planar tunable rf/microwave devices with magnetic ...1409/fulltext.pdf · verification of novel...

Planar Tunable RF/Microwave devices with magnetic, ferroelectric

and multiferroic materials

A Dissertation Presented

by

Jing Wu

To

The Department of Electrical and Computer Engineering

in partial fulfillment of the requirements

for the degree of

Doctor of Philosophy

in the field of

Electrical Engineering

Northeastern University

Boston, Massachusetts

August, 2012

2

NORTHEASTERN UNIVERSITY

Graduate School of Engineering

Thesis Title: Planar Tunable RF/Microwave devices with magnetic, ferroelectric and

multiferroic materials

Author: Jing Wu

Department: Electrical and Computer Engineering

Approved for Dissertation Requirement for the Doctor of Philosophy Degree

______________________________________________ ____________________

Dissertation Advisor: Professor Nian-Xiang Sun Date

______________________________________________ ____________________

Thesis Reader: Professor Philip Serafim Date

______________________________________________ ____________________

Thesis Reader: Professor Edwin Marengo Date

______________________________________________ ____________________

Department Chair: Ali Abur Date

Graduate School Notified of Acceptance:

______________________________________________ ____________________

Director of the Graduate School: Date

3

Acknowledgments

I would like to thank my advisor, Prof. Nian-Xiang Sun, for his constant help and

support during the time that I spent on my research. His patient guidance and novel

approach to the problems that I encountered was invaluable for my exploration and

learning, which help me become a better researcher.

I am grateful to Prof. Yuri K. Fetisov and Prof. Igor Zavislyak for their helpful

discussion on magnetostatic wave propagation, which helps me build in-depth

understanding of the physic concepts behind these RF devices.

I would also like to thank Prof. Philip Serafim and Prof. Edwin Marengo for

agreeing to be on my dissertation committee. Their advices on my thesis and dissertation

defense are invaluable.

Additionally, I would like to acknowledge the other members of our group.

Without the friendly help from the lab personnel and the scholarly and constructive work

environment within the group this process would have taken much longer. In particular, I

would like to thank Xi Yang, Ming Li, Ogheneyunume Obi, Xing Xing, Ming Liu, Jing Lou,

Yuan Gao, Tianxiang Nan and Shawn Beguhn for their invaluable help and collaboration

with my research.

Finally a special thank goes out to my family, who have always been behind me

whatever my goal at the time happened to be. Their love and support has helped me to

achieve my goals, and I will forever appreciate it.

4

Abstract

Modern ultra wideband communication systems and radars, and metrology systems

all need reconfigurable subsystems that are compact, lightweight, and power efficient. At

the same time, isolators with a large bandwidth are widely used in communication systems

for enhancing the isolation between the sensitive receiver and power transmitter.

Conventional Isolators based on the non-reciprocal ferromagnetic resonance (FMR) of

microwave ferrites in waveguide. However, these approaches are usually bulky. This

dissertation focuses on theoretical study, numerical evaluation and measurement

verification of novel planar RF/microwave devices with magnetic substrates and

superstrates, demonstrating tunable and non-reciprocal characteristics, so that size, weight

and cost of systems can be reduced.

The combination of ferrite thin films and planar microwave structure constituted a

major step in the miniaturization of such a non-reciprocal devices. A novel type of tunable

isolator was presented, which was based on a polycrystalline yttrium iron garnet (YIG)

slab loaded on a planar periodic serrated microstrip transmission line that generated

circular rotating magnetic field. The non-reciprocal direction of circular polarization

inside the YIG slab leads to over 19dB isolation and < 3.5dB insertion loss at 13.5GHz with

4kOe bias magnetic field applied perpendicular to the feed line. Furthermore, the tunable

resonant frequency of 4 ~ 13.5GHz was obtained for the isolator with the tuning magnetic

bias field 0.8kOe ~ 4kOe.

5

The non-reciprocal propagation behavior of magnetostatic surface wave in

microwave ferrites such as YIG also provides the possibility of realizing such a non-

reciprocal device. A new type of non-reciprocal C-band magnetic tunable bandpass filter

with ultra-wideband isolation is presented. The BPF was designed with a 45o rotated YIG

slab loaded on an inverted-L shaped microstrip transducer pair. This filter shows an

insertion loss of 1.6~2.3dB and an ultra-wideband isolation of more than 20dB, which was

attributed to the magnetostatic surface wave. The demonstrated prototype with dual

functionality of a tunable bandpass filter and an ultra-wideband isolator lead to compact

and low-cost reconfigurable RF communication systems with significantly enhanced

isolation between the transmitter and receiver.

A novel distributed phase shifter design that is tunable, compact, wideband, low-loss

and has high power handling will also be present. This phase shifter design consists of a

meander microstrip line, a PET actuator, and a Cu film perturber, which has been

designed, fabricated, and tested. This compact phase shifter with a meander line area of

18mm by 18mm has been demonstrated at S-band with a large phase shift of >360 o at 4

GHz with a maximum insertion loss of < 3 dB and a high power handling capability

of >30dBm was demonstrated. In addition, an ultra-wideband low-loss and compact phase

shifter that operates between 1GHz to 6GHz was successfully demonstrated. Such phase

shifter has great potential for applications in phased arrays and radars systems.

6

Table of Contents

Acknowledgments ......................................................................................................................... 1

Abstract .......................................................................................................................................... 4

List of Figures .............................................................................................................................. 10

Chapter 1: Introduction .............................................................................................................. 17

1.1 Motivation .......................................................................................................................... 17

1.2 Background ....................................................................................................................... 18

1.3 Microwave magnetic material and its property ............................................................. 19

1.3.1 Microwave ferrites ..................................................................................................... 19

1.3.2 Permeability tensors .................................................................................................. 21

1.3.3 Demagnetizing Field .................................................................................................. 23

1.3.4 Remanence magnetization and the hysteresis loop ................................................. 25

1.4. Mechanism of Microwave ferrite device ........................................................................ 26

1.4.1 Non-reciprocity .......................................................................................................... 26

1.4.2 Tunability.................................................................................................................... 28

1.5 Dissertation overview........................................................................................................ 31

1.6 Reference ........................................................................................................................... 33

Chapter 2: Simulations and Experiment Setups ........................................................................ 36

2.1 Ferrite device modeling in HFSS ..................................................................................... 36

2.1.1 Saturation magnetization ( ) and DC bias field ( ) in HFSS .................. 37

2.1.2 Delta H ( ) in HFSS ................................................................................................ 38

2.2 VNA for s-parameter and permeability measurement.................................................. 39

2.3 Electromagnet for applying DC bias field ...................................................................... 40

7

2.4 Reference ........................................................................................................................... 41

Chapter 3 Concept of magnetostatic surface wave .................................................................... 42

3.1 Motivation .......................................................................................................................... 42

3.2 Magnetostatic wave in tangential magnetized ferrite .................................................... 43

3.2.1 Magnetoquasistatic approximation .......................................................................... 43

3.2.2 Walker’s equation and magnetostatic modes .......................................................... 44

3.2.3 Magnetostatic surface wave in tangentially magnetized films (MSSW) ............... 45

3.2.4 Magnetostatic back volume wave in tangentially magnetized films ..................... 51

3.2.5 Summation of magnetostatic wave in tangentially magnetized films ................... 56

3.3 Magnetostatic wave in finite ferrite films ....................................................................... 58

3.3.1 Magnetostatic wave in ferrite films on metallic backed substrate ........................ 59

3.3.2 Magnetostatic wave in finite ferrite films (Straight Edge Resonator (SER)) ....... 61

3.4 Excitations of Magnetostatic wave .................................................................................. 65

3.5 Conclusion ......................................................................................................................... 70

3.6 Reference ........................................................................................................................... 70

Chapter 4 Bandpass Filters based on magnetostatic wave concepts......................................... 72

4.1 Motivation .......................................................................................................................... 72

4.2 Introduction of Previous BPF researches ....................................................................... 73

4.3 S-band magnetically and electrically tunable MSSW band pass filters ...................... 75

4.3.1 Filter design mechanism ............................................................................................ 76

4.3.2 Experimental and simulation verification ............................................................... 79

4.3.3 Magnetically and Electrically tunability .................................................................. 84

4.3.4 Conclusion and challenges ........................................................................................ 86

4.4. Reciprocal c-band Bandpass filters based on SER ....................................................... 88

8

4.4.1 Filter design mechanism ............................................................................................ 89

4.4.2 Simulations and Experimental verification ............................................................. 92

4.4.3 Magnetically tunability .............................................................................................. 96

4.4.4 Limitation of this design ............................................................................................ 99

4.5 Non-reciprocal c-band Bandpass filters based on rotated SER ................................... 99

4.5.1 The mechanism of the non-reflection boundary on a rotated YIG film ............. 100

4.5.2 Simulations and Experimental verification ........................................................... 104

4.5.3 Magnetically tunability ............................................................................................ 106

4.5.4 Summary for C-band non-reciprocal filter ........................................................... 111

4.6 Integrated bandpass filter with spin spray materials .................................................. 112

4.7 Conclusion ....................................................................................................................... 115

4.8 References ........................................................................................................................ 116

Chapter 5: Tunable Planar Isolator with Serrated Microstrip Structure ............................... 120

5.1 Introduction of isolator based on ferrite ....................................................................... 121

5.1.1 Ferromagnetic resonance isolator .......................................................................... 122

5.1.2 Field displacement isolator...................................................................................... 126

5.2 Serrated Microstrip Isolator Design Mechanism......................................................... 128

5.2.1 Previous Researches on Planar approaches of isolator designs .......................... 128

5.3.2 Serrated Microstrip Structure and Circular polarization ................................... 129

5.2.3 Magnetic field distribution of Serrated Microstrip Structure ............................. 131

5.3 Simulation verification ................................................................................................... 134

5.3.1 Effect of Ferrite films location with Serrated Microstrip Structure ................... 134

5.3.2 Designed Serrated Microstrip isolator with thicker YIG slab ............................. 138

5.4 Measurement verification .............................................................................................. 139

9

5.4 Conclusion ....................................................................................................................... 142

5.5 Reference ......................................................................................................................... 142

Chapter 6 Phase Shifters with Piezoelectric Transducer Controlled Metallic Perturber ...... 144

6.1 Introduction of tunable phase shifter researches ......................................................... 145

6.2 Device construction ......................................................................................................... 148

6.2.1 Device Construction ................................................................................................. 148

6.2.2 Piezoelectric transducer (PET) - PI PICMA® PL140.10 ...................................... 151

6.3 Theoretical analysis ........................................................................................................ 153

6.3.1 Equivalent Circuit Model for Meander Line with variable copper perturber .. 153

6.3.2 The insertion Loss Analysis..................................................................................... 154

6.4 Simulation Results .......................................................................................................... 156

6.5 Measurement Results...................................................................................................... 160

6.6. Extended design for 1-6GHz ......................................................................................... 165

6.7. Comparison with previous approaches ........................................................................ 171

6.8 Conclusions ...................................................................................................................... 172

6.9 References ........................................................................................................................ 173

Chapter 7 Conclusion ............................................................................................................... 176

10

List of Figures

Fig. 1. YIG elementary cell. Fe3+ in a-sites – empty circles, Fe3+ in d-sites –shaded circles,

Y3+ ions – filled circles. The positions of the oxygen atoms are not shown [10, 11] ..... 21

Fig. 1.2 Demagnetizing field of a magnetic plate with perpendicular external magnetic field

............................................................................................................................................... 24

Fig. 1.3 Demagnetizing field of a magnetic plate with tangential external magnetic field ... 24

Fig. 1.4 Hysteresis loops of magnetically YIG .......................................................................... 26

Fig 1.5, Spinning of electrons with right-handed polarization, with strong interaction with

RHPL wave propagation [12] ............................................................................................ 27

Fig. 1.7 versus on TTI-390 at 5.5 GHz [21] .......................................................... 29

Fig. 1.8. Calculated and measured FMR frequency against the external magnetic bias field

on YIG film ( ). ..................................................................................... 30

Fig. 2.1 The relation between magnetization moment and the Applied DC bias field H ..... 38

Fig.2.2 Vector network analyzer (Agilent PNA E8364A) ........................................................ 40

Fig.2.3 Current controlled Electromagnet................................................................................ 41

Fig. 3.1 Geometry for a tangential magnetized ferrite film. ................................................... 46

Fig. 3.2 Guided wave propagation in a tangential magnetized ferrite film. .......................... 46

Fig.3.3 Dispersion diagram for surface wave on infinite YIG slab (d=108um; H0=1500Oe,

4piMs=1750 Gauss) ............................................................................................................. 49

Fig.3.4 Potential profiles for surface wave on infinite YIG slab with forward ( ) and

backward ( - ) wave propagation at operating frequency . with Dc

bias field at z direction. ....................................................................................................... 50

Fig. 3.5 Surface wave propagation in a tangential magnetized ferrite film. .......................... 51

Fig.3.6 Potential profiles for back volume wave on infinite YIG slab ................................... 54

Fig.3.7 Dispersion relation for surface wave on infinite YIG slab (d=108um; H0=1600Oe,

4piMs=1750 Gauss) ............................................................................................................. 55

Fig. 3.8 Comparison of dispersion relation between Magnetostatic surface wave (MSSW)

and back volume wave (MSBVW), with DC bias field 1.6kOe, on YIG (thickness

108um, 4piMs 1750Gauss).................................................................................................. 57

11

Fig. 3.9 Geometry for a tangential magnetized ferrite film with metallic backed substrate 58

Fig. 3.10 Compare the dispersion relation for a tangential magnetized ferrite film

with/without metallic backed substrate ............................................................................ 60

Fig. 3.11 Geometry of straight edge resonator (SER)) ............................................................ 60

Fig. 3.12 MSSW propagation in straight edge resonator (SER)) .......................................... 61

Fig. 3.13. The dispersion relation for a YIG SER:

Bias field applied .................................................... 63

Fig. 3.14 The s-parameter of a bandpass filter utilizing YIM films width and standing wave

mode ; DC magnetic bias field 1500 Oe .................................................................. 64

Fig. 15. Transmission line model for magnetostatic wave excitation. ................................... 66

Fig. 3.16. Geometry of the transducers: Inverted L-shaped microstrip transducers with

parallel YIG alignment; ,

. ........................................................... 68

Fig. 3.17. Radiation resistance for coupling of transducers to top and bottom surface of the

YIG film. DC bias field is 1600 Oe. ................................................................................... 69

Fig. 3.18. Reciprocal excitations of microstrip transducer due to the reflection of the

straight edge. ....................................................................................................................... 69

Fig. 4.1 bandpass filter using two microstrip line antennas, realized by exciting the

magnetostatic surface waves (MSSW) reported by Srinivasan et. al: (a) schematic; (b)

s-parameters ........................................................................................................................ 75

Fig. 4.2. Geometry of the transducers. (a) Parallel microstrip transducers as used in [16]

and [7]. (b) L-shaped microstrip transducers as used in [14] and [15]. (c) T-shaped

microstrip transducers were proposed in this paper. ...................................................... 76

Fig. 4.3. Geometry of a T-shaped microwave transducer (top view and side view).

W1=1.18mm, W2=18.1mm, S1=9.0mm, S2=0.53mm, S4=1.2mm, H=1.28mm. ............ 78

Fig. 4.4. Schematic of the bandpass filter with single-sided YIG films ................................. 78

Fig. 4.5. Dispersion relation of Single crystal YIG film, which S3= 4mm and W3=10mm,

DC bias field at 200 Oe, Applied perpendicular to the feed lines. indicates the

standing wave modes indicates , as discussed in chapter 3.

............................................................................................................................................... 79

12

Fig. 4.5 S-parameters of the bandpass filter with 50-250 Gauss bias field ............................ 81

Fig. 4.6. 3-dB bandwidth versus magnetic bias field. S3=4mm, W3=10mm. ........................ 81

Fig. 4.7 Simulated and measured bandpass filter resonance frequency ................................ 83

Fig. 4.8. Simulated and measured bandpass filter 3-dB bandwidth. ..................................... 83

Fig. 4.9. Calculated and measured FMR frequency against the external magnetic bias field.

............................................................................................................................................... 84

Fig. 4.10. Measured electric field tunability of the bandpass filter ........................................ 85

Fig. 4.11 Transmission coefficient S21 of S-band bandpass filter utilizing single crystal

YIG film, with DC bias magnetic field 200 Oe. ................................................................ 87

Fig. 4.12 Transmission coefficient S21 in terms of different S3 (length of YIG film along the

propagation axis ), with DC bias magnetic field 200 Oe ................................................. 88

Fig. 4.13 Geometry of the transducers: Inverted L-shaped microstrip transducers with


...................................................................................... 91

Fig. 4.14. Dispersion relation of MSSW in a single crystal YIG film, which W4= 2mm and

L2=3mm, DC bias field at 1.6 kOe, Applied perpendicular to the feed lines. indicates

the standing wave modes indicates , as discussed in

chapter 3, eq. (3.48). ............................................................................................................ 92

Table 4.2 The resonance frequency of width and standing wave mode with DC

magnetic bias field 1600 Oe. ............................................................................................... 92

Fig. 4.15. Simulation result of bandpass filters based on YIG SER film, with DC magnetic

bias field 1600 Oe ................................................................................................................ 93

Fig. 4.16. Experimental result of bandpass filters based on YIG SER film , with DC

magnetic bias field 1600 Oe ................................................................................................ 94

Fig. 4.17. Resonance mode comparison between simulation and experimental data of the

proposed c-band bandpass filter ....................................................................................... 96

Fig. 4.18 Transmission coefficient (S21) of proposed C-band tunable band pass filter on

straight edge YIG film. The edge of the YIG film is parallel to the transducer and

perpendicular to DC bias magnetic field .......................................................................... 97

13



perpendicular to DC bias magnetic field .......................................................................... 98

Fig. 4.20 Comparison of transmission coefficient of proposed C-band tunable band pass

filter on straight edge YIG film with the FMR frequency calculated from Kittel’s

equation ................................................................................................................................ 98

Fig. 4.21 MSSW propagation in a tapered YIG film. [16] .................................................... 101

Fig. 4.21 MSSW propagation in a YIG film with different bias condition at edges or an

absorber. [12-15]. .............................................................................................................. 101

Fig. 4.22 MSSW propagation in a YIG film with a 45o inclined edge boundary at the YIG-

air boundary. ..................................................................................................................... 101


and back volume wave (MSBVW), with DC bias field 1.6kOe, on YIG (thickness

108um, 4piMs 1750Gauss)................................................................................................ 103

Fig. 4.24 Non-reciprocal c-band BPF on a rotated YIG fim. ................................................ 103

Fig. 4.25 Simulated s-parameter of our bandpass filter with parallel/rotated YIG slab

under DC bias field of 1.6 kOe. ........................................................................................ 105

Fig. 4.26 Measured s-parameter of our bandpass filter with parallel/rotated YIG slab

under DC bias field of 1.6 kOe. ........................................................................................ 106


rotated YIG film. ............................................................................................................... 107


rotated YIG film. ............................................................................................................... 108


rotated YIG film. ............................................................................................................... 108


rotated YIG film. ............................................................................................................... 109


filter on rotated YIG film with the FMR frequency calculated from Kittel’s equation

............................................................................................................................................. 109

14

Fig. 4.32 The insertion loss of the forward pass bands and the isolation of the backward

transmission. ...................................................................................................................... 110

Fig. 4.32 The 3-dB bandwidth of the forward pass bands for the fabricated c-band non-

reciprocal bandpass filter. ................................................................................................ 111

Fig. 4.33 Geometry of integrated band pass filter with MSSW concept .............................. 113

Fig. 4.34. Simulated results of integrated bandpass filter with parallelogram shape. ....... 114

Fig. 4.34. Simulated results of integrated bandpass filter with parallelogram shape, with

DC bias from 125Oe to 625 Oe ........................................................................................ 115

Fig. 5.1 Application of isolators in communication system. .................................................. 122

Fig. 5.2 Attenuation constants for circularly polarized plane waves in the ferrite medium

............................................................................................................................................. 124

Fig. 5.2 propagation constants for circularly polarized plane waves in the ferrite medium

............................................................................................................................................. 124

Fig. 5.3 Ferrite isolator with waveguide structure: (a) field distribution in waveguide; (b)

Ferrite location in waveguide. .......................................................................................... 125

Fig. 5.4 Forward and reverse attenuation constants for the resonance isolator (a) Versus

slab position. (b) Versus frequency.................................................................................. 125

Fig. 5.5 Field displacement isolator ......................................................................................... 127

Fig. 5.6. Geometry of the serrated microstrip isolator:

, and . The dashed line indicates the current flowing on the

substrate………………………………………………………………………………......130

Fig. 5.7. Microwave magnetic field distribution with the serrated structure ...................... 130

Fig. 5.8. The polarization of microwave magnetic field above and underneath the serrated

structure: (a) Forward transmission; (b) Backward transmission .............................. 132

Fig. 5.9. The summarized polarization of microwave magnetic field above and underneath

the serrated structure: (a) Forward transmission; (b) Backward transmission ......... 133

Fig. 5.11. Simulated s-parameter of the serrated isolator with different YIG placement with

DC bias field 4.4kOe, applied perpendicular to the feed line: YIG underneath serrated

structure…………………………………………………………………………………..136

15

Fig. 5.13. Simulated s-parameter of the serrated isolator with different YIG placement with

DC bias field 4.4kOe applied perpendicular to the feed line: YIG above serrated with

taperededges .…..………………………………………………………………………...138

Fig. 5.14. Simulated s-parameter of serrated microstrip isolator. ..................................... 139

Fig. 5.15. Measured s-parameter of serrated microstrip isolator ...................................... 140

Fig. 5.16 Return Loss of tunable serrated microstrip isolator with 4kOe magnetic field bias.

…..…………………………………………………………………………………….141

Fig. 5.17 Insertion loss and isolation of the tunable serrated microstrip isolator over

operating frequency. ......................................................................................................... 141

Fig. 6.1 Phase shifter design with PET controlled dielectric perturber by Chang et al.[9] 147

Fig. 6.2. Phase shifter design with PET controlled magneto-dielectric perturber by Yang et

al. ........................................................................................................................................ 148

Fig. 6.3. Schematic and photograph of the meander line phase shifter with PET controlled

metallic perturber. ............................................................................................................ 149

Fig. 6.4. Design dimensions for the meander line phase shifter, the grayed area shows the

size and position of the metallic perturber. .................................................................... 150

Fig. 6.5. Schematic and the equivalent circuit of piezoelectric transducer (PET) - PI

PICMA® PL140.10 ........................................................................................................... 152

Fig. 6.6. Approximated gap dimension with applied voltage (0~50V). The original gap is 2

mm. ..................................................................................................................................... 153

Fig. 6.7 Equivalent circuit of meander line with piezoelectric bending actuator ............... 154

Fig. 6.8. Simulated S21 of the meander line with different distances between the metallic

perturber and the substrate. ............................................................................................ 157


perturber and the substrate. ............................................................................................ 157

Fig. 6.10 Simulated relative phase shift of the phase shifter with different distances between

the metallic perturber and the substrate ........................................................................ 159

Fig. 6.11. Measured S21 of the meander line with different voltage applied on the PET. . 160

Fig. 6.12. Measured S11 of the meander line with different voltage applied on the PET. . 161

16

Fig. 6.13. Measured and simulated relative phase shift of the meander line phase shifter

with different voltage applied on the PET. The symbols indicate simulated results

from HFSS. ........................................................................................................................ 164

Fig. 6.14. Measured insertion loss of the meander line phase shifter with different input

power at 3 GHz.................................................................................................................. 165

Fig. 6. 15. Design dimensions for the extended meander line phase shifter. ....................... 166

Fig. 6.16. Measured relative phase shift of the extended meander line phase shifter with

different voltage applied on the PET .............................................................................. 167

Fig. 6.17. Measured S12 of the extended meander line with different voltage applied on the

PET. .................................................................................................................................... 170

Fig.6. 18. Measured S11 of the extended meander line with different voltage applied on the

PET. .................................................................................................................................... 170

17

Chapter 1: Introduction

1.1 Motivation


all need reconfigurable subsystems. Multi-band and multi-mode radios are becoming

prevalent and necessary in order to provide optimal data rates across a network with a

diverse and spotty landscape of coverage areas. As the number of required bands and

modes increases, the aggregate cost of discrete RF signal chains justifies the adoption of

tunable solutions.

More specifically, for example, the demand has been growing for bandpass filters

with improved performance on tunable operating frequency, low insertion loss, bandwidth,

linearity, size, weight, and power efficiency. Also, Compact tunable phase shifters with

large phase shift, low loss and high power handling capability are desired for a variety of

applications like phase array antennas. At the same time, tunable isolators with a large

bandwidth are widely used in communication systems for enhancing the isolation between

the sensitive receiver and power transmitter.

Conventional, these tunable and non-reciprocal microwave devices based on the

non-reciprocal ferromagnetic resonance (FMR) of microwave ferrites in waveguide are

usually bulky. This dissertation focuses on theoretical study, numerical evaluation and

measurement verification of novel planar microstrip RF/microwave structures with

18

magnetic substrates and superstrates loading, demonstrating tunable and non-reciprocal

characteristics, and insertion loss, size, weight and cost of systems can be reduced as well.

1.2 Background

The key concept for everything in this dissertation is the well-known Maxwell’s

equations, proposed by James Clark Maxwell in 1873, which are the foundation of

electromagnetic wave propagation in a medium [1]-[4].

(Gauss’s Law) (1.1)

(Faraday’s Law) (1.2)

(Gauss’s Law for magnetism) (1.3)

(Ampere’s Law) (1.4)

where:

is the electric displacement ( )

ρ is the charge density ( )

is the current density ( )

is the magnetic flux density ( )

H is the magnetic field intensity ( )

represents spatial location of any point in a 3-dimension space

represents time

This is the most general Maxwell’s equation. To describe the medium in which fields

exist, the constitutive relationships are required [1]-[5]:

(1.5)

19

(1.6)

(1.7)

where:

ς is the conductivity (mhos/m)

is the magnetization (amp/ )

is the permeability of free space (henrys/m), here π

is the dielectric constant of free space (farads/m), here

is the magnetic susceptibility;

For an isotropic, homogenous and non-dispersive medium, and are constant.

However, in reality many mediums are anisotropic, and dispersive. For example, the

permeability of magnetic materials can be written as a tensor due to the induced

magnetization:

[

] (1.8)

Each term of the tensor may be frequency and spatial dependent if the material is

dispersive and inhomogeneous.

1.3 Microwave magnetic material and its property

1.3.1 Microwave ferrites

20

Ferrimagnetic materials, or ferrites, are the most popular magnetic materials in RF

and microwave application. In this dissertation, we are interested in two practical types of

ferrites, which have cubic crystal structure: spinels and garnets [6].

Spinel ferrites exhibit a large static initial permeability, in the range of

. However, its permeability at high frequencies drops down to one at around 2 GHz.

Spinel ferrites are known as high relaxation loss materials, with typical ferrimagnetic loss

( ) in the order of 2-1000 Oe. Therefore, applications of spinel ferrites are usually limited

to low frequencies (MHz frequency).

The garnet ferrites have many applications in RF and microwave devices in past 20

years. G. Menzer first studied the cubic crystal structure of garnet ferrites in 1928. The

most famous garnet ferrite, yttrium iron garnet (Y3Fe5O12, or YIG), was first prepared by

F. Bertaut and F. Forrat [1]. YIG is an insulator with excellent high-frequency magnetic

properties. It has the narrowest known ferromagnetic resonance line and the lowest spin-

wave damping. Besides, YIG is a very low loss material at high frequencies. The FMR

linewidth, of a single crystal YIG was measured to be ~ 0.2 Oe at 3 GHz. Therefore,

many commercial magnetic microwave devices are made of YIG substrates.

The structure of YIG coincides with that of natural garnet [8, 9]. Its primitive

elementary cell is a half of cube with lattice constant . This cell consist of 4

octants each containing 1 formula unit of Y3Fe5O12. The mutual positions of atoms are

depicted on Fig. 1.1 [10, 11]. Atoms on the boundaries simultaneously belong to the

neighboring octants. The lattice has body-centered cubic structure. Positions of all atoms

21

are listed in [9]. A typical YIG saturation magnetization is around 1800 Gauss, with a

linewidth of for single crystal and for polycrystalline, which is very suitable

for microwave device applications.

Fig. 1. YIG elementary cell. Fe3+ in a-sites – empty circles, Fe3+ in d-sites –shaded circles,

Y3+ ions – filled circles. The positions of the oxygen atoms are not shown [10, 11]

1.3.2 Permeability tensors

At microwave frequencies, we are more interested in the net magnetization of ferrite,

which is defined as magnetic dipole moment per unit volume in response to the external

magnetic field. It can be written as:

(1.9)

22

where is the magnetic susceptibility tensor of the medium.

To make the problem simpler, first let us assume the external magnetic field is along

z-axis. Since most applications in this dissertation is signals at microwave frequency with a

DC bias field, the total magnetic field and total magnetization can be expressed as :

(1.10)

(1.11)

where is the applied bias field, is the DC bias magnetization, and is the AC

magnetic field and magnetization.

The equation of motion of the magnetic dipole moments can be derived as [12]:

[ ] (1.12)

where is gyromagnetic ratio, which is 2.8MHz/Gauss. For the study of magnetostaic

wave and magnetic resonance, we are primary interested in saturated single domain

materials. So, the static magnetic field and magnetization will be parallel to each

other in z-axis. Therefore, the first term of the right side of the equation zero. The fourth

term is small enough to be neglected, due to the small signal analysis. for the

saturation assumption. If the field can take the sinusoidal time dependent form , then

the equation of the magnetization can be written as:

[ ]

[ ]

[ ] (1.13)

23

where and .

By writing the vector and and fully expanding the Eq. (1.13), we

have the following matrix:

[

]

[

]

[

]

(1.14)

So we can write the permeability tensor as

[

]

, and

(1.15)

1.3.3 Demagnetizing Field

In most microwave applications, external bias magnetic fields are applied on ferrite

samples, in order to work in specific frequency bands. However, due to the magnetization

inside the ferrite, the net magnetic field can be very different with that in the air.

The demagnetizing field is a magnetic field due to the surface magnetic charges on

the interface between the magnetic material and non-magnetic material. It tends to reduce

the total magnetic moments inside the magnetic material and the internal magnetic field.

Let’s consider a magnetic plate with external bias magnetic field either perpendicular or

parallel to the plane, as shown in Fig. 1.2 and Fig. 1.3 .

24

Fig. 1.2 Demagnetizing field of a magnetic plate with perpendicular external magnetic field

Fig. 1.3 Demagnetizing field of a magnetic plate with tangential external magnetic field

M

𝐵𝑜 𝐻𝑜

𝐵𝑖 𝐻𝑖 Magnetic material

Air

Air

𝐻𝑜 𝐻𝑜 𝐻𝑖

Magnetic material

Air Air

25

To calculate demagnetizing field of a magnetic plate with perpendicular external

magnetic field (Fig. 1.2), it is assumed that all the magnetic moment was aligned along the

magnetization direction. Due to Gauss' theorem, normal component of is continuous on

the surface.

(1.16)

(1.17)

(1.18)

(1.19)

Where is the demagnetizing field of the magnetic plate is the applied field, is the

magnetizing factor. M is the magnetization along the normal direction.

To calculate demagnetizing field of a magnetic plate with tangential external

magnetic field (Fig. 1.3), it is assumed that all the magnetic moment was aligned along the

magnetization direction. The tangential component of is continuous on the surface.

Therefore, we have:

(1.20)

For other directions, article [13] shows more detailed derivations.

1.3.4 Remanence magnetization and the hysteresis loop

The remanence magnetization, , is the residue magnetization when the applied

field is

reduced to zero. The position of of YIG ferrite in a hysteresis loop is shown in Fig. 1.4

26

Fig. 1.4 Hysteresis loops of YIG

1.4. Mechanism of Microwave ferrite device

Microwave magnetic devices have had a major impact on the development of

microwave technology. As we discussed in the previous section, an electromagnetic wave

propagating through the ferrite encounters strong interaction with the spinning electrons

and give rise to desirable magnetic properties in ferrite. These properties have been utilized

to develop many microwave devices like, filters, isolators, phase shifters and circulators.

1.4.1 Non-reciprocity

The use of ferrites in a numbers of microwave devices is based on that propagation

constants for different modes of an electromagnetic wave are different (typically left

handed or right handed polarization). Under a proper external bias magnetic field, the

ferrite encounters strong interaction with the spinning electrons if the wave is right handed

27

polarized, while have weak interaction for the left handed polarized wave, as shown in fig.

1.5. [12] The difference in the interaction between ferrite and the EM wave will result in

different attenuation factor (magnitude) or Faraday rotation (polarization), Fig 1.6[12].

Also, the anisotropic permeability tensor of ferrites gives rise to different field or

potential displacement in the medium. For example, with a perpendicular in plane DC bias

field, the magnetostatic surface wave in ferrite will only propagate on one side of the ferrite

surface, while staying on the other side if the propagation direction is opposite. [14]

These two non-reciprocity properties can leads to a numbers of non-reciprocal

devices like circulators, isolator, non-reciprocal phase-shifters and filters.

Fig 1.5, Spinning of electrons with right-handed polarization, with strong interaction with

RHPL wave propagation [12]

28

Fig. 1.6 Faraday rotation when wave propagate in a ferrite sample along external bias field

[12]

1.4.2 Tunability

Another important property of ferrites is that their propagation constant is highly

depended by the external bias magnetic field. Therefore, one can tune the operating

frequency, bandwidth, or even reciprocity by tuning the different bias condition. These

tuning can be done the following method:

(i) Mechanically: direction or magnitude of bias field; [15],

(ii) Magnetically: electromagnet or hard magnet; [16]-[18],

(iii) Magneto-electrically: the bias condition can be tuned via magneto-electric

coupling on multiferroic structure with piezoelectric material bond to the ferrite film. The

stress induced by applied voltage will result in magnetic bias changes, leading to tuning of

FMR frequency [19].

(a) Tunable permeability

29

In many of the applications of ferrites in microwave devices the magnetic material is

only partially magnetized. The performance of tunable devices will be significantly

improved in unsaturated mode by allowing its operation in low-permeability (µr<1) range,

as shown in Fig. 1.7. The mechanism is based on Schloemann’s theory partially

magnetized ferrites [20], [21]. For the completely demagnetized state, the permeability in

this case is given by

[

]

(1.21)

The permeability of partially magnetized ferrites is given by

(1.22)

The permeability then only depends on the operating frequency omega and

magnetization . If omega is fixed for designed operating frequency, the permeability is

only set by its magnetized state.

Basically, the permeability can be tuned by the bias field applied, so is the operating

frequencies, and phase delays of the microwave devices.

Fig. 1.7 versus on TTI-390 at 5.5 GHz [21]

30

(b) Tunable ferromagnetic resonance frequency (FMR)

The strong interaction between the Spinning of electrons and the RF signal usually

happens when the magnetic material at ferromagnetic resonance. We can quickly estimate

of the FMR frequency by using Kittel’s equation [22]-[24].

√ (1.23)

where is the gyromagnetic constant of about 2.8 MHz/Oe, is the intrinsic in-plane

anisotropy field of the YIG film, and is the external bias field.

As expected, the measured resonance frequency of the bandpass filter matches

excellently with equation (1), which is shown in Fig. 1.8.

Fig. 1.8. Calculated and measured FMR frequency against the external magnetic bias field

on YIG film ( ).

31

1.5 Dissertation overview

Conventional, these tunable and non-reciprocal microwave devices based on the

non-reciprocal ferromagnetic resonance (FMR) of microwave ferrites in waveguide are

usually bulky. This dissertation will focus on theoretical study, numerical evaluation and

measurement verification of novel planar microstrip RF/microwave structures with

magnetic substrates and superstrates loading, demonstrating tunable and non-reciprocal

characteristics, and insertion loss, size, weight and cost of systems can be reduced as well.

In Chapter 2, we will briefly introduce the numerical modeling software and the

experimental measurement setups for the microwave ferrite devices discussed in this

dissertation. First, the modeling of ferrite material in Ansoft HFSS will be presented. Then

the whole experimental environment will be introduced, including VNA for s-parameter

measurement, Spin spray system for thin film deposition, electromagnet for applying DC

bias field, and VSM system for in plane and out plane hysteresis loop measurement.

In Chapter 3, we will provide a theoretical overview of electromagnetic wave

propagation in ferrite medium. More specifically, the propagation characteristics of

magnetostatic wave on a ferrite thin slab with an in-plane DC bias field will be investigated.

Magnetostaic surface wave (MSSW) will be excited when the bias field is perpendicular to

the wave propagation; Magnetostaic back volume wave (MSBVW) will be excited when the

bias field is parallel to the wave propagation. The dispersion relation under these two bias

conditions is also analyzed. Furthermore, the excitation structure of magnetostatic wave

32

for ferrites will be discussed. This chapter is introduced as the theoretical preparation for

the following chapters on microwave ferrite devices.

Chapter 4 will present my designs on tunable bandpass filters based on the

coupling between magnetostatic wave and EM wave. Both experimental and simulation

results of an s-band magnetically and electrically tunable bandpass filters (BPF) with

yttrium iron garnet (YIG) will be introduced. The designed bandpass filters can be tuned

by more than 50% of the central frequency with a magnetic bias field of 250 Oe. Then, a C-

band low loss straight-edge resonator band pass filter will be presented based on a similar

concept but with further discussion on the limitation on spurious resonance due to the

standing wave mode and finite width modes. Also, Simulation and experimental

verification will be presented for a new type of non-reciprocal C-band magnetic tunable

bandpass filter with dual functionality of ultra-wideband isolation.

Chapter 5 will present a novel planar tunable planar isolator with serrated

microstrip structure based on ferromagnetic resonance (FMR) of microwave ferrites. A

novel serrated microstrip structure will be presented to achieve circular polarization of

magnetic field, in terms of DC bias field. Current and field distribution will be analyzed

via HFSS simulations. The microwave ferrites experience LHCP (left-handed-handed

circular polarization) RF excitation magnetic fields in backward propagation while RHCP

(right-handed circular polarization) in forward propagation, leading to minimal

absorption in backward propagation while strong FMR absorption in forward propagation.

Simulation designs and experimental verification will be provided to understand the

33

mechanism behind this design. The non-reciprocal ferrite resonance absorption leads to

over 19dB isolation and 3.5 insertion loss at 13.5GHz with 4kOe bias magnetic field applied

perpendicular to the feed line.

Chapter 6 will present a compact, low-loss, wideband and high power handling

tunable phase shifters with piezoelectric transducer controlled metallic perturber. This

phase shifter design consists of a meander microstrip line, a PET actuator, and a Cu film

perturber, which has been designed, fabricated, and tested. This compact phase shifter

with a meander line area of 18mm by 18mm has been demonstrated at S-band with a large

phase shift of >360 o

at 4 GHz with a maximum insertion loss of < 3 dB and a high power

handling capability of >30dBm was demonstrated. In addition, an ultra-wideband low-loss

and compact phase shifter that operates between 1GHz to 6GHz was successfully

demonstrated. Such phase shifter has great potential for applications in phased arrays and

radars systems.

Chapter 7 will be the conclusion for the dissertation.

1.6 Reference

[1] C. Vittoria, Elements of microwave networks, World Scientific Publishing Co.,1998.

[2] D. M. Pozar, Microwave engineering, 3rd edition, John Wiley, Hoboken, NJ, 2005.

[3] R. F. Harrington, Time-harmonic electromagnetic field, Wiley-Interscience, NY, 2001.

[4] C. A. Balanis, Advanced Engineering Electromagnetics, John Wiley, Hoboken, NJ, 1989.

[5] C. Vittoria, Microwave Properties of magnetic films, World Scientific Publishing Co.,

34

1993.

[6] B. Lax and K. J. Button, Microwave Ferrites and Ferrimagnetics (McGraw-Hill Book

Company, Inc., 1962).

[7] F. Bertaut, F. Forrat, Cornpt, A. Rend, Sci. Paris. 1956, vol. 242, 382-384.

[8] Geller, S; Gilleo, MA. J. Phys. Chem. Solids., 1957, vol. 3, 30-36.

[9] Huber, DL. In Landolt-Börnstein Group III Crystal and Solid State Physics; Hellwege,

K.-H; Hellwege, AM; Ed; Numerical Data and Functional Relationships in Science and

Technology Series; Springer- Verlag Berlin: New York, NY, 1970; vol. 4: Part a, 315-

367.

[10] Plant, JS. J. Phys. C., 1977, vol. 10, 4805-4814.

[11] David M. Pozar, Microwave Engineering, Second Edition (John Wiley & Sons, Inc.,

New York, 1998).

[12] Carmine Vittoria, Magnetics, Dielectrics, and Wave Propagation with MATLAB®

Codes (CRC Press, Taylor & Francis Group, Boca Raton, 2011).

[13] Daniel D. Stancil, ―Theory of magnetostatic waves‖, Springer – Verlag, New York,

1993.

[14] T. Y. Yun and K. Chang, ―Piezoelectric-Transducer-Controlled tunable microwave

circuits,‖ IEEE Trans. Microw. Theory Tech. vol. 50, pp. 1303-1310, May 2002.

[15] J. Uher and W. J. R. Hoefer, ―Tunable microwave and millimeter-wave band-pass

filters,‖ IEEE Trans. Microw. Theory Tech. vol 39, pp. 643-653, Apr. 1991.

[16] B. K. Kuamr, D. L. Marvin, T. M. Christensen, R. E. Camley, and Z. Celinski, ―High-

frequency magnetic microstrip local bandpass filters,‖ Appl. Phys. Lett. vol 87, 222506,

Nov. 2005.

35

[17] N. Cramer, D. Lucic, R. E. Camley, and Z. Celinski, ―High attenuation tunable

microwave notch filters utilizing ferromagnetic resonance,‖ J. Appl. Phys. vol 87, pp.

6911-6913, May 2000.

[18] A. S. Tatarenko, V. Gheevarughese, and G. Srinivasan, ―Magnetoelectric microwave

bandpass filter,‖ Electron. Lett. vol 42, pp. 540-541 , Apr. 2006.

[19] Ernst Schlömann, ―Microwave Behavior of Partially Magnetized Ferrites,‖ J. Appl.

Phys. 41, 204 (1970).

[20] Jerome J. Green and Frank Sandy, ―Microwave Characterization of Partially

Magnetized Ferrites,‖ IEEE Trans. Microw. Theory Tech. 22, 641 (1974).

36

Chapter 2: Simulations and Experiment Setups

In Chapter 2, I will briefly introduce the numerical modeling software and the

experimental measurement setups for the microwave ferrite devices discussed in this

dissertation. First, the modeling of ferrite material in Ansoft HFSS will be presented. Then

the whole experimental environment will be introduced, including VNA for s-parameter

measurement, and electromagnet for applying DC bias field.

2.1 Ferrite device modeling in HFSS

HFSS is a high-performance full-wave electromagnetic (EM) field simulator for

arbitrary 3D volumetric passive device modeling that takes advantage of the familiar

Microsoft Windows graphical user interface. HFSS employs the Finite Element Method

(FEM), and can be used to calculate parameters such as S-Parameters, Resonant

Frequency, and Fields. [1]

The accuracy of HFSS simulation on non-ferrite device has been widely proved. In

this dissertation, we are interested in ferrite devices, which relied on the B-H nonlinear

material definition which model the interaction between a microwave signal and a ferrite

material whose magnetic dipole moments are aligned with an applied bias field. The

gyrotropic quality of the ferrite is evident in the permeability tensor which is Hermitian in

the lossless case. The Hermitian tensor form leads to the non-reciprocal nature of the

devices containing microwave ferrites. If the microwave signal is circularly polarized in the

same direction as the precession of the magnetic dipole moments, the signal interacts

37

strongly with the material. When the signal is polarized in the opposite direction to the

precession, the interaction will be weaker. Because the interaction between the signal and

material depends on the direction of the rotation, the signal propagates through a ferrite

material differently in different directions.

There are three parameters we can monitor when we simulate a RF device with

ferrite in HFSS: Saturation magnetization ( ), Delta H ( ) and DC bias field ( )

2.1.1 Saturation magnetization ( ) and DC bias field ( ) in HFSS

When a ferrite is placed in a uniform magnetic field, the magnetic dipole moments

of the material begin to align with the field. In HFSS, the bias field is applied along z- axis

by default. For different applications, the coordinate system should be rotated for align the

expected bias direction to z-axis. As the strength of the applied bias field increases, more of

the dipole moments align. The saturation magnetization , is a property which describes

the point at which all of the magnetic dipole moments of the material become aligned. At

this point, further increases in the applied bias field strength do not result in further

saturation. The relationship between the magnetic moment , and the applied bias field ,

is shown in Fig. 2.1.

Determined by the bias field, ferrites can work in two states: partially saturated or

fully saturated. For example, the critical bias field for Yttrium iron garnet (YIG, Y3Fe5O12)

is around 100~150 Oe. HFSS can only model the ferrite in the fully saturated state, where

the permeability tensor can be expressed as:

38

[

], (1.1)

, and

where , and , H0 is the DC bias field, and ω is the angular

frequency.

These models follow the wave propagation properties in ferrite, so the simulations are

proved to have a good agreement with measurement verification in the following chapters.

Fig. 2.1 The relation between magnetization moment and the Applied DC bias field H

2.1.2 Delta H ( ) in HFSS

39

Delta H is the full resonance line width at half-maximum, which is measured during

a ferromagnetic resonance measurement. It relates to how rapidly a precessional mode in

the biased ferrite will damp out when the excitation is removed. The factor doesn’t

appear in the permeability tensor; instead, the factor α appears. The factor α is computed

from:

α

(1.2)

The factor changes the and terms in the permeability tensor from real to complex, by

applying

, which makes the tensor complex non-symmetric and leads to

additional loss.

2.2 VNA for s-parameter and permeability measurement

All measurements in this dissertation are carried out via a vector network analyzer

(Agilent PNA E8364A). The photo of this Network analyzer is shown in Fig.2.2. The input

and output are at 1mW power level and well calibrated from 45MHz to 20GHz. S-

parameters can be measured and exported.

40

Fig.2.2 Vector network analyzer (Agilent PNA E8364A)

2.3 Electromagnet for applying DC bias field

Measurement of RF devices with ferrite usually requires DC magnetic bias field. We

use an electromagnet to vary the applied bias magnetic field, which can tuned either by the

separation of the two magnets or the current in the coil. Here is the typical operation: first

we mount the devices in between the magnets, then we adjust the separation to achieve a

resonable magnetic tuning scales and finally tune the supplied current and checked with

gauss meter for the desire bias field.

41

\

Fig.2.3 Current controlled Electromagnet

2.4 Reference

[1] HFSS user manual

42

Chapter 3 Concept of magnetostatic surface wave

3.1 Motivation


all need reconfigurable subsystems such as tunable bandpass filters that are compact,

lightweight, and power efficient [1]. At the same time, isolators with a large bandwidth are

widely used in communication systems for enhancing the isolation between the sensitive

receiver and power transmitter. If a new class of non-reciprocal RF devices that combines

the performance of a tunable bandpass filter and an ultra-wideband isolator is made

available, new RF system designs can be enabled which lead to compact and low-cost

reconfigurable RF communication systems with significantly enhanced isolation between

the transmitter and receiver.


microwave ferrites such as yttrium iron garnet (YIG) provides the possibility of realizing

such a tunable and non-reciprocal device [2-3]. Magnetostatic waves are formed when

electromagnetic waves couple to spin waves in magnetic materials. Under proper bias

condition, these waves can exhibit properties such as dispersive propagation, non-

reciprocity and frequency-selective nonlinearities. The goal of this chapter is to introduce

the concept of magnetostatic waves, which will be further utilized in the filter designs.

The study of this chapter can be divided in to three parts. First, an introduction will

be presented to Maxwell equations with given permeability tensor of magnetic material.

43

Under magnetoquasistatic approximation, when the wavelength in the medium is much

smaller than that of an ordinary electromagnetic wave at the same frequency, we can

obtain Walker’s Equation [4], which is the basic equation for magnetostatic modes in

homogeneous media. Second, boundary condition will be considered to deduce

magnetostatic surface wave propagation modes inside a finite ferrite slab under tangential

magnetization. Finally, the working excitation structure for magnetostatic wave in ferrite

slab will be discussed, and microstrip transducers with be designed via Ansoft HFSS

simulation. Non-reciprocity will be analyzed via radiation resistance equivalent model of

the transducers for magnetostatic wave excitation.

3.2 Magnetostatic wave in tangential magnetized ferrite

3.2.1 Magnetoquasistatic approximation [4]

First, let us consider uniform plane waves propagating in homogenous magnetic

material neglecting exchanges and anisotropy. The magnetic fields and magnetization

inside the material, and can be expressed as following:

(3.1)

(3.2)

Which can be divided to DC static fields , and time variable fields , .

The Maxwell’s equation then can be written as :

(3.3)

(3.4)

44

By crossing into Eq. (3.3) and substituted Eq. (3.4) for , given

(3.5)

(3.6)

Finally, since ,

(3.7)

For certain frequencies, | | , vanished as | | for large | |. Then the

wave propagation inside the homogeneous magnetic material can be described as:

(3.8)

(3.9)

(3.10)

(3.11)

This equation set is the Maxwell’s equation under magnetoquasistatic

approximation. Most cases discussed in this chapter will follow this limit.

3.2.2 Walker’s equation and magnetostatic modes [4]

The permeability tensor without exchange and anisotropy can be written as :

[

], (3.12)

, and

45

Where the bias field is supposed to lie along direction. where , and

, H0 is the DC bias field, and ω is the angular frequency.

Similar to the electric potential, since , we may define

(3.13)

where is the magnetostatic scalar potential.

By substitute 3.12 and 3.13 to 3.9, we can write the Walker’s equation:

(

)

(3.14)

(

) (3.15)

the Walker’s equation can be written as Eq. 3.15, when . The solutions are called

magnetostatic modes in homogeneous media.

3.2.3 Magnetostatic surface wave in tangentially magnetized films (MSSW) [4]

Now let us consider a thin ferrite film with DC bias field, applied tangential to the its

plane and normal to the propagation direction, as shown in fig. 3.1. In ferrite region (II),

the static magnetic field . There are several boundary conditions we can use to

take a trial solution.

(1) The magnetostatic scalar potential will decay to 0 at infinite along direction;

46

(2) The magnetostatic scalar potential will be continuous at the interface of ;

(3) The normal b will be continuous at the interface of ;

(4) The magnetostatic scalar potential will be uniform along direction if we excited the

spin wave to propagate in direction;

Fig. 3.1 Geometry for a tangential magnetized ferrite film.

Fig. 3.2 Guided wave propagation in a tangential magnetized ferrite film.

x

y

z

+d/2

-d/2

𝐻𝐷𝐶

I. Air

II. Ferrite

III. Air

HDC +d/2

-d/2

𝑒𝑖𝑘𝑦𝑦+𝑖𝑘𝑥𝑥 𝑒 𝑖𝑘𝑦𝑦+𝑖𝑘𝑥𝑥

47

Utilizing the above boundary conditions, we can analyze the guided wave in the film

as shown in Fig. 3.2. The plane waves are bouncing back and forth from the upper and

lower boundaries. The magnetostatic scalar potential can be written as:

+ (3.15)

(3.16)

+ (3.17)

Where v denotes the propagation direction, which is +1 for direction and -1 for

direction From the boundary condition (3), potential will be uniform along direction if

the fill is infinite. The Walker’s equation can be reduced as:

(

) (3.18)

(

) (3.19)

So, Eq. 3.19 leads to the relation

. If we are looking for a solution of wave

propagation in direction, should be real and should be imaginary. Therefore, the

potential in region II will not be oscillatory but contain growing and decaying exponentials.

Eq. 3.16 can be modified as following:

+

(3.20)

Here we can write | | , which is the propagation wave number along direction.

48

By applying boundary condition at for continuous , we have:

+

(3.21)

+

(3.22)

Another boundary condition is that should be

continuous at :

( +

) ( +

) (3.23)

( +

) ( +

) (3.24)

By solving eq. 3.21~ eq.3.24, the following tensor equation can be written:

[

] [ +

] (3.25)

The dispersion relation between k and frequency can be expressed by letting the

determinant of the coefficient matrix be 0 .

Where the k-ω relation is

+

(3.25)

, and

49

where , and , H0 is the DC bias field, and ω is the angular

frequency.

Based on eq. 3.25, Fig. 3.3 shows the dispersion diagram for magnetostaic wave on

an infinite YIG slab with thickness d=108um, and saturation magnetization 1750 Gauss.

The DC bias magnetic field 1500 Oe was applied in plane and perpendicular to the wave

propagation. This dispersion relation is unchanged even if the wave propagation is

reversed. There is only one mode in between 6.2GHz to 6.6GHz. However, the potential is

not reciprocal . By substituting Eq. (3.25) to Eq. (3.15), Eq. (3.17), Eq. and (3.20). We have

the potential distribution in all three regions. And they are not reciprocal.

0 2416 4832 7248 9664 12080

6.2

6.3

6.4

6.5

6.6

6.7

Infinite no Ground

Fre

qu

en

cy

(G

Hz)

kd

Fig.3.3 Dispersion diagram for surface wave on infinite YIG slab (d=108um; H0=1500Oe,

4piMs=1750 Gauss)

50

0.0 0.2 0.4 0.6 0.8 1.0-3

-2

-1

0

1

2

3

-d/2 Forward

-z propagation

+z propagation

y a

xis

(th

ickn

ess (

d))

Normalized Magnetic Potential

+d/2 Backward

Hdc

Fig.3.4 Potential profiles for surface wave on infinite YIG slab with forward ( ) and

backward ( ) wave propagation at operating frequency . with Dc bias

field at z direction.

+ (3.26)

(3.27)

+ , (3.28)

+ +

+

+

Figure 3.4 shows the normalized potential profiles for surface wave on infinite YIG

slab with forward ( ) and reverse ( ) wave propagation. The wave amplitude

decays exponentially from the interface of ferrite and the air. Therefore, we can imagine

that the surface wave will shift from one side of a film to the other side if the direction of

the propagation is reversed, given the same DC bias condition as shown in Fig. 3.5.

51

Fig. 3.5 Surface wave propagation in a tangential magnetized ferrite film.

3.2.4 Magnetostatic back volume wave in tangentially magnetized films [4]

In this section, we can consider the case with DC bias magnetic field applied

tangential to its plane and parallel to the propagation direction. The geometry for a

tangential magnetized ferrite film can be shown in Fig. 3.1. In ferrite region (II), the static

magnetic field is . There are several boundary conditions we can use to take a

trial solution.

(1) The magnetostatic scalar potential will decay to 0 at infinite along direction;

(2) The magnetostatic scalar potential will be continuous at the interface of ;

(3) The normal will be continuous at the interface of ;

(4) The magnetostatic scalar potential will be uniform along direction if we excited the

spin wave to propagate in direction;

HDC +d/2

-d/2

52

The wave will propagate along direction inside the ferrite, instead of direction.

So the Walker’s equation can be written as:

(

)

(3.29)

( )

(3.30)

Then similar to the surface case, the scalar potential in all three regions can be

written as:

+ (3.31)

(3.32)

+ (3.33)

By Applying the boundary condition at , we have :

By applying boundary condition at for continuous , we have:

(3.34)

(3.35)

Here, we can conclude , which is identified as odd mode.

Another boundary condition is that should be continuous at

:

(3.36)

53

(3.37)

These two equations are equivalent to the previous two. Substituting Eq. (3.36) to Eq.

(3.34) gives the dispersion relation:

(

) (3.38)

Substituting Eq. (3.29) give the dispersion relation for odd modes:

(

√ + ) √ (3.39)

For even modes, we can achieve it by a similar procedure:

(

√ + ) √ (3.40)

The even and odd mode then can be combined with identity (

)

(

√ +

) √ (3.41)

Based on the dispersion relation above, the odd and even mode potential functions are

given by :

+ (3.42)

(3.43)

(

) + (3.44)

+ (3.45)

(3.46)

54

(

) + (3.47)

Figure 3.6 shows the potential profiles on an infinite YIG slab with bias field applied

parallel to wave propagation. The potentials amplitude is distributed sinusoidal through

the volume of the film. There are fundamental modes like (for n=1) and

(n=2) , and some other high order harmonics. Fig 3.7 shows that the dispersion relation of

MSBVW is independent of the direction of propagation. On the other hand, all modes (n=1,

2, 3, 4, 5) have the same cut-off frequencies at , which can be calculated via

√ . There is no frequency range that only one mode exists. Also,

the group velocity seems to have opposite direction compared to the phase velocity.

Therefore, it is also called backward volume waves.

-1.0 -0.5 0.0 0.5 1.0-3

-2

-1

0

1

2

3

y a

xis

(th

ickness (

d))

Normalized Magnetic Potential

n=1

n=2+d/2

-d/2

Fig.3.6 Potential profiles for back volume wave on infinite YIG slab

55

0 2 4 6 8 104.5

5.0

5.5

6.0

6.5

Fre

qu

en

cy

(G

Hz)

kd

n=1

n=2

n=3

n=4

n=5

Fig.3.7 Dispersion relation for surface wave on infinite YIG slab (d=108um; H0=1600Oe,

4piMs=1750 Gauss)

56

3.2.5 Summation of magnetostatic wave in tangentially magnetized films

Table 3.1 comparison between magnetostatic surface wave and back volume wave

Magnetostatic surface wave Magnetostatic back volume wave

Wave

characteristics

Forward surface wave Backward volume wave

Applied Bias field In plane, perpendicular to wave

propagation

In plane, parallel to wave

propagation

Modes Single mode Multi modes, with same cut-off

frequencies

reciprocity Non-reciprocal wave

propagation with different

potential distribution

reciprocal wave propagation

independent of propagation

direction

Magnitude

distribution

Decays exponentially cross the

film thickness, maximum

locates at one side forward

propagation but the other side

for reverse propagation

Distributed sinusoidal cross the

volume of the film, including high

order harmonics

Group/phase

velocity

Same direction Opposite direction

57

0 2 4 6 8 104.5

5.0

5.5

6.0

6.5

7.0

n=5n=4

n=3

n=2

n=1

MSBVW

Fre

qu

en

cy (

GH

z)

kd

MSSWFMR @ 6.485GHz


and back volume wave (MSBVW), with DC bias field 1.6kOe, on YIG (thickness 108um,

4piMs 1750Gauss)

Table 3.1 shows the summation of magnetostatic wave in tangentially magnetized

films for both MSSW and MSBVW. Figure 3.8 compares the dispersion relation for these

two bias conditions. MSSW has a lower cut-off frequency above FMR and its wave

propagation is with single mode. MSBVWs have an upper cut-off frequency below FMR

and they are multi-modes. Therefore, there are always many modes existing at the same

time. For practical device designs, the volume waves will suffer from ripples due to the

58

multi-resonance wave modes, while surface wave usually have a very smooth band. In this

dissertation, we’ve focused on the surface wave for band pass filter designs.

Fig. 3.9 Geometry for a tangential magnetized ferrite film with metallic backed substrate

3.3 Magnetostatic wave in finite ferrite films [5]

In the previous section, we’ve discussed magnetostatic wave propagation in an

infinite large ferrite film with tangential magnetic bias field. However, in practical there

are finite boundary conditions which can change the wave propagation inside the ferrite

film.

x

y

z

+d/2

-d/2

𝐻𝐷𝐶

I. Air

II. Ferrite

III. Dielectric

t

IV. Ground

59

3.3.1 Magnetostatic wave in ferrite films on metallic backed substrate

Let us consider a ferrite film mounted on top of a microstrip structure, as shown in

Fig. 9. Compared with Fig. 1, region III is truncated by a metallic ground plane. The new

boundary condition can be expressed as the following:

(1) Continuous magnetic potential

,

(2) Magnetic potential

(3) Magnetic potential ,

(4) will be uniform along direction if we excited the spin wave to propagate in

direction;

Previous researches have deduced the dispersion relation for wave propagation in a

ferrite film placed with a metallic layer with a spatial separation : [5]. If goes to infinite,

this equation will be reduced to the case that is discussed in previous sections.

(3.48)

Fig. 10 shows the comparison of the dispersion relation for a tangential magnetized

ferrite film with/without metallic backed substrate when DC bias field is 1.5 kOe. The

ground plane only affects the dispersion relation when k is small. For a large k solution, the

difference between them is neglectable.

60

0 2416 4832 7248 9664 12080

6.2

6.3

6.4

6.5

6.6

6.7

Unground

GroundF

req

ue

nc

y (

GH

z)

k

Fig. 3.10 Compare the dispersion relation for a tangential magnetized ferrite film

with/without metallic backed substrate

Fig. 3.11 Geometry of straight edge resonator (SER))

x

y

z

+d/2

-d/2

𝐻𝐷𝐶

I. Air

II. Ferrite

III. Dielectric

t

IV. Ground

L

61

Fig. 3.12 MSSW propagation in straight edge resonator (SER))

3.3.2 Magnetostatic wave in finite ferrite films (Straight Edge Resonator (SER))[5]

For a practical filter design, a rectangular YIG films with straight edges are used.

Magnetostatic wave propagates in a finite medium, hits the edges, and reflected back. The

wave is bouncing back and forward, which forms standing wave modes. Additionally, finite

width of the films produces width mode resonance. Problems rise from the coupling to the

width modes and standing wave modes. Figure 3.12 shows an example of magnetostatic

surface wave propagating in a YIG film. The forward transmission happens on the bottom

interface, which the backward transmission is on the top surface. Eventually, they overlap

and form standing wave. It is similar to a cavity resonator, which resonate at different

discrete frequencies.

Suppose the YIG film has length L (x-axis) and width W (z- axis), as shown in Fig 11.

The DC bias field is applied along z axis, which is perpendicular to the wave propagation in

Forward

Backward

Standing Wave

Straight Edge

Straight Edge

62

x-axis, for surface waves. To find out the resonance frequency of the resonator, we can first

have a rough guess on the solution in the ferrite film (region II).

(3.49)

where +

is the solution found in the previous section (infinite

case). A new term has been added to response to the finite width W in z-axis. So,

The boundary condition can be expressed as following:

(1) Y-axis similar to the previous cases. So leads to a same dispersion relation as

infinite case.

(2) Z-axis, at the edge ( ):

(3) X-axis: standing wave condition:

+

Inside YIG

+

Outside YIG

Applying this in (1), we get the dispersion relation:

(3.49)

m= 1, 2, 3, 4, 5, corresponding to width mode

n= 1, 2 , 3, 4, 5, corresponding to standing wave resonance.

For each of the primary resonance ( ), the high order width

mode depends on the current distribution on the transducers.

63

represents transducers with an even current distribution. represents odd modes.

Figure 3.13 indicates the dispersion relation for all combos. Given the finite

width , finite length ,

corresponds to n=1, 2, 3, 4, 5. From the figure, we can read the resonance frequency of each

mode , as indicated in Table 3.2.

0 2416 4832 7248 9664 12080

6.2

6.3

6.4

6.5

6.6

6.7

m=1

m=2

m=3

m=4

m=5

min

Fre

qu

en

cy (

GH

z)

k

Fig. 3.13. The dispersion relation for a YIG SER:

Bias field applied

64

Table 3.2 The resonance frequency of width and standing wave mode with

DC magnetic bias field 1500 Oe.

GHz 1 2 3 4 5

1 6.48 6.5 6.55 6.59 6.61

2 6.35 6.45 6.52 6.56 6.59

3 N/A 6.37 6.47 6.53 6.57

4 N/A N/A 6.41 6.49 6.54

5 N/A N/A 6.34 6.43 6.50

6.2 6.3 6.4 6.5 6.6-25

-20

-15

-10

-5

0

S21

S12

S1

2&

S2

1(d

B)

Frequency (GHz)

Fig. 3.14 The s-parameter of a bandpass filter utilizing YIM films width and standing wave

mode ; DC magnetic bias field 1500 Oe

65

Table 3.2 indicate the resonance frequency of width and standing wave

mode with DC magnetic bias field 1500 Oe. Here the FMR frequency is

around √ . The frequency band

has been split by discrete resonant frequencies. When a bandpass

filter is designed using the same YIG film resonator. The s-parameter response was

shown in Fig 3.14. The splitting resonant frequency leads to many ripples in the pass

band (both S21-forward and S12-backward transmission), which can be a huge

drawback in the filter designs. More detailed design concerns and solutions will be

presented in chapter 4.

3.4 Excitations of Magnetostatic wave [6]

We’ve discussed the wave properties of the magnetostaic wave. Then, how can we

excite? Experimentally it is easy to excite the magnetostatic waves in thin films. Placing a

current carrying wire near the film will be enough to excite the spin wave. Most commonly,

microstrip structures with short pins to the ground plane at the end of the strip line are

utilized to achieve the excitation. Usually, the coupling between the current flowing on the

microstrip transducer and the spin wave propagate in the ferrite film can be model as an

equivalent lossy transmission line, are shown in Fig 3.14. As the incident wave propagates

along the transducer, the energy is lost to the magnetostatic wave.

66

Fig.3.15. Transmission line model for magnetostatic wave excitation.

There are plenty of previous researches on magnetostatic wave excitations. Adam et.

al. [8] adopted parallel microstrip lines as the transducers. However, the minimum

insertion loss of their bandpass filters is 10 dB, which is unsuitable for modern

communication system. Most recently, a T-shaped microstrip coupling structure and YIG

films were used to achieve a low-loss S-band tunable bandpass filter [9-10]. An L-shaped

microstrip transducer was reported in [11] and [7], which could enhance the coupling to a

minimum insertion loss of 5 dB .

In order to improve the insertion loss and isolation, and achieve the non-reciprocal

behavior at the same time, an inverted L-shaped transducer has been designed, are shown

in Fig 3.15. The transducer is designed on a 0.381mm (15mil) thick Rogers TMM 10i

substrate with and . The length of the transducer is ,

width , with a spatial separation . Single crystal YIG slab with

thickness about 108µm was placed on top of the transducers. The saturation magnetization

(4πMs) of the single crystal YIG slab is about 1750 Gauss and the FMR line width is less

than1 Oe at X-band (~9.8 GHz). The bias magnetic field H is perpendicular to the feed line.

The alignment of the YIG film is parallel to transducer, as well as the DC bias magnetic

field H. The YIG film then forms a straight edge resonator with finite width modes and

standing wave modes. The transducers will couple to these modes and deliver energy from

one port to the other.

67

The radiation resistant per unit length for surface waves travelling in

direction can be written as : [6]

[

+

+ + ] |

|

(3.50)

Where F indicates array factor for the microstrip transducer:

. is the width mode wave number, is the finite width of the YIG film. is the Bessel

function of zero order . is the vertical spacing between the transducer and YIG film,

usually it is around .

Because the surface wave exhibit field displacement non-reciprocity, as discussed in

the previous section. Besides, the resistance is proportional to , where is the space

between transducer and the wave propagation surface. The radiation resistance is

different for the two directions of propagation. The excitation is much stronger for the

mode localized at the surface near the transducer, while it is much weaker at the other side

(by attenuation of , is thickness of YIG film). The radiation resistance (under bias

field 1600 Oe) for our design is calculated as Fig 3.16. The resistance is close to 50 ohm,

around 6.8GHz for bottom coupling, while close to 0dbm for the top surface coupling.

Therefore, the energy coupled to the top surface is minimum, while that to bottom is

maximum, which leads to non-reciprocity of wave propagation.

These non-reciprocal coupling characteristics already suggest a potential use as an

isolator. However, the non-reciprocity can be destroyed by the reflection from the straight

edges. Suppose we have the forward wave propagation on the bottom surface of the ferrite

68

film, while backward wave on the top surface. As shown in Fig 3.17, although transducer 2

may have weak coupling to the top surface for the backward propagation, it can still

excited the forward wave on the bottom surface and get reflected to the top surface for

backward propagation. The surface wave can be bouncing forward and backward and

form a standing wave in the film, which result in reciprocal transmission. On the next

section, we will discuss the filter designs based on these microstrip transducers.

Fig 3.16. Geometry of the transducers: Inverted L-shaped microstrip transducers with


.

69

6 7 8 9 100

10

20

30

40

50

60

70

TOP layer

Bottom

Ra

dia

tio

n r

es

ista

nc

e

Freq (GHz)

Fig 3.17. Radiation resistance for coupling of transducers to top and bottom surface of the

YIG film. DC bias field is 1600 Oe.

Fig 3.18. Reciprocal excitations of microstrip transducer due to the reflection of the

straight edge.

Straight Edge

Straight Edge

Transducer 1 Transducer 2

Forward wave

Backward wave

70

3.5 Conclusion

In this chapter we’ve presented permeability tensor and wave propagation

properties of magnetic material under magnetoquasistatic approximation, when the

wavelength in the medium is much smaller than that of an ordinary electromagnetic wave

at the same frequency. Boundary conditions were considered to deduce magnetostatic

surface wave propagation modes inside a finite ferrite slab under tangential magnetization.

Also, the working excitation structure for magnetostatic wave in ferrite slab were discussed,

and microstrip transducers were designed via Ansoft HFSS simulation. Non-reciprocity

was analyzed via radiation resistance equivalent model of the transducers for

magnetostatic wave excitation.

3.6 Reference

[1] J. S. Hong and M. J. Lancaster, Microstrip Filters for RF/Microstrip Applications. New

York: Wiley, 2001.

[2] I. C. Hunter and J. D. Rhodes, ―Electronically tunable microwave bandpass filters,‖

IEEE Trans. Microw. Theory Tech., Vol. 30, pp. 1354-1360, Sept. 1982.


filters,‖ IEEE Trans. Microw. Theory Tech., vol 39, pp. 643-653, Apr. 1991.

[4] Daniel D. Stancil, ―Theory of magnetostatic waves‖, Springer-Verlag, 1993

[5] Kok Wai Chang and Waguih Ishak, "Magnetostatic surface wave straight-edge

71

resonators", Circuits, Systems, and Signal Processing, Vol 4, Numbers 1-2 (1985), pp

201-209

[6] P. R. Emtage, ―Interaction of magnetostatic waves with a current,‖ J. Appl. Phys., 49,

p.4475 (1978)


York: Wiley, 2001.

[8] J. D. Adam, L. E. Davis, G. F. Dionne, E. F. Schloemann, and S. N. Stitzer, ―Ferrite

Devices and Materials,‖ IEEE Trans. Microw. Theory Tech., vol. 50, pp. 721-737, Mar.

2002.

[9] P. W. Wong and I. C. Hunter, ―Electronically Reconfigurable Microwave Bandpass

Filter,‖ IEEE Trans. Microw. Theory Tech., vol. 57, pp. 3070-3079, Dec. 2009.

[10] Y. Murakami and S. Itoh, ―A bandpass filter using YIG film grown by LPE,‖ in IEEE

MTT-S Int. Microw. Symp. Dig., 1985, pp. 285-287.

[11] Y. Murakami, T. Ohgihara, and T. Okamoto, ―A 0.5-4.0-GHz tunable bandpass filter

using YIG film grown by LPE,‖ IEEE Trans. Microw. Theory Tech., vol 35, pp. 1192-

1198, Dec. 1987.

72

Chapter 4 Bandpass Filters based on magnetostatic wave concepts

4.1 Motivation


all need reconfigurable subsystems such as tunable bandpass filters that are compact,

lightweight, and power efficient [1]. At the same time, isolators with a large bandwidth are

widely used in communication systems for enhancing the isolation between the sensitive

receiver and power transmitter. If a new class of non-reciprocal RF devices that combines

the performance of a tunable bandpass filter and an ultra-wideband isolator is made

available, new RF system designs can be enabled which lead to compact and low-cost

reconfigurable RF communication systems with significantly enhanced isolation between

the transmitter and receiver.

As we’ve discussed in the previous chapter, the non-reciprocal propagation

behavior of magnetostatic surface wave in microwave ferrites such as yttrium iron garnet

(YIG) provides the possibility of realizing a non-reciprocal device [2-3]. Besides, the

magnetostatic surface wave can only excited in certain frequency band, as shown in the

dispersion relations from previous sections. The propagating frequency band is linearly

proportional to the magnitude of DC bias field, following the Kittel’s equation [26].

Therefore, by applying DC bias field parallel to microstrip transducers and proper align

the YIG film, one can achieve bandpass transmission performance with dual functionality

of an isolator.

73

In this Chapter, bandpass filters based on Magnetostatic wave concept will be

presented, with both reciprocal and non-reciprocal characteristics. The study of this

chapter can be divided in to several parts. First, a literature review will be presented to

introduce previous research on magnetostatic wave based filter. Second, an s-band

magnetically and electrically tunable bandpass filters (BPF) with yttrium iron garnet (YIG)

will be introduced. Both experimental and simulation results will be presented. Third, a C-

band low loss straight-edge resonator band pass filter will be presented based on a similar

concept as s-band filter. Then, Simulation and experimental verification will be presented

for a new type of non-reciprocal C-band magnetic tunable bandpass filter with dual

functionality of ultra-wideband isolation. Further parameter optimization will also been

discussed. Finally, this verified concept is used to several further extended designs like C-

band tunable circulator and integrated bandpass filter with spin spray NiCo ferrite.

4.2 Introduction of Previous BPF researches

Recently, with the dramatic growth of wireless communication technologies,

design and manufacturing of low cost microwave components are among the most critical

issues in the communications systems [1]. As one of the basic components of transceivers,

the use of low loss and small sized bandpass filters (BPF) has been continuously growing in

modern communication systems.

Generally speaking, the design of a BPF is subject to the size constraints of the

whole circuit system. Also, a single filter with only one working band may not fulfill the

requirements of multi-band systems. An ideal solution in such circumstance is a bandpass

filters with compact size and low loss, which could also be tuned for different working

74

frequency. Basically, there are four different types tunable bandpass filters, including

electronically tunable bandpass filters [2], magnetically tunable bandpass filters [3]-[5],

mechanically tunable bandpass filters [6], and magnetoelectric (ME) interaction tunable

bandpass filters [7]. Planar ferrite structures with straight edges have been applied in

filters utilizing the magnetostatic wave theory (MSW) [4]-[10]. Most recently, Srinivasan et.

al. [9], Fig 19, reported a bandpass filter using two microstrip line antennas, realized by

exciting the magnetostatic surface waves (MSSW) which can be tuned by electric field.

However, the designed bandpass filter has a large insertion loss of 5 dB, which may not be

suitable for modern communication systems.

(a)

75

Fig. 4.1 bandpass filter using two microstrip line antennas, realized by exciting the

magnetostatic surface waves (MSSW) reported by Srinivasan et. al: (a) schematic; (b) s-

parameters

4.3 S-band magnetically and electrically tunable MSSW band pass filters

In this section, we first present a design of magnetically and electrically tunable

bandpass filter in S-band (2~4 GHz), based on the magnetostatic surface wave utilizing

straight edge YIG films. A large resonant frequency shift of the primary resonant

frequency of 840 MHz, or equivalent to 54% of the central frequency of the bandpass filter

with bias fields of 50 ~ 250 Oe was obtained along with a low insertion loss of < 2dB. A

maximum 3-dB bandwidth of 40 MHz was also achieved when the bias field of 250 Oe was

applied perpendicular to the feed line. Also, limitations of this design will be discussed. In

S-band (2~4 GHz), the high-order width mode and standing wave modes are clearly

separated from the primary resonances, which leads to a series of high order spurious

resonance, downgrading the filter’s band pass performance.

76

4.3.1 Filter design mechanism

As a very important part in the design of a magnetostatic wave bandpass filter, a

transducer with compact coupling structure is needed. In [16], parallel microstrips were

adopted as the transducers, which are shown in Fig. 20 (a). However, the minimum

insertion loss of such bandpass filter is -10 dB that is unsuitable for modern

communication system. As shown in Fig. 20 (b), an L-shaped microstrip transducer was

proposed in [14] and [15], which could enhance the coupling to a minimum insertion loss of

-5 dB [15]. In order to improve the insertion loss problem in magnetostatic wave bandpass

filters, a T-shaped microstrip transducer was proposed in this section and is shown in Fig.

4.2 (c).

(a) (b) (c)

Fig. 4.2. Geometry of the transducers. (a) Parallel microstrip transducers as used in [16]

and [7]. (b) L-shaped microstrip transducers as used in [14] and [15]. (c) T-shaped

microstrip transducers were proposed in this paper.

The geometrical parameters of the T-shaped microstrip transducer include length

and the width of the microstrip, the distance between the two transducers; the length,

77

width and thickness of the YIG film. This structure is realized by patterned copper

cladding on the top surface of the underlying dielectric substrate. The width of the coupling

microstrip is 0.53mm and the length is 18.1mm as we adopted Rogers R3010 as the

substrate, which has a relative permittivity of 10.2 and a thickness of 1.28mm. All the

parameters are listed in the caption of Fig. 21.

Single-crystal YIG films that were grown on gadolinium gallium garnet (GGG)

substrate were used. The thickness of the YIG films are 100 um and the thickness of the

GGG substrate is 500 um. The single-crystal was cut along its (001) orientations to ensure

strong coupling. The saturation magnetization (4πMs) of the YIG films is about 1750 Gauss,

and the intrinsic anisotropy field is about 100 Oe. Due to its single-crystal nature, the FMR

linewidth of the YIG film is only <1 Oe measured at X-band (~9.8 GHz)

Single crystal YIG film was then introduced above the transducer, as indicated in

Fig. 22, in which S3= 4mm and mm and W3=10mm. In order to get a magnetically tunable

bandpass filter, the magnetic bias field (H) is applied perpendicular to the feed line from

zero to 250 Oe. More specifically, if the DC bias field is 200 Oe, the dispersion relation of

the MSSW in YIG can be plot as Fig 4.5, where the width modes ( seem to

merge due to the small separation of resonance frequencies, while the standing wave modes

(n=1, 2 ) seem to have large separations. For the primary

modes,

. As a result, these modes can be distinguished from each other.

78

Fig. 4.3. Geometry of a T-shaped microwave transducer (top view and side view).

W1=1.18mm, W2=18.1mm, S1=9.0mm, S2=0.53mm, S4=1.2mm, H=1.28mm.

Fig 4.4. Schematic of the bandpass filter with single-sided YIG films

79

0 1 2 3 4 51.8

2.0

2.2

2.4

2.6

2.82.71GHz

2.60GHz

2.41GHz

m=5

m=4

m=3

m=2

m=1

Fre

qu

en

cy (

GH

z)

n

2.17GHz

Fig. 4.5. Dispersion relation of Single crystal YIG film, which S3= 4mm and W3=10mm,

DC bias field at 200 Oe, Applied perpendicular to the feed lines. indicates the standing

wave modes

indicates

, as discussed in chapter 3.

4.3.2 Experimental and simulation verification

All the microwave measurements of the bandpass filter were done by a vector

network analyzer (Agilent PNA E8364A) with the frequency scanning from 1 to 3GHz.

The measured transmission coefficient (S21) and reflection coefficient (S11), as well

as the 3-dB bandwidth of bandpass filter with different bias magnetic field were plotted

and analyzed in Fig. 4.5 and Fig. 4.6.

From Fig. 4.5 we can see that the central resonant frequency (primary mode of

Fig.4.5) of the BPF with bias field of 50 Oe is about 1.561 GHz, the minimum insertion loss

is about -2.63 dB and the 3-dB bandwidth is 10 MHz. When the bias field increases to 200

80

Oe, the central frequency shifts upward to 2.172 GHz, this indicates a frequency up shift of

620 MHz relative to the former bandpass filter, and the 3-dB bandwidth is 38 MHz. This

agrees with the discussion for Fig 4.5 very well, where the primary resonance is 2.17GHz.

When we continue to increase the bias field, the central frequency continues shift upward

and the 3-dB bandwidth enhance as well. The central frequency is about 2.401 GHz and the

3-dB bandwidth is 40 MHz when the applied magnetic field is 250 Oe. In this case, the

frequency shift is about 840 MHz, or is equivalent to 54% of the central frequency of the

BPF with bias field of 50 Oe. The 3-dB bandwidth is greatly improved, which is almost four

times than the BPF with 50 Oe. Clearly, a magnetic tunable bandpass filter can be achieved

with single-crystal YIG film loaded over the T-shaped microstrip transducer under

different bias field.

As indicated in the Table I, the insertion loss was decreased with the increased

magnetic bias field, a minimum insertion loss of -0.98 dB was obtained when the bias field

is 150 Oe. After that the insertion loss increased with the increase of the bias field, which

may due to the increased magnetic loss tangent after 150 Oe.

81

Fig 4.5 S-parameters of the bandpass filter with 50-250 Gauss bias field

Fig 4.6. 3-dB bandwidth versus magnetic bias field. S3=4mm, W3=10mm.

82

TABLE 4.1 The Minimum insertion loss with different Magnetic Bias Field

Magnetic field 50Oe 75Oe 100Oe 125Oe

Insertion loss -2.63dB -2.24dB -1.69dB -1.44dB

150Oe 175Oe 200Oe 225Oe 250Oe

-0.98dB -1.02dB -1.09dB -1.26dB -1.64dB

In order to verify the measurement results on the magnetically tunable YIG band pass

filter, simulations done by HFSS were also carried out, by using the exact geometric and

physical parameters of the bandpass filter. Fig. 4.7 shows comparison of the resonance

frequency of the bandpass filter between simulated and measured data under different bias

magnetic field. Clearly, the simulated and measured resonance frequency of the bandpass

filter showed an excellent match.

Fig. 4.8 shows the 3-dB bandwidth comparison of the bandpass filter in measured and

simulated data. Although there are some quite large difference at certain bias magnetic

field (~20 MHz @ 200 Oe), which is likely due to the fact that the limited ability of HFSS in

simulating magnetic materials, the overall trend of the data showed nice agreement

between each other.

83

Fig. 4.7 Simulated and measured bandpass filter resonance frequency

Fig. 4.8. simulated and measured bandpass filter 3-dB bandwidth.

84

4.3.3 Magnetically and Electrically tunability

As a matter of fact, since the thickness of the YIG film is much smaller compare to its

length and width, we can quickly estimate of the resonance frequency of such bandpass

filter by using Kittel’s equation [17]-[19].

√ (4.1)

where is the gyromagnetic constant of about 2.8 MHz/Oe, Hk is the intrinsic in-plane

anisotropy field of the YIG film, and Hdc is the external bias field.

As expected, the measured resonace requency of the bandpass filter matches excellently

with equaiton (1), which is shown in Fig. 4.9.

Fig. 4.9. Calculated and measured FMR frequency against the external magnetic bias field.

85

Fig. 4.10. Measured electric field tunability of the bandpass filter

From Equ. 1, we can see that the resonate frequency of the YIG film can be changed

by both DC bias magnetic field and magnetic anisotropy field. This provides us the

opportunity to tune the bandpass filter without using bulky electromagnets. It has recently

been shown that by using a mechanically coupled magnetoelectric composite that consisting

both ferromagnetic and piezoelectric phases, the anisotropy of the ferromagnetic phase can

be easily change [20, 21].

The magnetoelectric coupling can be easily applied to the YIG film by bonding it to

a piezoelectric substrate. Although the magnetostriction constant for YIG films is very low,

typically less than 1 ppm, with proper engineering, it is still possible to get considerable

tunability. In our attempt, the PZN-PT single crystal was chosen as the piezoelectric

substrate, and the YIG film was directly bonded to it by epoxy. Two very thin layers of

86

copper were pre-deposited on the surfaces of the PZN-PT as electrodes, which can

introduce an in-plane strain in the YIG film by converse magnetoelectric coupling.

Fig. 7 shows the preliminary results that demonstrate the electric field tunability of

the bandpass filter. It is clear, by changing the electric field applied on the PZN-PT single

crystal, the center frequency of the bandpass filter can be tuned by about 200 MHz with an

8 kV/cm of electric field. This corresponds to a change in the magnetic anisotropy of about

50 Oe according to Eq. 4.1. This is a relative small tunability that is mainly due to the small

magnetostriction constant of YIG film. However, by properly choosing the magnetic

material with higher magnetostriction constant, the electric field tunability of the bandpass

filter can be dramatically improved. The detailed research will be presented in future

papers.

4.3.4 Conclusion and challenges

The designed bandpass filters can be tuned by more than 50% of the central

frequency with a magnetic bias field of 250 Oe. It is also possible to tune the resonant

frequency using electric fields by bonding the YIG film to piezoelectric substrate, and an

electric field tunability of about 200 MHz was obtained. However, it does have some

limitations in the applications due to the high-order spurious modes.

As we discussed in Fig. 4.5, the high order modes for 200 Oe bias field is

. The

primary resonance is at 2.17GHz, which has been proved to have good tunability and

bandwidth. Fig. 4.11 shows the s-parameter response, where additional resonances were

found around 2.4GHz with insertion loss of 2dB, 2.6GHz with -10dB, 2.7GHz with -10dB,

corresponding to different standing wave modes, which has a good agreement with the

87

dispersion relation in Fig. 4.5. The splitting due to finite width (m) seems have less impact.

They are merge to the primary standing wave resonance around to . These high

order modes can cause spurious resonances, which increased the rejection band of the band

pass filter.

1.5 2.0 2.5 3.0-20-18-16-14-12-10-8-6-4-20

S11

S21

S-p

ara

mete

r(d

B)

Freq (GHz)

Fig. 4.11 Transmission coefficient S21 of S-band bandpass filter utilizing single crystal

YIG film, with DC bias magnetic field 200 Oe.

88

1.6 1.8 2.0 2.2 2.4-25

-20

-15

-10

-5

0

YIG_W

3 mm

5 mm

7 mm

S12(d

B)

Freq (GHz)

Fig. 4.12 Transmission coefficient S21 in terms of different S3 (length of YIG film along the

propagation axis ), with DC bias magnetic field 200 Oe

In order to avoid these spurious resonances, further investigations have been done

on the geometry of the YIG film. From Fig. 4.12, we can see that the primary central

frequency shifted down and the resonant frequencies of different modes become closer

when S3 increases from 3 mm to 8 mm.

indicates the wave number in the

propagation direction. Apparently, a decreased S3 will increase the separation between two

resonance modes.

4.4. Reciprocal c-band Bandpass filters based on SER

We then expand this concept to the design of magnetically tunable bandpass filter in

C-band (4~8 GHz). A large resonant frequency shift of the primary resonant frequency

from 5GHz to 7GHz, with bias fields of 1.1 ~ 1.6 kOe was obtained along with a low

89

insertion loss of < 1.5dB. A maximum 3-dB bandwidth of 230 MHz was also achieved when

the bias field of 1.6kOe was applied perpendicular to the feed line.

Also, challenges of this design will be discussed. Compared with the S-band design,

the dimension of the YIG film is smaller ( for C-band compared to

for S-band). Therefore, the high-order width modes ( )

have larger separation than that of S-band. As the example in Fig. 4.13, the pass band of

this filter will be split by not only standing wave modes ( ), but also high-

order width modes ( ), which leads to a series of spurious resonance

(ripples in the pass band), downgrading the filter’s band pass performance.

4.4.1 Filter design mechanism

In order to improve the insertion loss and isolation, an inverted L-shaped

transducer has been designed, as shown in fig. 4.13. The transducer is designed on a

0.381mm (15mil) thick Rogers TMM 10i substrate with ε_r=9.8 and tanδ=0.002.

The geometrical parameters of the inverted-L shaped microstrip transducer

include length and the width of the microstrip, the distance between the two transducers;

the length, width and thickness of the YIG film. This structure is realized by patterned

copper cladding on the top surface of the underlying dielectric substrate. The width of the

coupling microstrip is 0.32mm and the length is 4.5mm as we adopted Rogers tmm 10i as

the substrate, which has a relative permittivity of 9.8 and a thickness of 0.381mm. All the

parameters are listed in the caption of Fig. 4.13.

90

Single crystal YIG slab with thickness about 108µm was placed on top of the

transducers, as shown in Fig. 1. The saturation magnetization (4πMs) of the single crystal

YIG slab is about 1750 Gauss and the FMR linewidth is less than1 Oe at X-band (~9.8

GHz). The bias magnetic field H is at X- band (~9.8 GHz). The bias magnetic field H is

applied perpendicular to the feed line.

Single crystal YIG film was then introduced above the transducer, as indicated in

Fig. 4.13, in which . In order to get a magnetically tunable

bandpass filter in C-band (5GHz to 7GHz in this dissertation), the magnetic bias field ( ) is

applied perpendicular to the feed line from 1.1 kOe to 1.6 kOe. More specifically, if the DC

bias field is 1.6 kOe, the dispersion relation of the MSSW in YIG was plot as Fig. 4.14.

indicates the standing wave modes

indicates

, as discussed in chapter 3,

eq. (3.48).The width modes ( seem to have as large separation of resonance

frequencies, as the standing wave modes (n=1, 2 ). So, the high order mode analysis is

much more complicate than the S-band case, where the width modes can be neglected. For

the primary modes, the resonance happens at

. Other resonances with (n,m) combo can be found in Table 4.2.

These modes are distinguished from each other, which leads to a pass band with many

ripples. In other word, the pass band will be split by these discrete resonances and is no

longer smooth.

91

Figure 4.13 Geometry of the transducers: Inverted L-shaped microstrip transducers with


0 1 2 3 4 56.5

6.6

6.7

6.8

6.9

7.0 m=4

m=3

m=2

m=1

Fre

qu

en

cy (

GH

z)

n

6.67GHz

6.8GHz

6.86GHz

6.88GHz

92

Fig. 4.14. Dispersion relation of MSSW in a single crystal YIG film, which W4= 2mm and

L2=3mm, DC bias field at 1.6 kOe, Applied perpendicular to the feed lines. indicates the

standing wave modes

indicates

, as discussed in chapter 3, eq. (3.48).

Table 4.2 the resonance frequency of width and standing wave mode with DC

magnetic bias field 1600 Oe.

GHz 1 2 3 4

1 6.67 6.56 N/A N/A

2 6.8 6.75 6.67 N/A

3 6.86 6.83 6.73 6.73

4 6.88 6.88 6.83 6.80

4.4.2 Simulations and Experimental verification

The proposed c-band bandpass filter was then simulated with Ansoft HFSS 12.1.

DC magnetic bias field 1600 Oe applied perpendicular to the feed line. The transmission

coefficient was calculated and shown in Fig. 4.15. We can see a very wide pass band with a

central resonance 6.7GHz with -1.8dB insertion loss and 170MHz 3-dB band width.

However, many discrete resonance modes can also be observed in the pass band: 6.56GHz

with 6dB loss, 6.67GHz with 4dB loss, 6.7dB with 1.8dB loss, and 6.88GHz with 5.4dB loss,

93

along with many other high order ones. These resonances split the major pass band and

cause the ripples. These observations match with the conclusion in figure 4.14 and table 4.2.

S12

S21

6.0 6.4 6.8 7.2 7.6 8.0-30

-20

-10

0

7GHz, -9dB

S-p

ara

me

ter(

dB

)

Freq (GHz)

6.70GHz , -1.8dB

6.88GHz, -5.4dB

6.67GHz, -4dB

6.56GHz,-6dB

6.80GHz -5.8dB

6.36GHz,-16dB

Fig. 4.15. Simulation result of bandpass filters based on YIG SER film, with DC magnetic

bias field 1600 Oe

94

S12

S21

6.0 6.4 6.8 7.2 7.6 8.0-30

-20

-10

0

S-p

ara

me

ter(

dB

)

Freq (GHz)

6.59GHz,

-6.3dB

6.65GHz, -4.3dB6.70GHz, -2.4dB

6.80GHz, -5.6dB

6.88GHz, -8.3dB

7.0GHz, <-22dB

6.40GHz, -22dB

Fig. 4.16. experimental result of bandpass filters based on YIG SER film , with DC

magnetic bias field 1600 Oe

Then the transmission coefficient was measured via network analyzer and shown in

Fig 4.16. We can see a similar pass band as the simulation with a central resonance 6.7GHz

with -2.4dB insertion loss and 160MHz 3-dB band width. The insertion loss increases from

1.6dB to 2.4dB, but the band becomes smoother, although it still contains lots of ripples, as

shown in Fig. 4.16.

The resonance modes from simulation and experiment were summarized in Table

4.3 and plotted in Fig. 4.17. The modes higher than the primary resonance (>6.7GHz)

corresponds to the standing wave modes ( ) , while those lower than primary

resonance (<6.7GHz) corresponds to the finite width modes ( ). In

experiments, the edges of YIG film were cut via a diamond saw. The edges are not ideally

95

straight edge, which leads to more loss from the reflection. Therefore, these high order

modes from experiment are proved to have higher insertion loss than those from the

simulation results. Also, the insertion loss of the primary resonance increased from 1.6dB

to 2.4dB, and the 3-dB band width decrease from 170MHz to 160MHz, because of other

fabrication losses, like copper defects on transmission line and non-uniform thickness of

YIG film. In one word, the simulation results match the experimental results very well on

primary resonance.

Table 4.3 Resonance mode comparison between simulation and experimental data of

the proposed c-band bandpass filter

Simulation 6.36GHz 6.56GHz 6.67GHz 6.7GHz 6.80GHz 6.88GHz 7.0GHz

-16dB -6dB -4dB -1.6dB -5.8dB -5.4dB -9dB

Experiment 6.40GHz 6.59GHz 6.65GHz 6.7GHz 6.80GHz 6.88GHz 7.0GHz

-22dB -6.3dB -4.3dB -2.4dB -5.6dB -8.3dB -22dB

96

6.5 6.6 6.7 6.8 6.9 7.0-25

-20

-15

-10

-5

0

Simulation

Experiemnt

Insert

ion

Lo

ss(d

B)

Freq (GHz)

Fig. 4.17. Resonance mode comparison between simulation and experimental data of the

proposed c-band bandpass filter

4.4.3 Magnetically tunability

As a matter of fact, since the thickness of the YIG film is much smaller compare to

its length and width, we can quickly estimate of the resonance frequency of such bandpass

filter by using Kittel’s equation [17]-[19].

√ (4.2)

where is the gyromagnetic constant of about 2.8 MHz/Oe, Hk is the intrinsic in-plane

anisotropy field of the YIG film, and Hdc is the external bias field.

Figure 4.18~4.20 shows the measured result of the fabricated C-band tunable band

pass filter on straight edge YIG film. The DC bias magnetic field varies from 1.1k Oe to

97

1.6kOe. The central resonance frequencies were tuned from 5.1GHz to 6.7GHz. A

tunability of 320MHz/100Oe bias shift has been observed. The high order modes under

these bias conditions are similar to those with 1.6kOe bias, as we discussed in the previous

section. Splitting resonances and ripples in the pass bands can be observed. Also, the pass

bands in S12 are identical to those in S21, so this band pass filter is reciprocal.

From Fig 4.20, we can see that the central frequencies of S12 and S21 are linearly

proportional to the bias field. These central frequencies have 130MHz difference compared

with the FMR frequencies calculated from the Kittel’s equation, which is the lower cut-off

frequency of pass band. The central frequencies of these pass band match the primary

resonances in the dispersion relation (Fig 4.14) very well.

4 6 8-40

-35

-30

-25

-20

-15

-10

-5

0

DC bias

1.1kOe

1.2kOe

1.3kOe

1.4kOe

1.5kOe

1.6kOe

S2

1(d

B)

Freq (GHz)



perpendicular to DC bias magnetic field

98

4 6 8-40

-35

-30

-25

-20

-15

-10

-5

0

DC bias

1.1kOe

1.2kOe

1.3kOe

1.4kOe

1.5kOe

1.6kOe

S1

2(d

B)

Freq (GHz)



perpendicular to DC bias magnetic field

1.1 1.2 1.3 1.4 1.5 1.64.85.05.25.45.65.86.06.26.46.66.8

S21

S12

FMR Frequency

Re

so

na

nc

e F

req

. (G

Hz)

Applied Bias field (Oe)


filter on straight edge YIG film with the FMR frequency calculated from Kittel’s equation.

99

4.4.4 Limitation of this design

All in all, we’ve investigate design of magnetically tunable bandpass filter in C-band

(4~8 GHz) with YIG SER. A large resonant frequency shift of the primary resonant

frequency from 5GHz to 7GHz, with bias fields of 1.1 ~ 1.6 kOe was obtained along with a

low insertion loss of < 1.5dB. A maximum 3-dB bandwidth of 230 MHz was also achieved

when the bias field of 1.6kOe was applied perpendicular to the feed line. However, this

design has two major limitations that we might improve in the following sections:

(1) Spurious resonances, or the high-order modes, split the major resonance to

many ripples. The pass bands are not smooth.

(2)The band pass transmission is reciprocal due to the reflection from the straight

edges.

4.5 Non-reciprocal c-band Bandpass filters based on rotated SER

In the previous section, MSSW based YIG devices have the unwanted reflected

waves from the straight edges, which will induce spurious resonance [11] due to the

standing wave modes, formed from the forward and backward wave.

In this section, starting from the analysis and simulation of magnetostatic wave

propagation in YIG slabs, a new method of suppressing the spurious resonance is proposed.

The YIG slab was rotated by a proper angle to diminish standing wave modes in order to

get a much smoother pass band. The designed C-band tunable bandpass filters show a

central frequency shift from 5.2 GHz to 7.0 GHz under in-plane magnetic fields from 1.1

kOe to 1.6 kOe with a reasonable insertion loss < 2.3 dB. Furthermore, the oblique angle

between the DC bias field and the propagation direction leads to non-reciprocal

transmission characteristics of the forward and backward MSSW, which provide more

100

than 20 dB isolation across all measured frequency range. The proposed device prototype,

which can perform simultaneously with the filtering and isolating functions, may be very

useful in practical applications of the filter and RF system design.

4.5.1 The mechanism of the non-reflection boundary on a rotated YIG film

The major spurious resonances are due to the unwanted reflected waves

from the straight edges. One can diminish them by using a non-reflection edge. For

example, several kinds of MSSW techniques have been reported to suppress the unwanted

reflection by depositing a film or attaching an additional ferrite material on to the edges of

YIG films to absorb the MSW [20]-[23]. Some simpler methods are: tapered the YIG film

edges at an angle (≠90o) [24]; local low bias field at the edge of the film [22]. The schematic

of a YIG resonator with a tapered edge is shown in Fig. 4.21. The reflection was diminished

and no backward transmission was excited. The MSSW was restricted on the bottom

interface of YIG film, which induces the non-reciprocal characteristics. However, in

practical designs, the tapering process of YIG can cause some other issues like non-uniform

thickness, cracks in YIG film due to damage, which make this approach not an ideal

solution. Fig 4.22 shows the diminishing of unwanted reflection from edge by applying

different DC bias condition , or applying a ferrite absorber around edge.

These approaches, however, need extra effort to implement, which makes the design of

band pass filter much more complicate.

101

Fig. 4.21 MSSW propagation in a tapered YIG film. [16]

Fig. 4.21 MSSW propagation in a YIG film with different bias condition at edges or an

absorber. [20-23].

Fig. 4.22 MSSW propagation in a YIG film with a 45o inclined edge boundary at the YIG-

air boundary.

Forward wave

Forward wave

𝐻𝐷𝐶

𝐻𝐷𝐶

Absorber

102

A new method of suppressing the spurious resonance is proposed. Let us first

consider a 45o edge boundary between YIG film and the air, as shown in fig. 4.22. The DC

bias magnetic field is applied in plane and perpendicular to the incident magnetostatic

surface wave (MSSW). After the reflection on the 45o edge boundary, the wave

propagation is parallel to the bias field. So the wave profile follows the magnetostatic back

volume wave (MSBVW), as discussed in chapter 3, (table 3.1). However, due to the

different dispersion relations of these two wave profiles, the allowed frequency band for

propagation modes are different, as shown in Fig 4.23. For example, suppose we applied

HDC=1600Oe to a YIG film with thickness 108um, 4piMs 1750Gauss, the MSSW

propagation is limited in 6.5GHz to 6.9GHz, where no propagation modes exist for

MSBVW. So, the reflection like Fig4.22 won’t happen. Instead, the reflection will decay

very fast and the energy dissipates fast along this path, because it is propagating in the stop

band of MSBVW.

In one word, the 45o rotated edge forms a non-reflection boundary for the MSSW,

which is very useful for utilizing the non-reciprocal characteristics of MSSW and avoid the

standing wave modes due to the reflection from the edges. By simply rotating the film by

45o, we do not need to apply either additional DC bias field and absorbers, or an additional

complicate process to taper the edge. Therefore, Compared with other approaches,

rotating a YIG film is much easier to be realized in a practical design.

103

0 2 4 6 8 104.5

5.0

5.5

6.0

6.5

7.0

n=5n=4

n=3

n=2

n=1

MSBVWF

req

ue

nc

y (

GH

z)

kd

MSSW


and back volume wave (MSBVW), with DC bias field 1.6kOe, on YIG (thickness 108um,

4piMs 1750Gauss)

Fig. 4.24 Non-reciprocal c-band BPF on a rotated YIG film.

𝟒𝟓𝒐

104

4.5.2 Simulations and Experimental verification

Based on the non-reflection boundary discussion in section 4.5.1, and the previous

reciprocal filter design in C-band, a non-reciprocal c-band BPF was proposed on a 45o

rotated YIG film. The alignment of the YIG slab can be adjusted through rotating around

its center, which can lead to a non-reciprocal s-parameter performance.

This proposed C-band bandpass non-reciprocal filter was then simulated with Ansoft

HFSS 12.1. More specifically, let us first investigate the DC magnetic bias field 1600 Oe

applied perpendicular to the feed line. The transmission coefficient was calculated and

shown in Fig 4.25.

We can see a very wide pass band for S21 (forward transmission), with a central

resonance 6.67GHz with -2dB insertion loss and 220MHz 3-dB band width. The pass band

is clear and smoother that the un-rotated case, although some small ripples can be found,

like 6.88GHz with 4dB insertion loss and 7GHz with -11dB insertion loss. On the other

hand, the insertion loss S12 (backward transmission) was greater than 18dB over the band

6GHz to 8GHz.

We can conclude that this filter has duel functionality of isolators. On the other

word, it is a non-reciprocal band pass filter. Then another question is that if the backward

transmission does not happen, where the energy goes. S22 is over 13dB, which means that

very little energy was reflected back to the port 2. So, the missing energy dissipates in the

YIG film.

Then the transmission coefficient was measured via network analyzer and shown in

Fig 4.26. We can see a similar pass band as the simulation with a central resonance

6.67GHz with -1.8dB insertion loss and 190MHz 3-dB band width. Compared with the

105

simulated results, the insertion loss decreases from 2dB to 1.8dB, and 3-dB bandwidth

increases from 230MHz to 190MHz. Also, the band becomes smoother due to the

suppression of the reflection through edges, although there is still a side lobe at 6.86GHz

with -11dB insertion loss, which can be neglected. The measured S22 is -20dB at 6.62GHz,

which confirms the analysis from the simulation that the energy dissipates in the medium

instead of reflecting back to the port. It is notable this type of design has a relatively high Q

of over 35 compared to other ferrite tunable bandpass filters.

6.0 6.5 7.0 7.5 8.0-30

-20

-10

0

S21

S12

S22

S-p

ara

me

ter(

dB

)

Frequency (GHz)

Fig. 4.25 Simulated s-parameter of our bandpass filter with parallel/rotated YIG slab

under DC bias field of 1.6 kOe.

106

6.0 6.5 7.0 7.5 8.0-30

-20

-10

0

S21

S12

S22

S-p

ara

mete

r(dB

)

Frequency (GHz)

Fig. 4.26 Measured s-parameter of our bandpass filter with parallel/rotated YIG slab

under DC bias field of 1.6 kOe.

4.5.3 Magnetically tunability

(1) Resonance frequency vs bias field

Figure 4.27~4.30 shows the measured result of the fabricated non-reciprocal C-band

tunable band pass filter on rotated YIG film. The DC bias magnetic field varies from 1.3k

Oe to 1.7kOe. The central resonance frequencies were tuned from 5.8GHz to 7.0GHz. A

tunability of 300MHz/100Oe bias shift has been observed. The results indicated a well-

shaped bandpass band with insertion loss between 1.8 ~ 3.0 dB, and bandwidth around

190MHz at 6.67GHz for 1.6 kOe bias field. The resonant frequencies follow the Kittel’s

equation [27] and can be tuned by DC magnetic fields, as shown in fig 4.31 Furthermore,

non-reciprocal performance was observed with isolation over 20dB between two

107

transmission directions, throughout the C-band 4GHz to 8GHz, and over15dB among

2GHz to 10GHz.

From Fig 4.31, we can see that the central frequencies of S21 are linearly

proportional to the bias field. These central frequencies have 200MHz difference compared

with the FMR frequencies calculated from the Kittel’s equation, which is the lower cut-off

frequency of pass band. The S11 (fig 4.29), and S22 (fig.4.30) shows little reflection back to

the excitation ports, which means the missing energy dissipates in the YIG film.

The central frequencies of these pass band match the primary resonances in the

dispersion relation (Fig 4.14) very well.

2 4 6 8 10-40

-35

-30

-25

-20

-15

-10

-5

0

DC bias H

1.3kOe

1.4kOe

1.5kOe

1.6kOe

1.7kOe

S2

1(d

B)

Freq (GHz)


rotated YIG film.

108

2 4 6 8 10-40

-35

-30

-25

-20

-15

-10

-5

0DC bias H

1.3kOe

1.4kOe

1.5kOe

1.6kOe

1.7kOeS

12

(dB

)

Freq (GHz)


rotated YIG film.

2 4 6 8 10-30

-25

-20

-15

-10

-5

0

DC bias H

1.3kOe

1.4kOe

1.5kOe

1.6kOe

1.7kOe

S1

1(d

B)

Freq (GHz)


rotated YIG film.

109

2 4 6 8 10-20

-15

-10

-5

0

DC bias H

1.3kOe

1.4kOe

1.5kOe

1.6kOe

1.7kOe

S2

2(d

B)

Freq (GHz)


rotated YIG film.

1.3 1.4 1.5 1.6 1.75.4

5.6

5.8

6.0

6.2

6.4

6.6

6.8

7.0 Measured central frequency

Kittel's Equation

Reso

nan

ce f

req

uen

cy (

GH

z)

DC Bias field (k Oe)


filter on rotated YIG film with the FMR frequency calculated from Kittel’s equation

110

(2) Insertion Loss and isolation vs central frequency

The insertion loss of the forward pass bands and the isolation of the backward

transmission are then plotted in fig. 4.32 (a) and (b), respectively. The insertion loss

increases from 1.8dB to 3dB, when the central resonance frequency increases. A possible

reason for higher insertion loss in lower frequency is the impedance mismatch. From fig

4.29 and fig 4.30, we can see the return loss is 8dB at 5.7GHz (1.3kOe bias field), while is

18dB at 7GHz. Proper optimization on the transducer width may help fix this mismatch

issue at whatever specific operating frequencies on a practical application. On the other

hand, the isolation is over 20dB for the whole tunable band.

5.6 6.0 6.4 6.8

-3.0

-2.8

-2.6

-2.4

-2.2

-2.0

-1.8 Insertion Loss

Ins

ert

ion

Lo

ss

(d

B)

Freq (GHz)5.6 6.0 6.4 6.8

-24

-23

-22

-21

-20

-19

-18

Isolations

iso

lati

on

(dB

)

Freq (GHz)

Fig. 4.32 The insertion loss of the forward pass bands and the isolation of the backward

transmission.

(3) Bandwidth vs central frequency

The 3-dB bandwidth of the pass bands were plotted in terms of central resonant

frequency, as shown in Fig. 4.33. The bandwidth is around 200MHz to 210MHz throughout

the entire tuning range. So, the Q ( ) of the filter increases as the central frequency

increases.

111

5.6 6.0 6.4 6.8180

190

200

210

220

bandwidth(MHz)

Ban

dw

idth

(MH

z)

Freq (GHz)

Fig. 4.32 The 3-dB bandwidth of the forward pass bands for the fabricated c-band non-

reciprocal bandpass filter.

4.5.4 Summary for C-band non-reciprocal filter

In summary, a novel non-reciprocal C-band magnetic tunable bandpass filter (BPFs)

with a YIG slab has been designed, fabricated and tested, which is based on an inverted L-

coupling structure loaded with a rotated single-crystal YIG slab. Magnetostatic surface

wave propagation in the rotated YIG leads to non-reciprocal behavior. The tunable

resonant frequency of 5.3 ~ 6.8GHz was obtained for the BPF with the magnetic bias field

1.1kOe ~ 1.6kOe, applied perpendicular to the feed line. At the same time, the BPF acts as

an ultra-wideband isolator with more than 22dB isolation at the pass band with insertion

loss of 1.6~3dB. The demonstrated nonreciprocal magnetically tunable bandpass filters

with isolator duel functionality should be promising in C-band RF front and other

microwave circuits.

112

4.6 Integrated bandpass filter with spin spray materials

Nowadays, integrated components for communication system are highly demanded.

The verified magnetostatic wave concept was then used to expand the filter designs to an

integrated solution. The material we used is NiCo ferrite, which can be deposited via the

spin spray thin film deposition process in our lab.

Top view 1 mm

850 um

70um

400um

Cross Section

15μm 5μm 15μm

6μm

2μm

2μm

Polyamide

Cu

Cu

NiCo Ferrite 1.5μm

113

Fig. 4.33 Geometry of integrated band pass filter with MSSW concept

The geometrical parameters of the S-shaped co-planar wave transducer include

length and the width of the microstrip, the distance between the two transducers, the length,

width and thickness of the NiCo ferrite film are shown in fig.4.33. This structure is realized

by patterned copper cladding on the top surface of the underlying dielectric substrate. The

width of the coupling microstrip is 15μm and the length is 1 mm as we adopted polyamide

as the substrate, which has a relative permittivity of 3.5 and a thickness of 6μm. The ends

of the two transducers are connected to the ground, in order to achieve maximum current

on the transducer. All the parameters are listed Fig. 4.33.

The NiCo ferrite is deposited via spin spray thin film deposition. The thickness of

the NiCo films is 2 um with parallelogram shape. The saturation magnetization (4πMs) of

the NiCo films is about 4800 Gauss, and the intrinsic anisotropy field is about 165 Oe. The

NiCo ferrite is then patterned underneath the transducer for magnetostatic wave, as

indicated in Fig. 4.34.

In order to get a magnetically tunable bandpass filter, the magnetic bias field (H) is

applied perpendicular to the feed line from zero to 125 Oe to 625 Oe. More specifically, if

the DC bias field is 500 Oe, the simulation transmission response was shown in Fig. 4.35.

The central frequency is at 5.4GHz, with insertion Loss: 1.98dB and -3dB Bandwidth:

400MHz, or 7.4%. The return loss is over 23dB. Furthermore, the central resonant

frequencies have been tuned from 3.7GHz to 5.9GHz with a varied DC bias 125 Oe to 625

Oe, which 440MHz/100Oe tunability. The transmission coefficient is reciprocal, due to the

114

small angle of the edges. This integrated design can lead to integrated bandpass filters for

compact and low-cost reconfigurable RF communication systems

1 2 3 4 5 6 7 8-30

-25

-20

-15

-10

-5

0

S12

S21

S11

S22

S-p

ara

me

ter(

dB

)

Freq (GHz)

Fig. 4.34. Simulated results of integrated bandpass filter with parallelogram shape.

1 2 3 4 5 6 7 8-30

-25

-20

-15

-10

-5

0 125 Oe

250Oe

375 Oe

500 Oe

625 Oe

S1

2(d

B)

Freq (GHz)

115

Fig. 4.35. Simulated results of integrated bandpass filter with parallelogram shape, with

DC bias from 125Oe to 625 Oe

4.7 Conclusion

In this Chapter, bandpass filters based on Magnetostatic wave concept were

presented, with both reciprocal and non-reciprocal characteristics. An s-band

magnetically and electrically tunable bandpass filters (BPF) with yttrium iron garnet (YIG)

will be introduced. A large resonant frequency shift of the primary resonant frequency of

840 MHz, or equivalent to 54% of the central frequency of the bandpass filter with bias

fields of 50 ~ 250 Oe was obtained along with a low insertion loss of < 2dB. A maximum 3-

dB bandwidth of 40 MHz was also achieved when the bias field of 250 Oe was applied

perpendicular to the feed line.

A C-band low loss straight-edge resonator band pass filter was presented based on

a similar concept as s-band filter. A large resonant frequency shift of the primary resonant

frequency from 5GHz to 7GHz, with bias fields of 1.1 ~ 1.6 kOe was obtained along with a

low insertion loss of < 1.5dB. A maximum 3-dB bandwidth of 230 MHz was also achieved

when the bias field of 1.6kOe was applied perpendicular to the feed line. Then, Simulation

and experimental verification will be presented for a new type of non-reciprocal C-band

magnetic tunable bandpass filter with dual functionality of ultra-wideband isolation.

The designed C-band tunable bandpass filters show a central frequency shift from

5.2 GHz to 7.0 GHz under in-plane magnetic fields from 1.1 kOe to 1.6 kOe with a

reasonable insertion loss < 2.3 dB. Furthermore, the oblique angle between the DC bias

field and the propagation direction leads to non-reciprocal transmission characteristics of

116

the forward and backward MSSW, which provide more than 20 dB isolation across all

measured frequency range. The proposed device prototype, which can perform

simultaneously with the filtering and isolating functions, may be very useful in practical

applications of the filter and RF system design.

4.8 References


York: Wiley, 2001.

[2] I. C. Hunter and J. D. Rhodes, ―Electronically tunable microwave bandpass filters,‖

IEEE Trans. Microw. Theory Tech., Vol. 30, pp. 1354-1360, Sept. 1982.


filters,‖ IEEE Trans. Microw. Theory Tech., vol 39, pp. 643-653, Apr. 1991.

[4] B. K. Kuamr, D. L. Marvin, T. M. Christensen, R. E. Camley, and Z. Celinski, ―High-

frequency magnetic microstrip local bandpass filters,‖ Appl. Phys. Lett., vol 87, 222506,

Nov. 2005.

[5] N. Cramer, D. Lucic, R. E. Camley, and Z. Celinski, ―High attenuation tunable

microwave notch filters utilizing ferromagnetic resonance,‖ J. Appl. Phys., vol 87, pp.

6911-6913, May 2000.

[6] T. Y. Yun and K. Chang, ―Piezoelectric-Transducer-Controlled tunable microwave

circuits,‖ IEEE Trans. Microw. Theory Tech., Vol. 50, pp. 1303-1310, May 2002.


bandpass filter,‖ Electron. Lett., vol 42, pp. 540-541 , Apr. 2006.

[8] C.S. Tsai, G. Qiu, H. Gao, L. W. Yang, G. P. Li, S. A. Nikitov, and Y. Gulyaev,

―Tunable wideband microwave band-stop and band-pass filters using YIG/GGG-GaAs

117

layer structures,‖ IEEE Trans. Magn., Vol. 41, pp. 3568-3570, Oct. 2005.

[9] C. S. Tsai and G. Qiu, ―Wideband microwave filters using ferromagnetic resonance

tuning in flip-chip YIG-GaAs layer structures,‖ IEEE Trans. Magn., Vol. 45, pp. 656-

660, Feb. 2009.

[10] G. M. Yang, X. Xing, A. Daigle, M. Liu, O. Obi, J. W. Wang, K. Naishadham, and N.

Sun, "Electronically tunable miniaturized antennas on magnetoelectric substrates with

enhanced performance," IEEE Trans. Magn., Vol. 44, No. 11, pp. 3091-3094, Nov. 2008.

[11] G. M. Yang, X. Xing, A. Daigle, M. Liu, O. Obi, S. Stoute, K. Naishadham, and N. X.

Sun, ―Tunable miniaturized patch antennas with self-biased multilayer magnetic films,‖

IEEE Trans. Antennas Propag., vol 57, pp. 2190-2193, July 2009.

[12] Y. Murakami and S. Itoh, ―A bandpass filter using YIG film grown by LPE,‖ in IEEE

MTT-S Int. Microw. Symp. Dig., 1985, pp. 285-287.



1198, Dec. 1987.

[14] S. M. Hanna and S. Zeroug, ―Single and coupled MSW resonators for microwave

channelizers,‖ IEEE Trans. Magn., Vol. 24, pp. 2808-2810, Nov. 1988.

[15] W. S. Ishak and K. W. Chang, ―Tunable microwave resonators using magnetostatic

wave in YIG films,‖ IEEE Trans. Microw. Theory Tech., vol 34, pp. 1383-1393, Dec.

1986.

[16] J. D. Adam and S. N. Stitzer, ―MSW frequency selective limiters at UHF,‖ IEEE Trans.

Magn., Vol. 40, No. 4, pp. 2844-2846, July 2004.

[17] Y.Ikuzawa and K. Abe, ―Resonant modes of magnetostatic waves in a normally

118

magnetized disk,‖ J. Appl. Phys., vol 48, pp. 3001-3007, July 1977.

[18] N. X. Sun, S.X. Wang, T. J. Silva and A. B. Kos, ―High frequency behavior and

damping of Fe-Co-N-based high-saturation soft magnetic films,‖ IEEE Trans. Magn.,

Vol. 38, No. 1, pp. 146-150, Jan. 2002.

[19] C. Kittel, Introduction to Solid State Physics. New York: Wiley, 1996.



1198, Dec. 1987.

[21] S. M. Hanna and S. Zeroug, ―Single and coupled MSW resonators for microwave

channelizers,‖ IEEE Trans. Magn., Vol. 24, pp. 2808-2810, Nov. 1988.

[22] W. S. Ishak and K. W. Chang, ―Tunable microwave resonators using magnetostatic

wave in YIG films,‖ IEEE Trans. Microw. Theory Tech., vol 34, pp. 1383-1393, Dec.

1986.

[23] J. D. Adam and S. N. Stitzer, ―MSW frequency selective limiters at UHF,‖ IEEE Trans.

Magn., Vol. 40, No. 4, pp. 2844-2846, July 2004.


bandpass filter,‖ Electron. Lett., vol 42, pp. 540-541 , Apr. 2006.

[25] G. M. Yang, J. Lou, G. Y. Wen, Y. Q. Jin and N. X. Sun, "Magnetically Tunable

Bandpass Filters with YIG-GGG/ YIG-GGG-YIG Sandwich Structures", International

Microwave Symposium (IMS) 2011, Baltimore, MD.

[26] Kok-Wai Chang and W. S. Ishak, ―Magnetostatic surface wave straight-edge

resonators,‖ Trans. Circuits, Syst., Signal Proc., vol. 4, no. 1-2, pp. 201-209, 1985.

119

[27] J. H. Collins, D. M. Hastie, J. M. Owens, and C. V. Smith, Jr., "Magnetostatic wave

terminations," Appl. Phys., vol. 49, pp. 1800-1802, 1978

120

Chapter 5: Tunable Planar Isolator with Serrated Microstrip

Structure

Modern communication systems, radars, and metrology systems all need tunable

components that are compact, lightweight, and power efficient. Tunable isolators are

highly desired in communication systems for enhancing the isolation between the sensitive

receiver and power transmitter. The integration of passive devices using a ferrite, such as

circulators and isolators, has become one focus of research for electronic applications in the

microwave range.

Isolators based on the non-reciprocal ferromagnetic resonance (FMR) of

microwave ferrites in waveguide or on planar transmission lines have been widely used [1-

7]. The microwave ferrites experience LHCP (left-handed-handed circular polarization)

RF excitation magnetic fields in forward propagation while RHCP (right-handed circular

polarization) in backward propagation, leading to minimal absorption in forward

propagation while strong FMR absorption in backward propagation. Another class of

isolators is based on field displacement. The energy from the backward travelling signal is

absorbed in a resistive film [2]-[4]. However, the resist absorbers are usually very sensitive

to the location of the ferrite, and they can hardly have tunability via magnetic field.

In this Chapter, a tunable planar isolator with serrated microstrip structure based

on ferromagnetic resonance (FMR) of microwave ferrites will be presented, with both

121

tunable and non-reciprocal characteristics. The study of this chapter can be divided in to

several parts. First, a literature review will be presented to introduce previous researches

on isolators. Second, a novel serrated microstrip structure will be presented to achieve

circular polarization of magnetic field, in terms of DC bias field. Current and field

distribution will be analyzed via HFSS simulations. Then, attenuation factor of wave

propagation in magnetic material at the FMR frequency with serrated microstrip structure

will be discussed. Finally, simulation designs and experimental verification will be provided

for the proposed tunable planar isolator with serrated microstrip structure.

5.1 Introduction of isolator based on ferrite

An isolator is a passive non-reciprocal 2-port device which permits RF

energy to pass through it in one direction while absorbing energy in the reverse direction.

Isolators are widely used for decoupling of circuit stages in cascade amplifier stages and

suppress reflection between oscillators and multipliers, as shown in Fig. Tunable isolators

are highly desired in communication systems for enhancing the isolation between the

sensitive receiver and power transmitter.

There are two types of ferrite isolators: (1) ferromagnetic resonance isolator,

which is based on non-reciprocal ferromagnetic resonance (FMR) of microwave ferrites in

waveguide or on planar transmission lines; (2) field displacement isolator, which is based

on absorption in a resistive film for the backward travelling signal.

122

Fig. 5.1 Application of isolators in communication system.

5.1.1 Ferromagnetic resonance isolator

To better understand the interaction between the circular polarized EM wave and

the DC magnetic bias field, let us first introduce the effective permeability under circular

polarization. The magnetic field then can be expressed as:

RHCP: + + (5.1)

LHCP: (5.2)

where RHCP indicates right-handed circular polarization in terms of the DC bias magnetic

field, LHCP in terms of left-handed circular polarization.

By expressing the permeability as a tensor, as in Eq. (1.15) we can calculate the

magnetization as:

+

+ (5.3)

123

+ + (5.4)

So the permeability is then expressed as :

+ (

)

Suppose we have an infinite ferrite medium with saturation magnetization

, linewidth , permittivity , given a DC bias

field the propagation constant inside the ferrite is then calculated as :

√

where ,

, which estimates the loss

from the linewidth .A clear comparison between attenuation constant was plotted in

Fig 5.2. The attenuation constant of LHCP is so small that we have times it by 1000 to

compare with the RHCP. A stop band was found for RHCP at 12GHz to 16GHz, while the

attenuation for LHCP is neglectable. Similarly, propagation constant was plotted in Fig

5.3. In the stop band (12GHz to 16GHz), + is close to zero, while is linearly

proportional to the frequency.

The difference of attenuation and propagation constant, regard of RH or LH

circular polarization can lead to Ferromagnetic resonance isolator designs, as long as one

can place the ferrite medium at the location where forward and backward transmission

have different polarization.

124

4 8 12 16 200

200

400

600

800

1000

1200 RHCP

LHCP*1000

Att

en

uati

on

co

nsta

nt

Freq (GHz)

Stop Band

Fig. 5.2 Attenuation constants for circularly polarized plane waves in the ferrite medium

4 8 12 16 200

400

800

1200

1600 RHCP

LHCP

Pro

pag

ati

on

co

nsta

nt

Freq (GHz)

Fig. 5.2 propagation constants for circularly polarized plane waves in the ferrite medium

125

(a) (b)

Fig. 5.3 Ferrite isolator with waveguide structure: (a) field distribution in waveguide; (b)

Ferrite location in waveguide.

Fig. 5.4 Forward and reverse attenuation constants for the resonance isolator (a) Versus

slab position. (b) Versus frequency.

126

For example, a waveguide operating in mode has the magnetic field

distribution like fig. 5.3(a). Suppose the wave is propagating along z –axis, the field

component can be expressed as:

(5.5)

(5.6)

If let / , we have

. At the locations

, a pure LHCP or

RHCP wave are expected. From Fig. 5.4, we can see the difference of attenuation constant

for forward and reverse transmission.

The operating frequency of these isolators highly depends on the FMR

frequency. So this type of isolator is called ferromagnetic resonance isolator. The basic

characteristics are:

(1) Bias field perpendicular to the propagation direction;

(2) Ferrites are located at some location with circular polarization RHCP and LHCP

(3) The operating frequency of these isolators can be tuned by the FMR frequency.

(4)Narrow bandwidth due to the limit FMR band width

5.1.2 Field displacement isolator

Another type of isolator is field displacement isolator. Consider a waveguide loaded

with a ferrite film, the electric field distributions are different for the forward and

backward transmission because of the loss characteristic of RHCP, as shown in Fig 5.5. As

a result, if one place a lossy resistive film on the location of the ferrite, the forward

transmission won’t be affected, while the reverse wave will be attenuated.

127

This type of isolator has the following characteristics:

(1)Ferrite film is located at the center, so it is hard to dissipate heat. This approach is not

good for high power application

(2) Very sensitive to the location of the ferrite.

(3) The operation frequency does not depend on FMR frequency, so only small bias field is

required. On the other hand, the frequency cannot be tuned.

(4)They have wider bandwidth, depending on the resistive film, not the FMR frequency.

Fig. 5.5 Field displacement isolator

128

5.2 Serrated Microstrip Isolator Design Mechanism

5.2.1 Previous Researches on Planar approaches of isolator designs

The conventional ferrite isolators on waveguides are usually bulky and not

convenient to apply on modern communication systems. The combination of ferrite thin

films and planar microwave structure constituted a major step in the miniaturization of

such ferrites [5-8].

Wen [7] first realized a coplanar isolator with rods of magnetic material located in

the slots between the coplanar waveguide. A transverse DC magnetic field applied parallel

to the surface of the substrate is required to provide appropriate bias conditions. Low

insertion losses < 2 dB and high isolation of 38 dB were achieved at 6 GHz for a line length

of 2 cm. In this approach, high-k TiO2 rutile substrate with a dielectric constant of r=130

is required in order to produce the circularly polarized microwave magnetic field and

furthermore the device is non-integrated due to the slot cut.

Bayard [5] realized a coplanar isolator with ferrofluid between the conductors. An

isolation of 13 dB and insertion losses of 10 dB were measured for a line length of 1 cm

under a polarizing field of 340 kA/m. Capraro et al. [8] reported the transmission

coefficients that showed a non-reciprocal effect, which reached 5.4 dB per cm of line length

at 50 GHz for a 26.5μm thick BaM film. These approaches have large insertion loss of over

10 dB, which may not be suitable for modern communication systems.

129

5.3.2 Serrated Microstrip Structure and Circular polarization

Ferrite resonance isolators are usually based on different attenuation constants for

both directions of propagation, forward and backward. At the FMR frequency, EM waves

with RHCP, in terms of the DC magnetic bias field or magnetization, will have strong

coupling with the ferrite; while LHCP (left-handed-handed circular polarization) will have

weak couplings.

Figure 5.1 shows a new planar approach to generate RHCP and LHCP on

microstrip lines. The microstrip line is cut via periodic slots, forming a serrated geometry

with multiple fingers. The substrate we used is Rogers TMM 10i ( and

), with a thickness of 0.381mm. A polycrystalline Yttrium Iron Garnet (YIG) film was

then placed covering the serrated part, with dimension 4 mm x 5 mm. The saturation

magnetization (4πMs) of the YIG films is about 1750 Gauss with the FMR linewidth of the

YIG film around 20 Oe measured at X-band (8 GHz).

W1

W2

S2 S

1 H

130

Fig. 5.6. Geometry of the serrated microstrip isolator:

, and . The dashed line indicates the current flowing on

the substrate.

Fig. 5.7. Microwave magnetic field distribution with the serrated structure

For the original microstrip line, the current flows mainly on the edge along y axis as

schematically shown in Fig. 5.6. Hx and Hz components dominate the magnetic field

distribution. The disruption of the serrate structure forces the current flowing around the

new edges, which generated rotating magnetic field with Hy and Hz components.

When the DC bias field is applied along x- axis, the polarization of the magnetic

field can either be RH or LH, in terms of the DC magnetic bias field or magnetization, as

shown in fig. 5.7. When YIG films are placed either above or underneath the serrated

131

structure, opposite distributions of circular polarization can lead to different attenuation

constants for both directions of propagation, forward and backward. The location, with the

maximum attainable ratio of RHCP to LHCP, can be the optimal placement for YIG films

to achieve best insertion/isolation performance.

5.2.3 Magnetic field distribution of Serrated Microstrip Structure

Unlike the field distribution in waveguides, the analytical close form distribution

equations for the serrated structure can be rather complicated. We used Ansoft HFSS full

wave simulator to analyze the magnetic field distribution. Figure 5.8 shows the circular

polarization of magnetic field above and underneath the serrated structure.

For forward input, fig 5.9 (a), we found RHCP magnetic field above the serrated

structure, with LHCP in the corner region of the YIG film, which is at the interconnection

between serrated line and the feed line. The polarization is opposite underneath the

serrated line: LHCP for major part and RHCP for interconnection part.

Similarly, for backward input, fig 5.9 (b), we found LHCP magnetic field above the

serrated structure, with RHCP in the corner region of the YIG film, which is at the

interconnection between serrated line and the feed line. The polarization is opposite

underneath the serrated line: RHCP for major part and LHCP for interconnection part.

It is notable that the polarization at the interconnection between serrated part and

the feed line are opposite to the serrated part, which may increase the insertion loss or add

an additional isolation band. At the FMR frequency, YIG will have strong coupling with

RHCP waves, while have weak coupling with LHCP. Different attenuation constants of

132

forward and backward propagation can lead to non-reciprocal characteristics and isolating

behavior by properly load the ferrite film with the serrated microstrip line.

(a)

(b)

Fig. 5.8. The polarization of microwave magnetic field above and underneath the

serrated structure: (a) Forward transmission; (b) Backward transmission

Bias Field

133

(a)

(b)

Fig. 5.9. The summarized polarization of microwave magnetic field above and

underneath the serrated structure: (a) Forward transmission; (b) Backward transmission

H

Sub

YIG

Fwd Input Port1

H

Sub

YIG

Bwd Input Port2

134

5.3 Simulation verification

5.3.1 Effect of Ferrite films location with Serrated Microstrip Structure

In order to verify the distribution of circular polarization, the isolator with different

placements of YIG thin film (20μm) was analyzed via HFSS, and the simulation results

were shown in Fig. 5.10~5.13. Four cases are investigated:

(1) YIG above microstrip

Figure 5.10 shows the S21 and S12 of the case when the YIG film was placed covering

serrated structure. Insertion loss of 3.5dB at 14.5GHz for backward propagation (S12,

LHCP) and isolation of 17.6dB for forward propagation (S21, RHCP) were observed.

Besides, a side lobe can be observed at 15.1GHz with an opposite insertion/isolation

characteristics (2.4dB and 9dB), due to the edge effect from the interconnection shown in

Fig. 5.7.

(2) YIG underneath microstrip

In Fig. 5.11, YIG film was placed underneath serrated structure. Insertion loss of

5dB at 14.5GHz for forward propagation (S21, LHCP) and isolation of 13dB for backward

propagation (S12, RHCP) were observed. Similarly, there is a side lobe with 2.5dB/8.5dB at

15.2GHz.

(3) YIG both above and underneath microstrip

135

In Fig. 5.12, YIG film was placed both above and underneath. The isolator then

becomes reciprocal, with isolation 23dB at 14.4GHz (main lobe) and 11dB at 15.4GHz (side

lobe).

(4) YIG above microstrip with tapered edge

Figure 5.13 shows the S21 and S12 of the case when the YIG film was placed above

serrated structure as untapped case. But, the straight edges of the YIG film at the

interconnection were tapered to suppress the contribution from the unwanted opposite

circular polarization. The insertion loss of backward wave (S12) at 15.4GHz (side lobe) was

reduced from 9dB to 5dB. The insertion loss and isolation at 14.4GHz are similar to the

untapped case.

Clearly, YIG films placed either above or underneath can lead to non-reciprocal

characteristics. YIG film with tapered edge above exhibits better suppression on edge

effects, which is consistent with the circular polarized microwave magnetic field

distribution.

136

12 13 14 15 16 17-20

-15

-10

-5

0

S12

S21

S1

2 &

S2

1(d

B)

Freq (GHz)Fig.5.10. Simulated s-parameter of the serrated isolator with different YIG placement

with DC bias field 4.4kOe, applied perpendicular to the feed line: YIG above serrated

structure.

12 13 14 15 16 17-20

-15

-10

-5

0

S12

S21

S12 &

S21(d

B)

Freq (GHz) Fig.5.11. Simulated s-parameter of the serrated isolator with different YIG placement

with DC bias field 4.4kOe, applied perpendicular to the feed line: YIG underneath serrated

137

structure.

12 13 14 15 16 17-25

-20

-15

-10

-5

0

S12

S21

S12 &

S21(d

B)

Freq (GHz)

Fig.5.12. Simulated s-parameter of the serrated isolator with

different YIG placement with DC bias field 4.4kOe, applied perpendicular to the feed line:

YIG placed both above and underneath the microstrip.

138

12 13 14 15 16 17-20

-15

-10

-5

0

S12

S21

S1

2 &

S2

1(d

B)

Freq (GHz) Fig.5.13. Simulated s-parameter of the serrated isolator with different YIG placement

with DC bias field 4.4kOe, applied perpendicular to the feed line: YIG above serrated with

tapered edges

5.3.2 Designed Serrated Microstrip isolator with thicker YIG slab

A 400μm thick YIG slab with tapered edge ( 90o) was then placed above the

serrated part. DC magnetic bias field was applied perpendicular to the feed line, from 0 Oe

to 4kOe. Figure 5.14 shows the simulated s-parameter results. With 4kOe bias, the

insertion loss of the backward propagation is 5dB at 13.5GHz, while the isolation is 17.5dB

for the forward propagation.

139

S12-0.8kOe S21-0.8kOe

S12-1.6kOe S21-1.6kOe

S12-2.4kOe S21-2.4kOe

S12-3.2kOe S21-3.2kOe

S12-4.0kOe S21-4.0kOe

2 4 6 8 10 12 14-20

-15

-10

-5

0

S12 &

S21(d

B)

Freq (GHz)

Fig.5.14. Simulated s-parameter of serrated microstrip isolator.

5.4 Measurement verification

The designed serrated microstrip isolator was then fabricated and measured via a

vector network analyzer (Agilent PNA E8364A). A 400μm thick YIG slab with tapered

edge ( 90o) was then placed above the serrated part. DC magnetic bias field was applied

perpendicular to the feed line, from 0 Oe to 4kOe. Figure 15 shows the measured s-

parameter results. With 4kOe bias, the insertion loss of the backward propagation is 3.5dB

at 13.5GHz, while the isolation is 19.3dB for the forward propagation, compared to the

simulation result 5.2dB/17.5dB.

Fig.16 shows that the return losses of both the forward (S11) and backward (S22 )

transmission with 4kOe magnetic field bias are greater than 10dB, which indicated that the

missing energy was dissipated in the YIG slab instead of reflecting back to port 1.

140

Fig.17 shows the insertion loss and isolation of the tunable serrated microstrip

isolator over operating frequency. The isolation increases from 5dB to 19.3dB, as the

resonance frequency goes up, due to the increasing of electronic length, while the insertion

loss remain low (2.5dB ~ 3.5 dB). Therefore, the proposed isolator may perform better in

higher frequencies. The resonant frequencies of the serrated microstrip isolator can be

tuned by changing the DC bias field and follow the Kittel’s equation [11].

S12-0.8kOe S21-0.8kOe

S12-1.6kOe S21-1.6kOe

S12-2.4kOe S21-2.4kOe

S12-3.2kOe S21-3.2kOe

S12-4.0kOe S21-4.0kOe

2 4 6 8 10 12 14-20

-15

-10

-5

0

S12 &

S21(d

B)

Freq (GHz)

Fig.5.15. Measured s-parameter of serrated microstrip isolator

141

2 4 6 8 10 12 14-40

-30

-20

-10

0 S11

S22

Re

turn

Lo

ss

(dB

)

Frequency (GHz)

Fig.5.16 Return Loss of tunable serrated microstrip isolator with 4kOe magnetic

field bias.

2 4 6 8 10 12 140

4

8

12

16

20 Meas. Insertion

Meas. Isolation

Sim. Insertion

Sim. Isolation

Insert

ion

& Iso

lati

on

(dB

)

Freq (GHz) Fig.5.17 Insertion loss and isolation of the tunable serrated microstrip isolator over

operating frequency.

142

5.4 Conclusion

In summary, a novel serrated microstrip isolator has been presented. Microstrip

lines with periodic serrated structure were shown to generate circularly polarized

microwave magnetic field, allowing forward propagation LHCP, and strong ferromagnetic

resonance absorption of the YIG slab at forward propagation. The non-reciprocal ferrite

resonance absorption leads to over 19dB isolation and 3.5 insertion loss at 13.5GHz with

4kOe bias magnetic field applied perpendicular to the feed line. Furthermore, the tunable

resonant frequency of 4 ~ 13.5GHz was obtained for the isolator with the tuning magnetic

bias field 0.8kOe ~ 4kOe. The proposed serrated microstrip isolator prototype can have

many applications in RF front and other microwave circuits.

5.5 Reference

[1] D. M. Pozar, Microwave Engineering, Third edition, New York: J. Wiley & Sons, 2005

[2] J. J. Kostelnick, "Field displacement isolator," US Patent 3035235, 1962

[3] K. J. Button, "Theoretical Analysis of the Operation of the Field-Displacement Ferrite

Isolator, " IEEE Trans. Microwave Theory & Tech., vol 6, pp. 303 -308, July 1958

[4] T. M. F. Elshafiey, J. T. Aberle, E. B. El-Sharawy, "Full wave analysis of edge-guided

mode microstrip isolator," IEEE Trans. Microwave Theory & Tech., vol.44, no.12,

pp.2661-2668, Dec 1996

143

[5] B. Bayard, D.Vincent, C. R. Simovski, and G. Noyel, ―Electromagnetic study of a

ferrite coplanar isolator suitable for integration,‖ IEEE Trans. Microwave Theory &

Tech., vol. 51, no. 7, pp. 1809–1814, Jul. 2003.

[6] J. D. Adam, L. E. Davis, G. F. Dionne, E. F. Schloemann, and S. N. Stilzer, ―Ferrite

devices and materials,‖ IEEE Trans. Microwave Theory & Tech., vol. 50, no. 3, pp. 721–

737, Mar. 2002.

[7] C. P.Wen, ―Coplanar waveguide: A surface strip transmission line suitable for

nonreciprocal gyromagnetic device applications,‖ IEEE Trans. Microw. Theory Tech.,

vol. MTT-17, no. 12, pp. 1087–1090, Dec. 1969.

[8] Capraro, S.; Rouiller, T.; Le Berre, M.; Chatelon, J.-P.; Bayard, B.; Barbier, D.;

Rousseau, J.J.; , "Feasibility of an Integrated Self Biased Coplanar Isolator With

Barium Ferrite Films," IEEE Trans.Components and Packaging Technologies, vol.30,

no.3, pp.411-415, Sept. 2007

[9] G. M. Yang, J. Lou, G. Y. Wen, Y. Q. Jin and N. X. Sun, "Magnetically Tunable

Bandpass Filters with YIG-GGG/ YIG-GGG-YIG Sandwich Structures", International

Microwave Symposium (IMS) 2011, Baltimore, MD.

[10] Schlomann, E.; , "On the Theory of the Ferrite Resonance Isolator," IEEE Trans.

Microwave Theory & Tech., vol.8, no.2, pp.199-206, March 1960

[11] C. Kittel, Introduction to Solid State Physics. New York: Wiley, 1996.

144

Chapter 6 Phase Shifters with Piezoelectric Transducer Controlled

Metallic Perturber

Phase shifters are essential microwave components that provide controllable phase

shifts of microwave/RF signals. They are widely used for beam steering and beam forming

for phased arrays, phase equalizers, and timing recovery circuits [1]. With thousands of

phase shifters that are usually required for a phased-array antenna system, it is crucial to

have phase shifters with small sizes, light weights and low costs. It is also important for

phase shifter to have low loss, minimized power consumption and large power handling

capability.

In this chapter, we will present a novel distributed phase shifter design that is

tunable, compact, wideband, low-loss and has high power handling. This phase shifter

design consists of a meander microstrip line, a PET actuator, and a Cu film perturber,

which has been designed, fabricated, and tested. This compact phase shifter with a

meander line area of 18mm by 18mm has been demonstrated at S-band with a large phase

shift of >360 o

at 4 GHz with a maximum insertion loss of < 3 dB and a high power handling

capability of >30dBm was demonstrated. In addition, an ultra-wideband low-loss and

compact phase shifter that operates between 1GHz to 6GHz was successfully demonstrated.

Such phase shifter has great potential for applications in phased arrays and radars systems.

145

6.1 Introduction of tunable phase shifter researches

Phase shifters are used to change the transmission phase angle (phase of S21) of a

network. Ideal phase shifters provide low insertion loss, and equal amplitude (or loss) in all

phase states. While the loss of a phase shifter is often overcome using an amplifier stage,

the less loss, the less power that is needed to overcome it. Most phase shifters are reciprocal

networks, meaning that they work effectively on signals passing in either direction. Phase

shifters can be controlled electrically, magnetically or mechanically.

The applications of microwave phase shifters are numerous, perhaps the most

important application is within a phased array antenna system (a.k.a. electrically steerable

array, or ESA), in which the phase of a large number of radiating elements are controlled

to force the electro-magnetic wave to add up at a particular angle to the array. The total

phase variation of a phase shifter need only be 360 degrees to control an ESA of moderate

bandwidth.

Different techniques and approaches have been adopted for achieving phase shift in

RF/microwave components, such as magnetic field tuned ferrite based phase shifters [2],

ferroelectric varactors based phase shifters [3], p-i-n diodes [4], field-effect transistor (FET)

switches [5], and RF micro-electro-mechanical systems (MEMS) switched line phase

shifters [6]. Nevertheless, state of the art phase shifters listed above have their own

limitations. Ferrite phase shifters have large power handling capability, but typically have

limited bandwidth, large size, high power consumption and slow tuning. FET switches, p-i-

146

n diodes, and ferroelectric varactor based phase shifters typically have high insertion loss

at W-band, and exhibit limited frequency range. RF MEMS phase shifters show good

performance on bandwidth, insertion loss, size and power consumption [7-8]; however,

they show limited power handling of < 1W (30dBm). These limitations prevent their

applications in mission critical phased arrays, such as high power radars and electronic

warfare.

Chang et al. reported a new type of phase shifters with dielectric perturber

controlled by piezoelectric transducers (PET) on a planar microstrip transmission line such

has been reported [9]-[12], as shown in Fig. 6.1. With the introduction of the dielectric

perturber that is closely placed above a microstrip transmission line, the characteristic

impedance of the line is only slightly altered, while its effective dielectric constant can be

changed significantly, which leads to phase shift. However, such phase shifters still have

problems, such as limited phase shift, large size, and high insertion loss when the dielectric

perturber is closely placed on the microstrip for achieving large phase shifter. For example,

a phase shifter with the size of about 30 mm can only produce a controlled phase shift of

less than 80° in S-band [9], which is far away from the typical requirement for a 360° phase

shift.

Most recently, we have reported a similar phase shifter design with PET controlled

magneto-dielectric perturber,[2], as shown in Fig. 6.2, which leads to significantly enhanced

phase change (> 2×) compared to PET controlled dielectric perturber approach due to the

increased miniaturization factor, related to the high permeability of the magneto-dielectric

147

disturber. At the same time, the increased permeability of the magneto-dielectric disturber

lead to better wave impedance match to the free space and therefore, much lower reflection

due to the loading of the perturber and less insertion loss [2]. This leads to high phase shift

per dB loss of >500/dB insertion loss. However, this approach has its own limited

bandwidth of less than 3 GHz due to the increased loss tangent of the self-biased magneto-

dielectric perturber, and it still could not meet the need for ultra-wide band phased arrays,

such as electronic warfare.

Fig. 6.1 Phase shifter design with PET controlled dielectric perturber by Chang et al.[9]

148

Fig. 6.2 Phase shifter design with PET controlled magneto-dielectric perturber by Yang

et al. [2]

6.2 Device construction

6.2.1Device Construction

Similar to the previous PET phase shifter using dielectric perturber, the structure of

the designed phase shifter is shown in Fig.6.3. The PET used in the design is a

commercially available piezoelectric bending actuator (PI PICMA® PL140.10) which

features a multilayer structure that reduces the voltage that needed for large deflection.

The dimension of the PET is about 45 mm in length and 11 mm in width, and can be

deflected up and down for a total range of 2 mm with a control voltage ranging from zero

to 60V.

149

Fig. 6.3. Schematic and photograph of the meander line phase shifter with PET controlled

metallic perturber.

The meander line was designed to possess a characteristic impedance of 50 Ω, which has

a conductor width of 0.356 mm. With each of the segments of the meander line being 10.8

mm and each of the corners being 0.71 mm, the total length of the meander line is about 4.5

inches within an area of 12.812.8 mm, as shown in Fig.6.4. Also shown in Fig. 4 is the

dimension and position of the metallic perturber, which is a 12.8 mm 12.8 mm copper

square that covers majority part of the meander line. Without the metallic perturber, the

meander line structure is essentially a transmission line with a working frequency range of

0~4 GHz. The maximum insertion loss of the meander line is less than 1 dB at < 4 GHz.

150

Fig. 6.4. Design dimensions for the meander line phase shifter, the grayed area shows the

size and position of the metallic perturber.

For broadband true-time delay phase shifters (e.g. 1 ~ 6GHz), there is an important

design trade-off between the highest and lowest operating frequencies. That is, the size of

the phase shifter should be smaller than half wavelength at the highest frequency, e.g. 25

mm at 6GHz; and a large enough phase shifts should be achieved at the lowest frequency,

say 90o. Clearly, we need to make the phase shifter small enough to fit size requirement,

while achieve a moderate phase shift at lower frequencies at the same time. A substrate

with relatively high K was used for the meander line design. Rogers TMM 10i has a

151

nominal dielectric constant of 9.8 and a thickness of 0.38 mm was chosen to accomplish

both longer length of the meander line and higher power handling requirement.

6.2.2 Piezoelectric transducer (PET) - PI PICMA® PL140.10

PICMA®-series multilayer bender piezo actuators as shown in Fig 6.5, provide a

deflection of up to 2 mm, forces up to 2 N (200 grams) and response times in the

millisecond range. These multilayer piezoelectric components are manufactured from

ceramic layers of only about 50 µm thickness. They feature internal silver-palladium

electrodes and ceramic insulation applied in a cofiring process. The benders have two outer

active areas and one central electrode network dividing the actuator in two segments of

equal capacitance, similar to a classical parallel bimorph.

The maximum travelling distance of the PET is 2 mm for 60V applied DC voltage. If

we placed the meander line under PET with a gap separation , we can approximate the

gap dimension with applied voltage using – (according to PL140 data

sheet, Piezo University), where V is the voltage applied on the PET. For example, in our

experiment, we have measured the original gap , then for 50V DC voltage, the

gap is 0.13mm. The tuning of traveling distance is linear proportional as the applied

voltage, as shown in Fig. 6.6.

152

Fig. 6.5. Schematic and the equivalent circuit of piezoelectric transducer (PET) - PI

PICMA® PL140.10

153

0 10 20 30 40 500.0

0.4

0.8

1.2

1.6

2.0

gap

sep

ara

tio

n (

mm

)

Applied DC voltage (V)

Fig. 6.6. Approximated gap dimension with applied voltage (0~50V). The original gap is 2

mm.

6.3 Theoretical analysis

6.3.1 Equivalent Circuit Model for Meander Line with variable copper perturber

Microstrip meander line structure is widely used in phase shifter designs due to

their broadband, low insertion loss, and ease of manufacturing. The characteristics

impedance Z and phase velocity of a typical microstrip transmission line vph can be

expresses as

√

(6.1)

√

(6.2)

where L and C indicates the equivalent capacitance and inductance.

154

As a distributed transmission line, meander lines with piezoelectric bending

actuator can be also modeled as an L-C circuit, as shown in Fig. 6.7. The variable distance

from the copper perturber to the meander line leads to an equivalent variable capacitor.

Therefore, the variable phase constant βvar caused by the perturbation can be calculated as:

√ (6.3)

The variable capacitance Cvar can be tuned electrically by applying variable voltage

on the piezoelectric bending actuator. Hence, the phase shift can be estimated as:

)(360 minmax CCCCLfl o (6.4)

where Cmax and Cmin denotes the capacitance variance.

Fig. 6.7 Equivalent circuit of meander line with piezoelectric bending actuator

6.3.2The insertion Loss Analysis

For microstrip meander lines, most losses are contributed by dielectric and

conductor losses, given that the radiation loss is small. The dielectric loss d in dB/cm [13]

caused by the finite conductivity of the dielectric layers is given by

155

eff

r

r

eff

d

d

11*)

tan(*686.8

, (6.5)

where the substrate loss tangent tanδ=0.002; εr =9.8 denotes the dielectric constant of the

substrate; εeff denotes the effective dielectric constant for the microstrip transmission line;

λd denotes the wavelength in the substrate.

The conductor loss c [14-16] can be obtained from

(dB/cm) 686.8WZ

R

c

Sc ,

2sR (6.6)

Where SR denotes the surface impedance; W denotes the width of the strip line; ζ denotes

the conductivity; Zc denotes the characteristic impedance; w denotes the angular operating

frequency.

With a piezoelectric bending actuator, a variable capacitance leads to variable

characteristics impedance. The return loss due to perturber perturber in dB/cm will increase

due to the impedance mismatch to a standard 50 Ω port, which can be described as

)log(*20min

max

CCC

CCCperturber

(6.7)

156

The final form of the loss calculation is a function of loss metal thickness, strip

width and conductivity, frequency and distance to the perturber. The insertion loss in unit

of decibels for a perturbed length of the phase shifter is given by

Δl*) + + (=LossInsertion perturberdc (6.8)

6.4 Simulation Results

Simulations of the device were carried out by HFSS before the meander line S-band

transmission line was fabricated. To match the travelling distance of the PET of 2 mm, the

maximum and minimum distances between the metallic perturber and the substrate were

set to be 1.80 mm and 0.13 mm respectively.

157


perturber and the substrate.


perturber and the substrate.

Figure 6.8 shows the transmission coefficient (S21) of the meander line phase shifter with

different distances between the metallic perturber and the substrate. Clearly when the

metallic perturber is far away from the substrate (1.8 mm), the insertion loss of the phase

shifter stays at a relatively low level of < 1 dB throughout the entire S-band. However,

when the metallic perturber approaches the substrate, the insertion loss starts to increase

due to the impedance mismatch introduced by the metallic perturber. Nevertheless, the

158

maximum insertion loss of the phase shifter is less than 2 dB at a 0.13 mm spacing between

the metallic perturber and the meander line.

Figure 6.9 shows the reflection coefficient (S11) of the phase shifter with different

metallic perturber distances. As one may expect, when the distance between the perturber

and the substrate is 1.8 mm, the return loss –is greater than 20 dB; while with the

perturber getting closer to the substrate, the return loss eventually reaches a minimal level

of about 8 dB for a 0.13 mm distance.

The S11 and S21 spectra show clear ripples associated with the meander line structure, as

shown in Figs. 4 and 5. The amplitude of the ripples increases with the approaching of the

metallic perturber to the substrate, and their positions as well as their separations also vary.

This is attributed to the change of the capacitance per unit length C of the transmission line

due to the metallic perturber. This increased C leads to changes of the characteristic

impedance of the meander line transmission line expressed by 0Z /L C , where L is the

inductance per length of the meander transmission line, and therefore decreased return

loss and increased insertion loss as shown in Figs. 4 and 5. At the same time, the increased

C also decreases the phase velocity of the meander line, 1/phaseV LC . As a result of such

changes of the phase velocity of the microstrip line, the relative phase shift changes

dramatically as a function of the distance between the metallic perturber and the substrate,

as shown in Fig. 6.10.

159

Fig. 6.10 Simulated relative phase shift of the phase shifter with different distances between

the metallic perturber and the substrate

From Fig. 6.10, it is very clear that the phase shift of the meander line can be readily

tuned by varying the distance between metallic perturber and the substrate, although it’s

not a linear function of the distance. For example, the phase shift is only 28o

when the

disturber-meander line gap is 1.12 mm at 4 GHz, and is 54o when the distance is 0.80 mm.

However, the phase shift reaches a value of 266 o

and 352 o

at a gap of 0.20 mm and 0.13

mm, respectively.

160

Fig. 6.11. Measured S21 of the meander line with different voltage applied on the PET.

6.5 Measurement Results

The meander line was fabricated by PCB fabrication technique and the phase

shifter was assembled as schematically shown in Fig. 1. Measurement of the meander line

phase shifter was done on an Agilent PNA series vector network analyzer. With a control

voltage applied on the PET changing from zero to 50 V, the distance between the metallic

perturber and the substrate can be tuned. It should be mentioned that due to the difficulty

of accurately measuring the distance between the perturber and the meander line, the

applied voltage should only be used for reference purpose to compare to the actual distance.

161

However, after careful calibration, these two values should be able to be preciously linked

to each other.

Figure 6.11 shows the transmission coefficient of the meander line phase shifter with

different voltage applied on the PET. When the voltage is zero volts, which corresponds to

the largest distance between the metallic perturber and the meander line, the insertion loss

shows very flat response with the maximum loss being 1 dB, which matches well with

simulated data shown in Fig. 6.9. With the increase of the voltage applied on the PET, the

distance between the metallic perturber and the substrate was reduced, which led to

degraded insertion loss.

Fig. 6.12. Measured S11 of the meander line with different voltage applied on the PET.

162

Since the performance of the phase shifter is very sensitive to the distance between

the perturber and the meander line, and waviness of the perturber surface may introduce

additional loss in the device. As we can see from Fig. 6.12, compared to simulated results,

the insertion loss of the device is slightly larger at higher voltage. Nevertheless, the overall

insertion loss is still less than 2 dB over the entire S-Band.

Similar to the simulated results, the measured reflection coefficient has the same

trend, as shown in Fig. 12. For a control voltage of zero volt, the return loss stays at very

low level of ~25 dB. For higher voltages however, a maximum return loss of 7 dB is

observed for 50 V of control voltage, which is in close match with the simulated data.

The maximum travelling distance of the PET is 2 mm for 60V applied DC voltage.

Starting from a 1.8 mm gap with 0V, the PET bended down and the gap between the

perturber and the meander can be approximated as (1.8 – 2*V/60) mm (PL140 Data sheet,

Piezo University), where V is the applied voltage on the PET. For 50V DC voltage, the gap

is 0.13mm, where the measured relative phase shift has a maximum phase shift of 362 o at 4

GHz as shown in Fig. 13. HFSS simulation showed 352o phase shift, indicating a decent

match between measurement and simulation results. Also, compared to the published

phase shifter based on dielectric perturber, this accounts for one order of magnitude

enhancement [5]. Furthermore, it can be found that the relative phase shift is very

sensitivity to the voltage change at higher control voltages as well. The phase shift from 40

to 50 volts contributes to almost 70% of the total phase shift range. This agrees well with

the simulated results that the phase shift is particularly sensitive to the distance between

the perturber and the substrate when the distance is small. This phenomenon leads to the

conclusion that it is possible to use a much smaller tunable distance between the metallic

163

disturber and the meander line, which means that large phase shift can be achieved with a

shorter PET and/or at a smaller voltage span in order to gain majority of the phase shift

capability. As an alternative, one can start with a smaller distance between the perturber

and the substrate as an initial reference state, and a much lower control voltage of 20V can

lead to a phase shift of 300o. This will dramatically reduce the need for high control voltage

and is needed to reduce the power consumption of the device. Compared to other phase

shifter designs, this phase shifter design showed significantly enhanced phase shift and

lower loss [9].

Unlike most semiconductor based planar phase shifters that can only handle very

limited microwave input power of <30dBm [1-4], our phase shifter design with a PET

controlled metallic disturber on meander line has the potential to handle a much larger

range of input power since the phase shifter has just copper and dielectric substrates. As a

result, power handling of such phase shifters will mainly be limited by Joule heating at

large RF/microwave power level. We

164

Fig. 6.13. Measured and simulated relative phase shift of the meander line phase shifter

with different voltage applied on the PET. The symbols indicate simulated results from

HFSS.

165

Fig. 6.14. Measured insertion loss of the meander line phase shifter with different input

power at 3 GHz.

measured the insertion loss of our phase shifter at 3 GHz under different microwave input

powers at 3GHz, with both zero and 50 V applied to the PET, as shown in Fig. 10. Clearly,

the insertion losses of both cases stay nearly straight at different microwave input power

level, with only negligible increase in the insertion loss at a control voltage of 50V and at 30

dBm. Maximum power level was only tested to up to 30dBm due to the limited power

output level in our labs, while simple extrapolation of the two curves in Fig. 6.14 indicate

that the phase shifter shows much higher power handling capability than 30dBm. The high

microwave power handling capability of the meander line phase shifter is critical for high

power phased array radars.

6.6. Extended design for 1-6GHz

Some applications, such as satellite communication and radar system, require

controllable phase shifts in wider band, 1GHz to 6GHz etc, which covers L band, S band,

and part of C band. Hence, it is also important for phase shifters to have a wide working

bandwidth and the properties of low profile, low loss, minimized power consumption and

large power handling capability. Fig. 6.15 shows an extended meander line phase shifter

working from 1GHz to 6GHz. The meander line was designed to have the conductor width

of 14 mils. With each of the segments of the meander line being 5.58 mm and each of the

corners being 0.508 mm, the total length of the meander line is about 223 mm within an

166

area of 18 18 mm. The same metallic perturber has been use to tune the capacitance

through different heights.

Fig. 6. 15. Design dimensions for the extended meander line phase shifter.

It should be mentioned that the performance of the phase shifter is very sensitive to the

distance between the perturber and the meander line. Besides, the bending actuator brings

an inclined copper surface, which leads to additional insertion loss and non-linearity of

phase shifts. These are more critical at closer distance. Therefore, in the extended meander

line approach, the perturber was placed at the closest distance, and completely parallel to

the meander line, when the voltage is 0 volts. Then, it would be bent up when higher

voltages were applied. With the metallic perturber far away from the substrate, the phase

shift due to the metallic surface will be neglected. So, we set the 25V applied voltage as the

reference point for relative phase shift measurement.

167

Fig. 6.16. Measured relative phase shift of the extended meander line phase shifter with

different voltage applied on the PET

Table 6.1 Measured relative phase shift of the extended meander line phase shifter

at 6GHz with different voltage applied on the PET

Applied

Voltage (v)

Phase

shifts (o)

IL

(dB)

RL

(dB)

0 806 3.8 11.6

3.5 520 2.9 19.4

8.0 343 2.8 21.2

12 192 2.5 24.0

15 100 2.9 27.3

168

25 0 3.0 31.9

Fig.6.16 shows the phase shifts of the meander line phase shifter with different

voltage applied on the PET. It is very clear that the phase shift of the meander line can be

readily tuned by varying the distance between metallic perturber and the substrate

through variable voltage applied. The measured relative phase shift showed a maximum

phase shift of 367 o

at the center frequency 3.5 GHz with a control voltage of 0 V on the

PET, 88 o

at 1GHz and 807 o

at 6GHz. With the increase of the voltage applied on the PET,

the distance between the metallic perturber and the substrate was increased. Then, the

reduced capacitance leads to smaller phase shifts. For example, if we set 6GHz as working

frequency, we get the following phase shifts as Table 6.1.

Fig. 6.17 show the transmission coefficient (S21) of the meander line phase shifter

with different voltage applied on the metallic perturber. Clearly, with the higher voltage

(25V), where the metallic perturber was far away from the substrate, the insertion loss of

the phase shifter stays at a relatively low level of < 2 dB throughout the entire band of 1-

6GHz. However, when the applied voltage was reduced, the metallic perturber approaches

the substrate. The insertion loss starts to degrade to 3.8dB at 6GHz, which is the maximum

insertion loss throughout the entire band. However, it should be mentioned that 360 o

phase

shift is sufficient for most applications. In our design, the phase shift exceeded the 360 o

phase shift requirement in the frequency band of 3.5 - 6GHz, with the majority of bad

insertion loss cases. A customized voltage set can be used to achieve the required phase

shift while maintaining relatively low insertion loss. For example, at 6GHz, the tuning

range of 8V to 25V can achieve 360 o

phase shift, with the maximum insertion loss 2.85dB;

169

at 5GHz, the tuning range of 3.5V to 25V can achieve 360 o

phase shift, with the maximum

insertion loss 3.53dB.

Fig. 6.18 shows the return loss (S11) of the meander line phase shifter with different

voltage applied on the metallic perturber. A high S11 (6.5dB) was observed when the voltage

is 0V, and the perturber was very close to the meander line. Once the voltage was increase,

and the metallic perturber was far enough and had less impact on the meander line, S11

went beyond 10dB.

Compared to the original design (working at 2-4GHz), the extended meander line

shifter has a small insertion loss increase. Loss was then analyzed by applying equations (4)

and (5). The estimated α of the meander line at 6GHz is 0.1035 dB/cm for conductivity loss

and 0.0262dB/cm for dielectric loss. The total effective length of the meander line is 22.2976

cm. Therefore, the total loss can be estimated as 2.3dB for conductivity loss, 0.58dB for

dielectric loss, 0.8dB for metallic perturber according to the measurement results in Table

I, and the rest 0.12dB for impedance mismatching of original perfect conductor meander

line. Apparently, the majority of the loss comes from finite conductivity of copper

transmission line, which is also the bottleneck of meander-line phase shifter. However, it

achieved much wider bandwidth (1-6GHz), which is very important for some application

desired of wide operation frequency band.

170

Fig. 6.17. Measured S12 of the extended meander line with different voltage applied on the

PET.

Fig.6. 18. Measured S11 of the extended meander line with different voltage applied on the

PET.

171

6.7. Comparison with previous approaches

Table 6.2 Performance comparison of phase shifters with different device techniques.

Reference Device Tech. Fre

qG

Hz

Compare

Freq.

(GHz)

Total

Phase

shifts

IL

(dB)

Degree

/dB

loss

Size or

Area

(mm)

DC power

consumptio

n

or DC

voltage

[4] SiGe

Pin diodes

7~11 10 320 11 29 3.83.8 45mW

[17] FET switches 4~8 6 360 5.7 63 1.720.81 0mW

[18] RF MEMS 7~11 9.45 270 1.4 192 40 mm2 N/A

[19] Ferroelectric

varactors

0~7 7 170 2.3 74 46 25V

[2] PET

Magneto-

dielectric

perturber

1~5 5 40 0.5 80 2010 50V

[20] PET

dielectric

perturber

1~6 6 75 1 75 70.432 40V

Our work PET metallic 1 ~ 6 6 806 3.8 212 12.812.8 50V

172

perturber

Table 6.2 shows the performance comparison of the fabricated phase shifter in this

work with the other reported phase shifters. The measured degree/dB low insertion loss of

212 are found to be better than those of the previously phase shifters. Also, the device size

is the smallest among PET phase shifters, although larger than others.

6.8 Conclusions

A novel type of phase shifter was proposed and demonstrated utilizing a

piezoelectric transducer (PET) controlled metallic transducer on meander transmission

line. Compared to phase shifters with PET controlled dielectric or magnetodielectric

perturber, the phase shifter with PET controlled metallic perturber exhibited significantly

enhanced phase shift (>10x) and bandwidth, reduced size and insertion loss. A compact S-

Band meander line phase shifter with metallic perturber controlled by a PET has been

designed, fabricated and tested. The total dimension of the meander line is only 18 by 18

mm square. Compared to dielectric perturber that only exhibits very limited phase shift at

S-Band, our design reached a phase shift of 360o with a low controlling voltage of 25 V at

3.5 GHz, along with a wide operating bandwidth from 1 GHz to 6GHz. In addition, there is

no fundamental limit of the frequency range for such a phase shifter, as the frequency limit

is mainly from the design of the meander line. While the meander line can be easily

designed for frequencies of S-band was demonstrated in this work, similar phase shifter

designs can be made for X-band, K-band, W-band and beyond from our simulations, and

even extremely wideband phase shifter can be achieved with a straight transmission line

173

and a PET controlled metallic disturber. High power handling of 30dBm has been

experimentally demonstrated in a compact S-band phase shifter, with an expected power

handling limit of >50dBm. With the combined low insertion loss, large phase change,

compacted size, high microwave power handling capability, and the extend abilities to

other frequency bands, the new meander line phase shifter with PET controlled metallic

perturber show great potential for different phased array systems.

6.9 References

[1] B. York, A. Nagra, and J. Speck, ―Thin-film ferroelectrics: Deposition methods and

applications,‖ in IEEE MTT-S Int. Microw. Symp., Boston, MA, Jun. 2000.

[2] G. M. Yang, O. Obi, G. Wen, Y. Q. Jin, and N. X. Sun, ―Novel Compact and Low-Loss

Phase Shifters with Magnetodielectric Disturber,‖ IEEE Microw. Wireless Compon.

Lett, vol. 21, no. 5, May 2011

[3] J. B. L. Rao, D. P. Patel, and V. Krichevsky, ―Voltage-controlled ferroelectric lens

phased arrays,‖ IEEE Trans. Antennas Propagat., vol. 47, pp. 458–468, Mar. 1999.

[4] M. Teshiba, R. V.Leeuwen, G. Sakamoto, and T. Cisco, "A SiGe MMIC 6-Bit PIN

Diode Phase Shifter" , IEEE Microw. wireless Comp. Lett., VOL. 12, NO. 12 Dec.2002

[5] A. S. Nagra, and R. A. York, ―Distributed analog phase shifters with low insertion loss,‖

IEEE Trans. Microw. Theory Tech., Vol. 47, pp. 1705-1711, Sep. 1999.

[6] B. Pillans, S. Eshelman, A. Malczewski, J. Ehmke, C. Goldsmith, ―Ka-band RF MEMS

phase shifters,‖ IEEE Microw. Guided wave Lett., vol 9, pp. 520-522, Dec. 1999.

[7] N. S. Barker, G. M. Rebeiz, "Optimization of Distributed MEMS Transmission-Line

Phase Shifters—U-Band and W-Band Designs", IEEE Trans. Microw. Theory Tech.,

174

Vol. 48, NO. 11, Nov. 2000

[8] G.M. Rebeiz, G.L. Tan, J.S. Hayden, "RF MEMS Phase Shifters: Design and

Application", Microwave Magazine, June 2002

[9] T. Y. Yun and K. Chang, ―Analysis and optimization of a phase shifter controlled by a

piezoelectric transducer,‖ IEEE Trans. Microw. Theory Tech., Vol. 50, pp. 105-111, Jan.

2002.

[10] T. Y. Yun and K. Chang, ―A low-cost 8 to 26.5 GHz phased array antenna using a

piezoelectric transducer controlled phase shifter,‖ IEEE Trans. Antennas Propag., vol.

49, pp. 1290-1298, Sept. 2001.

[11] T. Y. Yun and K. Chang, ―A low-loss time-delay phase shiter controlled by

piezoelectric transducer to perturb microstrip line,‖ IEEE Microw. Guided wave Lett.,

vol 10, pp. 96-98, Mar. 2000.

[12] J. M. Pond, S. W. Kirchoefer, H. S. Newman, W. J. Kim, W. Chang, and J. S. Horwitz,

―Ferroelectric thin films on ferrites for tunable microwave device applications,‖

Proceedings of the 2000 12th IEEE International Symposium on Applications of

Ferroelectrics, 2000.

[13] Jia-Sheng Hong, M. J. Lancaster, ―Microstrip filters for RF/Microwave

Applications‖ Page 83. formula 4.18,4.19

[14] Brian C Wadell, ―Transmission Line Design Handbook‖ , Artech House 1991

[15] Harold A. Wheeler, Transmission-line properties of a strip on a dielectric sheet on a

plane", IEEE Tran. Microwave Theory Tech., vol. MTT-25, pp. 631-647, Aug. 1977

[16] M. V. Schneider, "Microstrip lines for microwave integrated circuits," Bell Syst Tech.

J., vol. 48, pp. 1422-1444, 1969.

175

[17] J.G. Yang; K. Yang, "Ka-Band 5-Bit MMIC Phase Shifter Using InGaAs PIN

Switching Diodes," IEEE Microw. Wireless Compon. Lett, vol.21, no.3, pp.151-153,

March 2011

[18] M. Hangai,M. Hieda, N. Yunoue,Y. Sasaki and M. Miyazaki, "S- and C-Band Ultra-

Compact Phase Shifters Based on All-Pass Networks", IEEE Trans. Microw. Theory

Tech., vol. 58, No. 1, pp. 44-47, Jan. 2010

[19] A. Malczewski, S. Eshelman, B. Pillans, J. Ehmke, and C. L. Goldsmith, "X-Band RF

MEMS Phase Shifters for Phased Array Applications" IEEE Microw. Guided wave

Lett., vol. 9, No. 12, pp. 517-519, Dec 1999

[20] S. Sheng, P. Wang, X. Chen, X.Y. Zhang, and C. K. Ong ―Two paralleled

Ba0.25Sr0.75TiO3 ferroelectric varactors series connected coplanar waveguide

microwave phase shifter‖, J. Appl. Phys. 105, 114509 , 2009

[21] S. G. Kim, T. Y. Yun, and K. Chang, "Time-Delay Phase Shifter Controlled by

Piezoelectric Transducer on Coplanar Waveguide," IEEE Microw. Wireless Compon.

Lett, vol.13, No. 1, pp. 19, Jan 2003

[22] C. Kim and K. Chang, ―A reflection-type phase shifter controlled by a piezoelectric

transducer‖ Microwave and Optical Technology Letters, vol. 53, No. 4, pp. 938-940,

April 2011

176

Chapter 7 Conclusion

In this dissertation, I combine the ferrite thin films and planar microwave structure

to realize tunable and non-reciprocal devices, including bandpass filters, isolators and

phase shifters.

A novel type of tunable isolator was presented, which was based on a polycrystalline

yttrium iron garnet (YIG) slab loaded on a planar periodic serrated microstrip

transmission line that generated circular rotating magnetic field. The non-reciprocal

direction of circular polarization inside the YIG slab leads to over 19dB isolation and <

3.5dB insertion loss at 13.5GHz with 4kOe bias magnetic field applied perpendicular to the

feed line. Furthermore, the tunable resonant frequency of 4 ~ 13.5GHz was obtained for

the isolator with the tuning magnetic bias field 0.8kOe ~ 4kOe.


microwave ferrites such as YIG also provides the possibility of realizing such a non-

reciprocal device. A new type of non-reciprocal C-band magnetic tunable bandpass filter

with ultra-wideband isolation is presented. The BPF was designed with a 45o rotated YIG

slab loaded on an inverted-L shaped microstrip transducer pair. This filter shows an

insertion loss of 1.6~2.3dB and an ultra-wideband isolation of more than 20dB, which was

attributed to the magnetostatic surface wave. The demonstrated prototype with dual

functionality of a tunable bandpass filter and an ultra-wideband isolator lead to compact

and low-cost reconfigurable RF communication systems with significantly enhanced

isolation between the transmitter and receiver.

177

A novel distributed phase shifter design that is tunable, compact, wideband, low-loss

and has high power handling will also be present. This phase shifter design consists of a

meander microstrip line, a PET actuator, and a Cu film perturber, which has been

designed, fabricated, and tested. This compact phase shifter with a meander line area of

18mm by 18mm has been demonstrated at S-band with a large phase shift of >360 o at 4

GHz with a maximum insertion loss of < 3 dB and a high power handling capability

of >30dBm was demonstrated. In addition, an ultra-wideband low-loss and compact phase

shifter that operates between 1GHz to 6GHz was successfully demonstrated. Such phase

shifter has great potential for applications in phased arrays and radars systems.

planar tunable rf/microwave devices with magnetic ...1409/fulltext.pdf · verification of novel...

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