.2.2
Design and Simulation
A. RT/Duroid-based 8-12GHz Passive Band-pass Filter
The passive BPF that provides a passband of 8-12 GHz for the RT/Duroidbased BPF module is comprised of four half-wave open-circuited stubs that
are λg /2 long with three connecting lines λg /4 long, where λg is the guided
wavelength in RT/Duroid substrate at the mid-band frequency.
The Chebyshev LPF which has sharp cut off response was chosen as the
46
prototype filter and then transformed to band-pass response to form a BPF.
In the prototype filter design, four stubs (n=4) and passband ripple lower
than 0.1 dB were specified. Given the filter degree n, the BPFs characteristics
depend on the characteristic impedances of the stubs and the connecting
lines. The width (W ) of each stub and connecting line were computed using
Eqs. 3.2-3.5 [5, 172].
εr − 1
0.61
W
2
×[ln(B−1]+0.39−
>2
), f or
W = d× ((B−1)−ln(2B−1)+
π
2εr − 1
εr
d
(3.2)
W
8 × eA
, f or
<2
W = d × 2A
e −2
d
(3.3)
in which
Zi
A=
60
(
εr + 1
0.11
εr + 1
)+
(0.23 +
)
2
εr − 1
εr
60π 2
B=
√
Zi × ε r
(3.4)
(3.5)
where Zi are the impedances, εr =10.3 is the relative dielectric constant of
RT/Duroid 6010LM substrate, and d=254 μm is the substrate thickness.
47
(a)
S-Parameter S21(dB)
5
0
-5
-10
-15
-20
-25
Simulated Result
Experimental Result
-30
-35
-40
5
6
7
8
9
10 11 12 13 14 15
Frequency (GHz)
(b)
Figure 3.8: (a) Layout of the passive BPF; (b)Simulated and measured transmission characteristics (S21 ) of the passive BPF.
48
Table 3.3: Width and Length of 8-12 GHz Passive BPF
W (μm)
L(μm)
W0
223
L0
2865
W1
261
L1
5706
W12
390
L12
2800
W2
800
L2
5386
W23
470
L23
2773
W3
848
L3
5368
W34
242
L34
2862
W4
306
L4
5666
The half-wave and quart-wave lengths (L=λg /2 and λg /4) for the stubs and
connecting lines were calculated using Eq. 3.6 for the guided wavelength,
λ0
300
=
λg = √
√ (mm)
εre
f (GHz) εre
(3.6)
where f (GHz) =10 GHz is the mid-band frequency and εre is the effective
relative dielectric constant.
The final dimensions of the width (W ) and length (L) of the stubs and the
connecting lines are listed in Table 3.3. The layout is shown in Fig. 3.8(a).
The measured transmission characteristics show a passband of 7.8-11.8 GHz
with an insertion loss of 2.5 dB (Fig. 3.8(b)). A good agreement between the
measured results and the simulated results obtained using AWR Microwave
Office Simulator is clearly seen.
B. RT/Duroid-based Tunable Band-stop Filters
Each of the two YIG/GGG-RT/Duroid-based BSFs with large tunability in
its stopband center frequency and BW was realized using three identical nine-
49
element SILPFs. The SILPF has 223 μm wide line as a 50 Ω transmission
line and 767 μm and 70 μm wide lines as the low and high characteristic
impedances of 25 Ω and 80 Ω, respectively. Note that the latter correspond
to the shunt capacitances and the series inductances, respectively. AWR
Microwave Office was used to design, simulate and optimize the SILPFs. As
mentioned previously, the multi-element SILPFs together with a nonuniform
bias magnetic field can drastically widen the resultant stop-band bandwidth
of the BSF [52, 53, 55].
C. RT/Duroid-based Tunable Band-pass Filter Module and Simulation
By integrating a pair of the BSFs described in Section B at both ends of
the 8-12 GHz passive BPF described in Section A, a tunable BPF module
as shown in the Fig. 3.9 was constructed. The Ansoft HFSS was used to
simulate its tunability resulting from the nonuniform bias magnetic fields,
which was taken from the measurement data. In simulation, the following material parameters of the YIG film were used:4πMs = 1760 Oe, εre
=14.7, ΔH=1 Oe, Gyromagnetic ratio γ =2.8 × 106 Hz/Oe and the size of
6.0mm×8.0mm×100μm. The simulated transmission characteristics of the
resulting RT/Duroid-based BPF module are then compared with the experimental results in Fig. 3.8(b).
50
Figure 3.9: The schematic of the tunable X-band Band-pass Filter module.
3.2.3
Experimental Results and Discussion
A. Fabrication of the RT/Duroid-based BPF Module
The X-band BPF module was fabricated on a 254 μm thick RT/Duroid
6010LM substrate with 17 μm thick copper films using photolithographic
technique. The Y-directed bias magnetic field, H0 ,was generated using two
pairs of identical Nd-Fe-B permanent magnets (0.75” in diameter and 0.5”
in thickness) attached to a pair of iron yokes, respectively, to complete the
magnetic circuit. Two pieces of 100 μm thick YIG film samples each with
dimension of 6.0×8.0mm2 along the X and Y directions were laid directly
upon the three-segment SILPFs. To avoid mutual interference of the magnetic fields, a 1 cm gap between the pairs of iron yokes was maintained. Since
the bias magnetic fields in the YIG/GGG sample was varied by tuning the
51
gap (d) between the permanent magnet pairs, by programming the magnetic
fields applied in the YIG/GGG layer structure, the passband of the BPF
module could be tuned and tailored.
B. Experimental Results on Passband Tuning
1) Tuning toward the High-End Band
By applying the bias magnetic fields of 990 and 1,825 Oe, respectively, on
the two BSFs, the passband was tuned upwardly from 7.8 to 9.8 GHz. When
the center magnetic fields were increased to 1,700 and 2,360 Oe, respectively,
the passband was further tuned to 11.2 GHz, and with the center frequency
at 11.5 GHz, a 3 dB BW of 1.0 GHz, and a tuning range of 3.4 GHz were
accomplished (See the red diamond line in Fig. 3.10(a)).
2) Tuning toward the Low-End Band
Similarly, the passband was tuned from the high-end frequency toward the
low-end frequency. When the bias magnetic fields of 990 and 3,180 Oe were
applied, respectively, to the two BSFs, the passband was lowered from the
high-end at 11.8 to 9.4 GHz. It was completely tuned to the lower end,
namely, 7.8 GHz, when the magnetic fields were programmed at 2,570 and
3,180 Oe, as shown in the red diamond line in Fig. 3.10(b). The downward
tuning of the full 4.0 GHz passband was then realized with the center frequency at 7.9 GHz and the associated 3 dB BW of 1.1 GHz.
52
3) Tuning toward the Center Frequency Band
Fig. 3.10(c) shows the simultaneous tuning of the passband from the highand low-end bands to the center frequency at 9.8 GHz. When the magnetic
fields were centered at 1,450 and 3,350 Oe, respectively, the passband was
compressed from 7.8-11.8 GHz to 8.8-10.6 GHz. It was further narrowed to
9.6-10.0 GHz, when the magnetic fields were set at 1,725 and 3,180 Oe. Thus,
the tuning range was 3.6 GHz with a 3 dB BW of 1.2 GHz.
The center frequency, the 3 dB BW and the tuning range of the RT/Duroidbased X-band BPF module together with the bias magnetic fields used are
listed in Table 3.4. The results clearly demonstrate the large tunability of
the BPF module. A good agreement between the simulated and experimental results in both the center frequency and the BW is also clearly seen in
Fig. 3.10(a)-Fig. 3.10(c). Since the power sensors used in the measurement
had a limited dynamic range of about 30 dB, the experimental results show
flatter stop-bands than the simulated results.
As shown in Fig. 3.10, the measured insertion loss (S21 ) of the BPF module is
5.3 dB. The relatively high insertion loss mainly resulted from the mismatch
of the transmission line caused by variation in the effective dielectric constant
of the RT/Duroid substrate. The effective dielectric constant associated with
the air and dielectric regions of the quasi-TEM microstrip line would be
different after the flip-chip YIG/GGG layer was laid.
53
No magnetic filed applied
Simulated result
S-Parameter S21(dB)
0
990 and 1,825Oe applied
1,700 and 2,360Oe applied
-5
-10
-15
-20
-25
-30
-35
-40
4
5
6
7
8
9 10 11 12 13 14 15 16
Frequency (GHz)
(a)
No magnetic field applied
Simulated Result
S-Parameter S21(dB)
0
990 and 3,180Oe applied
2,570 and 3,180Oe applied
-5
-10
-15
-20
-25
-30
-35
-40
4
5
6
7
8
9 10 11 12 13 14 15 16
Frequency (GHz)
(b)
No magnetic field applied
Simulated result
S-parameter S21(dB)
0
1,450 and 3,350Oe applied
1,725 and 3,180Oe applied
-5
-10
-15
-20
-25
-30
-35
-40
4
5
6
7
8
9 10 11 12 13 14 15 16
Frequency (GHz)
(c)
Figure 3.10: Tuning of the passband of the BPF module toward (a) the high end, till 11.2
GHz, (b) the low end, with full passband (7.8-11.8 GHz) tuning realized, and (c) the center,
with passband narrowed to 9.6-10.0 GHz.
54
Table 3.4: The Measured Tunability of X-band BPF Module
8-12GHz BPF
Tuning Toward
High End Band
Tuning Toward
low End Band
Tuning Toward
Center Freq.
Fields
Applied(Oe)
None
1,700 and 2,360
Center
Freq.(GHz)
9.8
11.5
Tuning
Range(GHz)
N/A
7.8-11.2
3dB BW
(GHz),(%)
4.7
1.0(78.7%)
2,570 and 3,180
7.95
11.8-7.8
1.1(76.7%)
1,725 and 3,180
9.8
7.8-9.6 and
11.8-11.0
1.2(74.5%)
In conclusion, a tunable X-band BPF module consisting of an 8-12 GHz passive BPF and two tunable BSFs with large tunability has been realized using
the non-conducting and inexpensive RT/Duroid substrate. The measured
tuning ranges toward the high-end, the low-end and the center bands are,
respectively, 3.4, 4.0, and 3.6 GHz with the corresponding 3 dB BWs of 1.0,
1.1 and 1.2 GHz in good agreement with the simulation results. The average
measured insertion loss is 5.3 dB. By optimizing the design, a lower insertion
loss than 5.3 dB should be achievable.
3.3
A Composite Tunable X-band BPF Module
As detailed in Section 3.2, an X-band BPF module using a YIG/GGG thin
film upon RT/Duroid substrate has demonstrated large frequency tunability [54]. Compared to the GaAs substrate, RT/Duroid 6010 substrate is of
much lower material cost and capable of easier integration with other RF
55
S 21
8
S 21
f(GHz)
12
S
f(GHz)
26.5
+
L2
C1 C3
L4
L6
C5
L8
21
8
12
f(GHz)
=
C 7 C9
Open-circuited Stubs (ii) SILPF
(i) X-band Passive BPF
(iii) Composite-BPF
(a)
H01
H02
Y
X
Microwave
Output
Microwave
Input
Composite BPF No .2
Composite BPF No .1
(b)
Figure 3.11: (a) The design of composite-BPF (iii) by combing four open-circuited stubs of
an X-band BPF (i) with the four inductive elements of a SILPF (ii) which can function as a
BPF and a tunable BSF simultaneously. (b). A compact tunable BPF module using a pair
of composite-BPFs connected in cascade.
components and subsystems. However, its relatively large circuit area and
higher insertion loss are less than desirable. Therefore, a new composite-BPF
that has significantly smaller size and lower insertion loss was proposed [56].
By connecting a pair of such composite-BPFs in cascade, an X-band tunable BPF module of smaller circuit area, lower insertion loss and superior
frequency tunability and selectivity has been realized [56].
56
3.3.1
Device Architecture and Working Principle
The new composite-BPF was realized by combining four half-wave opencircuited stubs of a passive X-band BPF with four inductive elements (L2 ,
L4 , L6 and L8 ) of a 9-element SILPF as shown in Fig. 3.11(a). As mentioned previously, the multi-element SILPF is capable of significantly enhancing the FMR absorption level and functioning as a tunable BSF in flip-chip
YIG/GGG thin-film layer structures [52–55]. The composite-BPF also shows
a large passband of 8-12 GHz. Therefore, the newly devised composite-BPF
(see Fig. 3.11(a)) provides the dual functions as an X-band BPF and a tunable BSF when a tunable magnetic field is applied. By connecting a pair of
such composite-BPFs in cascade, and applying separate bias magnetic fields,
H0 , a tunable X-band BPF module is realized as shown in Fig. 3.11(b). In
operation, the incoming microwave is coupled into the YIG/GGG layer, and
the peak absorption of the microwave power occurs when its carrier frequency
coincides with the FMR frequency of the YIG/GGG layer. By applying individual and tunable bias magnetic fields to the two YIG films, the corresponding peak absorption frequencies of the two resulting composite-BPFs
serve to tune the center frequency and the BW of the BPF module toward
its high-end, low-end and center frequencies (See Fig. 3.12).
57
S21
S 21
+
8
12 f(GHz)
8
12 f(GHz)
H01
Microwave
Input
H02
CompositeBPF No.1
CompositeBPF No.2
S21
Microwave
Output
8
S 21
S21
12 f(GHz)
8
(a)
12 f(GHz)
S 21
8
(b)
12 f(GHz)
8
(c)
12
f(GHz)
Figure 3.12: Superposition of the two stop-bands from composite-BPF No.1 and No.2 connected in cascade upon their 8-12 GHz passbands and facilitate tuning of the passband
toward (a) the high end, (b) the low end, and (c) the center.
3.3.2
Design and Verification
A. RT/Duroid-based Composite-BPF Design
The SILPF and the passive microstrip X-band BPF were first designed. The
9-element SILPF utilizes 238.3 μm wide line as a 50 Ω transmission line and
588.8 μm and 87 μm wide lines as the low and high characteristic impedances
of 30 Ω and 80 Ω respectively. The X-band passive BPF consists of four halfwave open-circuited stubs that are λg /2 long with three connecting lines of
λg /4 long, where λg is the guided wavelength in RT/Duroid substrate at the
mid-band frequency [1, 5].
The composite-BPF employed four λg /2 long open-circuited stubs inserting
58
into four inductive elements (L2 , L4 , L6 and L8 ) of the SILPF as shown
in Fig. 3.11(a)). The positions of the stubs were set to preserve the BPFs
band-pass characteristics by specifying the inductive elements width, WL ,
and lengths, d1 and d2 , as shown in Fig. 3.13(c). As an example, when stub2
and stub3 were combined with inductive elements L4 and L6 , by determining
WL and d2 , the impedance Z23 and physical length L23 computed based on
Eq. 3.7 to Eq. 3.8 (see Fig. 3.13(b)) were used to replace the X-band BPFs
connecting line Z23 and λg /4 in Fig. 3.13(a). As a result, the band-pass
function of the X-band BPF was incorporated with that of the steppedimpedance structure which significantly enhanced the FMR peak absorption
as previously demonstrated [52–55].
8h
WL
60
)
+ 0.25
Z = √ ln(
εre WL
h
(3.7)
WL
120π WL
+ 1.393 + 0.677ln(
+ 1.444)}−1
Z= √ {
εre h
h
(3.8)
and for WL /h ≥1,
where WL is the width of the inductive elements, h is the thickness of the
RT/Duroid substrate, namely, 254 μm, and εre is the relative effective dielectric constant of the substrate [5].
59
23
23
23
L
4
d2
d2
stub2
stub3
WL
lC1
d1
d1
d2
d2
lC 5
lC 3
l2
W2
W2
d1 d1
lC1
lC 3
l2
l1
W1
d2
d2
l1
W1
Figure 3.13: (a) to (b). By specifying WL and d2 , the X-band BPFs open-circuited stubs
can be embedded into a SILPF to preserve the band-pass function. (c). Layout of the
composite-BPF.
60
Table 3.5: The Dimensions of The Composite-BPF(Unit: μm)
W1
303
W2
353
WL
141
l1
5,910
l2
6,262
lc1
147
lc3
607
lc5
792
d1
180
d2
675
As described above, a set of initial design values were used for the first calculation and then Software AWR Microwave Office was utilized to optimize
the dimensions of the composite-BPFs architecture. The final dimensions of
the composite-BPF are listed in Table 3.5.
B. Verification on Composite-BPFs Dual Functions
The composite-BPF design presented in the last Subsection was fabricated on
a 254 μm thick RT/Duroid 6010 substrate using photolithographic technique.
The measured transmission characteristics (See Fig. 3.14(a)-Fig. 3.14(b))
show an edge passband of 7.9 to 12.2 GHz and an insertion loss of 1.6 dB.
By laying a 2mm ×10mm ×100 μm YIG/GGG thin-film upon the RT/Duroidbased composite-BPF and applying a bias field of 2,690 Oe, a peak absorption was seen to occur at the mid-band frequency of 10.25 GHz as shown in
Fig. 3.14(a). Fig. 3.14(b) shows the peak absorptions measured from a 50 Ω
microstrip, a SILPF and the composite-BPF. The results clearly show that
the composite-BPF has the highest peak absorption which demonstrated that
the composite-BPF could also function as a BSF.
61
S-Paramter S21(dB)
5
0
-5
-10
-15
-20
-25
-30
-35
-40
-45
No magnetic field applied
2,690Oe field applied
4
5
6
7
8
9 10 11 12 13 14 15 16
Frequency (GHz)
(a)
S-Paramter S21(dB)
5
0
50 Ohm microstrip
SILPF
single composite BPF
-5
-10
-15
-20
-25
-30
8.0
8.5
9.0
9.5 10.0 10.5 11.0 11.5 12.0 12.5
Frequency (GHz)
(b)
Figure 3.14: (a).The measured S21 (dB) shows a passband from 7.9-12.2 GHz, 1.6 dB insertion
loss, and a peak absorption at 10.25 GHz with 2,690 Oe field applied. (b). Peak absorption
comparison among three different structures.
62
3.3.3
Experimental Results and Discussion
A. RT/Duroid-based Composite BPF Configuration
By connecting a pair of composite-BPF presented above in cascade, a tunable
BPF module was realized (See Fig. 3.11(b)). Fig. 3.15 shows the measured
passband of 7.9-11.9 GHz and insertion loss of 2.1 dB. Compared to the single
composite-BPF, the tunable BPF module designed has a sharper frequency
response with 30dB/3dB shape factor of 1.2, which is smaller than that of
the single-composite BPF, namely, 1.48. Note that such sharp frequency response is highly desirable for enhancing 3 dB BW tuning range and frequency
tunability and selectivity to be discussed in the below Section.
In order to widen the peak absorption BW of the two stop bands at the
high- and low- ends, a pair of identical SILPFs was connected to the pair of
composite-BPFs as shown in Fig. 3.16 [52, 53, 55]. The measured transmission characteristics show a passband from 7.9 to 12.0 GHz, center frequency
of 10.0 GHz, an insertion loss of 2.5 dB, and the maximum 3 dB BW of 4.7
GHz (See Fig. 3.17(a)-Fig. 3.17(c), in black).
B. Experimental Results on Passband Tuning
1) Tunability Study
63
S-Parameter S21(dB)
10
5
0
-5
-10
-15
-20
-25
-30
-35
-40
-45
Simulated result for BPF module;
Measured result for BPF module;
Measured result for single composite-BPF
4
5
6
7
8
9 10 11 12 13 14 15 16
Frequency (GHz)
Figure 3.15: The simulated (in blue) result shows good agreement with the measured (in red)
transmission characteristics of the tunable BPF module consisting of cascaded compositeBPFs in RT/Duroid substrate. It also shows a sharper frequency response than that of the
single composite-BPF (in black).
The tunability of passband for the BPF modules toward the high-end, lowend and the center frequencies was studied. A pair of identical YIG/GGG
layers with 100 μm thick YIG film and the dimension of 2.0×10.0 mm2 were
laid upon the composite BPF No.1 and No.2, respectively, along the X- and
Y- directions. The YIG/GGG layers were grown using liquid phase epitaxy
(LPE) technique and furnished by Shin-Etsu Chemical Co., Japan. The Ydirected bias magnetic field, H0 ,was generated using two pairs of identical
Nd-Fe-B permanent magnets (0.75” in diameter and 0.5” in thickness) at-
64
Figure 3.16: The schematic of the RT/Duroid-based X-band BPF module.
tached to a pair of iron yokes, respectively, to complete the magnetic circuit
[52–55]. The desirable magnetic fields were obtained by tuning the gap of the
magnet pairs along the Y-axis mechanically, therefore, there was no electrical
power consumed. When the center magnetic field was set at 1,780 Oe, the
corresponding maximum magnetic circuit dimension along the X- and Y- directions was 1.62”× 3.15”.The minimum dimension was 1.62”× 2.78” when
the center magnetic field was set at the maximum value of 3,250 Oe.
By tuning the center bias magnetic fields upon the YIG films to 1,780 and
2,670 Oe , respectively, the low-end frequency of the resulting passband was
tuned upwardly toward the high-end frequency from 8.0 to 11.8 GHz as shown
in Fig. 3.17(a). This shift of low-end frequency was a result of superposition
65
of the two FMR absorption bands created by the two magnetic fields (1,780
and 2,670 Oe) applied, respectively, to the YIG films laid upon the composite
BPF No.1 and No.2 [50, 51, 54]. A minimum 3 dB BW of 0.6 GHz and a
BW tuning range of 4.1 GHz were measured. Similarly, the passband was
tuned from the high-end frequency toward the low-end frequency. When the
center bias magnetic fields were tuned to 2,450 and 3,250 Oe,respectively, the
high-end frequency of the passband was lowered from the 12.0 to 8.0 GHz as
shown in Fig. 3.17(b). The measured performance was a center frequency of
7.0 GHz, a minimum 3 dB BW of 0.4 GHz, and a BW tuning range of 4.3
GHz.
Finally, when the magnetic fields were tuned to 1,780 and 3,250 Oe, respectively, the edge passband was compressed from the low-end 7.9 GHz and the
high-end 12.0 GHz to the center frequency 9.9 GHz as shown in Fig. 3.17(c),
demonstrating the simultaneous tuning of passband from the high-end and
low-end frequencies to the center frequency of 10.0 GHz. The corresponding
3 dB BW of 0.5 GHz and a BW tuning range of 4.2 GHz were achieved.
2) Comparison and Analysis
Table 3.6 shows a comparison of the experimental results obtained with the
newly designed BPF module with that of the one reported earlier [54] and
presented in the previous Section 3.2. The comparison clearly shows that
the newly realized BPF module has a more compact device structure with
66
No magnetic field applied
1,780 and 2,670 Oe centered upon the YIG films
No magnetic field applied
2,670 and 3,550 Oe centered upon the YIG films
0
S-Paramter S21(dB)
S-Paramter S21(dB)
5
5
0
-5
-10
-15
-20
-25
-30
-35
-40
-45
-5
-10
-15
-20
-25
-30
-35
-40
-45
4
5
6
7
8
9 10 11 12 13 14 15 16
4
5
6
7
8
9 10 11 12 13 14 15 16
Frequency (GHz)
Frequency (GHz)
(a)
(b)
5
No magnetic field applid
1,780 and 3,250 Oe centered upon the YIG films
S-Paramter S21(dB)
0
-5
-10
-15
-20
-25
-30
-35
-40
-45
4
5
6
7
8
9 10 11 12 13 14 15 16
Frequency (GHz)
(c)
Figure 3.17: Tuning of the passband of the BPF module toward (a). the high-end, till 11.8
GHz; (b). the low-end, with full passband tuning realized, and (c). the center, with a narrow
passband centered at 9.9 GHz.
67
Table 3.6: Comparison Between Two X-Band BPF Modules
Circuit Area
Insertion Loss (dB)
High End
3 dB BW and
Low End
(tuning range)(GHz)
The Center
The newly
realized BPF
Module
2.3 × 1.2
2.5
0.6(4.1)
0.4 (4.3)
0.5 (4.2)
Recently
Reported BPF
Module [54]
4.25 × 1.15
5.3
1.0(3.7)
1.1 (3.6)
1.2 (3.5)
Reduced
By (%)
43.5%
52.8%
40%
63.6%
58.3%
circuit area reduced by 43.5%, namely, from 4.25×1.15 cm2 to 2.3×1.2 cm2 .
This device size reduction should be important for the modern high-speed
and high-frequency circuits in terms of functionality and production cost.
Due to its compact structure and lesser microstrip mitered bends used in the
design, the insertion loss was reduced by 52.8%, namely, from 5.3 dB to 2.5
dB. Also, the sharper frequency response obtained by employing a pair of
composite-BPF in cascade reduces the minimum 3 dB BW by 40%, 63.6%
and 58.3%, respectively, toward the high-end, low-end and the center, while
both modules have the same maximum 3 dB BW of 4.7 GHz, namely, from
1.0 to 0.6 GHz, 1.1 to 0.4 GHz and 1.2 to 0.5 GHz, respectively. Note that
the smaller the minimum 3 dB BW, the larger the BW tuning range and,
thus, better frequency tunability and selectivity. Clearly, the newly devised
X-band BPF module has shown desirable features such as greater compact
structure, smaller device dimensions, lower insertion loss, and superior frequency tunability.
In conclusion, a compact tunable X-band BPF module which consists of a
68
pair of tunable composite-BPFs with large tunability in center frequency and
BW has been realized using YIG/GGG layer structure on RT/Duroid 6010
substrate. The measured insertion loss was 2.5 dB, and the 3 dB BW tuning
ranges toward the high-end, the low-end and the center frequencies were,
respectively, 4.1, 4.3, and 4.2 GHz with the corresponding 3 dB BWs of 0.6,
0.4, and 0.5 GHz. Compared to the BPF module realized earlier, the newly
realized BPF module has significantly smaller device size and lower insertion
loss, and superior frequency tunability as well as selectivity.
3.4
A Varactor and FMR-Tuned BPF Module
The two FMR-tuned X-band BPF modules presented in Sections 3.2 and 3.3
have demonstrated large frequency tunability using YIG/GGG thin film on
inexpensive RT/Duroid substrate [54, 56]. The large tunability of these two
BPF modules was accomplished by superimposing the two FMR-tuned stopbands generated using a pair of BSF upon an X-band passive BPF/compositeBPF [54, 56]. Therefore, their tuning ranges were limited by the passband of
the passive BPF/composite BPF having a fixed center frequency and BW.
In order to overcome this limitation and further enlarge the tuning range,
a tunable X-band passive composite-BPF was realized by connecting four
varactors to its four open-circuited stubs and applying the reverse bias voltages to the varactors. In comparison with the other tuning techniques, the
69
varactor-tuned BPFs are characterized by a fast tuning speed over a wide
frequency range, compact structure, and light weight [169, 173–177], while
the thin-film FMR-tuned BPFs possess attractive features such as very high
carrier frequency, high selectivity, multi-octave tuning range, spurious-free
response, and inherent compatibility with planar microwave circuitry such as
MMIC [39–44]. The combined technique of the electrical/varactor and magnetic/FMR tunings enabled realization of a new BPF module with superior
frequency tunability and versatile frequency selectivity [57].
3.4.1
Device Architecture and Working Principle
The architecture of the new BPF module is shown in Fig. 3.18. It consists
of a pair of BSF each with three identical multi-element SILPFs, a bias-T
structured RF choke, and an X-band passive composite-BPF loaded with four
varactors at the four open-circuited stubs.
In operation, the variation in capacitance of the varactor arising from the
applied reverse bias voltages through the RF choke causes changes in the
electrical length of the open-circuited stub and results in an electrically tuned
passband [174–176]. Note that by means of such tuning a large passband (4.7
GHz or higher) but fixed BW was obtained at a given reverse bias voltage.
Therefore, FMR-tuning was utilized to facilitate improved frequency selectivity by tuning the BW. The FMR-tuning was realized by laying one YIG/GGG
70
Figure 3.18: The architecture of the newly realized BPF module using a pair of FMR-tuned
BSFs and a varactor-tuned X-band passive composite-BPF.
thin film (5×12mm2 ×100 μm in size) each upon a BSF composed of three
SILPF segments together with non-uniform magnetic fields. As reported
in [53–56], a SILPF can function as a BSF when a ferromagnetic YIG/GGG
thin-film is laid upon a microstrip line and with application of a bias magnetic
field. The basic BSF utilizes the FMR absorption mechanism which can be
tuned by the applied magnetic fields. The capability of multi-element SILPF
over a 50 Ω microstrip for significant enhancement in FMR peak absorption
level was first demonstrated with the flip-chip YIG/GGG layer structure on
GaAs substrate [53]. The microstrip meander-line constructed by connecting
the three identical SILPFs in series together with the non-uniform magnetic
field was to further enhance the peak absorption level and enlarge the absorption BW [55]. The resultant passband tuning by means of superimposing
71
two such FMR-tuned stopbands upon the fixed passband of a passive BPF
[54] was discussed previously in Section 3.2 . In short, the combination of
the varactor- and FMR- tuning techniques has demonstrated capability to
facilitate a versatile passband tunability over a large frequency band.
3.4.2
Design and Simulation
A. X-band Passive Composite-BPF Design
The X-band passive composite-BPF that combines four half-wave open-circuited
stubs of a passive X-band BPF with four inductive elements of a nine-element
SILPF has demonstrated its capability to function capable of functioning as a
BSF and a BPF [56]. The detailed design procedures and experimental verifications have been reported in [56]. The passive composite-BPF was utilized
to realized of this new BPF module because it provided larger gaps between
the adjacent open-circuited stubs and thus allowing for easy installation of
the varactors.
In the realization, an X-band passive composite-BPF was first designed using
the procedures reported in [56]. The ends of the open-circuited stubs were
then shaped to the same dimensions as that of the varactors for packaging
purpose as shown in Fig. 3.19. The physical length of the varactor’s lead beam
was regarded as a transmission line segment connected to the stub and taken
72
W50:
lC1
d1
W1
lC 3
lC 5
d2
l1 W2
l2
lv
lv
Wv
WL
Wv
Figure 3.19: The layout of the X-band passive composite-BPF with a symmetrical structure.
into account in the initial design calculation [56]. AWR Microwave Office
Simulator was subsequently used to perform simulation and optimization,
during which each varactor was simplified as a capacitor in series with a
resistor in an electrical model. The finalized layout and architecture of the
X-band passive composite-BPF is shown in Fig. 3.19. It has a symmetrical
structure with respect to the red dash-dotted central line with the dimensions
listed in Table 3.7.
Table 3.7: The Dimension of the Composite BPF
W idths(μm)
Lengths(μm)
WL
150
L1
1013
W1
500
L2
1138
73
W2
602
Lv
550
Wv
550
Lc1
138
d1
902
Lc3
607
d2
943
Lc5
702
B. RF Choke Design and Simulation
As shown in Fig. 3.20(b), the bias-T structured RF choke was used for feeding
a dc supply from port 3 through dc bias pad to the BPF module such that the
RF transmission from port 1 to port 2 was unaffected by the dc connection.
In essence, such RF choke design functions as a band-stop filter to short out
RF transmission over its stop band, while maintaining a perfect transmission
for the dc current [5]. The radial stub was utilized in the design since it has
lower impedance, more compact area and broader bandwidth when compared
with a conventional quarter-wave open-circuited stub [5, 178–181]. In order
to obtain a wider stopband, a pair of radial stubs of different radii connected
in cascade was utilized.
In the design the stub angle α of the RF choke that affects its BW was
chosen as 90◦ . The width of feeding line used to connect the radial stub pairs
was chosen as narrow as 58.2 μm with the corresponding impedance of 80
Ω since the narrower the width, the wider the stopband and the better the
performance [5]. The outer radius R0 of the RF choke which determines the
attenuation frequency was computed using Eq. 3.9 as follows
√
logR0 = Alog( εr fg0 ) + Blog(H) + Clog(r0 ) + D
(3.9)
where r0 and R0 are the inner and outer radii, respectively, H and εr are the
74
substrate thickness and dielectric constant, and λg0 is the resonance frequency
in GHz [178, 179]. The coefficients A, B, C, D are, respectively, valued at
-0.8510, 0.0614, 0.0877 and -0.8695 according to [179]. The final layout and
dimensions of the RF choke are shown in Fig. 3.20(b).
90
0
90
90
Figure 3.20: (a). Architecture of the radial stub, (b). A microstrip RF choke using a pair of
radial stubs in cascade is capable of providing a wider stopband.
The simulated results in Fig. 3.21 clearly shows that the designed RF choke
has an ideal broadband transmission characteristics (S21 ) from 6 GHz to 19
GHz, while maintaining an effective RF choke (S31 ) over the desired frequency
band.
75
10
S-Parameter (dB)
0
-10
-20
-30
S21(dB)
S11(dB)
S31(dB)
-40
-50
-60
2
4
6
8 10 12 14 16 18 20 22 24
Frequency (GHz)
Figure 3.21: Simulated performance of the microstrip RF choke.
3.4.3
Experimental Results and Discussion
The X-band passive composite-BPF module was fabricated on a 254 μm
thick RT/Duroid 6010 substrate using photolithographic technique. Four
GaAs Hyperabrupt varactor diodes (provided by Aeroflex/Metelics Inc. with
model number MGV-125-08 and operating frequency up to 40 GHz) were
connected to the ends of the open-circuited stubs using silver paste. Fig. 3.22
is a photo of the completed module.
76
Figure 3.22: The varactor and FMR-tuned BPF module.
A. Electrical tuning using varactors
Electronic tuning of passband was accomplished by applying the same reverse bias voltage to the four varactors connected to the ends of the four
open-circuited stubs of the X-band composite-BPF. When the reverse bias
voltage was set at threshold value, i.e., 2 V, the measured 3 dB passband
was from 7.7-12.4 GHz, with a BW of 4.7 GHz and a center frequency of
10 GHz. Continuous increase in the reverse bias voltage till the varactor’s
breakdown voltage, namely, 22 V, the passband was tuned to 11.4-17.5 GHz
(see Fig. 3.23(a), in blue) with an increased BW of 6.1 GHz and a higher
center frequency of 14.45 GHz. In summary, the resultant 3 dB BW of this
77
newly realized X-band passive composite-BPF module was enlarged from 4.7
to 6.1 GHz by the 2 and 22 V reverse bias voltages, respectively, with the corresponding frequency span of 9.8 GHz, namely, from 7.7 GHz to 17.5 GHz, as
shown in Fig. 3.23(b). The measured insertion loss was 6.3 dB. The relatively
large insertion loss was mainly caused by the significant series resistance (R)
of the varactor diodes. As clearly seen in Fig. 3.23(c), the larger the series
resistance the poorer the simulated transmission characteristics are.
B. Magnetic tuning using FMR
The varactor-tuned passive composite BPF module has demonstrated a large
passband tuning range from X- to Ku-band as shown in Fig. 3.23(a). However, it lacks the capability of further tuning and control in the BW and
center frequency, which can be facilitated by employment of the FMR-tuned
BSFs. The FMR-tuned BPFs are characterized by high carrier frequency,
high selectivity, very large and dynamic tuning range through BW control,
free of spurious frequency response, while maintaining a compact circuit area
[54, 56].
The FMR tuning was accomplished by placing the magnetic YIG/GGG layer
upon the microstrip SILPF meander line structure and applying bias magnetic fields. The incoming microwave propagating along the microstrip structure was coupled into the YIG/GGG layer and the peak absorption of the
78
10
-2V
-6V
-12V
-18V
-22V
-2V
-10
-20
S-Parameter S21 (dB)
S-Parameter S21(dB)
0
-30
-22V
-40
-50
-60
7.7 GHz 9.8 GHz Span 17.5 GHz
0
6.1GHz BW
-10
12.4 GHz
4.7 GHz
BW
-20
-2V
-22V
11.4 GHz
-30
-40
-50
-60
4
6
8
10 12 14 16 18 20 22 24
4
6
8
10 12 14 16 18 20 22 24
Frequency (GHz)
Frequency (GHz)
(a)
(b)
0
S-Parameter S21(dB)
-5
-10
-15
R=0.5 ohm
R=1.0ohm
R=1.5ohm
R=2.0ohm
-20
-25
-30
-35
-40
5
6
7
8
9
10 11 12 13 14 15 16
Frequency (GHz)
(c)
Figure 3.23: (a).By increasing the reverse bias voltages applied to the varactors from 2 to 22
V, the 3 dB passband was continuously tuned from 7.7-12.4 GHz to 11.4-17.5 GHz. (b).The
corresponding 3 dB BW were enlarged from 4.7 GHz to 6.1 GHz indicating a frequency span
of 9.8 GHz, namely from 7.7-17.5 GHz.(c).The series resistance of the varactors degrades the
transmission characteristics.
79
microwave power occurred when its frequency coincided with the FMR frequency of the YIG/GGG layer. The FMR frequency (fr ) varied with an
external bias magnetic field (H0 ) in accordance with Eq. 3.1.
The FMR-tuned band-pass filtering was accomplished by superimposing two
magnetically-tuned stopbands from a pair of BSF upon the passband of the
X-band passive composite-BPF presented in [54]. Each of the Y-directed
bias magnetic fields, H0 , was generated using a pair of identical Nd-Fe-B
permanent magnets (0.75” in diameter and 0.5” in thickness) attached to
a pair of iron yoke, respectively, to complete the magnetic circuit as shown
in Fig. 3.24. The tunable stopbands of the BSF pair were controlled by
varying the gaps, d1 and d2 , in Fig. 3.24, between the magnet pairs, and their
superposition upon the passband of the passive composite-BPF facilitated
tuning of the resultant passband towards the high-end, low-end, and any
frequency region within the passband.
1). Tuning toward the high-end frequency
By setting the reverse bias voltage at 22 V (see Fig. 3.25(a), in blue) and
tuning the center bias magnetic fields to 3,250 and 4,200 Oe, respectively,
upon the two YIG films, the low-end frequency of the passband was tuned
upwardly toward the high-end frequency from 11.4 to 16.1 GHz as shown in
Fig. 3.25(a). This shift of the low-end frequency was a result of the superposition of the two FMR absorption bands created by the two bias magnetic fields
80
0.5''
0.5''
Iron Yoke
Iron Yoke
0.75''
0.75''
Nd-Fe-B
Magnet
Nd-Fe-B
Magnet
YIG/GGG
Sample
Microwave
d1 Input
YIG/GGG
Sample
Microwave
Output
Device
Device
y
z
Nd-Fe-B
Magnet
Nd-Fe-B
Magnet
Iron Yoke
Iron Yoke
d2
x
Figure 3.24: Arrangement for producing nonuniform bias magnetic fields in YIG/GGG layer.
applied, respectively, to the YIG films laid upon the pair of BSF [52, 53, 55].
The measured center frequency was 16.8 GHz and the 3 dB BW was reduced
from 6.1 GHz to 1.4 GHz.
2). Tuning toward the low-end frequency
Similarly, the passband was tuned from the high-end frequency toward the
low-end frequency when the reverse bias voltage was set at the threshold
voltage of 2 V and the center bias magnetic fields were tuned to 2,650 and
3,500 Oe, respectively. As shown in Fig. 3.25(b), the high-end frequency of
the passband was lowered to 8.7 GHz, with a center frequency of 8.2 GHz
and the 3 dB BW was drastically reduced from 4.7 GHz to 1.0 GHz.
81
3). Tuning within the passband
The combination of the varactor- and FMR-tuning facilitates the passband
and its BW to be tuned to any frequency region within the maximum frequency coverage, namely, 7.7-17.5 GHz, obtained by setting the reverse bias
voltage at 2 and 22 V (see Fig. 3.25(c), in black dash line). For example, by
setting the reverse bias voltage at 4 V and the bias magnetic fields at 2,350
and 4,150 Oe, an 8.3-9.5 GHz passband with a 3 dB BW of 1.2 GHz (see
Fig. 3.25(c), in red) was measured. Similarly, the passband was tuned to
the frequency range of 11.2-12.2 GHz, with a center frequency of 11.7 GHz
and a 3 dB BW of 1.0 GHz when a 10.0 V reverse bias voltage and 1,800
and 3,120 Oe bias magnetic fields were applied. As a last example shown
in Fig. 3.25(c) in blue, the passband was narrowed to the range of 14.7-15.7
GHz with a center frequency of 15.2 GHz and a 3 dB BW of 1.0 GHz at
the reverse bias voltage and bias magnetic fields of 16 V, 2,950 and 3,250
Oe, respectively. Clearly, other passband and 3 dB BWs can be obtained by
first setting the bias voltage and then adjusting the bias magnetic fields as
demonstrated previously in [54]. Thus, the above measured results demonstrate that the newly realized BPF module possess versatile tuning capability
in both the passband center frequency and the corresponding BW.
In conclusion, a new BPF module which consists of a pair of magneticallytuned BSF, an RF choke, and an X-band passive composite-BPF with four
82
varactors connected to four open-circuited stubs on inexpensive RT/Duroid
6010 substrate has demonstrated versatile frequency tunability in center frequency and BW. Initially, the passband was varactor-tuned from 7.7-12.4
GHz to 11.4-17.5 GHz when the reverse bias voltage was varied from 2 to
22 V. The corresponding 3 dB BW was enlarged from 4.7 GHz to 6.1 GHz,
and the total frequency span was 9.8 GHz, namely from 7.7 GHz to 17.5
GHz. Then, the pair of the FMR-tuned BSF continuously compressed the
resultant passband toward the high end and low end frequencies with the 3
dB BW and frequency span drastically reduced to the range of 1.4 GHz and
1.0 GHz, respectively. By first setting the bias voltage and then adjusting
the bias magnetic fields, other passband and 3 dB BWs can also be obtained.
Thus, the combination of the varactor- and FMR- tuning enabled the resultant passband and its BW to be tuned freely with both large frequency
tunability and greatly improved frequency selectivity within the X- and Kubands.
83
10
-2V, no magnetic field
10
-22V, no magnetic field.
9.8 GHz
6.1 GHz
0
S-Parameter S21(dB)
S-Parameter S21(dB)
3250 and 4200 Oe fields, and -22V applied
1.4 GHz
9.8 GHz
4.7 GHz
0
1 GHz
-10
-10
-20
-20
-30
-30
-40
-40
-50
-50
-60
-2V, no magnetic field;
-22V, no magnetic field
2650 and 3500 Oe fields, and -2V applied
-60
4
6
8
10 12 14 16 18 20 22 24
4
6
Frequency (GHz)
8
10 12 14 16 18 20 22 24
Frequency (GHz)
(a)
(b)
10
-10V, 1800 and 3120 Oe fields
-4V, 2350 and 4150 Oe fields
S-Parameter S21(dB)
-16V, 2950 and 3250 Oe fields
-2V and -22V, no fields
9.8 GHz
0
1.2GHz
1GHz
1GHz
-10
-20
-30
-40
-50
-60
4
6
8
10 12 14 16 18 20 22 24
Frequency (GHz)
(c)
Figure 3.25: Tuning and narrowing of the passband of the new BPF module toward: (a). the
high-end; (b). the low-end, and (c). any frequency region within the maximum frequency
coverage of a span 9.8 GHz.
84
3.5
A Magnetically- and Electrically- Tunable Microwave
Phase Shifter
In Section 3.4, employment of the combined a magnetic- and electrical- tuning
technique for realization of a versatile BPF module for frequency tuning and
selection was presented in detail. In this section, application of the combined
tuning technique for realization of a new type of tunable microwave phase
shifter capable of large phase shift and moderate insertion loss variation [148]
is presented.
3.5.1
Device Architecture
The architecture of the new phase shifter is shown in Fig. 3.26(a). The
magnetically- tuned element phase shifter was realized by placing a YIG/GGG
thin film upon the 3-segment SILPFs meander line structure and inserted in
a magnetic field generated by a pair of NdFeB permanent magnets as shown
in Fig. 3.26(b). The electrically- tuned element phase shifter was realized
by connecting four varactors to the four open-circuited stubs of a passive
composite-BPF designed using the procedures presented in Ref.[57] and Section 3.4 and fabricated on RT/Duroid 6010 substrate. The passive compositeBPF was introduced because it would provide a larger spacing between the
adjacent open-circuited stubs and, thus, allowing for easy placement of the
85
varactors . The bias-T RF choke facilitated by a pair of radial stubs was also
included for feeding the dc supply through a dc bias pad such that the RF
transmission was unaffected by the dc connection [57].
Figure 3.26: (a) The architecture of the newly realized magnetically- and electrically- tuned
composite phase shifter, (b).Geometry of a microstrip transmission line with a YIG/GGG
film laid on a GaAs/Duroid substrate.
86
3.5.2
Experimental Results
A. Magnetically-Tuned Element Phase Shifter
The magnetically-tuned element phase shifter using the YIG/GGG-GaAs
layer structure was studied first. The theoretical calculation based on a
metal/dielectrics/YIG/metal layer structure predicts phase shifting at frequencies that neighbor the FMR frequency with large dynamic range and
small insertion loss variation [140, 171]. Fig. 3.27(a) and Fig. 3.27(b) show
the calculated phase shift and propagation loss at the operating frequency of
9.66 GHz with the bias magnetic field tuned from 2,610 to 3,320 Oe. For example, a phase shift of 122◦ /cm and an insertion loss variation of 0.3 dB were
predicted. Subsequent experimental study utilized the microstrip structure
with the YIG/GGG thin film flipped over the 350 um thick GaAs substrate
as shown in Fig. 3.26(b)).The YIG film has a nominal thickness of 6.8 μm and
a linewidth of 0.8 Oe at 9.2 GHz, saturation magnetization (4πMs ) of 1,750
Oe, and an anisotropy field (Han ) of 100 Oe. The external bias magnetic field
shown in Fig. 3.26(b)was applied in parallel to the microwave propagation
direction (the Y-axis). As mentioned previously, a pair of NdFeB permanent
magnets was used to provide the bias magnetic fields.
Fig. 3.28(a)-Fig. 3.28(b) show the measured phase shift (a) and the measured
S11 and S21 magnitudes (b) in the frequency range from 9.50 to 9.70 GHz.
87
9.50
0.1
9.52
9.54
9.56
9.58
9.60
9.62
9.64
9.66
9.68
9.70
0.1
Propagation Attenuation (dB)
3,320Oe
0.0
0.0
-0.1
-0.1
2,610 Oe
-0.2
-0.2
-0.3
-0.3
0.3dB
-0.4
-0.4
-0.5
-0.5
9.66GHz
-0.6
9.50
9.52
9.54
9.56
9.58
9.60
9.62
9.64
9.66
9.68
-0.6
9.70
Frequency (GHz)
(a)
9.50
-400
9.52
9.54
9.56
9.58
9.60
9.62
9.64
9.66
9.68
9.70
-400
Phase Shift (degree/cm)
3,320Oe
-425
-425
-450
-450
-475
-475
2,610 Oe
-500
-500
-525
-525
122o/cm
-550
-550
-575
-575
9.66GHz
-600
9.50
9.52
9.54
9.56
9.58
9.60
9.62
9.64
9.66
9.68
-600
9.70
Frequency (GHz)
(b)
Figure 3.27: (a).Calculated propagation loss and (b) phase shift at 9.66 GHz by tuning the
bias magnetic field from 2,610 to 3,320 Oe.
88
The measured phase shift of 53◦ (117.8◦ /cm) at 9.66 GHz with the bias
magnetic fields tuned from 2,610 to 3,320 Oe, shows a close agreement with
the theoretical prediction. The insertion loss variation of 2.05 dB and a
return loss larger than 11 dB are clearly shown in Fig. 3.28(b). The phase
shifts of 35◦ (77.8 ◦ /cm), 46.0◦ (102.2 ◦ /cm), and 66.0◦ (146.7 ◦ /cm) with
insertion loss variation of 1.1 dB and return loss greater than 11 dB were also
measured at the operating frequencies of 5.2, 7.75, and 11.5 GHz, respectively.
A microstrip meander line structure with two or three identical SILPFs in
cascade was constructed and utilized to obtain even greater phase shifts. For
example, the corresponding phase shifts were increased to 104.5◦ and 136.7◦ ,
respectively, with the same amount of magnetic field tuning, namely, from
2,610 and 3,320 Oe, with a moderate insertion loss variation of 2.95 dB at
the operating frequency of 9.66 GHz.
B. Magnetically- and Electrically- Tuned Composite Phase Shifter
To further increase the phase shift tuning range, an electrically- tuned varactor element phase shifter was constructed and integrated with the magneticallytuned element phase shifter just presented. The composite-BPF platform depicted in Fig. 3.26(a)) was fabricated on an inexpensive RT/Duroid 6010 substrate (254 μm thick) using photolithographic technique. Four Aeroflex/Metelics
GaAs Hyperabrupt varactor diodes (model number MGV-125-08) were con-
89
9.50 9.52 9.54 9.56 9.58 9.60 9.62 9.64 9.66 9.68 9.70
Phase Shift (degree)
30
30
3,320Oe
20
20
10
10
0
0
-10
-20
-10
2,610Oe
-20
-30
-30
-40
-40
-50
9.66GHz
-60
-50
-60
9.50 9.52 9.54 9.56 9.58 9.60 9.62 9.64 9.66 9.68 9.70
Frequency (GHz)
(a)
9.50 9.52 9.54 9.56 9.58 9.60 9.62 9.64 9.66 9.68 9.70
-2
3,320Oe
-2
-3
-4
-4
2,610Oe S
21
-8
-5
-6
-7
-10
3,320Oe
S11
-8
S21 (dB)
S11 (dB)
-6
-9
-12
-14
-10
2,610Oe
9.66GHz
-11
-12
9.50 9.52 9.54 9.56 9.58 9.60 9.62 9.64 9.66 9.68 9.70
Frequency (GHz)
(b)
(b)
Figure 3.28: Measured (a). S21 phase shift in degree, and (b). S21 and S11 magnitudes with
magnetic fields tuned from 2,610 to 3,320 Oe in the frequency range of 9.50 to 9.70 GHz.
90
nected to the ends of the four open-circuited stubs placed along the microstrip
using silver paste, and then tested by a vector network analyzer (Agilent
N5230A).
The combined magnetic- and electric- tunings was accomplished by first applying the same reversed bias voltage to the four varactors to facilitate electrical tuning of the phase shift. As shown in Fig. 3.29(a), by increasing the
voltage from -6 V to -18V, the resultant phase shift was increased continuously. For example, a maximum differential phase shift of 280◦ (23.3 ◦ /V)
was achieved using the voltage tuning at 10.37 GHz. Fig. 3.29(b) shows the
corresponding passband tuned by the revised bias voltage with an absolute
insertion loss measured around 5.3 dB, which was mainly caused by the significant series resistance (R) of the varactor diodes [57]. Clearly, the shaded
region in Fig. 3.29(a), corresponding to the frequency range 10.37 to 12.35
GHz suggests inherent capability of large phase shift and a relatively low
insertion loss variation of ± 0.6 dB. Thus, it maybe concluded that magnetic
tuning using FMR can be utilized to further increase the phase shift.
Subsequently, the phase shift was magnetically- tuned by placing a YIG/GGG
thin film with dimension of 6.8 μm × 8 mm × 8mm upon the 3-segment meander line structure and applying an external bias magnetic field to it. The
FMR frequency was set at 10.6 GHz (see the embedded figure of Fig. 3.30(b))
where the lowest insertion loss variation of ± 0.3 dB occurred due to electrical91
Phase Shift (degree)
0
12.35GHz
-200
-18V
o
280
-400
o
147.5
-6V
-9V
-12V
-15V
-18V
-600
-800
-6V
10.37 GHz
-1000
9
10
11
12
13
Frequency (GHz)
(a)
0
S21(dB)
-10
-20
-6V
-9V
-12V
-15V
-18V
-30
-40
6
8
10
12
14
Frequency (GHz)
16
(b)
Figure 3.29: The measured (a) phase shift in degree, and (b) S21 (dB) of an electricallytuned phase shifter by increasing the reversed bias voltage from 6V to 18V.
92
Phase Shift (degree)
100
10.87GHz
0
-100
-200
3,450Oe
-300
172.5o
-400
10.37 GHz
-500
10.0
2,700Oe
10.4
10.8
11.2
Frequency (GHz)
(a)
-2
3,450Oe
±1 dB
-4
2,700Oe
-8
0
-10
FMR
-10
S21(dB)
S21(dB)
-6
-20
-12
-30
-18V
-40
-14
10.20
-50
10.87 GHz
6
8 10 12 14 16 18
Frequency (GHz)
10.35
10.50
10.65
10.80
10.95
Frequency (GHz)
(b)
Figure 3.30: (a) Measured phase shift versus magnetic field, (b) the corresponding insertion
loss variation.
93
Total Phase Shift (degree)
400
350
Electrically-tuned
300
( -6V to -18V )
250
10.37 GHz
10.60 GHz
10.73 GHz
10.87 GHz
200
150
100
Magnetically-tuned
50
(2,700 Oe to 3,450 Oe)
0
Combined Electric and Magnetic Tunings
Figure 3.31: Total phase shifts achieved by combined magnetic and electric tunings.
tuning to further increase the phase shift. As shown in Fig. 3.30(a), by tuning
the magnetic field from 2,700 to 3,450 Oe, a further phase shift of 172.5◦ was
obtained with the corresponding insertion loss variation of ±1 dB at 10.87
GHz (See Fig. 3.30(b)).) Clearly, the frequency range from 10.37 to 10.87
GHz shadowed in Fig. 3.30(a) is the region capable of large phase shift and
small insertion loss variation as shown in Fig. 3.30(b)). As a result of combined magnetic and electric tunings, a total phase shift well over 360◦ , namely
406.5◦ in maximum, and a moderate insertion loss variation of 2.8 dB were
accomplished at 10.87 GHz. As shown in Fig. 3.31, for the frequency range
from 10.37 to 10.87 GHz, the measured total phase shifts are also larger than
94
360◦ with an insertion loss variation of ± 1.5 dB. Furthermore, by varying
the magnetic fields to set the FMR at a frequency within 10.35 to 12.35 GHz
with relatively small insertion loss variation (See Fig. 3.29(a)), a similarly
large total phase shift can also be achieved by using the combined tuning
technique.
In conclusion, a new microwave phase shifter that simultaneously employs
magnetic tuning of FMR in a YIG film and electrical tuning of varactors has
been constructed and tested. By setting the reversed bias voltage of 18 V
to the varactors together with application of bias magnetic field of 3,450 Oe
to the YIG film, a total phase shift of 406.5◦ with an insertion loss variation of ± 1.5 dB from 10.37 to 10.87 GHz was achieved. Such composite
phase shifter has demonstrated capability for providing a phase shift well
over 360◦ ,continuous tuning and thus potential for wideband applications.
In contrast to the hybrid tuned phase shifters that utilized either ferroelectric/ferromagnetic bilayer structures [144–147] or MSWs [145, 146], the composite phase shifter reported in [148] and presented here has demonstrated
significantly larger phase shift, smaller drive voltages, and small insertion loss
variation over a wide range of operating frequency .
95
Chapter 4
Propagation Characteristics in 1-D
and 2-D Magnonic Crystals:
Verification and Applications
Walker’s equation provided in Chapter 2 was employed to analyze the propagation characteristics in one-dimensional (1-D) and two-dimensional (2-D)
magnonic crystals (MCs) with the eigenvalue equations derived in matrix
form Ref.[104–106] by Professor Chen S. Tsai’s group. By solving the eigenvalue equations, the band structures associated with magnetostatic volume
waves (MSVWS) in 1-D and 2-D MCs at normal and oblique incidence have
been found and verified experimentally, and are first presented in this chapter. Applications of the magnetostatic backward volume waves (MSBVWs)
excited in 1-D and 2-D MCs for realization of tunable microwave filters and
96
phase shifters are then described and discussed.
4.1
MSWs in a Non-structured YIG Thin Film
The frequency response of the MSWs excited in a non-structured ferromagnetic yttrium iron garnet(YIG) thin film was measured and compared with
the simulated results. A square yttrium iron garnet/gadolinium gallium garnet (YIG/GGG) thin film with dimension of 8mm× 8mm × 100μm was used
for the purpose. The bias magnetic fields were generated by a pair of Nd-FeB permanent magnets (0.75” in diameter and 0.5” in thickness) attached to
an iron yoke to complete the magnetic circuit as reported in Ref.[54–57]. All
three types of MSWs were excited by setting the directions of the magnetic
fields as shown in Fig. 2.7.
The measured and simulated MSWs were compared in Fig. 4.2 with a close
agreement clearly seen. The simulation was carried out using Ansoft HFSS
software and the model shown in Fig. 4.1(a). Note that both simulated and
measured results show many fluctuating absorption peaks, which were caused
by the destructive/constructive interferences of the reflected MSWs from the
edges of the YIG thin-film. A YIG thin film of parallelogram shape as shown
in Fig. 4.1(b) was prepared to replace the original sample of rectangular
shape [80]. As shown in Fig. 4.3(a) and Fig. 4.3(b), both simulation and
97
(a)
(b)
Figure 4.1: MSWs excited in a non-structured YIG/GGG thin film of a (a) square, and (b)
parallelogram shape.
experimental results showed that the YIG thin film of parallelogram shape
was capable of eliminating the undesirable fluctuations. Such findings was
then applied to the subsequent 1-D and 2-D MCs experiments.
98
S21(dB)
-5
-10
-15
-20
-25
-30
-35
-40
-45
-50
-55
-60
X=5mm, Y=2mm
Simulation Result
Expremental Result
4.8
5.2
5.6
6.0
6.4
6.8
7.2
7.6
8.0
Frequency (GHz)
(a) HFSS simulation and experimental result
of MSFVW.
(b) HFSS simulation and experimental result
of MSFVW.
(c) HFSS simulation and experimental result of (d) HFSS simulation and experimental result of
MSBVW.
MSBVW.
(e) HFSS simulation and experimental result of (f) HFSS simulation and experimental result of
MSSW.
MSSW.
Figure 4.2: The simulation and experimental comparisons of MSWs in a rectangular
YIG/GGG sample.
99
!"#$%!&
'!!( &"#$%!&
(a)
Squre Shape
Parallelogram Shape
Fields Applied:1375 Oe.
YIG:8mm x 8mm x100um.
-20
-25
S21(dB)
-30
-35
-40
-45
-50
-55
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
Frequency (GHz)
(b)
Figure 4.3: The comparison of the MSBVWs excited in a non-structured rectangular and a
parallelogram YIG thin film with (a). simulated, (b) experimental results.
100
4.2
Propagation Characteristics of MSVWs in 1-D Magnonic
Crystal with Normal Incidence
The analytical approach based on Walkers equation presented in Ref. [104]
was used to calculate the band structures of the MSVWs in 1-D MC at normal
incidence and then verified experimentally. The validity of the analytical approach in determining and identifying the bandgaps of MSVWs in structures
with periodic variation in YIG thin film thickness was demonstrated.
4.2.1
Band Structures Calculation and Verification
Fig. 4.5 shows the calculated band structure of the MSFVW by using the
theoretical approach reported in Ref. [104] of a 1-D MC with geometrical
parameters: d1 = 10 μm, d2 = 5 μm, a1 = 5 μm, and a2 = 5 μm, where d1 ,
d2 , a1 , and a2 are defined in Fig. 4.4. The band structure shows clearly the
d1
d2
a1
a2
Figure 4.4: Unit cell in a 1-D MC. d1 and d2 are the thicknesses of non-etched and etched
magnetic layer, respectively. a1 and a2 are the widths of non-etched and etched layers, and
the lattice constant a = a1 + a2 .
101
Figure 4.5: Band structure of a 1-D magnonic crystal for MSFVW with parameters of
Ms = 140 G, H0 = 1850 Oe, n = 2, d1 = 10 μm, d2 = 5 μm, a1 = 5 μm, and a2 = 5 μm.
bandgaps expected in a MC.
The 1-D MC was designed and fabricated using standard photolithographic
technique. The SiO2 was first grown on the top surface of the YIG film as
the mask and orthophosphoric acid was used subsequently for wet etching
[182–185]. To suppress unwanted fluctuations, a parallelogram shape was
etched on a square YIG thin film and the periodic channel structure was
thereafter fabricated. The 3-D schematic of the designed 1-D MC is shown
in Fig. 4.6(a). The dimension of a unit cell is illustrated in Fig. 4.4. The
period length of the unit cell a is 200 μm, with the etched channel width a2
102
Periodic structure
with 20 periods
YIG
GGG
Input
50 Ω Microstrip
Tranceiver
Output
(a)
(b)
Figure 4.6: (a). The 3-D model of the 1-D MC sample; (b). the SEM image of the 1-D MC
structure.
103
of 50 μm , and height of the etched channel d2 of 65 μm after etching off 35
μm. The SEM image is shown in Fig. 4.6(b).
The MSWs were excited and received by mounting the 1-D MC upon a delay
line structure. The arrangement for excitation and reception of the MSFVWs
and MSBVWs is shown in Fig. 4.7, in which K represents the wave vector
and M0 the direction of the external fields generated from the permanent
magnet pairs.
The analytical results were first compared with the early results for band
gaps reported by others [124]. In [124], the experimental results suggest
that the bandgaps fall approximately at 7.160, 7.120, 7.070, and 7.030 GHz.
Fig. 4.8 shows the bandgaps (circled frequencies) predicted using our method,
namely, 7.157, 7.133, 7.091, and 7.024 GHz. Clearly, the results calculated
by our method are in good agreement with that reported in [124].
A series of experiments at different bias magnetic fields were also carried out
on MSBVWs and MSFVWs. They consistently showed very good agreement
between the experimental and the calculated results. The effect of magnonic
bandgaps on the MSBVW is shown in Fig. 4.9. The 20 unit cells MC used
was fabricated using photolithography and wet etching. A pair of 50 Ω transmission lines with 5 mm separation was used as a transceiver. The measured
spectrum of Fig. 4.9(a) obtained at the bias field of 1,650 Oe clearly shows
the three bandgaps, A, B, and C, created by the MC.
104
0
(a)
K
M0
(b)
Figure 4.7: Experimental setup for (a) MSFVWs, and (b) MSBVWs excitation and bandgap
tunability test.
105
7.25
Frequency (GHz)
7.2
7.15
7.1
7.05
7
6.95
6.9
0
0.1
0.2
0.3
k (2/a)
0.4
0.5
y
Figure 4.8: The band structure calculated by our approach with the geometry and material
parameters presented in [124].
The calculated band structure of the MC with nearly identical parameters presented in Fig. 4.9(b) clearly shows the existence of bandgaps. The
bandgaps A’, B’, and C’ are the first three calculated bandgaps corresponding
to the measured bandgaps A, B, and C, respectively, in Fig. 4.9(a). Table 4.1
lists the frequencies of the first three magnonic bandgaps. Clearly, an excellent agreement between the experimental and calculated results was obtained.
Experiments were also conducted to excite MSFVWs in 1-D MC. The measured spectrum of MSFVWs at a bias field of 1,350 Oe is shown in Fig. 4.10(a).
A comparison between Fig. 4.10(a) and the calculated band structure shown
106
%!
% (a) Experimental result of 1-D MC with bias magnetic field of 1650 Oe.
7
Frequency (GHz)
6.5
A’
B’
C’
6
5.5
5
4.5
0
0.1
0.2
0.3
ky (2/a)
0.4
0.5
(b) Theoretical result of 1-D MC with bias magnetic field of 1650 Oe.
Figure 4.9: (a) Measured spectrum of MSBVW in a MC with the following parameters:
Ms = 140 G, H0 ≈ 1650 Oe, d1 = 100 μm, d2 ≈ 80 μm, a1 ≈ 85 μm, and a2 ≈ 75 μm.
(b) Calculated band structure of MSBVW in the 1-D MC with the following parameters:
Ms = 140 G, H0 = 1650 Oe, n = 2, d1 = 100 μm, d2 = 80 μm, a1 = 85 μm, and a2 = 75 μm.
107
Table 4.1: Comparison of the first two bandgap frequencies between experimental and theoretical results with bias magnetic field H0 of 1,650 Oe.
Experimetal
Calculated
Difference (%)
Mid-gap Frequency
A: 6.565 B: 6.14
A’: 6.516 B’: 6.216
0.75%
1.23%
(GHz)
C: 5.935
C’: 5.893
0.71%
Table 4.2: Comparison of the first two bandgap frequencies between experimental and theoretical results with bias magnetic field H0 of 1,350 Oe.
Experimetal
Calculated
Difference (%)
Mid-gap Frequency (GHz)
A: 3.94
B: 4.29
A’: 3.9545 B’: 4.3235
0.37%
0.78%
in Fig. 4.10(b) as listed in Table 4.2 also shows a close agreement between
the two.
The tunability of the MSBVWs and that of the MSFVWs were studied subsequently. As shown in Fig. 4.11(a), by increasing the bias magnetic field from
1,150 Oe to 2,030 Oe, three bandgaps of the MSFVWs marked A, B and C,
respectively, were identified. The tunability of the bandgaps toward a higher
frequency with the increase of the bias magnetic field was also clearly demonstrated. Similarly, the tunability of the bandgaps marked D-G of the MSBVWs in a MC under different bias magnetic fields is shown in Fig. 4.11(b).
The comparison between the experimental and theoretical results is presented
in Table 4.3 and a good agreement between the two results was achieved, suggesting the validity of the approach biased on Walker’s equation in bandgaps
calculation at normal incidence.
108
(a) Experimental result of 1-D MC with bias magnetic field of 1350 Oe.
6
Frequency (GHz)
5.5
5
4.5
B’
A’
4
3.5
0
0.1
0.2
0.3
k (2/a)
0.4
0.5
y
(b) Theoretical result of 1-D MC with bias magnetic field of 1350 Oe.
Figure 4.10: The experimental and theoretical results of MSFVW propagating in 1-D MC
with bias magnetic field, H0 , of 1350 Oe.
109
Measured MSFVWs Bandgaps
Insertion Loss S21(dB)
-10
-20
H0=1150Oe
H0=1570Oe
H0=2030Oe
-30
B
-40
C
A
-50
-60
-70
(Dotted lines): Non-structured YIG film.
( Solid lines): 1-D Magnonic Crystals.
3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5
Frequency (GHz)
(a)
Measured MSBVWs Bandgaps
Insertion Loss S21(dB)
-10
(Dotted lines): Non-structured YIG film.
( Solid lines): 1-D Magnonic Crystals.
-20
-30
-40
D
E
F
G
-50
H0=1075Oe
H0=1475Oe
-60
3.5
4.0
4.5
5.0
5.5
Frequency (GHz)
6.0
6.5
(b)
Figure 4.11: Measured bandgaps under different magnetic fields of (a). MSFVW, bandgaps
marked as A-C and (b). MSBVWs, bandgaps marked as D-G.
110
Table 4.3: Comparison between measured MSFVWs and MSBVWs in a 1-D MC with analytically calculated Results. UNIT:[GHz]
MSFVWs Mid-gap Freq.
MSBVWs Mid-gap Freq.
Experimetal
A: 3.73 B: 4.98 C: 6.23 D:4.33 E:5.45 F:5.64 G:6.05
Calculated
A’: 3.76 B’: 4.89 C’: 6.23 D’:4.21 E’:5.11 F’:5.71 G’:5.99
Difference (%) 0.93%
1.82%
1.08%
2.8%
1.08% 1.19% 0.93%
In conclusion, the validity of the eigenvalue equations derived from Walker’s
equation for analysis of the propagation characteristics of MSVWS in 1-D
MC with periodic variation in magnetic layer thickness has been established.
An excellent agreement between the calculated bandgaps for the MSVWs
using the proposed approach and the experimental results has been achieved.
Tuning of the bandgaps in MSFVWs and MSBVWs via a bias magnetic field
has also been demonstrated.
111
4.3
Propagation Characteristics of MSVWs in 1-D MC
with Oblique Incidence
In the last Section, the results of theoretical and experimental studies on the
bandgaps of MSVWs in 1-D MC with periodic variation in YIG/GGG layer
thickness at normal incidence [104] are presented. The results of subsequent
theoretical and experimental studies for the case of oblique incidence [105]
are presented in this Section.
4.3.1
Bandgaps Calculation and Verification
The relative propagation direction of the incident MSVWs with respect to
the y-oriented 1-D MC is shown in Fig. 4.12 in which k and θ are the wave
number and the incident angle of the MSVWs, respectively. The bias magnetic field H0 is applied along the y or the z direction to excite the MSFVWs
or MSBVWs, respectively.
The bandgaps of the MSVWS in a 1-D MC at oblique incidence were calculated by using the approach reported in [105]. In order to elucidate the
propagation characteristics at different incident angles, 2-D band structures
were constructed to present the calculated results. Fig. 4.13 and Fig. 4.14 are
such 2-D band structures for the MSFVWs and the MSBVWs, respectively,
with the incident angle ranging from -45◦ to 45◦ in the 1-D MC with unit cell
112
Figure 4.12: Oblique incidence of MSVWs upon a 1-D MC, when k is the wave number of
the MSVWs and θ is the incident angle.
dimensions of a1 = 50 μm,a2 = 50 μm, a = 100 μm , d1 = 100 μm, and d2 =
80 μm as shown in Fig. 4.4.
The theoretical approach enabled efficient calculation of the band structures
at different θ together with the corresponding bandgap information clearly
demonstrated on the 2-D band structures. For example, from Fig. 4.13 for
the MSFVWs, the first band (in blue to green) can be readily found to be
from 5.531 GHz to 6.453 GHz at θ = 0◦ and from 5.531 GHz to 6.804 GHz
at θ = 45◦ , respectively. Similarly, the second band (in green to orange) are
readily found to be from 6.597 GHz to 7.152 GHz at θ = 0◦ and from 6.935
GHz to 7.152 GHz at θ = 45◦ , respectively. Furthermore, Fig. 4.15(a) and
113
= 0o
Frequency (GHz)
8
7.5
7
Bandgap
6.5
0.5
6
5.5
0
0
0.1
0.2
0.3
0.4
k (2S/a)
0.5 -0.5 k (2S/a)
x
y
Figure 4.13: 2-D band structure of the MSFVWs in a 1-D MC. The range of incident angle
θ is from -45◦ to 45◦ . The dimensions of the unit cell are a1 = 50 μm, a2 = 50 μm, a =
100 μm , d1 = 100 μm, and d2 = 80 μm as shown in Fig. 4.4. The saturation magnetization
4πMs is 1760 G. The bias magnetic field is 1975 Oe.
4.15(b) clearly show the variation of bandgaps at versus the incident angle
for the MSFVWs and the MSBVWs, respectively. The mid-gap frequency
of the bandgap increases as the incident angle increases. Experiments were
thereafter conducted to verify the correctness of the calculated results [105].
4.3.2
A. MSFVWs, Incident Angle θ = 0◦ , 14◦ , and 25◦ ; Bias
magnetic field H0 =1650Oe
Experiments were first carried out to verify the calculated bandgaps of the
MSVWs propagating in the 1-D MC as shown in Fig. 4.16(a) with oblique
114
Frequency (GHz)
8
Bandgap
7.5
= 0o
7
6.5
6
5.5
0
0.5
0.1
0
0.2
0.3
0.4
0.5 -0.5
k (2S/a)
k (2S/a)
x
y
Figure 4.14: 2-D band structure of the MSBVWs in a 1-D MC. The range of incident angle
θ is from -45◦ to 45◦ . The dimensions of the unit cell, the saturation magnetization, and the
bias magnetic field are given in the caption of Fig. 4.13.
incidence using the same measurement setup as the one used previously [104].
The periodic channels of the 1-D MC sample was formed by wet etching upon
the YIG/GGG thin-film with a thickness of 100 μm. The unit cell of the
periodic structure has the dimensions of a1 = 90μm, a2 = 70μm, d1 = 100
μm, and d2 = 80μm . Variation of the incident angle was accomplished by
rotating the 1-D MC sample while maintaining the position of the microstrip
transducers and the direction of the bias magnetic field (see Fig. 4.16(b)).
As shown in Figs. 4.17 (a), (c), and (e), the circled dips marked with letters
A to D are the measured bandgaps of the MSFVWs with the incident angles
of 0◦ , 14◦ , and 25◦ , respectively, at the bias magnetic field of 1,650 Oe. The
115
(a)
(b)
Figure 4.15: Variation of bandgaps with the incident angle:(a) MSFVWs,(b) MSBVWs.
The mid-gap frequency of the bandgap increases as the incident angle increases, while the
width of the bandgap decreases as the incident angle increases.
116
1-D MC
θ
Microstrip
Transducers
Figure 4.16: (a) The unit cell of a 1-D MC with periodic variation in layer thickness. a1
and a2 , and d1 and d2 are, respectively, the width and the thickness of unetched and etched
parts of the YIG film. (b) Geometry of a 1-D MC and microstrip transducers.
corresponding calculated band structures are shown in Figs. 4.17 (b), (d), and
(f), respectively, with the bandgaps marked A’ to D’. A comparison between
the experimental and the theoretical results is presented in Table 4.4. Note
that a very slight difference (<1%) between the two results was observed.
4.3.3
B. MSBVWs, Incident Angle θ = 0◦ , 14◦ , and 25◦ ; Bias
magnetic field H0 = 1,385 Oe
Similarly, experiments were carried out to measure the bandgaps of the MSBVWs at the incident angles of 0◦ , 14◦ , and 25◦ , and the bias magnetic field
of 1,385 Oe. Variation of the incident angle was also accomplished in the
same manner as in the experiments with the MSFVWs. Fig. 4.18(a) shows
117
6.5
Insertion Loss S21(dB)
A
MSFVW
0
θ=0
H0=1650Oe
-30
Frequency (GHz)
-25
-35
-40
6
5.5
5
A'
-45
4.4
4.6
4.8
5.0
4.5
0
5.2
0.1
Frequency (GHz)
6.5
MSFVW
0
θ=14
H0=1650Oe
Frequency (GHz)
Insertion Loss S21(dB)
B
-30
-35
-40
4.6
4.8
5.0
Frequency (GHz)
6
5.5
5
B'
4.5
0
5.2
0.1
(c)
C
Frequency (GHz)
Insertion Loss S21(dB)
-40
4.6
0.4
0.5
6
-30
-50
0.2
0.3
ky (2S/a)
(d)
MSFVW
D θ=250
H0=1650Oe
-20
0.5
(b)
-20
-45
4.4
0.4
y
(a)
-25
0.2
0.3
k (2S/a)
4.8
5.0
5.2
Frequency (GHz)
5.4
5.5
5
D'
C'
4.5
0
0.1
0.2
0.3
k (2S/a)
0.4
0.5
y
(e)
(f)
Figure 4.17: Experimental and calculated results of the MSFVWs propagating in a 1-D MC
with incident angle (a), (b):θ = 0◦ ; (c), (d):θ = 14◦ ; (e), (f):θ = 25◦ under a bias magnetic
field of 1,650 Oe. (a) Experimental Resutls,θ = 0◦ ; (b) Calculated Results θ = 0◦ ; (c)
Experimental Resutls,θ = 14◦ ; (d) Calculated Results θ = 14◦ ; (e) Experimental Resutls,θ
= 25◦ ; (f)Calculated Results θ = 25◦ .
118
Table 4.4: Calculated and Measured MSFVWS Bandgaps Comparison
Incident Angle
Experimetal
Calculated
Difference (%)
Mid-gap Frequency(GHz)
θ=0
θ = 14 ◦
θ = 25 ◦
A: 4.82 B: 4.83
C: 4.81 D:5.01
A’: 4.80 B’: 4.82 C’: 4.78 D’:4.98
0.40%
0.20%
0.62%
0.60%
◦
the measured bandgaps of the MSBVWs with the incident angle of 0◦ and
the bias magnetic field of 1,385 Oe. The calculated band structures and
bandgaps are shown in Fig. 4.18 (b). The measured and calculated bandgaps
of the MSBVWs with the incident angle of 14◦ , and 25◦ are shown in Fig. 4.18
(c) and (e), and (d) and (f), respectively. Again, as shown in Table 4.5, an
excellent agreement between the experimental and the theoretical results was
achieved.
Table 4.5: Calculated and Measured MSBVWS Bandgaps Comparison
(a) θ = 0◦
Angle
Experimetal
Calculated
Difference (%)
A: 4.620
A’: 4.721
2.16%
Mid-gap
B: 4.99
B’: 4.891
2.00%
Frequency(GHz)
C: 5.172 D:5.461
C’: 5.162 D’:5.482
0.19%
0.36%
E:5.761
E’:5.760
0%
(b) θ = 14◦
Angle
Experimetal
Calculated
Difference (%)
θ = 14◦ , Mid-gap Frequency(GHz)
F: 5.044 G:5.243
H: 5.436 I:5.723 J:5.787
F’: 5.043 G’: 5.242 H’: 5.446 I’:5.656 J’:5.804
0.02%
0.02%
0.18%
1.17%
0.29%
(c) θ = 25◦
Angle
Experimetal
Calculated
Difference (%)
K: 5.04
K’: 5.13
1.78%
θ = 14◦ , Mid-gap
L:5.24
M: 5.36
L’: 5.29 M’: 5.43
1.00%
1.30%
119
Frequency(GHz)
N:5.36 O:5.68
N’:5.59 O’:5.72
0.54% 0.70%
P:5.84
P’=5.81
0.51%
-10
MSBVWs
0
θ =0
H0=1385 Oe
-30
6
Frequency (GHz)
Insertion Loss S21 (dB)
-20
-40
BC
-50
-60
D
A
4.8
5.2
D'
5.5
C'
5 B'
A'
4.5
E
-70
4.4
E'
5.6
Frequency (GHz)
4
0
6.0
0.1
0.2
0.3
ky (2S/a)
(a)
0.4
0.5
(b)
-10
-20
6
H0=1385Oe
-30
-40
H
F
-50
I J
5.6
G
4.8
5.2
J'
I'
Frequency (GHz)
Insertion Loss S21(dB)
MSBVW
0
θ =14
H'
5.5
G'
F'
5
4.5
0
6.0
0.1
Frequency (GHz)
P
M
NO
6
P'
5.8
Frequency (GHz)
Insertion Loss S21(dB)
-30
K L
0.5
(d)
MSBVW
0
θ =25
H0=1385 Oe
-40
0.4
y
(c)
-20
0.2
0.3
k (2S/a)
O'
N'
5.6
M'
5.4
5.2
L'
K'
5
-50
4.8
5.2
5.6
4.8
0
6.0
0.1
0.2
0.3
0.4
0.5
k (2S/a)
y
Frequency (GHz)
(e)
(f)
Figure 4.18: Experimental and calculated results of the MSBVWs propagating in a 1-D MC
with incident angle (a), (b):θ = 0◦ ; (c), (d):θ = 14◦ ; (e), (f):θ = 25◦ under a bias magnetic
field of 1,385 Oe. (a) Experimental Resutls,θ = 0◦ ; (b) Calculated Results θ = 0◦ ; (c)
Experimental Resutls,θ = 14◦ ; (d) Calculated Results θ = 14◦ ; (e) Experimental Resutls,θ
= 25◦ ; (f)Calculated Results θ = 25◦ .
120
In summary, as shown in Tables 4.4 and 4.5, the measured bandgaps of
the MSFVWs and the MSBVWs at the three incident angles of 0◦ , 14◦ ,
and 25◦ are all in excellent agreement with the calculated results using the
approach reported in Ref. [105]. One additional bandgap was created as the
incident angle was increased from 14◦ , and 25◦ . Thus, the capability of the
new analytical approach for calculation of the bandgaps of both types of the
MSVWs at oblique incidence in the 1-D MCs has been clearly demonstrated.
4.4
Propagation Characteristics of MSVWs in 2-D Magnonic
Crystal
In Sections 4.2 and 4.3, the propagation characteristics of the MSVWs in the
1-D MC at normal and oblique incidence [104, 105] are presented. The research was further extended to the propagation characteristics of the MSVWs
in 2-D MCs, at normal and oblique incidence and the findings are presented
in this Section.
4.4.1
Bandgaps Calculation and Verification
The theoretical approach based on Walker’s equation [106] was again employed to analyze the 2-D MC band structure. Fig. 4.19 (a) and (b) show the
geometric profile of the 2-D MCs in square lattice used in the numerical cal121
Figure 4.19: (a) Geometry and reduced first Brillouin zone in 2-D MCs of square lattice
culation, in which a is the lattice constant, R is the radius of the etched hole,
d1 and d2 are the thicknesses of unetched and etched YIG layer, respectively.
The resulting band structure is presented along the first reduced Brillouin
zone, Γ-X-M , as shown in Fig. 4.19(c), in which Γ: kx = 0, ky = 0, X: kx =
π/a, ky = 0, and M : kx = π/a, ky = π/a.
Figs. 4.20(a)-(d) are the calculated band structures for MSVWs which show
the first three passbands (PBs) and the first bandgap obtained with H0 =
1,650 Oe, MS = 1,750 Gauss for a YIG layer, with the geometric parameters: a = 200 μm, R = 0.32a, and d1 = 100μm, and d2 = 55 and 35 μm.
Specifically, the colored lines represent the passbands in which the MSVWs
can propagate through the periodic structure at different frequencies. The
horizontal darkened bands designate the bandgaps in which the MSVWs cannot propagate in the MCs due to the destructive interference. Besides, the
dispersion relations of the passbands are also readily available. As clearly
122
(a)
(b)
(c)
(d)
Figure 4.20: Calculated band structures of MSVWs in a 2-D MC at H0 = 1650 Oe, MS =
1750 Gauss, and the geometric parameters:a = 200 μm, R = 0.32a, and d1 = 100μm, and
the corresponding wave numbers:Γ: kx = 0, ky = 0; X: kx = 0.5(2π/a) = 157.08 cm−1 ,ky =
0; M : kx = ky =0.5(2π/a) = 157.08 cm−1 : (a) MSFVWs, d2 = 55μm, (b) MSFVWs, d2 =
35μm, (c) MSBVWs, d2 = 55μm, (d) MSBVWs, d2 = 35μm.
123
seen from Figs. 4.20, the mid-gap frequency and the bandgap width change
drastically as d2 was varied from 55 to 35 μm. Therefore, the thickness variation achieved by varying d2 is an important parameter to obtain the band
structures desired.
Fig. 4.21(a) and (b) show the calculated bandgaps versus the incidence angle
for the MSVWs. The blue line and the green line are for the first and the
second bands, respectively. The area in between corresponds to the bandgap
at respective incidence angle. It shows that at all incidence angles (-45◦ to
45◦ ) a bandgap exists from 8.844 to 8.853 GHz for the MSFVWs and 5.891
to 5.935 GHz for the MSBVWs. This is in stark contrast to the case with the
1-D MCs. For example, at 6.5 GHz, the bandgap only ranges from -15◦ to
15◦ of incidence angle as shown in Fig. 4.21(c) for the MSFVWs in the 1-D
MCs.
The approach based on Walkers equation has thus demonstrated its capability
for fast calculation and design of the desired band structure through a joint
setting of the bias magnetic field H0 and the periodic geometric parameters,
e.g. d2 . Its correctness was thereafter verified experimentally.
A. MSFVWs in a 2-D MC
Experiments were conducted to verify the calculated bandgaps of the MSVWs
propagating in the 2-D MCs. The samples were prepared by photolithogra124
(a)
(b)
(c)
Figure 4.21: Calculated bandgaps versus the incidence angle of the MSVWs: (a) For the
MSFVWs in a 2-D MC. Dark area shows that the bandgap exists at all incidence angles; (b)
For the MSBVWs in a 2-D MC. Dark area shows that the bandgap exists at all incidence
angles; and (c) For the MSFVWs in a 1-D MC. The dark area shows a limited range of
incidence angle.
125
(a)
(b)
Figure 4.22: The optical image of the 2-D MC sample with square lattice (a) and the setup
for experiments (b).
phy and wet-etching techniques on a 100μm YIG/GGG thin film as shown
in Fig. 4.22(a). The 2-D periodic etched holes of square lattice has the dimensions of a = 200 μm, R = 0.32a, d1 = 100 μm, and d2 = 52 μm with
reference to Fig. 4.19(a) and Fig. 4.19(b). Note that the hexagonal shape of
the etched holes was due to preferential etching. The MSVWs were excited
and received by a pair of 50 copper microstrip transmission lines as shown
in Fig. 4.22(b).
126
Table 4.6: Comparison of mid-gap frequency and bandgap width at Γ-X and M -Γ between
experimental results and calculated results for MSFVWs.
H0 (Oe)
Experimetal
Calculated
Mid-gap Freq./Bandgap width(GHz)
3000
3125
3250
A: 8.50/0.022 B: 8.88/0.020 C: 9.28/0.025
A’:8.49/0.009 B’:8.85/0.011 C’: 9.28/0.009
Firstly, the MSFVWs were excited by applying a bias magnetic field H0 in
the direction perpendicular to both the wave propagation direction and the
sample plane, namely, the Z-axis. Measurements of the insertion losses were
carried out to determine the bandgaps of the MSFVWs at H0 of 3,000, 3,125,
and 3,250 Oe. As shown in Fig. 4.23, the corresponding bandgaps A, B,
and C of 8.50, 8.88, and 9.28 GHz, respectively, are clearly seen. These
measured values are in a very good agreement with the calculated results
designated in the colored areas A’, B’, and C’ in Fig. 4.24 with the mid-gap
frequencies of 8.49, 8.85, and 9.28 GHz, respectively. A comparison between
the experimental results and the calculated bandgaps at the three values of
H0 are shown in Table 4.6, and it shows a very good agreement.
B. MSBVWs in a 2-D MC
Subsequently, the MSBVWs were excited by applying H0 in parallel direction
to the propagation direction as shown in Fig. 4.22(b). Fig. 4.25 shows the
measured bandgaps A, B, and C at H0 = 1,160, 1,375, and 1,600 Oe, respectively. As shown in Fig. 4.26, the calculated bandgaps marked A’, B’ and
127
Figure 4.23: Comparison between experimental results and calculated results of MSFVWs
at three H0 : 3,000, 3,125, and 3,250 Oe. The passband and bandgaps could be adjusted by
tuning the H0 .
C’ with the corresponding mid-gap frequencies of 5.61, 6.25, and 6.91 GHz,
respectively, are in a very good agreement with the measured values. Table
4.7 lists both the measured and calculated bandgaps and bandgap widths at
the three values of H0 . Clearly, the tunibility of the pass and stop bands by
the bias magnetic field has been demonstrated.
Experiments were also carried out to measure the angular dependence of the
bandgap associated with the 2-D MCs. The variation of incidence angles
of the MSBVWs was facilitated by rotating the 2-D MC sample around the
Z-axis as depicted in Fig. 4.27.
As shown in Fig. 4.28, the bandgaps A, B, C, and D are clearly seen in the
128
Figure 4.24: Calculated band structures of the MSFVWs at three H0 : 3,000, 3,125, and
3,250 Oe.
129
Figure 4.25: Comparison between measured and calculated results of the MSBVWs at three
values of H0 : 1,160, 1,375, and 1,600 Oe. The passband and bandgaps were tuned by varying
the H0 .
Table 4.7: Comparison of Mid-gap frequency and bandgap width at Γ-X and M -Γ between
experimental results and calculated results for MSFVWs.
H0 (Oe)
Experimetal
Calculated
Mid-gap Freq./Bandgap width(GHz)
1,160
1,375
1,600
A: 5.55/0.035 B: 6.19/0.020 C: 6.89/0.040
A’:5.61/0.025 B’:6.25/0.021 C’: 6.91/0.031
measured insertion losses of the MSBVWs propagating in the 2-D MC sample
at the incidence angle of 0◦ , 10◦ , 20◦ , and 30◦ , respectively, at H0 = 1,600 Oe.
Table 4.8 shows the mid-gap frequency of each bandgap and a high degree
of consistency across different incidence angles was observed. In other words,
the bandgap of MSBVWs in the 2-D MCs at a given frequency exists in a
much larger range of incidence angle than in the 1-D MCs [104, 105],.
In conclusion, an expanded analytical approach based on Walkers equation
130
Figure 4.26: Calculated band structures for MSBVWs at three values of H0 : 1,160, 1,375,
and 1,600 Oe.
Table 4.8: Mid-gap Frequencies of the Bandgaps of MSBVWs versus the Incidence Angle
Incident Angle
Experimental
Mid-gap Frequency (GHz)
θ=0◦
θ=10◦ θ=20◦
θ=30◦
A: 6.90 B: 6.90 C: 6.92 D:6.88
131
Figure 4.27: Relative direction of incident MSBVWs and the 2-D MC. The incidence angle
of the MSBVWs (θ) was varied by rotating the sample around the Z-axis.
was employed to study the propagation characteristics versus the bias magnetic field for both types of the MSVWs in 2-D MCs made of periodic thickness variation of square lattice in an YIG layer. Experiments were conducted
to verify the calculated results, and very good agreements between the measured and calculated results were obtained.
4.5
Magnonic Crystal Based Tunable Microwave Filters and Phase Shifter
In this Section, the applications of the MSBVWs excited in a 1-D and 2D MC for realization of magnetically tunable microwave filters and phase
shifters are presented.
132
Figure 4.28: Insertion loss measurement of MSBVWs in the 2-D MC sample at the incidence
angles of 0◦ , 10◦ , 20◦ , and 30◦ , and H0 =1,600 Oe.
4.5.1
MC-Based Tunable Microwave Filter
By applying a bias magnetic field (H0 ) of 1,200 Oe on the 1-D MC, the
excited MSBVW is seen to function as a BPF as shown in Fig. 4.29(a)(in
black). Furthermore, the bandgap arising from the periodic structure of the
MC facilitates filtering function of a BSF at a center frequency of 4.95 GHz
with a 3 dB BW of 100 MHz. By slightly decreasing the bias magnetic field
from 1,200 Oe to 1,180 Oe or slightly increasing the field from 1,200 Oe to
1,250 Oe, the center frequency of the BSF was tuned to 4.875 GHz and 5.05
GHz, respectively, as shown in Fig. 4.29(a). Similar results were also obtained
133
in a 2-D MC. By setting the bias magnetic field at 1,265 Oe, a BSF embedded
in a BPF with a center frequency of 4.90 GHz and a 3 dB BW of 90 MHz
was measured as shown in Fig. 4.29(b), a small variation of the fields by ±
15 Oe centered at 1,265 Oe, the BSF’s center frequencies were tuned to 4.9
and 4.975 GHz, respectively, with the corresponding 3 dB BW remained at
90 MHz.
4.5.2
MC-Based Tunable Phase Shifter
The capability of tunable phase shifting via the MSBVWs excited in a 1-D
and 2-D MCs and thus realization of magnetically tunable phase shifter were
also stuided. As shown in Fig. 4.30(a), by increasing the bias magnetic field
applied on the 1-D MC from 1,180 to 1,200 Oe, a differential phase shift of
about 78◦ in average and an insertion loss variation of ±1.5 dB were measured
in a frequency range from 4.70 to 4.85 GHz. Further tuning of the bias field
from 1,200 to 1,250 Oe produced a phase shift of about 267
◦
at an insertion
loss of ± 1.5 dB for the frequency range from 4.70 to 4.85 GHz as shown in
Fig. 4.31(a) and Fig. 4.31(b), respectively.
The differential phase shift on the left and right passbands of the bandgap in
a 2-D MC as shown in Fig 4.29(b) was also studied. As shown in Fig. 4.32(a),
by tuning the field from 1,250 to 1,265 Oe, a maximum phase shift of 190.7◦ at
4.82 GHz was measured on the left passband with an insertion loss variation
134
-10
S21(dB)
-20
1-D MC, 1,180 Oe applied
1-D MC, 1,200 Oe applied
1-D MC, 1,250 Oe applied
-30
-40
-50
-60
4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8
Frequency (GHz)
(a)
-10
S21(dB)
-20
2D MC 1,250Oe ;
2D MC 1,280 Oe
left passband
2D MC 1,265Oe;
right passband
-30
-40
-50
-60
4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8
Frequency (GHz)
(b)
Figure 4.29: Excitation of MSBVWs to function as a tunable BPF with a BSF embedded in
(a) 1-D MC with 1,180, 1,200 and 1,250 Oe applied, and (b) 2-D MC with 1,250 Oe, 1,265
Oe and 1,280 Oe applied, respectively.
135
of ± 1.5 dB in the frequency range from 4.76 to 4.85 GHz. Further tuning of
the magnetic field from 1,265 to 1,280 Oe, a maximum phase shift of 151.3◦
was measured at 4.87 GHz for the frequency range from 4.81 to 4.90 GHz
with an insertion loss variation of ± 1.5 dB. Similarly, by adjusting the bias
field from 1,250 to 1,650 Oe, an average differential phase shift of 148.5◦ was
obtained on the right passband with an insertion loss variation ± 1 dB for the
frequency range from 4.975 to 5.1 GHz. Further increase of the bias magnetic
field to 1,280 Oe resulted in an average phase shift of 258.5◦ with ± 1 dB
insertion loss variation for the frequency range from 5.02 to 5.16 GHz (See
Fig. 4.32(b)).
4.5.3
Discussion
As presented in the last two subsections, the bandgaps associated with the
MSBVWs in 1-D and 2-D MCs are capable of functioning as BSFs. The
measured 3 dB BW of the resulting BSFs are around 90 MHz which is much
smaller than that of FMR-tuned BSFs [55]. For example, a 3 dB BW of 1.3
GHz was measured at a FMR peak absorption frequency of 5.2 GHz with
a bias magnetic field of 1,020 Oe. Note that the smaller the 3 dB BW,
the better the frequency selectivity. Furthermore, a maximum phase shift
of 172.5◦ with a tuning rate of 0.23◦ /Oe was measured with the FMR-tuned
phase shifter [148]. In contrast, as presented in previous subsections, the
136
MC-based tunable phase shifter has demonstrated a much larger phase shift
up to 309◦ with 50 Oe variation (6.08◦ /Oe) in 1-D MC or 321◦ with 15 Oe
variation (21.4◦ /Oe) in 2-D MC. It has demonstrated a much larger tuning
rate.
137
-10
1-D MC, 1,200 Oe applied
1-D MC, 1,180 Oe applied
S21(dB)
-20
4.7
4.85
-30
-40
-50
-60
4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8
Frequency (GHz)
(a)
Phase Shift (Degree)
0
1-D MC, 1,180 Oe applied
1-D MC, 1,200 Oe applied
o
83.3
-400
-800
o
89.5
-1200
Δ S21 (dB) = ± 1.5 dB
4.7
4.85
-1600
4.65
4.70
4.75
4.80
4.85
4.90
Frequency (GHz)
(b)
Figure 4.30: The measured (a) S21 (dB) and (b) the corresponding phase shift in a 1-D MC
with a field of 1,180 and 1,200 Oe applied.
138
-10
1-D MC, 1,250 Oe applied
1-D MC, 1,200 Oe applied
S21(dB)
4.925
4.75
-20
-30
-40
-50
-60
4.2
4.5
4.8
5.1
5.4
5.7
Frequency (GHz)
(a)
Phase Shift (Degree)
0
1-D MC, 1,200 Oe applied
1-D MC, 1,250 Oe applied
o
253.5
-400
-800
o
-1200
291.1
-1600
Δ S21 (dB) = ± 1.5 dB
4.75
-2000
4.70
4.925
4.75
4.80
4.85
4.90
4.95
Frequency (GHz)
(b)
Figure 4.31: The measured (a) S21 (dB) and (b) the corresponding phase shift in a 1-D MC
with a field of 1,200 and 1,250 Oe applied.
139
0
Phase Shift (Degree)
1,250 Oe;
1,265 Oe;
4.81
-400
1,280 Oe
4.90
Δ S21 (dB) = ± 1.5 dB
o
136.5
o
140.8
-800
o
117.5
o
-1200
160.4
4.76
Δ S21 (dB) = ± 1.5 dB
4.85
-1600
4.72
4.76
4.80
4.84
4.88
4.92
Frequency (GHz)
(a)
0
o
125.8
5.02
Phase Shift (Degree)
5.16
Δ S21 (dB) = ± 1 dB
o
236.9
-400
-800
o
o
280.1
181.3
-1200
Δ S21 (dB) = ± 1 dB
5.10
4.975
-1600
4.96
1,250 Oe;
5.00
1,265 Oe;
5.04
5.08
5.12
1,280 Oe
5.16
5.20
Frequency (GHz)
(b)
Figure 4.32: Measured differential phase shift in the (a). left passband and (b)right passband
of the bandgap with fields 1,250, 1,265 and 1,280 Oe applied on a 2-D MC structure.
140
Chapter 5
Conclusion
Tunable wideband microwave filters and phase shifters are essential devices
in wideband communications and radar systems. Such devices realized by
magnetic-tuning technique are attractive because of their unique features
such as high carrier frequency, high selectivity, multi-octave tuning range capability, spurious-free response, and inherent compatibility with other planar
microwave circuits. In this dissertation research, ferromagnetic resonance
(FMR)- and magnetostatic volume waves (MSVWs)-based tuning techniques
were employed for realization of such high-performance devices.
FMR-tuned microwave filters and phase shifters using bulk or thin film ferrite, e.g. YIG films, have long been constructed and utilized in wideband
applications. In this dissertation research, FMR-tuned BPF modules and
phase shifters using YIG/GGG flip-chip layer structures on GaAs or Duroid
141
substrate were studied at length.Three magnetically-tuned wideband BPF
modules, namely, 1. incorporation of cascaded BSF pairs, 2. incorporation
of an X-band passive BPF and two tunable BSFs, and 3. incorporation of a
pair of X-band composite-BPFs were successively devised and constructed.
An advanced BPF module with versatile frequency tunability facilitated using
the combination of electric-tuning with varactor and magnetic-tuning based
on FMR was also realized. The combined tuning technique was also employed
to develop a new tunable microwave phase shifter capable of providing a large
phase shift at a moderate insertion loss variation. In comparison with the
counterparts realized using magnetoelectric effect (ME), such combined tuning technique has demonstrated a wider tuning range and more versatile in
frequency control as well as a significant larger phase shift.
The MSVWs-tuned microwave filters and phase shifters using a 1-D and 2D MCs in YIG/GGG thin films were explored subsequently.The calculated
bandgaps associated with the MSVWs in the 1-D and 2-D MCs were verified
experimentally. The magnetically-tuned bandgaps created in the 1-D and 2-D
MCs were shown to function as tunable BSFs. Furthermore, the large phase
shifts associated with the left and right flat passbands of the bandgap was
verified experimentally. Compared with the FMR-tuned BSF and the phase
shifter, the MSWs-tuned counterparts have demonstrated a much smaller
3 dB BW and, thus, better frequency selectivity and a much larger phase
tuning rate, respectively.
142
The tunable wideband microwave filters and phase shifters studied and presented in this dissertation, when fully developed, could find applications in
wideband communication and signal process systems. The theoretical and experimental approaches as well as the device fabrication techniques established
should provide a valuable resource for further research and development on
the field.
143
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