Magnetoelectric(ME) composites and functional
Magnetoelectric(ME) composites and
functional devices based on ME effect
Junqi Gao
Dissertation submitted to the faculty of the
Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
In
Materials Science and Engineering
Dwight D. Viehland (Chair)
Jiefang Li
David Clark
Guo-Quan Lu
May 06 2013
Blacksburg, Virginia
Keywords: Magnetoelectric, magnetic sensor, low noise circuit, noise modeling,
geomagnetic field sensing, energy harvester
© Copyright 2013, Junqi Gao
Magnetoelectric(ME) composites and
functional devices based on ME effect
Junqi Gao
ABSTRACT
Magnetoelectric (ME) effect, a cross-coupling effect between magnetic and electric
orders, has stimulated lots of investigations due to the potential for applications as
multifunctional devices. In this thesis, I have investigated and optimized the ME effect in
Metglas/piezo-fibers ME composites with a multi-push pull configuration. Moreover, I
have also proposed several devices based on such composites.
In this thesis, several methods for ME composites optimization have been
investigated. (i) the ME coefficients can be enhanced greatly by using single crystal
fibers with high piezoelectric properties; (ii) the influence of volume ratio between
Metglas and piezo-fibers on ME coefficients has been studied both experimentally and
theoretically. Modulating the volume ratio can increase the ME coefficient greatly; and
(iii) the annealing process can change the properties of Metglas, which can enhance the
ME response as well. Moreover, one differential structure for ME composites has been
proposed, which can reject the external vibration noise by a factor of 10 to 20 dB. This
differential structure may allow for practical applications of such sensors in real-world
environments.
Based on optimized ME composites, two types of AC magnetic sensor have been
developed. The objective is to develop one alternative type of magnetic sensor with low
noise, low cost and room-temperature operation; that makes the sensor competitive with
the commercially available magnetic sensor, such as Fluxgate, GMR, SQUID, etc.
Conventional passive sensors have been fully investigated, including the design of sensor
working at specific frequency range, sensitivity, noise density characterization, etc.
Furthermore, the extremely low frequency (< 10-3 Hz) magnetic sensor has undergone a
redesign of the charge amplifier circuit. Additionally, the noise model has been
established to simulate the noise density for this device which can predict the noise floor
precisely. Based on theoretical noise analysis, the noise floor can be eliminated greatly.
Moreover, another active magnetic senor based on nonlinear ME voltage coefficient is
also developed. Such sensor is not required for external DC bias that can help the sensor
for sensor arrays application.
Inspired by the bio-behaviors in nature, the geomagnetic sensor is designed for
sensing geomagnetic fields; it is also potentially used for positioning systems based on
the geomagnetic field. In this section, some works for DC sensor optimization have been
performed, including the different piezo-fibers, driving frequency and magnetic flux
concentration. Meanwhile, the lock-in circuit is designed for the magnetic sensor to
replace of the commercial instruments. Finally, the man-portable multi-axial geomagnetic
sensor has been developed which has the highest resolution of 10 nT for DC magnetic
field. Based on the geomagnetic sensor, some demonstrations have been finished, such as
orientation monitor, magnetic field mapping, and geomagnetic sensing.
iii
Other devices have been also developed besides the magnetic sensor: (i) magnetic
energy harvesters are developed under the resonant frequency condition. Especially, one
60 Hz magnetic harvester is designed which can harvester the magnetic energy source
generated by instruments; and (ii) frequency multiplication tuned by geomagnetic field is
investigated which potentially can be used for frequency multiplier or geomagnetic
guidance devices.
iv
To my parents, sister and wife
v
Acknowledgements
I would like to express my sincere gratitude to my advisor, Professor Dwight
Viehland, for his support on my Ph.D study and research: for his patience, motivation,
enthusiasm, and immense knowledge. His guidance helped me in all the time of research
and writing of this thesis.
I have tremendous respect to Professor Dwight Viehland for his professional
knowledge and passion for the research. I benefited a lot from his “Structure Properties
Materials” class, the discussions about the project, the intelligent suggestions on my
research, his patience on correcting my papers, and his valuable instruction on my
presentation. His high enthusiasm and hard-work on research influenced me greatly and
will be very helpful in my future career.
Equally important, Professor Jiefang Li has given me great help and guidance in
almost all of the projects that I have worked during my Ph.D research. Professor Li gave
me several suggestions on research ideas and experimental setup. She generously shared
with me all her senior experience on sensor design and characterization without any
reservations. I definitely would not be successful in many of my research without her
help.
I would also like to thank my committee member Professor David Clark. I learned a
lot on the knowledge of ceramic science from his “Advanced Physical Ceramics” class.
Professor Clark gave me several professional instructions on presentations, and valuable
training on research. I really appreciate his questions and comments on my Ph.D qualifier
and preliminary exams.
My sincere thank also goes to Professor Guo-Quan Lu, who serves as my committee
member for my defense. I benefited a lot from his “Advanced materials thermodynamics”
class, especially the training about the proposal writing. I really appreciate the knowledge
and skills obtained from Professor Lu.
I would like to thank Professor Shashank Priya. I benefited a lot from his “Energy
Harvesting” class, especially the theoretical model and analysis on piezoelectric materials
based vibration energy harvester. Dr. Priya also gave me significant guidance on my
vi
project that is related to geomagnetic sensor design. I always acquired new knowledge
each time I discussed with him.
I would like to thank Dr. Junyi Zhai and Dr. Zengping Xing. They have given me
knowledge on the ME materials, measurement setup, and circuit design since I joined the
research group. Their valuable experience made my research go much easier.
I would like to thank Dr. Davresh Hasanyan. He shared with me lots of hermetical
models and calculations about the magnetoelectric effect, which gave me deep insight
about the fundamental research on functional materials. His strong theory convinced my
many ideas.
I would like to thank Dr. Yaodong Yang for his creative ideas on the optimizations
and applications of ME composites. We collaborated together happily for lots of
measurements.
I would like to thank Dr. Liangguo Shen for his great help on the lock-in circuit
design that made my project run fast.
I would like to thank Dr. David Gray, David Berry for their great guidance and
discussion on the experimental setup and magnetic sensor design.
I would like to thank Dr. Yaojin Wang, Menghui Li, and Ying Shen for great
discussion on the ME materials and applications. We worked together to make great
progress on the development of the ME sensor. It will always be good memory to work
with you.
I would also like to thank Dr. Yan Li, Dr. Jianjun Yao, Dr. Wenwei Ge, Zhiguang
Wang, Yanxi Li, and Chengtao Luo, members in Professor Dwight Viehland’s group.
They gave me a lot of knowledge on quite different research areas that extended my
research experience widely.
Last, but most importantly, I wish to express my deepest appreciation to my family. I
am eternally indebted to my parents, Zhenjin Gao and LiZhen Cao, for their endless
support over the years. I would like to thank my sister, Yanqi Gao for her encouragement
and help as it was most required. In particular, I would like to express my gratitude to my
wife, Ying Shen. She gave me lots of support, help and encourage both in my Ph.D study
and life.
vii
Table of contents
ABSTRACT ....................................................................................................................... ii
DEDICATION................................................................................................................... v
ACKNOWLEDGEMENT ............................................................................................... vi
TALBE OF CONTENTS .............................................................................................. viii
LIST OF TABLE ............................................................................................................. xi
LIST OF FIGURES ........................................................................................................ xii
1. Introduction ................................................................................................................... 1
1.1 Development of Magnetoelectric effect ...................................................................... 1
1.1.1 Magnetoelectric Materials ...................................................................................... 1
1.1.2 Workding mode of ME lamianted composites ...................................................... 11
1.2 Potential devices based on ME effect ....................................................................... 18
1.2.1 Magnetic sensors .................................................................................................. 18
1.2.2 Energy harvesters ................................................................................................. 22
1.2.3 Other decices ........................................................................................................ 24
1.3 Noise souruces and their elminations........................................................................ 26
1.3.1 External noise ....................................................................................................... 26
1.3.2 Internal noise ........................................................................................................ 29
1.4 Summary of this section ............................................................................................ 35
2. Purpose of thesis .......................................................................................................... 36
3.Magnetoelectric composites ........................................................................................ 41
3.1 Metglas/Piezo-fbiers ME lamiantes composites ....................................................... 41
3.2 Improvement of ME coefficients .............................................................................. 42
3.2.1 Compasrison of different piezo-fibers.................................................................. 42
viii
3.2.2 Volume ratio effect ............................................................................................... 51
3.2.3 Heat treatments..................................................................................................... 64
3.3 Vibration noise rejection ........................................................................................... 67
3.4 Summary of this section ............................................................................................ 78
4. AC magnetic sensor .................................................................................................... 79
4.1 Introduction ............................................................................................................... 79
4.2 Passive magnetic sensor unit..................................................................................... 79
4.3 Extremely low frequency magnetic sensor ............................................................... 92
4.3.1 Charge amplifier circuit design ............................................................................ 92
4.3.2 Charge noise model .............................................................................................. 98
4.3.3 ELF magnetic sensor optimization..................................................................... 105
4.4 Active magnetic sensor unit .................................................................................... 122
4.4.1 Sensor design and characterization .................................................................... 122
4.4.2 Optimization of active magnetic sensor ............................................................. 134
4.5 Summary of this section .......................................................................................... 146
5. DC magnetic sensor .................................................................................................. 149
5.1 Introduction ............................................................................................................. 149
5.2 Improvement of sensitivity ..................................................................................... 152
5.2.1 Different piezo-fibers ......................................................................................... 153
5.2.2 Magnetic flux concentration .............................................................................. 159
5.3 Man portable magnetic sensor ................................................................................ 166
5.3.1 Lock-in detection circuit .................................................................................... 166
5.3.2 Sensor performances .......................................................................................... 171
5.4 Geomagnetic field detection ................................................................................... 175
5.4.1 2-axial magnetic sensor ...................................................................................... 176
5.4.2 3-axial magnetic sensor ...................................................................................... 178
5.4.3 Mobile magnetic sensor unit .............................................................................. 180
5.4.4 Demonstrations for geomagnetic field sensor .................................................... 182
5.5 Summary of this section .......................................................................................... 188
ix
6. Other devices based on ME effect ........................................................................... 189
6.1 Introduction ............................................................................................................. 189
6.2 Bi-layered ME composites ...................................................................................... 190
6.2.1 Design of bi-layered ME composites ................................................................. 191
6.2.2 Tunability of resonant frequency ....................................................................... 199
6.3 Energy harvester...................................................................................................... 206
6.3.1 Multi-push pull ME harvester ............................................................................ 206
6.3.2 Bi-layered ME harvester .................................................................................... 210
6.4 Frequency multiplier ............................................................................................... 214
6.5 Summary of this section .......................................................................................... 224
x
LIST OF TABLES
Table 1.1 ME coefficients for different ME composites .................................................. 10
Table 3.1 Piezoelectric properties of some materials ....................................................... 43
Table 3.2 Materials parameters for ME coefficients calculation ...................................... 60
Table 4.1 ME composites properties ................................................................................ 99
Table 4.2 Circuit components used for charge amplifier .................................................. 99
Table 4.3 Comparisons of op-amp chips ........................................................................ 112
Table 4.4 Components used for circuit design................................................................ 113
Table 5.1 Critical piezoelectric properties for PZT and PMN-PT fibers ........................ 153
Table 5.2 Geomagnetic field measurements at two positions by using 3-axial sensor... 178
Table 5.3 Geomagnetic field intensity along North direction......................................... 178
Table 5.4 Geomagnetic field intensity along Vertical direction ..................................... 178
Table 5.5 Inclination Angle ............................................................................................ 178
Table 6.1 Materials parameters for Metglas, PZT used for theoretical modeling .......... 204
Table 6.2 Geomagnetic field intensity of Virginia Tech area ......................................... 219
xi
LIST OF FIGURES
Figure 1.1 Schematic illuminations of idea ME coupling effect in multiferroic materials 2
Figure 1.2 Schematic illustrations of bulk composites with three common connectivity
schemes: (a) 0-3 particulate composite, (b) 2-2 laminate composites, and (c)
1-3 fiber/rode composites. ............................................................................... 6
Figure 1.3 Transverse and longitudinal ME voltage coefficients as function of dc
magnetic field at 100 Hz for Zn-doped NFO and PZT multilayer structure. .. 7
Figure 1.4 (a) An optical and (b) scanning electron micrograph of the fractured surface of
the sandwiched PZT/NFO/PZT ceramics. ....................................................... 8
Figure 1.5 Schematic illustration of the various ME coupling modes: (a) L-L; (b) T-L; (c)
L-T; and (d) T-T. ........................................................................................... 12
Figure 1.6 Schematic of push-pull mode. ......................................................................... 14
Figure 1.7 Schematic illustration of multi-push pull configuration. ................................. 15
Figure 1.8 Self biased Ni/Metglas/PZT ME composites: (a) Metglas/Ni/PZT
configuration, (b) Ni/Metglas/PZT configuration; and (c) Magnetostriction
coefficients for Ni, KNNLS-NZF, and KNNLS-NZF/Ni/KNNLS-NZF. ..... 17
Figure 1.9 (a) Photograph of the prototype ME detection system. A: batteries (below the
PCB board); B: optimized dc magnetic bias (NbFeB); C: Teflon tube (ME
sensor is held inside); D: aluminum box; E: low noise charge amplifier; F:
output jack; G: power switch; and (b) response of detection unit to small AC
magnetic field at 1 Hz. .................................................................................. 19
Figure 1.10 (a) Schematic illustration of DC magnetic sensor; (b) Photo of geomagnetic
field detection; and (c) Output signals along different directions in Earth
plain. .............................................................................................................. 21
Figure 1.11 (a) Multimodal energy harvester; and (b) Vibration energy harvester
prototype. ....................................................................................................... 23
Figure 1.12 (a) Equivalent circuit of gyrator; (b) ME gyrator design; (c) Inductor
converted to inductor; and (d) resistor to resistor with inverse resistance .... 25
Figure 1.13 (a) Schematic illustration of symmetrical structure design; and (b)
comparison of output signals under thermal fluctuations in time domain .... 28
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Figure 1.14 (a) Voltage noise model; and (b) current noise model. ................................. 31
Figure 1.15 (a) Equivalent noise model for magnetic sensor; and (b) Output noise level of
circuit and sensor unit. ................................................................................... 34
Figure 3.1 The ME voltage coefficient ME as a function of the static magnetic field Hdc
for Metglas-PZT, Metglas-PMN-PT, and Metglas-PZN-PT laminate
composites, as indicated. Inset shows a representative picture of a laminate
composite....................................................................................................... 45
Figure 3.2 (a) Picture of our low noise circuit along with the ME sensor in a box. The ME
output voltage as a function of time for the (b) PZT, (c) PMN-PT and (d)
PZN-PT based sensors, respectively. The corresponding field sensitivities are
as indicated. (e) Noise level for various detection units. ............................... 48
Figure 3.3 Noise spectra for the PZT, PMN-PT, and PZN-PT laminates with wide band
circuit. Inset shows the wide band circuitry response as the function of the
frequency. ...................................................................................................... 50
Figure 3.4 (a) Schematic diagram of ME composites configuration consisting of an ID
electrodes, core composite and symmetric Metglas actuators on the bottom
and top of the core composite. (b) Illustration of the numerous alternating
push-pull mode units. (c) Optical microscopy image of a longitudinally poled
push-pull element in the core composite. (d) and (e) Photographs of ME
composites. .................................................................................................... 52
Figure 3.5 2-D ID electrode schematic showing the electric field lines. .......................... 54
Figure 3.6 Schematic of L-L model. ................................................................................. 55
Figure 3.7 Magneto-electric voltage coefficients V as a function of the static dc
magnetic field Hdc for various PZT fiber-Metglas laminate composites. The
inset shows a schematic of the structure........................................................ 59
Figure 3.8 Comparison of experimental data and estimated values. ................................ 61
Figure 3.9 (a) Lowest detectable magnetic field for the PZT fiber-metglas laminate
composites as a function of the number of metglas layers N on either side of
PZT at 1 Hz for constant signal-to-noise ratio SNR > 2. (b)-(f) Output
voltage waveforms for the laminates with different metglas layers N in the
time domain. (g) Example voltage noise level for the low noise charge
amplifier as a function of time. ..................................................................... 63
Figure 3.10 ME voltage coefficient a as a function of the static dc magnetic field Hdc for
various PZT fiber-Metglas laminate composites after heat treated with
Metglas layer. ................................................................................................ 65
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Figure 3.11 Comparison of AC magnetic sensitivity for the PZT fiber/Metglas laminated
composites as a function of the different annealed temperature of Metglas
layer. .............................................................................................................. 66
Figure 3.12 (a) Schematic of our new differential mode ME laminate sensor; (b) poling
profile of multi-push/pull, dual PZT composite structure; and (c) schematic
of the experimental signal path. .................................................................... 70
Figure 3.13 (a) Time-domain equivalent magnetic response of differential mode sensor to
incident vibrational signal; (b) power spectral density of top, bottom and
time-domain summation of top and bottom; and (c) phase shift between top
and bottom PZT layers as a function of frequency calculated from a linear
time invariant transfer function. .................................................................... 73
Figure 3.14 (a) Time-domain response of top PZT layer, bottom and sum of individual
signals in response to an incident magnetic field; and (b) power spectral
density response of a sensor to a 10 Hz magnetic field. ................................ 75
Figure 3.15 Comparison of noise cancellation for a differential ME structure sensor and a
non-differential ME structure sensor. ............................................................ 77
Figure 4.1 (a) Schematic illustrations of Metglas/PMN-PT ME composites; and (b) ME
voltage coefficient ME and ME charge coefficient me for Metglas/PMN-PT
laminates as function of Hdc. ......................................................................... 81
Figure 4.2 Transfer function of detection circuit. ............................................................. 83
Figure 4.3 Equivalent magnetic noise density spectra: (a) Voltage noise density detected
by dynamic signal analyzer; and (b) equivalent magnetic noise density after
conversion. .................................................................................................... 84
Figure 4.4 Transfer function of low frequency detection circuit. ..................................... 87
Figure 4.5 Output signal in response to the incident magnetic field: (a) low frequency
detection sensor circuit, and (b) wide band frequency detection sensor unit. 88
Figure 4.6 Linearity of magnetic sensor assembled with low frequency circuit. ............. 90
Figure 4.7 Equivalent magnetic noise spectra. ................................................................. 91
Figure 4.8 (a) Charge amplifier design for quasi-static magnetic sensor, and (b) predicted
and measured transfer functions of the circuit. ............................................. 94
Figure 4.9 ME charge coefficients at quasi-static frequency range. The insert is the output
voltage of circuit in response to a 10 mHz input charge. .............................. 97
Figure 4.10 Estimated and measured equivalent magnetic noise of the magnetic sensor
based on previous noise model. ................................................................... 100
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Figure 4.11 (a) Theoretical model for noise sources in our ME magnetic sensor; and (b)
estimated and measured equivalent magnetic noise of the sensor. ............. 104
Figure 4.12 (a) Transfer function of two sensors, and (b) coherency between two sensors.
..................................................................................................................... 106
Figure 4.13 Comparisons of equivalent magnetic noise with and without high vacuum
conditions. ................................................................................................... 108
Figure 4.14 Comparison of equivalent magnetic noise spectra at normal and high vacuum
conditions for ELF magnetic sensors. ......................................................... 110
Figure 4.15 Estimated and measured equivalent magnetic noise of the ELF magnetic
sensor based on Metglas/PMN-PT ME composites. The insert is a schematic
illustration of the ME composites. .............................................................. 111
Figure 4.16 (a) Calculated voltage noise densities for LMC6042 and LMC6442
operational amplifiers, and (b) comparisons of calculated magnetic noise
spectra for magnetic sensors based on optimized and previously reported
detection circuits. ......................................................................................... 114
Figure 4.17 (a) Predicted and measured transfer functions of the new detection circuit;
and (b) estimated and measured equivalent magnetic noise floors of an
optimized magnetic sensor. ......................................................................... 116
Figure 4.18 Transfer functions of the 0.001 Hz detection circuit. .................................. 118
Figure 4.19 (a) Waveform of magnetic sensor in time domain, and (b) magnetic power
spectra of magnetic sensor. The red dash line indicates the theoretical
prediction result. .......................................................................................... 121
Figure 4.20 Modulation process of active mode ME sensor. ......................................... 124
Figure 4.21 (a) Schematic of our custom-built lock-in circuit; and (b) photo of a lock-in
circuit. .......................................................................................................... 127
Figure 4.22 (a) Experimental setup for the active sensor test; and (b) H-coils calibration
results at 1 Hz and 7.875 mHz..................................................................... 131
Figure 4.23 (a) Output signal from active sensor as function of incident magnetic field;
and (b) sensitivity of sensor as frequency range from 7.8125 mHz to 1 Hz.
..................................................................................................................... 132
Figure 4.24 Equivalent magnetic noise density spectra of active magnetic sensor. ....... 133
Figure 4.25 Equivalent magnetic noise density spectra of active magnetic sensor. ....... 135
Figure 4.26 (a) Sensitivity of modulated sensor as frequency range from 6 mHz to 200 Hz;
and (b) equivalent magnetic noise density spectra of active magnetic sensor.
..................................................................................................................... 136
xv
Figure 4.27 (a) Sensitivity of modulated sensor as frequency range from 6 mHz to 200 Hz;
and (b) equivalent magnetic noise density spectra of active magnetic sensor.
..................................................................................................................... 138
Figure 4.28 (a) Induced output signals in response to the incident magnetic field; and (b)
noise spectra of the sensor at various driving signals, respectively. ........... 140
Figure 4.29 Equivalent magnetic noise density spectra for the sensors under different
driving signals. ............................................................................................ 141
Figure 4.30 Sensitivity, voltage noise density and equivalent magnetic noise density at
1Hz for active sensor as function of driving signals. .................................. 143
Figure 4.31 (a) Local geomagnetic field noise measurements along different directions;
and (b) comparisons of noise spectra measured by active sensor and fluxgate.
The insert of the figure indicates the experimental setup. ........................... 145
Figure 5.1 Geomagnetic sensing by sea turtles. .............................................................. 151
Figure 5.2 αME-Hdc for Metglas/PZT composites. .......................................................... 152
Figure 5.3 ME voltage coefficient of Metglas/PZT and Metglas/PMN-PT laminates: (a)
ME as the function of dc bias Hdc at f = 1 kHz, and (b) ME as a function of
ac magnetic drive frequency. ....................................................................... 154
Figure 5.4 DC magnetic field sensitivities for (a) PZT based; (b) PMN-PT based
composites. .................................................................................................. 156
Figure 5.5 Sensitivity of MEtglas/PMN-PT laminate to small DC magnetic field changes
at ac drive field of Hac = 0.1 Oe at the resonant frequency. ........................ 158
Figure 5.6 (a) Schematic representation of 3-D Mangetostatic model layout including
large, permanent magnetic HDC bias generators, and (b) vector map of the
y-z (axial-height) component of the H field in the presence of the high-mu
Metglas. Insert: non-ideal B-H relationship used to define magnetostatic
behavior of high mu Metglas in FEM. ........................................................ 160
Figure 5.7 (a) In-plane magnetic field strength along centerplane of Metglas foils in
response to arbitrarily low DC bias field, as simulated by Maxwell 3D, and (b)
line scan traces of magnetic flux density along the axially centerline of
Metglas foils for 80mm and 100mm geometries. ........................................ 162
Figure 5.8 ME voltage coefficient of laminate sensor with different Metglas lengths as a
function of DC bias Hdc in response to a 1Oe, 1 kHz AC magnetic excitation.
..................................................................................................................... 164
Figure 5.9 Comparison of the sensitivity for Metglas/PZT laminates to small DC
magnetic field changes under AC drive conditions of at f =1 kHz and Hac=0.1
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Oe: (a) ME sensor with 8 cm long Metlgas, and (b) ME sensor with 10 cm
long Metglas. ............................................................................................... 165
Figure 5.10 (a) Schematic of our custom-built lock-in circuit; (b) photo of a prototype
lock-in circuit. ............................................................................................. 167
Figure 5.11 Waveforms of driving signal generated by oscillator in time domain: (a) 1
kHz; and (b) 32.7 kHz. ................................................................................ 169
Figure 5.12 Sensitivity of composites to small DC magnetic field changes under AC
driving conditions at f=1 kHz and Hac=0.1 Oe generated by (a) lock-in
amplifier (SR-850); and (b) lock-in circuit. ................................................ 170
Figure 5.13 Illustration of capability of our DC magnetometer to localize a magnetic
dipole: (a) schematic of experimental setup, (b) magnetic flux distribution of
the magnetic dipole, and (c) position measurement. ................................... 173
Figure 5.14 Real space DC magnetic field test: (a) photo of test location, and (b) output
signal from DC magnetometer over spatial grid about test location. .......... 174
Figure 5.15 Multi-axial detection magnetic sensor: (a) 2-axis; and (b) 3-axis. .............. 175
Figure 5.16 (a) Experimental setup for 2-axial geomagnetic sensor; and (b) orientation
determined based on geomagnetic field. ..................................................... 177
Figure 5.17 Geomagnetic field measurements around Blacksburg area. The insert shows
the 3-axial magnetic sensor used in the test. ............................................... 179
Figure 5.18 (a) Rigid package for 3-axial magnetic senor; and (b) characterization of
sensitivity for each axis sensor. ................................................................... 181
Figure 5.19 (a) Labview program for rotation monitor; and (b) experimental setup for
monitoring the orientation in 3-D space. ..................................................... 183
Figure 5.20 (a) magnetic field mapping demonstration performed at parking lot; and
(b)-(d) magnetic field mapping results measured by the sensors. ............... 185
Figure 5.21 (a) Geomagnetic field sensing in open environment; and (b) magnetic fields
for the process. ............................................................................................ 187
Figure 6.1 Schematics of Metglas/PZT ME laminate sensors: (a) L-L mode sensor, and (b)
bending mode. ............................................................................................. 192
Figure 6.2 ME voltage coefficients of L-L and bending mode ME laminates: (a) ME as a
function of dc magnetic bias Hdc at f = 1 kHz, and (b) ME as a function of ac
magnetic drive frequency. The insert shows ME for the L-L mode for 103
<f<105 Hz. ................................................................................................... 194
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Figure 6.3 (a) Noise levels for the L-L and bending mode sensors; and (b) ME output
voltage as a function of time for the L-L and bending mode sensors. The
corresponding peak-to-peak ac field sensitivities are listed. ....................... 196
Figure 6.4 Equivalent magnetic noise spectra for the L-L and bending mode sensors for
102< f <103 Hz. ............................................................................................ 198
Figure 6.5 (a) Impedance spectra of Metglass/PZT bending laminates with various tip
masses; and (b) ME voltage coefficients for Metglas/PZT laminates as a
function of frequency with various tip masses. The insert is a schematic of
the bending mode laminates. ....................................................................... 201
Figure 6.6 (a) Theoretical model for magnetoelectric bi-layer laminates, and (b) estimated
ME voltage coefficients as a function of frequency. ................................... 205
Figure 6.7 Output voltage and power as a function of load resistance load for
Metglas/PMN-PT laminates at the resonance frequency. ........................... 207
Figure 6.8 Illustration of ability to charge batteries of ME detection units by magnetic
energy harvesting: (a) experimental setup, and (b) testing results. ............. 209
Figure 6.9 (a) ME voltage coefficient of 60 Hz magnetic energy harvester as a function of
AC magnetic drive frequency; and (b) output voltage and power as a function
of resistance load at the bending mode resonance frequency...................... 211
Figure 6.10 Demonstration of ability to capture 60 Hz electromagnetic energy by using
ME magnetic harvester: (a) photo of experimental setup, and (b) output
voltage signal in the time domain................................................................ 213
Figure 6.11 (a) Waveforms of driving ac magnetic field and output signal in time domain;
and (b) induced frequency doubling signal as a function of dc magnetic bias
Hdc. The insert shows schematic of frequency multiplier based on
Metglas/PZT ME composites. ..................................................................... 216
Figure 6.12 Waveforms of driving ac magnetic field and output signal in the time domain
at various frequencies: (a) 100 Hz, (b) 1 kHz, and (c) 2 kHz. .................... 218
Figure 6.13 (a) Schematics of frequency multiplier under geomagnetic field; the ratio of
the induced second to first harmonic signals V2f/Vf along various directions:
(b) in horizontal plane, and (c) in vertical plane. The inserts show the
waveforms in the time domain. ................................................................... 221
Figure 6.14 Magnetostriction and effective linear piezomagnetic coefficient for the
Metglas/PZT ME composites. ..................................................................... 223
xviii
1. Introduction
1.1 Development of Magnetoelectric effect
1.1.1 Magnetoelectric Materials
Magnetoelectric (ME) effect is characterized by electric polarization changes in
response to an applied magnetic field (H), or conversely, a magnetization changes
with an applied electric field (E).1-3 The direct ME coupling effect of the materials
can be characterized by a parameter designed as ME voltage coefficient αME, which
is described by the induced electric field (δE) by an applied magnetic field (δH):
αME= δE/ δH=δV/(tδH)
(1.1)
where δV is induced voltage as applied magnetic field, t is the thickness. On the
other hand, the converse ME coupling effect is defined as induced magnetic field by
an applied electric field.4 Figure 1.1 shows the idea ME coupling effect in
multiferroic materials. Ideally, electric (magnetic) polarization would show the
hysteresis response to applied magnetic (electric) field.5 Based on strong ME
coupling effect, some novel multifunctional devices can be developed.
1
Figure 1.1 Schematic illuminations of idea ME coupling effect in multi-ferroic
materials
2
The concept of magnetoelectric effect can be traced back to predictions based
on crystal symmetry theory by Curie in 1894.6 However, over half of century passed,
and only was, the electrically induced and magnetically induced ME effects
observed in anti-ferromagnetic single phase crystal of Cr2O3 by G.N.Astrov and
G.T.Rado in 1960 and 1961,7, 8 respectively. These works confirmed the reality of
ME effect experimentally, which were the milestones in the research of ME effect.
Later, more single phase ME materials were reported.
However, the ME voltage coefficients for single phase materials are not high:
the values of αME for these materials are on the order of several mV/cm-Oe. For
example, the ME voltage coefficient is only about 20 mV/cm-Oe in Cr2O3 single
crystal. The basic problem in single phase materials is that the electronic
configurations which favor magnetization are antagonistic to those that favor
polarization. This problem makes the ME coupling effect is either weak or occurred
at low temperature, in which case, makes it hard for single phase materials to be
useful for devices in practical applications.
Obviously, it is necessary to explore possible composites when the reasonable
ME effect could not be obtained or optimized in single phase materials. In 1972, van
Suchtelen first proposed the concept of ME effect in ceramic composites. The
composite materials contain one magnetostrictive phase and piezoelectric phase,
achieving ME coupling effect via elastic interaction. The following expressions
show the process of how to obtain direct or converse ME effect:9
3
magnetic mechanical

,
mechanical
electric
electric
mechanical
ME E effect=

.
mechanical magnetic
ME H effect=
(1.2)
According to this design, some ME ceramic composites were first reported by
the Philips Research Lab.10 For example, they studied ME composites using BaTiO3
as the piezoelectric phase and Ni(Co,Mn)Fe2O4, as piezomagnetic phase in 1978. In
their study, the ME voltage coefficient for this composites was up to 80 mV/cm-Oe.
Although it did not get the remarkable values (> 1V/cm-Oe) as expected, it did prove
the design concept and possibility of obtaining higher ME coefficients. In the 1990s,
several theoretical work on ME ceramics were developed to understand the coupling
effect between two phases, and to predict the ME coefficient in ceramic composites.
However, a rare giant ME coupling effect was reported experimentally at that time.
Meanwhile, some groups prepared particulate ceramic composites by conventional
processing. This method is much easier and cost effective. There are several
challenges that limited the property of ME composites: (i) chemical reactions
between the constituent phases or during sintering; (ii) non-ideal interfacial
boundary makes the stress transfer inefficient, (iii) much smaller resistivity of the
magnetostrictive phase compared to that of piezoelectric phase results in poor
polarization of the piezoelectric phase and discharge as applied magnetic field; and
(iv) non-optimum alignment of the magnetization of the magnetostrictive phase on
applying DC bias.
Since 2000, ME laminated composites consisting of magnetostrictive and
piezoelectric phases were reported to have giant ME voltage coefficients. The values
4
of αME for these laminated composites were enhanced by over 500× compared to
other ME materials.11-13 In detail, laminated composites are designed with “2-2”
connectivity schemes, as shown in Figure 1-2.9 The biggest advantage of 2-2
connectivity is that the leakage problem due to high concentration of the ferrite
phase with low resistivity in the particulate composites can be reduced. So, 2-2
connectivity can improve the poling condition of a piezoelectric layer resulting in
enhancement of the ME effect.
Laminated composites have been constructed by co-sintering or mechanical
epoxy bonding methods.13-16 Co-sintered ME laminated composites have been made
from perovskite ferroelectric and ferrite magnetostrictive ceramics. For example,
bi-layer or multi-layer Pb(Zr, Ti)O3 (PZT) and NiFe2O4(NFO) and so on. Another
characteristic for laminated composites is the anisotropic response to external
magnetic bias.14 Figure 1.3 shows the dc magnetic field dependent ME coefficient
for NZFO and PZT composites. The ME voltage coefficients for transverse mode is
around 400 mV/cm-Oe, while the value for longitudinal mode is less than 100
V/cm-Oe.
Although the co-sintering method is easy to perform, there are several
limitations that influence the property of composites: (i) chemical reaction at higher
sintering temperature; (ii) non-idea interfacial boundary between two phases, like
porous in ceramics, as shown in Figure 1.4;17 and (iii) limited materials selection.18,
19
The first two reasons make the ME coefficients for laminated composites
fabricated by co-sintering exhibit smaller values than the value predicted by model
works.
5
Figure 1.2 Schematic illustrations of bulk composites with three common
connectivity schemes: (a) 0-3 particulate composite, (b) 2-2 laminate composites,
and (c) 1-3 fiber/rode composites.
6
Figure 1.3 Transverse and longitudinal ME voltage coefficients as function of dc
magnetic field at 100 Hz for Zn-doped NFO and PZT multilayer structure.
7
Figure 1.4 (a) An optical and (b) scanning electron micrograph of the fractured
surface of the sandwiched PZT/NFO/PZT ceramics.
8
On the other hand, an epoxy bonding method is much more suitable for
magnetic alloy and piezoelectric ceramic based ME laminated composites. By this
method, materials with completely different properties can be bonded together
mechanically,20,
21
such as the PZT/ Terfenol-D alloy. Terfenol-D is a
magnetostrictive alloy with extremely high magnetostriction coefficients that could
enable the achievement of further enhancement in ME coefficients. However, it is
impossible to form composites by using the co-sintering method: the high sintering
temperature for PZT would oxidize Terfenol-D. Epoxy bonding can solve this
problem easily without high temperature sintering. Dong et al. have reported that the
giant ME coefficient in PZT/Terfenol-D laminated composites.22 The value of αME
can reach as high as 4.6 V/cm-Oe at quasi-static frequency and up to 40 V/cm-Oe at
the electromechanical resonance drive conditions: this value is one order higher than
the value of ferrite/PZT system. More investigations on magnetic alloys and ceramic
systems have been developed, such as Fe-Ga alloy, Galfenol or Metglas and PZT,
PMN-PT or PVDF layers. Table 1.1 list the ME coefficients for some ME
composites.
9
Table 1.1 ME coefficients for different ME composites
ME composites
ME coefficient (mV/cm-Oe)
Ref.
Ceramic Composites:
(0-3)NZFO/PZT
[email protected]
Ref.23
(2-2) NCZF/PZT/NCZF
[email protected]
Ref.24
10.3×[email protected]
Ref.25
1.43×103
Ref.26
22×103
Ref.27
Ceramic-Alloy Composites
(2-2) Terfenol-D/PMN-PT
(2-2) Terfenol-D/PVDF
(2-2) Metglas/PZT
10
1.1.2 Working mode of ME laminated composites
Besides the numerous types of materials that have been studied for enhanced
ME effects, several investigations have focused on the geometry and the polarization
or magnetization direction with respect to long axis of the laminated composites.
The results show that different ways to bond the composites can generate significant
different ME coefficients and optimum DC bias, even for the same phases. Basically,
there are four operation modes according to the poling or magnetization directions
with respect to long axis.28
Figure 1.5 shows four basic types of operation modes. These are the
longitudinally magnetized and longitudinally poled (L-L) mode, the transversely
magnetized and longitudinally poled (T-L) mode, the longitudinally magnetized and
transversely poled (L-T) mode, and the transversely magnetized and transversely
poled (T-T) mode.
As mentioned above, different operation modes can affect the ME response
dramatically. Generally, the L-L mode normally shows the largest ME voltage
coefficient among these four operation modes according to the experimental results.
To explain it easily, we can say that the L-L mode uses the d33 of the piezoelectric
phase while others operate using d31. For typical piezoelectric ceramics, the value of
d33 is larger than d31. Take PZT-5, one of the commercially available piezoelectric
phases, for example: d33 is 400 pC/N while d31 is just -175 pC/N.
11
Figure 1.5 Schematic illustration of the various ME coupling modes: (a) L-L; (b)
T-L; (c) L-T; and (d) T-T.
12
However, there are several limitations for this operation mode: (i) a high poling
voltage. Due to the geometry of laminates (Length (l) >width (w)> thickness (t)),
much higher poling voltage is required for L-L mode than that needed for L-T, T-T
mode; (ii) a low capacitance, that makes the composites be affected by the stray
capacitance of the measurement system, and low charge output. In order to solve
these problems, the L-L push-pull mode was proposed, as shown in Figure 1.6.16
Compared to traditional L-L mode, push-pull mode can enhance the capacitance by
4× with the same dimensions. Meanwhile, it decreased the poling voltage.
Interestingly, Dong et al. proposed a multi-push pull structure for Metglas/PZT
laminated composites.27 Figure 1.7 shows the structure of this design: PZT fibers of
100 um in thickness were oriented along their long axis to form a piezoelectric layer.
Two interdigitated Kapton®-based electrodes were then bonded to the top and
bottom surfaces of the piezoelectric layer. Metglas foils were then laminated to both
the top and bottom surfaces of the PZT composite cores. In fact, we can separate this
configuration into numerous small units, as shown in insert of Figure 1.7. Each unit
can be taken as a “push-pull” mode. Due to the thickness of Metglas foils is very
thin, the thin piezo-fiber used for this system is required to reach high ME voltage
coefficient, such as 100 um in this case. This structure can enhance the capacitance
dramatically, which is quite valuable for Metglas alloy based ME laminated
composites.
13
Figure 1.6 Schematic of push-pull mode.
14
Figure 1.7 Schematic illustration of multi-push pull configuration.
15
Besides these typical symmetrical modes, there are also many asymmetric
designs, such as the bi-layer bending structure.29-32 Moreover, recently, graded
magnetization ME composites have been proposed which show a non-zero ME
coefficients at zero bias, as illustrated in Figure 1.8 (a) and (b).33 Interestingly, the
ME voltage can be tuned by changing the arrangement of magnetostrictive layers.
The origin for a self bias effect comes from the different magnetic properties of two
piezomagnetic phases and the strain-mediated coupling between them. One direct
observation for KNNLS-NZF/Ni/KNNLS-NZF composites is present in Figure 1.8
(c).34 From this figure, one can see, compared to pure Ni or KNNLS-NZF
individually, the magnetostriction coefficient curve for combination of KNNLS-NZF
and Ni was shifted to the left resulting in the remaining strain at zero dc magnetic
bias. This shift could be the reason for the non-zero ME effect at zero magnetic field.
16
Figure 1.8 Self biased Ni/Metglas/PZT ME composites: (a) Metglas/Ni/PZT
configuration, (b) Ni/Metglas/PZT configuration; and (c) Magnetostriction
coefficients for Ni, KNNLS-NZF, and KNNLS-NZF/Ni/KNNLS-NZF.
17
1.2 Potential devices based on ME effect
Giant ME coupling effects in laminated composites gives the material the
potential for applications as multifunctional devices, such as sensors,35, 36 memory
devices,37, 38energy harvesters,39, 40 transducer41 and so on.
1.2.1 Magnetic Sensors
There are some commercially available magnetic sensors in the market: giant
magneto-resistive (GMR), flux-gate, and superconducting quantum interference
devices (SQUID). They have low noise floors in the order of 10-10 T / Hz , 10-12
T / Hz and 10-14 T / Hz respectively, in the frequency range of 1<f<103
Hz.42-44 However, there are some limitations to these conventional magnetic sensors
in applications. For example, SQUIDs require extremely low operational
temperatures, fluxgates have magnetic hysteresis and offset values under zero
magnetic fields, and both fluxgate and GMRs require considerable power. So, one
novel AC magnetic sensor is highly desired to satisfy the following requirements: (i)
high sensitivity or low noise at static frequency range (~pT/√Hz at 1 Hz); (ii) low
power: long-term operation; (iii) compact size; and (iv) low cost.
Xing et al. designed one passive AC magnetic sensor based on charge amplifier
circuit. Based on Terfenoal-D/PZT composites with L-T mode, the sensitivity of 2.6
nT at 1 Hz can be measured, as shown in Figure 1.9.45 Later, using push-pull mode,
Zhai et al have proposed one passive AC magnetic sensor with much lower noise
density (20 pT/√Hz @ 1 Hz) at room temperature.46
18
Figure 1.9 (a) Photograph of the prototype ME detection system. A: batteries (below
the PCB board); B: optimized dc magnetic bias (NbFeB); C: Teflon tube (ME sensor
is held inside); D: aluminum box; E: low noise charge amplifier; F: output jack; G:
power switch; and (b) response of detection unit to small AC magnetic field at 1 Hz.
19
However, there are still researches needed to further improve the AC magnetic
sensor: (i) increase the sensitivity; (ii) decrease the equivalent magnetic noise at the
quasi-static frequency range; (iii) external noise rejection; and (iv) small package.
Besides AC magnetic sensors, an active DC magnetic sensor was also
developed. In this measurement, Dong et al. developed a lock-in amplifier method to
drive the ME composites, as shown in Figure 1.10.47 A small AC current was
generated from a lock-in amplifier to directly excite the driving coils wrapped
around the composites. The incident magnetic field was applied along a long axial
direction. Based on the ME effect, the composites can convert the small DC
magnetic field to an electric signal monitored by a lock-in amplifier as well. By this
method, the small DC magnetic field variations as small as 10 nT can be detected
using Terfenol-D/PZT composites driving at frequency of 84 kHz and Hac = 71 mOe.
Moreover, Zhai et al. used the similar method to design one geomagnetic detection
sensor based on Metglas/PZT laminated composites.35 Figure 1.10 (b) shows the
experimental setup: the sensor was placed on the inside of the globe which can rotate
along three different directions. Thus, the geomagnetic intensity along the
north-south axis, east-west axis, and earth plan can be detected. Figure 1.10(c)
presents the test result of the Earth plane. These results confirm that the ME
composites also have the potential for applications in DC magnetic field sensor.
However, in spite of this potential, an actual application has not yet been achieved.
One of the biggest problems is using a lock-in amplifier in this method. This method
limits the mobility as a detection unit. A different method is highly desired to
develop which would have the similar functions as the lock-in amplifier.
20
Figure 1.10 (a) Schematic illustration of DC magnetic sensor; (b) Photo of
geomagnetic field detection; and (c) Output signals along different directions in
Earth plain.
21
1.2.2 Energy harvesters
Magnetoelectric bulk composites can be also used for energy harvesting devices
which can generate useful electric energy by harvesting energy sources that cannot
be utilized directly in the environment, such as solar, thermal, vibration, and
magnetic energies. Specifically, for ME laminated composites, it would be possible
to harvest vibration energy via piezoelectric effect and electromagnetic energy via
ME effect. These hybrid harvesters are expected to enhance energy collection and
conversion efficiency.
For example, by using an ME laminated composites attached to a cantilever
beam with a tip mass, a multimodal energy harvester was developed which can
harvest energy from both of magnetic field and mechanical vibration.48 By driving
the harvester at 20 Hz with a magnetic field of 2 Oe and mechanical vibration
amplitude of 50 mg, an open-circuit output voltage of 8 V can be generated, as
shown in Figure 1.11 (a). Also, other groups designed a prototype of vibration
energy harvester by using a Terfenol-D/PZT sandwich structure ME transducer
which can generate a load power of 1.05 mW across a 564.7 kohm electric load
driving with an acceleration of 1 g at resonance frequency of 51 Hz (Figure 1.11
(b)).49, 50
Compared to piezoelectric or electromagnetic harvesters, the conversion
efficiency of an ME harvester is still at a lower level.51 There is a lot of room for
enhancement.
22
Figure 1.11 (a) Multimodal energy harvester; and (b) Vibration energy harvester
prototype.
23
1.2.3 Other Devices
Besides these main applications, some other multifunctional devices based on
ME composites have been designed as well. For example, ME composites based
gyrator was developed.52 A gyrator is a passive, two-port electric network. Figure
1.12 (a) shows the equivalent circuit of gyrator. The gyrator looks like the voltage
transformer via inductive interaction between coils. The gyrator can achieve the
impedance inversion function, which means that it can convert an inductor (capacitor)
to a capacitor (inductor). Through calculations, ME composites are predicted to have
this function. Figure 1.12 (b) shows the device’s design according to the equivalent
circuit. (c) and (d) present through ME gyrator, the capacitor can be converted to
inductor, resistor to resistor with an inverse resistance.
Recently, a simple ME-based frequency multiplier made up of FeBSiC and PZT
wrapped with a coil has been proposed.53 It shows the steady frequency doubling
behaviors at various frequencies. Moreover, the small DC bias can switch device on
or off. Zhang et al. designed one resonance frequency multiplier.54 The multiplying
signal can be generated when the input frequency of AC magnetic field is around 1/n
of mechanical resonance frequency of device. Interestingly, such frequency
multiplying behavior can be tuned by using external DC bias. Compared to
traditional frequency multipliers, these devices are passive components and can be
used in broad frequency range, probably offering a potential application in the
electric industry
24
Figure 1.12 (a) Equivalent circuit of gyrator; (b) ME gyrator design; (c) Inductor
converted to inductor; and (d) resistor to resistor with inverse resistance.
25
1.3 Noise sources and their eliminations
The main research for my thesis is about the improvement of AC and DC
magnetic sensors based on ME laminated composites. So, the noise analysis is
mainly considered for these detection units. Generally, noise is referred to as any
unexpected or unwanted disturbance that reduces the resolution of signal.55 It plays
an important role in electronic devices, especially for the measurement of minute
signals. The sensitivity of sensors is limited by noise level: so, reducing the noise is
quite helpful for enhancement in sensitivity of detection unit. According to sources,
noise can be classified as external noise and internal noise. We will discuss these
classification separately to show how they can affect the ME detection unit, and
what some works have been done to reject their influences.
1.3.1 External noise
External noise is referred to as the interactions between a detection unit and the
environment. These interactions can be electric, magnetic, chemical, thermal,
vibration, and so on. Due to an AC magnetic sensor that contains materials and
electronic circuit parts, the noise sources that affect any parts would influence the
detection unit. The main noise sources that can disturb materials are vibrations and
external
thermal
noises.
On
the
other
hand,
electromagnetic
coupling,
electrochemical noises are the main factors for circuit parts. Although conductive
coupling is also common as noise sources for electrics, it has little effect due to
individual circuit used for each sensor without sharing common grounding or
common power supply.
26
Thermal noise should be named as external thermal noise or thermal fluctuation
noise. That noise affects the ME-based magnetic sensor via pyroelectric effect which
refers to the fact that some materials with lower crystal symmetry can generate an
electrical potential when they are heated or cooled.56 In our case, PZT belongs to a
4mm point group, which just has the pyroelectric effect. Thus, most of PZT-based
magnetic sensors would be affected by thermal fluctuation noise. Previous
investigation
show
designs
of
one
symmetrical
bimorph
structure
for
Terfenol-D/PZT laminated composites which shows great thermal noise rejection
ability, as shown in Figure 1.13.57 The idea is to separate the signal and noise with
different deformations resulted from a magnetic field and thermal fluctuations. We
can see that the sensor is used in a mechanically symmetrical design that would
generate elongating or shrinking deformation along horizontal plane. However, the
bending mode deformation would be excited as applied magnetic field due to
reversed magnetization directions two pieces of Terfenol-D plates by using U-shape
magnets. The comparative results clearly exhibit the ability of noise rejection.
Vibration noise affects the ME-based sensor via piezoelectric effect. Because
piezoelectric effect is a natural phenomenon of the materials, it is impossible to
remove by changing other materials unless new ME materials systems are found. In
lab conditions, we can use a vibration isolation table to reject the effect of vibration
noise. However, for real environments, there is no effective method to reject the
vibration noise: thus, this lack of effective method has limited the ME sensor
applications greatly. Xing et al. analyzed the external noise effect on ME composites
27
with various configurations and proposed potential methods to design the sensor
which can reject vibration or thermal noise.58
Figure 1.13 (a) Schematic illustration of symmetrical structure design; and (b)
comparison of output signals under thermal fluctuations in time domain.
28
For the circuit portion, Electromagnetic Interference (EMI) is occurred almost
all over the Earth due to the development of communication techniques. For
example, we have strong 60 Hz EMI noise due to the power supply all over America.
EMI noise can be reduced by proper shielding, grounding, and filtering techniques.
Electrochemical noise59 refers to a fluctuation in corrosion potential or corrosion
current flow. This effect takes place as a chemical reaction occurs between two
different inductors, forming micro batteries. At high humanity environment, the
sensor or the front end of the amplifier is contaminated, this electrochemical noise
always appears. To reduce this effect, it is very important to keep the detection unit
clean and dry.
1.3.2 Internal noise
Even if we can eliminate or reject all external noise mentioned above, a circuit
or ME composites would still exhibit inherent noise. This form of noise is random in
nature, such as thermal agitation of electrons in resistors and the random generation
and recombination of electron-hole pairs in semiconductors. This inherent noise is
also defined as intrinsic or internal noise. Basically, we have thermal noise, shot
noise, Flicker noise, and Avalanche noise.60, 61
Thermal noise, or Johnson noise, is present in all passive resistance components,
including the stray resistances of non-ideal capacitor and capacitor.62, 63 The origin of
thermal noise is from random thermal motion of electrons (or holes in p-type
semiconductor). From the name, it is easy to see that this noise is directly related to
temperature. In fact, thermal noise in a resistor can be described as a voltage noise
29
source with power density of eR in series with a noiseless resistor, as shown in Figure
1.14 (a). The voltage noise density of thermal noise can be calculated by:60
eR (V / Hz )  4kTR ;
(1.3)
where k = 1.38×10-23 J/K is Boltzmann’s constant, T is absolute temperature in
kelvins, and R is resistance value. From the formula, one can see that the voltage
noise density is independent with frequency, but directly affected by temperature and
resistance used. By using an equivalent circuit mode, the voltage noise model can be
transferred to a current noise source in parallel with an ideal resistor, as shown in
Figure 1.14 (b). The current noise density can be expressed as:
iR ( A / Hz ) 
4kT
;
R
(1.4)
Shot noise arises whenever charges cross a potential barrier, such as in
transistors. As electrons encounter a potential barrier, energy will accumulate until
they have enough energy to pass the barrier. Shot noise has uniform power density
given as:60
in ( A / Hz )  2qI ;
(1.5)
where q=1.6×10-19 C is an electron charge, and I is the dc current through a barrier.
Once again, the shot noise is also independent with frequency, and also not related to
temperature.
30
Figure 1.14 (a) Voltage noise model; and (b) current noise model.
31
Flicker noise, also called 1/f noise, or contact noise, is present in all active and
some passive devices. The origins of Flicker noise are various, depending on the
device type. Basically, it is related to the capture or release charge carrier as current
flows in the active devices. That can result in random fluctuation in the current. The
noise power density can be written as:60
in ( A / Hz )  K
Ia
;
f
(1.6)
where K is a device constant, I is the dc current, and a is another device constant in
range from ½ to 2.
The biggest difference between Flicker noise and the previous two noises is the
frequency dependent power density. The power density can be increased sharply at
low frequency range. That is a big problem for our low frequency measurement (f <
1 Hz), because it is also found in some resistors as a flowing current. In this case,
this noise is also called excess noise because it appears in addition to the thermal
noise, and it would have a main contribution on noise density as extremely low
frequency. Different types of resistors have various excess noises. The resistor of the
wirewound type is the quietest in terms of 1/f noise; however, it is high cost. Carbon
composition types can be noisier by as much as an order of magnitude. Carbon-film
and metal film types have intermediated performance compared to wirewound and
carbon composition.
Avalanche noise is found in p-n junctions as operated in reverse breakdown
mode. Under the strong reverse electric field in p-n junction, electrons have enough
kinetic energy to create additional election-hole pairs by collision against the atoms
32
of the crystal lattice. These additional pairs can create other pairs that result in noise
spikes as current flowing through the reverse biased junction.
All of these noises have limited the signal-to-noise ratio (SNR) for magnetic
sensors based on ME composites. Since the external noise can be reduced
dramatically in lab conditions, the internal noises are the dominant factors that need
to be optimized.
Previously, Xing et al. designed the charge amplifier based AC magnetic sensor
that can be operated at quasi-static frequency (0.16 Hz ~ 10 Hz).45 This design is a
passive device with high sensitivity. Moreover, they also analyze the internal noise
in this detection unit at quasi static frequency range, as shown in Figure 1.15 (a).64 In
the model, ME composites was considered as a charge source induced as applied
magnetic field in parallel with a capacitor and resistor. Another part is the detection
circuit consisting of an op-amp, feedback resistor, and capacitor. The thermal noise,
shot noise and other internal noise sources were analyzed in this model. The output
noise level was characterized for the circuit itself and connected with one ME
composites (Figure 1.15 (b)). The results showed that the dominant noise source of
detection unit was from the ME composites part. Thus, more investigations have
been focused on how to optimize that portion, including external noise rejection,
capacitance and dimension effects,65 and array study.66 These works can increase the
ME coefficient or decrease noise level, in another word, it can enhance the SNR
value of the detection unit.
33
Figure 1.15 (a) Equivalent noise model for magnetic sensor; and (b) Output noise
level of circuit and sensor unit.
34
1.4 Summary of this section
In the past ten years, ME laminated composites have been developed rapidly
due to giant ME coefficients compared to other connectivity schemes, especially for
Metglas/piezo-fibers
with
multi-push
pull
structure.
Meanwhile,
several
multifunctional devices based on ME effect have been proposed, such as sensors,
harvester and so on. However, there is significant work to be done, including (i)
further improvement of ME voltage coefficients; (ii) external noise rejection; (iii)
optimum of detection circuit; and (iv) new detection method for DC sensor. These
are the purposes of my thesis.
35
2. Purpose of the thesis
The purpose of my dissertation is to optimize the ME coupling effect for
Metglas/piezo-fiber laminate composites, and develop devices based on ME
composites. Specifically, the following topics are the main area I studied in the
thesis.
(1) ME composites
Previous investigations have found ME laminate composites consisting of
Metglas foils with high magnetic permeability and piezo-fiber with great
piezoelectricity have giant ME coefficient of of ME  22 V/cm-Oe under small
optimum DC magnetic biases. Such ME composites have the potential to develop
the multifunctional devices, such as magnetic sensors, memory storages. All of my
researches were focused on improving the ME coefficients for Metglas/piezo-fiber
composites, including different piezoelectric materials, volume ratio, thermal
treatment, and preliminary array study.
Besides improving the ME coefficient, another challenge for the ME
composites is to reduce the equivalent magnetic noise floor, which is impacted by
environmental or external noise sources. Some examples include thermal
fluctuations coupled into the noise via the pyroelectric effect and mechanical
vibrations coupled via the piezoelectric effect pose significant obstacles for practical
application of ME composites based devices. In my thesis, I have proposed a
36
symmetric differential structure for Metglas/Pb(Zr,Ti)O3 (PZT) fiber-based ME
composites which can reject the vibration noise effectively.
(2) AC magnetic sensor
Previously, the passive AC magnetic sensor based on ME composites has been
developed; this passive device is quite highly sensitive to small AC magnetic fields.
The practical application of such magnetic sensor is determined not only by the
output signal of the sensor in response to an incident magnetic field, but also by the
equivalent magnetic noise which limits the detection sensitivity in principle. In
Section 3.2, I have shown the works on improving ME coefficient that can optimize
the sensor’s output signal to an incident magnetic field. Moreover, reducing the
equivalent magnetic noise is another important part of this thesis. In my research, I
developed a new method to characterize the sensor’s noise: taking materials and
circuit as a whole unit to study. In this method, the detection circuit noise is also the
important factor that needs to be taken into account.
To understand the main noise sources in this unit, a static charge model for the
sensor was developed. The effect of composites and electronic circuit on the
equivalent magnetic noise was studied and optimized. Based on the noise model, the
extremely low frequency magnetic sensor (<1 mHz) with low noise level was
proposed. Furthermore, one active magnetic sensor based on amplitude
modulation-demodulation method has been also developed. The motivation for using
this technique is to modulate the low frequency magnetic signal to the relative high
frequency range which has lower noise floor. Accordingly, the signal to noise ratio is
expected to be enhanced.
37
(3) DC magnetic sensor
The DC magnetic sensor has been designed in previous works. By using the
active method, the sensor can sense small DC magnetic field variations driven by AC
magnetic field. Interestingly, the novel global positioning system (GPS) based on
geomagnetic field was proposed. Previous investigations have shown the DC
magnetic sensor can sense the intensity and inclination angle for local geomagnetic
field accurately. This capability offers the potential application on underwater
guidance system based on geomagnetic field. However, in these reports, only 1-axis
sensor was developed that required to rotate the sensor to sense the magnetic field
along a different direction. Moreover, the traditional method needs to use a
commercial lock-in amplifier (SR-850) to drive the sensor and process induced
signal from ME composites that is not convenience for application. In my research, I
proposed a man-portable multi-axial DC magnetic sensor that can be operated
anywhere easily.
Firstly, some works were focused on the improvement of DC magnetic
sensitivity for ME composites, including different piezoelectric materials, magnetic
flux concentration, and driving frequency. Meanwhile, in order to replace the
commercial lock-in amplifier, I fabricated a battery operated multi-axial lock in the
circuit which had the comparable capacity of commercial one. After assembling the
sensor and circuit in a compact box, some measurements were performed, such as
target localization, and magnetic field distribution mapping. More importantly, I took
the DC magnetic sensor to test the geomagnetic field outside which show the great
accuracy compared to the database.
38
(4) Other devices and applications
Previously, ME composites have been approved to have ability of harvesting the
vibration and magnetic energy. However, the output power for the previous harvester
was not high enough. In my research, a magnetic energy harvester based on
Metglas/PMN-PT composites can be used to charge a Ni-Mn hybrid battery pack as
driving at resonance frequency. Meanwhile, based on bending mode ME composites,
I proposed one 60 Hz magnetic energy harvester which had potential to integrate on
power supply to harvest energy.
39
3.
Magnetoelectric composites
3.1 Metglas/Piezo-fibers ME laminated composites
Metglas is a thin amorphous metal alloy ribbon produced by using a rapid
solidification process.67 The amorphous alloy Fe81B13.5Si3.5C2 is specially designed
as Metglas 2605SC68, and has been used to serve as the magnetostrictive phase in
my investigations. Metglas 2605SC, which exhibits strong magnetic flux
concentration effect, has an extremely high relative permeability that is over
40,000.27 Moreover, Metglas 2605SC can reach a maximum magnetostriciton of λ >
40 ppm at very low magnetic field biases of Hdc< 2 Oe.69 On the other hand,
Pb(Zr,Ti)O3
(PZT),
Pb(Mg1/3,Nb2/3)O3-30at%PbTiO3
(PMN-PT)
and
Pb(Zn1/3,Nb2/3)O3-4.5at%PbTiO3 (PZN-PT) were used as the piezoelectric phase in
my research.
Previous investigations have indicated long-type sandwiched laminate
structures comprised of Metglas and Pb(Zr,Ti)O3 (PZT) fiber layers with multi-push
pull configurations had several advantages compared to other ME composites and
structures: (i) high ME voltage coefficients, (ii) small required DC magnetic biases,
and (iii) an anisotropic response to incident magnetic field.
There still remains some factors needing study in order to optimize the ME
coefficients. I studied several questions in my research:
41
i) Are there any methods to further improve the ME voltage coefficient for
Metglas/PZT ME composites? We already know that Metglas/PZT has a high ME
coefficient. High permeability Metglas foils can reduce the DC magnetic field biases
dramatically compared to Terfenol-D. PZT is a commercially available piezoelectric
material with good properties. For this specific structure, I wanted to know if it was
possible to improve the ME effect by using other piezo-fibers. What is the best
volume ratio between magnetostrictive and piezoelectric phases? Can Metglas layers
be improved?
ii) Can we design different configurations that can reject external noise, such as
thermal and vibration noises? External noise is one of the biggest challenges for
sensor application based on piezoelectric materials.
We know that piezoelectric
materials will introduce thermal fluctuation noise via the pyroelectric effect, which
can generate charges that influence the signal to incident magnetic field. Moreover,
piezoelectric layers will couple to vibration noises in practical applications, due to
the strain induced by this noise source. Thus, it is highly desired to design a structure
that can reject these noise sources without losing ME voltage coefficients.
3.2 Improvement of ME coefficients
3.2.1 Comparison of different piezo-fibers
Different piezo-fibers have various piezoelectric properties and mechanical
coupling effects. This can result in enhancements of the ME voltage coefficients by
using better raw materials. In this study, three piezoelectric fibers was selected for
research: Pb(Zr,Ti)O3 (PZT), Pb(Mg1/3,Nb2/3)O3-30at%PbTiO3 or PMN-PT, and
42
Pb(Zn1/3,Nb2/3)O3-4.5at%PbTiO3 (PZN-PT). Table 3.1 lists the basic properties for
these materials.
Table 3.1 Piezoelectric properties of some materials
Piezo-fibers
d33 (pC/N)
d31(pC/N)
g33 (mV-m/N)
g31 (mV-m/N)
k33
PZT 3195 STD a)
350
-175
24.2
-11.0
0.70
PMN-PT b)
2365
-1283
39.11
-21.22
0.93
PZN-PT c)
2400
-1400
45.9
-20.9
0.90
a) Cited from CTS, Albuquerque, NM
b) Cited from Ref 70
c) Cited from Microfine Materials Technologies Pte Ltd, Singapore
To compare the ME effect for the three different ME composites,
I obtained
PZT (CTS, Albuquerque, NM), PMN-PT single crystals (Shanghai Institute of
Ceramics, Shanghai, China), PZN-PT single crystals (Microfine Materials
Technologies Pte Ltd, Singapore), and Metglas foils (Metglas Inc, Anderson, SC).
Piezoelectric fibers of 200m thickness were then cut to the dimensions of
2.5cm  0.4cm, and both surfaces of the fibers were adhered to thin
polymer-insulating films with inter-digitated (ID) electrodes using an epoxy resin.
This electrode pattern allowed us to symmetrically pole the piezoelectric fibers in a
back-to-back pattern along their length axis. Next, these structures were laminated
together between four Metglas layers of dimension 8cm  0.4cm using an epoxy. The
thickness of each Metglas layer was 25 m, as shown in the insert of Figure 3.1.
The ME coefficient ME was first measured as a function of DC magnetic
field Hdc for various laminates using a lock-in amplifier method. A pair of Helmholtz
43
coils was used to generate an AC magnetic field of Hac=1 Oe at a frequency of f=1
kHz. The Hdc was applied along the longitudinal axis of the laminates. Figure 3.1
shows ME as a function of Hdc for Metglas-PZT, Metglas-PMN-PT, and
Metglas-PZN-PT laminates. We can see that for all three laminates, ME increases
with increasing dc magnetic bias up to about Hdc=3 Oe, reaches a maximum, and
subsequently decreases as Hdc increases further. The values of ME for the
Metglas-PMN-PT and Metglas-PZN-PT fiber laminates are nearly equal and both
are notably higher than that for Metglas-PZT. The maximum value of ME for
PMN-PT and PZN-PT-based laminates is about 8.5V/cm-Oe, which is about 2.8
times larger than that for the PZT based ones of similar size. Higher ME coefficients
are expected to get better sensitivity and lower noise floors for the AC magnetic
sensor.
44
Figure 3.1 The ME voltage coefficient ME as a function of the static magnetic field
Hdc for Metglas-PZT, Metglas-PMN-PT, and Metglas-PZN-PT laminate composites,
as indicated. Inset shows a representative picture of a laminate composite.
45
I then assembled the ME composites and charge amplifier circuits into battery
operated sensor detection units (Figure 3.2 (a)). In order to bias the ME laminate to
the highest value of ME near the inflection point in the αME–H curve, small
permanent magnets were attached to the composites. The detection units were
designed to operate over the bandwidth of 1<f<103Hz. Firstly, the AC magnetic-field
sensitivity was characterized. A small AC magnetic field was applied along the
longitudinal direction of the sensors by inputting an AC signal generated by a
lock-in amplifier (SR-850) at a frequency of f = 1Hz into the Helmholtz coils. The
output voltages from the sensors in response to the small incident magnetic field and
the noise levels of sensors without any external magnetic field were measured in the
time domain using an oscilloscope (Agilent 54624A). The peak-to-peak voltage
noise level was about 6 mV. Thus, the applied AC magnetic field was varied to keep
the peak-to-peak output voltage constant at about 12 mV where the signal magnitude
was 2 times larger than the value of noise level: this was done in order to compare
the magnetic field sensitivity for different sensors under the same conditions.
Figure 3.2 shows the magnetic field sensitivity results. Panel (a) shows a photo
of the detection circuit. This box contains the ME laminate, the low noise detection
circuit, and several batteries that served as the power supply for the circuit.
Panels
(b), (c), and (d) show the time domain output waveforms for the Metglas-PZT,
Metglas-PMN-PT, and Metglas-PZN-PT laminates, respectively. The corresponding
magnetic field sensitivities are also provided in the graphs. The magnetic-field
sensitivities are 0.6 nT for both the PMN-PT and PZN-PT based laminates, which
are about 1.7 times higher than the 1 nT for PZT based ones. This increase in
46
sensitivity originates from the increase in ME for PMN-PT and PZN-PT laminated
composites. Panel (e) shows an example noise level from the low noise circuit in
real time for Hac=0 Oe. One can see that the peak-to-peak noise level is about 6 mV
yielding a signal-to-noise ratio above 2, which again has been kept constant during
the sensitivity measurements for the various laminates.
Finally, the noise floors for the three sensor units were measured in the
frequency range of 10<f<103 Hz by using dynamic analyzer. Over this frequency
range, the gain factor (V/pC) was characterized, as shown in the insert of Figure 3.3.
I then obtained the following sensor transfer function, by which to convert the noise
floor in V / Hz to that in T / Hz using the gain:
Conversion factor (V / Oe) 
 me ( pC / Oe)
1 pC / V
Noise floor (V / Hz )
Noise floor (T / Hz ) 
104
Conversion factor (V / Oe)
(4.1)
Please note that I included a 60 Hz notch filter in the circuit to reject 60 Hz
electromagnetic induction. In order to obtain the real noise floor for the ME sensor
units, rather than that of the environment, the sensor units were tested in a mu-metal
chamber without any signal input.
47
(a)
PZT
(b)
0.01
0.00
-0.01
Corresponds to 1 nT
(c)
0.01
PMN-PT
Output voltage (V)
0.00
-0.01
Corresponds to 0.6 nT
(d)
0.01
PZN-PT
0.00
-0.01
Corresponds to 0.6 nT
(e)
0.01
Noise level
0.00
-0.01
0
2
4
Time (Sec)
6
8
Figure 3.2 (a) Picture of our low noise circuit along with the ME sensor in a box. The ME
output voltage as a function of time for the (b) PZT, (c) PMN-PT and (d) PZN-PT based sensors,
respectively. The corresponding field sensitivities are as indicated. (e) Noise level for various
detection units.
48
Figure 3.3 shows the noise floor spectra for all three sensor units. From this
figure, we can observe that the noise floors for the Metglas-PMN-PT and
Metglas-PZN-PT laminates are about 6  10-11 T / Hz in the frequency range of f
=10-100 Hz and about 2  10-11 T / Hz in the range of
f=100-1000 Hz. This was
much lower than that for the Metglas-PZT laminate which is 1.5  10-10 T / Hz and
7  10-11 T / Hz in the low and high frequency range, respectively. The reduction of
the noise floor resulted from the increase of ME for the laminates that had single
crystal fibers, due to the much larger piezoelectric d33 coefficient for PMN-PT and
PZN-PT relative to PZT.
The findings demonstrate that selection of better materials can enhance the ME
coefficients dramatically, resulting in the improvement of sensitivity and decrease of
noise floors for the AC magnetic sensors based on laminated composites. However,
the cost of single crystals was much higher than that of PZT fibers, and the
operational temperature span for single crystals based sensor would be narrower
compared to PZT based ones. Recently, highly orientated PMN-PT fibers were
commercialized that can decrease the cost without sacrificing much in terms of the
piezoelectric properties.
49
Figure 3.3 Noise spectra for the PZT, PMN-PT, and PZN-PT laminates with wide
band circuit. Inset shows the wide band circuitry response as the function of the
frequency.
50
3.2.2 Volume ratio effect
As mentioned in the introduction part, the volume ratio between piezoelectric
and magnetostrictive phases is an important parameter for ME composites. The ME
voltage coefficients can be enhanced greatly at optimum volume ratio. However, no
previous report has focused on the study of the volume ratio effect on
Metglas/piezo-fibers composites.
The schematic structure of our Metglas/PZT laminated composites is shown in
Figure 3.4.71
It is a more complicated structure than traditional modes, not only
due to numerous units, but also to the non-ideal poling current. Typically, for poling
along the thickness direction, the electrodes need to deposit on both top and bottom
surfaces; for poling along the length direction, the electrodes are placed two edges.
However, it is impossible to do such an ideal design. The fibers used in this structure
were only 180 um in thickness and 4 cm in length. Thus, it is not easy to put
electrode directly, which furthermore would require extremely high voltages to pole.
By using Interdigitated (ID) electrodes, poling along the length direction can be
achieved by smaller voltage, as the PZT layer was separated into small poling unit
with a push-pull mode configuration. Each push-pull unit can be considered as two
L-L modes in parallel connection.
51
Figure 3.4 (a) Schematic diagram of ME composites configuration consisting of an
ID electrodes, core composite and symmetric Metglas actuators on the bottom and
top of the core composite. (b) Illustration of the numerous alternating push-pull
mode units. (c) Optical microscopy image of a longitudinally poled push-pull
element in the core composite. (d) and (e) Photographs of ME composites.
52
However, I need to make some assumptions in dividing an “L-L mode” theory
that describes the real case. (i) Homogenous poling current between the two
electrodes. This is an important assumption in the model development, because the
poling current of the ID electrodes was not uniform. In fact, it had a dead zone and
active zone, as shown in Figure 3.5. 72 (ii) The epoxy between each Metglas layers is
uniform, and this has identical mechanical properties. Figure 3.6 indicates the
conceptual model used to analyze the problem.
53
Figure 3.5 2-D ID electrode schematic showing the electric field lines.
54
Figure 3.6 Schematic of L-L model.
55
In this model, I considered N layers of Metglas foils in ME composites on each
side, 2 ID electrodes and 2 (N+1) layers epoxy. More considerations complicate the
model more than previous static model.
The constitutive equations for the piezoelectric phase can be written as:
Si  p sij pTj  pdki p Ek
(3.2)
Dk  pdki pTi  p kn p En
(3.3)
p
p
where
P
phase.
p
Si and
p
T j are strain and stress tensor components of the piezoelectric
Ek , p En and
p
displacement. p sij and
Dk are the vector components of the electric field and electric
p
d ki are compliance and piezoelectric coefficient, and
p
 kn is
the permittivity matrix of the piezoelectric phase.
The n-th Metglas layer is described by the following constitutive equations:
m
m
where n=(1,2,…,2N)
piezoelectric phase.
m
m
Si and
Si  m sij( n ) mTj( n )  m q(kin ) m H k
(3.4)
Ti ( n )  m kn( n ) m H n
(3.5)
Bk  m qki
(n)
m
m
T j are strain and stress tensor components of the
H k , m H n and
m
Bk are the vector components of the magnetic
field and magnetic flux induction. m sij and
coefficients, and
m
m
qki are compliance and piezomagnetic
kn is the permittivity matrix of the magnetostrictive phase.
Besides the traditional equations for piezoelectric and magnetostrictive phase, I
need to consider the stains in epoxy layers and electrode layers:
g
e
Si  g sij( n ) mT j( n )
Si  e sij mT j
56
(3.6)
where n=(1,2,…,2(N+1))
the epoxy layers.
e
g
Si and
Si and
e
Tj
g
T j are strain and stress tensor components of
strain and stress tensor components of the
electrode layer.
In order to simplify the equations, the following assumptions were made firstly:
(i) no stress in “2” direction; (ii) no shear stress; and (iii) homogenous mechanical
property for epoxy and electrode layers.
Boundary conditions:
S1n  p S1
3.7
S  S3
3.8
S  S1
3.9
S3n  p S3
3.10
e
S1  S1
3.11
e
S3  S3
3.12
2 mT1n hmn  2 gT1n hgn  2 eT1hc  pT1hp  0
3.13
2 mT3n hmn  2 gT3n hgn  2 eT3hc  pT3hp  0
3.14
m
m
g
p
n
1
g
N
N 1
n 1
N
n 1
N 1
n 1
n
3
p
p
p
n 1
p
D3  0
3.15
Through the equations 3.7-3.12, I can express the stress in Metglas, epoxy and
electrode by using the terms of
p
T1 , pT3 . By using equations 3.13-3.14, pT1 , pT3 can be
written as the function of E3 and H3.
Finally, based on open circuit condition, the ME voltage coefficients can be
calculated by following equations:
 ME , L L 
E3
d31[ B2 A4  B4 A2 ]  d33[ B4 A1  B2 A3 ]

.
H 3  33[ A1 A4  A2 A3 ]  d31[ B3 A2  B1 A4 ]  d33[ B1 A3  B2 A1 ]
where,
57
3.16
A1  2a1hm N  2 g1hg ( N  1)  2 1hc  hp
A2  2a2 hm N  2 g 2 hg ( N  1)  2 2 hc
A3  2a3 hm N  2 g 4 hg ( N  1)  2 4 hc
A4  2a4 hm N  2 g5 hg ( N  1)  2 5 hc  hp
B1  2 f1hm N  2 g3hg ( N  1)  2 3hc
B2  2 f 2 hm N
B3  2 f3 hm N  2 g 6 hg ( N  1)  2 6 hc
B4  2 f 4 hm N
Then, I did experiments to compare the model data. The fabrication for ME
composites is the same as previous process. The difference is the dimensions for
PZT is 4 cm × 1cm and Metglas is 8cm × 1 cm. And the cut Metglas pieces were
then stacked one on top of each other, bonded with epoxy resin, and were pressed
using a hydraulic press to minimize the epoxy thickness in-between Metglas foils. To
study the effect of Metglas layers, various layers of Metglas stacks were made (2, 4,
6, 8, and 10). Metglas stacks with equal number of layers were then attached at the
top and bottom of the ID electrode-PZT-ID electrode structure with epoxy, in order
to obtain the ME laminate layered structures.
Figure 3.7 shows the ME voltage coefficients as functions of DC magnetic field
Hdc. From this figure, it can be seen that ME is nearly zero at Hdc = 0; increased as
Hdc was increased; reached a maximum at a particular field point; and subsequently
decreased as Hdc was further increased.
One can also clearly see that the maximum
value of ME increased with increasing number of Metglas layers until N = 6, after
which it began to decrease with further increase in N.
required for the maximum V response also increased with N.
58
Furthermore, the Hdc
Figure 3.7 Magneto-electric voltage coefficients V as a function of the static dc
magnetic field Hdc for various PZT fiber-Metglas laminate composites. The inset
shows a schematic of the structure.
59
I recorded the maximum ME values at the optimum Hdc bias, and compared the
data to the model predications. The materials parameters are given in Table 3.2.
Table 3.2 Materials parameters for ME coefficients calculation
Elastic constants
−12
(10
2
−1
mN )
PZT a)
Metglas b)
Electrode c) Epoxy c)
15.3 (ps11)
10 (ms11,ms33)
440
(es11,es33)
315(gs11,gs33)
-5.2 (ms12)
-110 (es12)
-78 (gs12)
20
20
17.3 (ps11)
-5 (ps13)
p
-185( d31)
Piezoelectric constant
-12
440(pd33)
(10 pC/N)
-21.3(mq31)
Piezomagnetic coefficient
50.3(mq33)
(10-9 m/A)
1750
Dielectric constant
p
( ε33/ε0 )
180
25
Thickness (μm)
a) Cited from CTS, Albuquerque, NM
b) Cited from Ref 73
c) Cited from Ref 74
Figure 3.8 presents a comparison of the experimental results and estimated
values. We can see that the measured data follow the trend predictions, although the
values were smaller compared to the predicted behavior. The reasons may be: (i) the
poling of the PZT was not sufficient compared to the model assumption; (ii) the
epoxy layer reduced the strain transfer between the interfaces. To reduce the
thickness of the epoxy, a spin coating method has been used. Such an optimized
fabrication process can reduce the thickness of the epoxy from 20 μm down to 4 μm,
as observed by optical microscopy.75 The ME coefficient for the composites
fabricated by this process was improved by a factor of 1.5× compared to previous
method; and (iii) strain transfer across interfaces results in energy loss.
60
Figure 3.8 Comparison of experimental data and estimated values.
61
Moreover, I also found a sensitivity improvement by using an optimized volume
ratio. Figure 3.9 presents the magnetic field sensitivity results.
Part (a) shows the
lowest detectable magnetic field as a function of the number of Metglas layers N.
Parts (b) through (f) show the output waveform as a function of real time for the
structures with different number of Metglas layers N, as shown in the figures. The
corresponding field sensitivities are also marked in the graphs. Part (g) shows an
example of the voltage noise spectrum in real time from our low noise charge
amplifier.
From part (a), we can see that the structure with 2 Metglas layers can
detect a magnetic field of 0.8 nT with a SNR > 2.
With increasing N, the magnetic
field sensitivity increased almost linearly with N up to 6 layers. The structure with
N = 6 was capable of detecting a magnetic field as small as 0.3 nT (with a SNR > 2).
This is a 2.7 times increase in sensitivity relative to the 2 layered structure. This
increase in sensitivity is a direct consequence of the increase in the ME voltage and
charge coefficients that resulted from an increase in the effective interfacial volume
with increasing Metglas thickness. In parts (b) - (f), one can see that the noise level
is much smaller than the peak-to-peak output waveforms.
The graphs also clearly
show that the waveform profile for N = 6 was much cleaner than that for N = 2, even
though the applied Hac was much smaller.
62
Lowest detectable
field (nT)
1.2
0.9
0.6
(a)
0.3
0.0
0.01
2
4
6
8
10
Number of metglas layers, N
N=2
0.00
-0.01
0.01
Corresponds to 0.8 nT
(b)
Corresponds to 0.5 nT
(c)
Corresponds to 0.3 nT
(d)
Corresponds to 0.6 nT
(e)
Corresponds to 1.0 nT
(f)
N=4
0.00
Output voltage (V)
-0.01
0.01
N=6
0.00
-0.01
0.01
N=8
0.00
-0.01
0.01
N = 10
0.00
-0.01
0.01
Noise level
0.00
-0.01
(g)
0
2
4
Time (s)
6
8
Figure 3.9 (a) Lowest detectable magnetic field for the PZT fiber-metglas laminate
composites as a function of the number of metglas layers N on either side of PZT at
1 Hz for constant signal-to-noise ratio SNR > 2. (b)-(f) Output voltage waveforms
for the laminates with different metglas layers N in the time domain. (g) Example
voltage noise level for the low noise charge amplifier as a function of time.
63
3.2.3 Heat treatments
In addition to the piezo-fiber phase, the Metglas phase was also studied with
regards to how to improve the ME coefficient.76 Some previous investigations have
shown that the electromechanical factor k33 of Metglas 2605 can be improved by
heat treatment.77 The value of the k33 was found to be increased with increasing
annealing temperature between 385°C and 400°C, and to decline sharply above
400°C. Thus, it may be possible to improve the ME coefficients by increasing the
magnetomechanical factors of Metglas.
I used Metglas 2605 from Metglas Inc (Conway, SC) and annealed the foils at
different temperatures: 300°C, 350°C and 400°C. After heat treatment, the foils were
bonded to PZT to fabricate the laminated composites. Figure 3.10 shows the ME
coefficient as a function of Hdc. One can see that the ME coefficient was increased
with increasing annealing temperature from 300°C to 350°C, and was dramatically
decreased by annealing at 400 °C. This trend agrees with the experimental data for
k33 in Ref 69.
Next, the magnetic field sensitivity and output noise measurements for the
heterostructures were characterized. The output voltage and the noise level for the
different structures with various Metglas layers were then measured using an
oscilloscope. The noise amplitude of our charge amplifier detection circuit was
about 7 mV. The applied Hac was varied to keep the peak-to-peak output voltage
constant at about 15 mV (to maintain a signal to noise ratio SNR > 2). This
allowed us to compare the field sensitivities measured at constant SNR for the
different structures. In Figure 3.11, it can be seen that the ME sensors with Metglas
64
annealed under 350 ºC had larger magnetic-field sensitivity than the others. The
value was almost 1.4 times larger than for the laminate annealed at 300 ºC, and about
1.5 times than the one annealed at 400 ºC.
Figure 3.10 ME voltage coefficient a as a function of the static dc magnetic field Hdc
for various PZT fiber-Metglas laminate composites after heat treated with Metglas
layer.
65
Figure 3.11 Comparison of AC magnetic sensitivity for the PZT fiber/Metglas
laminated composites as a function of the different annealed temperature of Metglas
layer.
.
66
3.3 Vibration noise rejection
One of the biggest challenges for ME sensors is to reduce the equivalent
magnetic noise floor, which are impacted by environmental or external noise sources.
Thermal fluctuation coupled into the noise via the pyroelectric effect and mechanical
vibration coupled via the piezoelectric effect pose significant obstacles for practical
applications of ME sensors.
To eliminate vibration noise, I proposed a differential structure for Metglas/PZT
laminates.78 Sensors fabricated with this differential mode structure can attenuate
external vibration noise by about 10-20dB at different frequencies, while
simultaneously having a doubled ME voltage coefficient. Interestingly, in additional
to offering a means of mitigating vibration noise, this ME structure offers the
potential to be a hybrid sensor, separating magnetic and acoustical signals.
Figure 3.12 (a) illustrates our new laminate structure design for vibrational noise
cancellation. Unlike other Metglas/PZT/Metglas sandwich structures, two layers of
PZT were used to create a differential symmetric structure. Five PZT fibers were
oriented along the longitudinal axis to form composite PZT layers 10 mm wide and
40 mm long. Two such PZT layers were fabricated, and epoxied to either side of a
double-sided ID electrode. A single-sided electrode with identical geometry was then
bonded bare to the top and bottom surfaces of the PZT layers in a multi-push-pull
geometry. The PZT composite was then poled under 2 kV/mm for 15 minutes at
room temperature. Metglas foils (Vitrovac Inc. Hanau, German) were cut to 10 mm
in width and 80 mm in length.
Three Metglas foils were then laminated to both the
top and bottom of the dual PZT laminate core.
67
Figure 3.12 (b) shows the poling configuration of the structure. In our design,
the two PZT fiber layers were poled along the same orientation.
Due to the
symmetrical nature of the structure, the double-sided electrode in the middle acts as
a neutral plane. Application of a magnetic field along the longitudinal direction of
the laminate will cause the sensor to contract or elongate longitudinally.
Contraction or expansion in the plane of the sensor will result in an identical charge
in each PZT layer. Parallel electrical connection of the PZT layers would therefore
result in a doubling of the signal.
Conversely, an applied external vibration signal
will tend to cause an asymmetric (bending mode) deformation. Simultaneous
elongation of the top PZT and contraction of the bottom PZT will result in charges of
opposite polarity in the PZT layers. Parallel electrical connection of the PZT,
therefore, results in an attenuation of the output signal.
A schematic of the experimental setup for the evaluation of the differential mode
structure of the Metglas/PZT laminates is shown in Figure 3.12 (c).
Information
about the relative amplitude of and the phase shift between the top and bottom PZT
layer is important to understanding the different deformation modes excited by an
applied magnetic signal relative to those excited by an applied vibrational signal. In
order to analyze the signal from each PZT layer individually, the charge generated by
each PZT layer was converted to a voltage, via integration using custom-built charge
amplifier circuits. The raw voltage signals were recorded using a CR 5000
Datalogger and uploaded to a PC for analysis using MATLAB.
Vibrational signals
were generated using an LDS V203 10/32 shaker. The shaker was driven by a 10
Hz sinusoidal output signal from a SR850 lock-in amplifier augmented by an LDS
68
PA25E power amplifier. Magnetic test fields of frequency 10 Hz were generated
using the output of the lock-in amplifier, and then fed into a custom-built 100 turn
Helmholtz coil with a 45 mm radius.
To compare the two signals generated by each sensor, the charge outputs were
converted into equivalent magnetic signals using a calibration factor. The
magnetoelectric charge coefficient (αMEQ) was measured for each sensor by exposing
the sensor to a calibrated magnetic field.
69
Figure 3.12 (a) Schematic of our new differential mode ME laminate sensor; (b)
poling profile of multi-push/pull, dual PZT composite structure; and (c) schematic of
the experimental signal path.
70
First, the response of the sensors to an induced vibration signal was measured
and analyzed. Using the calibration factor given above, the equivalent magnetic
signal was calculated from the output voltage of each charge amplifier.
The response of each layer of the differential sensor, as well as the summation of
the constituent signals, is presented in Figure 3.13 (a).
In this figure, the blue line
shows the output signal from the top PZT layer, the red dashed line is the signal
generated by the bottom PZT layer, and the black dashed line is the time-domain
summation of the top and bottom PZT layers.
Figure 3.13 (a) shows that the
amplitude of the combined signal (black trace) is significantly attenuated relative to
either of the two constituent output signals (red and blue traces). In order to more
accurately analyze the data, the power spectral density (PSD) of each component
signal and of the time-domain summation of the two signals was calculated using
MATLAB. Additionally, a linear, time-invariant transfer function between the
constituent output signals was estimated using built-in MATLAB commands. The
phase shift between top and bottom PZT layers as a function of frequency can then
be calculated from the estimated transfer function.
Figure 3.13 (b) shows the power density of the output signals of the top, bottom
and time-domain summation over the frequency range from DC to 55 Hz. At the
vibration drive frequency of 10 Hz, the amplitude of the summation signal was 5
times smaller than either that of the top or bottom PZT layers (10-8 T/√Hz versus
5×10-8 T/√Hz, respectively). In addition, the second, third, fourth and fifth harmonic
signals (20, 30, 40, and 50 Hz) exhibited the same trends. The summation signal of
the third harmonic was tenfold attenuated. In fact, the differential structure ME
71
sensor also shows the significant cancellation to the vibration noise at frequency
range from 10 Hz to hundreds Hz.
Figure 3.13 (c) shows the calculated phase shift between the output signals as
function of frequency upon exposing the differential ME structure to a 10 Hz
vibrational signal. At 10 Hz, as well as at the higher order harmonics, the phase shift
between the top and bottom PZT layers was quite close to 180˚. This phase shift data
supports our hypotheses that vibration signals tend to excite the differential ME
structure in a bending mode deformation, where the top and bottom layers are phase
shifted, and enabling cancellation of that vibration signal in summation.
72
(a)
(b)
(c)
Figure 3.13 (a) Time-domain equivalent magnetic response of differential mode
sensor to incident vibrational signal; (b) power spectral density of top, bottom and
time-domain summation of top and bottom; and (c) phase shift between top and
bottom PZT layers as a function of frequency calculated from a linear time invariant
transfer function.
73
To examine the response of the sensor to an incident magnetic field, the shaker
was replaced by a 90 mm, 100 turn Helmholtz coil driven at a frequency of 10 Hz by
a SR850 lock-in amplifier. Figure 3.14 (a) shows the time domain response of the
sensor to an incident 10 Hz magnetic field. The signals from the top and bottom PZT
layers are nearly in-phase, resulting in an approximate doubling of the output signal
upon summation. The relative phase shift between top and bottom PZT layers at 10
Hz was only 0.6˚, which evidences the fact that incident magnetic fields result in a
longitudinal mode deformation of the differential ME structure.
The power spectral density response to the 10 Hz magnetic field over the range
of DC to 55 Hz is shown in Figure 3.14 (b). Characteristic of the ME laminate
sensor’s magnetic response, the 10 Hz first harmonic signal was dominant relative to
the higher harmonic signals (20 Hz, 30 Hz, etc.). The power spectral density of the
summation signal was doubled in amplitude relative to the individual component
layers at 10 Hz (1.4 µT/√Hz vs. 0.7 µT/√Hz, respectively).
74
(a)
(b)
Figure 3.14 (a) Time-domain response of top PZT layer, bottom and sum of
individual signals in response to an incident magnetic field; and (b) power spectral
density response of a sensor to a 10 Hz magnetic field.
75
Finally, the capability for vibration signal cancellation of our new differential
ME structure was compared to that of a non-differential one of similar geometry.
Following analysis similar to that above, the different working modes under various
excitation sources were studied. The results demonstrate that the new differential
structure has the ability to reject an incident vibration signal by summation of the
signals of top and bottom PZT layers. In this measurement, the top and bottom PZT
layers were connected in parallel at first, and a single charge amplifier was used to
collect the signal. Simultaneously, a second non-differential ME laminate connected
to another charge amplifier was used as a control group. Both of these two signals
were observed together by an oscilloscope. The shaker was put in the middle of the
differential and non-differential ME structures and a 10 Hz driving signal was
excited.
Figure 3.15 shows the signals from the differential and non-differential ME
sensors, obtained directly from the oscilloscope. In this figure, the signal amplitude
of the non-differential sensor was about 80 mV, whereas, that of the differential ME
structure was only about 20 mV.
Clearly, our new differential structure shows excellent capacities with regards to
vibration signal cancellation. Furthermore, the fact that we can separate magnetic
and vibration signals is important in and of itself. Hybrid sensors capable of data
fusion between two separated signals of an environment could be enabled.
76
Output Signal (V)
0.08
Non-differential
Differential
0.04
0.00
-0.04
-0.08
0.0
0.2
0.4
0.6
0.8
Time (seconds)
Figure 3.15 Comparison of noise cancellation for a differential ME structure sensor
and a non-differential ME structure sensor.
77
3.4 Summary of this section
In summary, investigations directed at enhancing the ME voltage coefficient
have been performed, such as different piezo-fibers, volume ratios, and heat
treatments. In addition, I have proposed a differential structure for Metglas/PZT
laminate to reject the external vibration noise.
(i) Using PMN-PT and PZN-PT single crystal fibers, one can improve the ME
voltage coefficient by over 2× compared to PZT fibers. The sensitivity for
magnetic sensors based on those single crystal fibers is likewise enhanced. The
drawback is the high cost of the crystals, which can be reduced a little by using
highly orientated PMN-PT fibers that also have high piezoelectric properties.
(ii) The volume ratio between Metglas and PZT layers was found to have a
significant influence on the ME effect. The findings show that the ME
coefficient can be increased by 1.4×, offering another effective means by which
to optimize the ME laminates.
(iii) Heat treatment can affect the electromechanical factor for Metglas 2605. By
annealing the Metglas foils at 350°C, the ME coefficients of the laminate was
found to be increased.
(iv) A differential structure was developed that can notably reject the vibration noise.
Additional investigations are needed to optimize this structure to realize its full
rejection efficiency.
78
4.
AC magnetic sensor
4.1 Introduction
I have developed a novel type of AC magnetic sensor, based on ME composites,
which has advantages over the presently available ones. The sensors need to meet
the following requirements: (i) high sensitivity or low noise at quasi-static
frequencies (~pT/√Hz at 1 Hz); (ii) low power consumption offering the potential for
long-term operation; (iii) compact size; and (iv) low cost.
In addition to the external noise that I mentioned in the last chapter, the internal
noise in the detection unit needs investigations. Such internal noise is an important
aspect to identifying the potential of ME laminate as AC magnetic sensors. In this
chapter, I will discuss the internal noise sources in AC magnetic sensors and address
some methods by which to attenuate the spectral noise density.
4.2 Passive magnetic sensor unit
Considering the giant internal impedance of ME laminates, an induced charge
detection method has been developed to detect the induced signals from ME
composites in response to the incident magnetic field. Quasi-static models of the ME
composite and detection circuit have been investigated in previous studies.45,
64
Figure 4.1 (a) shows a photograph of a passive magnetic sensor detection unit: it
contains an analog charge amplifier circuit and a ME laminated composites. Two
79
small dc magnets were used to bias the laminate to work at the optimized me value,
as shown in Figure 4.1 (b). Based on different application requirements, the
detection circuit can be modified to optimize the ME magnetic sensor unit to
particular frequency ranges.
One of the most important parameters to evaluate magnetic sensors is the
spectra noise density (SND) which limits the detection sensitivity of a sensor unit.
Previous measurements were mainly concerned themselves with the SND over a
broad frequency range, which is not necessarily accurate to describe a sensors
performance at a specific frequency. Meanwhile, the SND was measured using a
commercially available charge amplifier (Kistler 5015). Though this method is
capable of detecting the noise, one must bear in mind that the charge amplifier noise
itself cannot be neglected.
80
Figure 4.1 (a) Schematic illustrations of Metglas/PMN-PT ME composites; and (b)
ME voltage coefficient ME and ME charge coefficient me for Metglas/PMN-PT
laminates as function of Hdc.
81
In this thesis, a low noise charge amplifier was developed and assembled with
ME composites to form a magnetic sensor unit, and the noise sources were
characterized for the unit instead of only the composites part. Based on this method,
the transfer function in units of V/pC for each magnetic sensor unit has been
identified. Figure 4.2 shows the transfer function of a detection circuit with designed
to have a frequency bandwidth of 1 to 1600 Hz. Considering the strong
Electromagnetic Interference (EMI) at 60 Hz resulting from power lines, a notch
filter was induced in the circuit to attenuate the signal at this specific frequency.
Clearly, my lab-made circuit has demonstrated to have a uniform gain factor of
about 1 V/pC over the frequency range from 1 Hz to 1600 Hz, except near 60 Hz.
A Metglas/PZT ME laminate was then assembled with this wide band
frequency circuit as the magnetic sensor unit shown in Figure 4.1. The intrinsic
magnetic noise for this unit was characterized in a magnetic shielding chamber to
reject the external magnetic noise and EMI. The SND was detected by using a
dynamic signal analyzer in units of V/√Hz. The detected signal was then converted
to equivalent magnetic noise in units of T/√Hz by the following equation:79
Conversion factor (V / Oe) 
 me ( pC / Oe)
1 pC / V
Noise floor (V / Hz )
Noise floor (T / Hz ) 
104
Conversion factor (V / Oe)
(4.1)
where, ɑme is the ME charge coefficient at the optimized bias. For this detection unit,
the ME charge coefficient was ɑme = 200 pC/Oe.
82
Figure 4.2 Transfer function of detection circuit.
83
Figure 4.3 Equivalent magnetic noise density spectra: (a) Voltage noise density
detected by dynamic signal analyzer; and (b) equivalent magnetic noise density after
conversion.
84
Figure 4.3 (a) shows the direct measurement of the voltage noise density of the
sensor unit by using a dynamic signal analyzer (SR-785) over the frequency range
from 1.8 Hz to 1600 Hz. From this figure, the noise density near 60 Hz was
decreased sharply due to the notch filer mentioned above: the noise density was only
about 1.49 nV/√Hz at 60 Hz. However, the intrinsic magnetic noise density
calculated using Equation 4.1 presents a different noise sources from that of the
voltage noise density, as shown in Figure 4.3 (b). From the spectrum, one can see the
magnetic noise at 60 Hz was still much higher than the values at other frequencies.
This was a direct result of EMI interference, although the sensor unit was placed in a
magnetic shielding chamber. In detail, the magnetic noise at 1.8 Hz was almost
7×10-10 T/√Hz, which decreased with frequency increasing. The noise density was
about 5×10-11 T/√Hz at 1000 Hz, which was dominantly influenced by the 1/f noise
in the electronic circuit and materials. The detailed noise model will be discussed in
the following section.
In addition to the wide band detection unit, a low frequency detection unit has
also been designed to work over the frequency range from 0.8 Hz to 10 Hz. This
narrower bandwidth detection unit was developed to reduce the noise floor. The
output voltage noise as function of frequency bandwidth can be described as:
fH
En  (  en2 ( f )df )1/ 2;
(4.2)
fL
where En is the mean square value of voltage noise, en(f) is the spectral noise density
which is dependent on frequency f, and fL, fH are the lower and upper limits of the
frequency band of interest, respectively.
85
Equation 4.2 clearly indicates that a narrower frequency bandwidth may have a
lower output noise, as given a similar voltage noise density. Figure 4.4 shows the
gain factor of a low frequency detection circuit. It can be seen that the circuit had a
totally different transfer function than the wide band ones. It had a homogenous gain
only over the frequency range of 1 Hz to 10 Hz, with a 3-dB point near 12.5 Hz.
This type of circuit, assembled with a ME laminates, can be used for low frequency
magnetic field detection with reduced equivalent magnetic noise floors.
In order to demonstrate the benefit of the low frequency circuit, a Metglas/PZT
laminates was assembled with both the low frequency and wide bandwidth circuits.
During the measurements, a pair of H-coils driven by lock-in amplifier was used to
generate AC magnetic fields at 1 Hz and 10 Hz for these two sensor units. The
output signals from the sensors were monitored by an oscilloscope in the time
domain. The AC magnetic field was modulated to keep the signal-to-noise ratio
constant at the value of SNR=2.
86
Figure 4.4 Transfer function of low frequency detection circuit.
87
Figure 4.5 Output signal in response to the incident magnetic field: (a) low
frequency detection sensor circuit, and (b) wide band frequency detection sensor
unit.
88
Figure 4.5 shows the measurement results for these two magnetic sensors. Panel
(a) indicates the low frequency magnetic sensor in response to AC magnetic field at
frequency of 1 Hz with the amplitude of 0.4 nT. The amplitude of signal is about
12.5 mV, which is two times larger than output noise. Panel (b) shows the output
signal from the wide band magnetic sensor in response to AC magnetic field at
frequency of 10 Hz with amplitude of 2.5 nT, that corresponds to an amplitude of
114 mV in order to satisfy the SNR=2. From this comparison, it can be seen that the
wide band magnetic sensor has a larger voltage noise compared to the low frequency
one. Moreover, the small spikes at 60 Hz were also observed in this unit due to the
detectable frequency range from 1 Hz to 1600 Hz, although 60 Hz notch filter has
been designed in detection circuit. The specific detection circuit can enhance the
performance of magnetic sensor according to the practical application.
Considering that the low frequency circuit has better performance, more
characterizations have been performed to study the sensor assembled with low
frequency circuit. Firstly, the linearity of the sensor was measured. During the test,
an incident magnetic field as small as 0.88 nT at 1 Hz was applied to the magnetic
sensor, and then the amplitude of the field was increased gradually. Figure 4.6 shows
the output signal as function of incident magnetic field. From the figure, one can see
that the ME composites based sensor shows great linearity in response to the
external field with the dynamic range. Moreover, the dynamic range can be
determined by using the similar measurement. In detail, the waveform of the
magnetic sensor indicated the distortion as applied the field over 106 nT. Thus, the
dynamic range was considered as below 100 nT.
89
Figure 4.6 Linearity of magnetic sensor assembled with low frequency circuit.
90
The equivalent magnetic noise density spectra were then measured as absence
of magnetic field. The result was shown in Figure 4.7. From the figure, one can see
the magnetic noise was about 15 pT/√Hz at 1 Hz.
Figure 4.7 Equivalent magnetic noise spectra.
91
4.3 Extremely low frequency magnetic sensor
Besides the noise floor, another important consideration for design of magnetic
sensor is the frequency bandwidth of detectable magnetic fields. Some specific
applications require extremely low frequency detection. For example, the
magnetoencephalography (MEG) measurements span a frequency range from about
10 mHz to 1 kHz.80 However, previous investigations show the frequency bandwidth
of 1 Hz < f <1 kHz.81 In this section, one quasi-static frequency detection sensor unit
based on Metglas/Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) ME laminated composites
was developed.82 In detail, an extremely low frequency (ELF) charge amplifier
circuits were designed with cutoff frequencies of f <1 mHz, which allowed us to
characterize ME effect at frequency range down to f ≤ 1 mHz.
4.3.1 Charge amplifier circuit design
Firstly, the 10 mHz magnetic sensor was developed. In order to characterize the
ME effect for Metglas/PMN-PT laminated composites and to fabricate the magnetic
sensor at quasi-static frequency, a charge amplifier with extremely low cut-off
frequency (fc ≤ 10 mHz) was proposed. The circuit design was partially based on a
previous report,45 as illustrated in Figure 4.8 (a). The biggest challenge for this
circuit design was to reduce the cut-off frequency to be fc ≤ 10 mHz, while
maintaining a reasonable circuit transfer function (V/pC), otherwise the output
voltage would be significantly reduced. In addition, the circuit noise was another
important factor that needed to be taken into account.
92
Figure 4.8 (a) illustrates the charge amplifier as containing two parts:
pre-amplifier and band-pass filter stages. The transfer function in (V/pC) of the
preamplifier part can be written as:
H1 ( s) 
where the Rf and Cf
1 sR f C f
;
C f 1  sR f C f
(4.3)
are the feedback resistor and capacitor, respectively. s is a
complex frequency. For a sine wave signal drive, s= jω: where ω=2πf is the angular
frequency. Meanwhile, the cut-off frequency of the pre-amplifier part was
determined by Rf and Cf as well, given as:
fc 
1
.
2 R f C f
(4.4)
In order to design an extremely low frequency charge amplifier, the value of fc
should be smaller than 10 mHz. However, one is not free to choose arbitrary values
of Rf and Cf to control fc. There are several other factors that need to be considered.
For example, the bias current of the op-amp needs to be sufficient to avoid saturation,
and also the leakage charge from the capacitor must be small.45 As the circuit is
operated at the bandwidth range: f > fc for preamplifier part, the transfer function can
be simplified as:
H1 ( s ) 
1
.
Cf
93
(4.5)
Figure 4.8 (a) Charge amplifier design for quasi-static magnetic sensor, and (b)
predicted and measured transfer functions of the circuit.
94
In my design, I chose feedback capacitors and resistors with values of Cf = 1000
pF and Rf =50 Gohm, respectively. Thus, the cut-off frequency was fixed at fc =
3.184 mHz, which satisfied the requirements for detection of magnetic signals for
frequencies as low as f =10-2 Hz. Unfortunately, the amplitude of the transfer
function given in (3) for this pre-amplifier stage was decreased by a factor of 10×,
compared to previously reported detection circuit.29 However, the filter stage of the
circuit (see Figure 2(a)) can be used to increase the transfer function. The transfer
function in (V/V) of this filter can be written as:
H 2 ( s)  
R2 R1C1s
1
.
R1 R1C1s  1 R2C2 s  1
(4.6)
This second stage was a single bandpass filter which sets the bandwidth of the
signal to be:
1
1
 fbp 
.
2 R1C1
2 R2C2
(4.7)
In considering these two functions for the filter stage, I set the bandpass filter to
work over the frequency bandwidth of 1.59 mHz <fbp <7.96 Hz. The transfer
function was then designed to be 200 (V/V), and the overall gain factor for both
stages together in (V/pC) was:
H ( s)  H1 ( s)  H 2 ( s) 
1
V
 200  0.2 (
).
1000 p
pC
(4.8)
Figure 4.8 (b) shows the predicted and experimental values for the transfer
function of the charge amplifier detection unit. During the measurement, one 440 pF
capacitor was connected to the charge amplifier circuit. An AC signal with amplitude
of 10 mVrms was applied to the capacitor at various frequencies, and the output
95
voltage from circuit was then monitored by a dynamic signal analyzer (SR-785).
Finally, the transfer function was calculated by using the output voltage divided by
the input charge. From the figure, one can see that the values match quite well. The
experimentally-observed cut-off frequencies were 3.56 mHz and 7.58 Hz, which are
quite closed to the predicted ones.
Finally, I assembled the ME laminated composites and charge amplifier circuit
together into battery-operated magnetic sensor detection units, as shown in Figure
4.1 (a). In this unit, two small dc magnets were used to bias the composites with
optimum me value.82 I then characterized the ME charge coefficients at extremely
low frequency range. During the test, the H-coils was used to generate 10 nT AC
magnetic field to the magnetic sensor at various frequencies, the signals were
monitored by dynamic signal analyzer to analysis the amplitudes and then were
displayed by an oscilloscope to present the waveforms. Figure 4.9 present the values
of me over the frequency range of 7×10-3 Hz < f < 20 Hz: the values of me were
constant around 1900×10-8 C/T which was closed to the value at 1 kHz. The insert
shows the waveform of sensor’s response to a 10 mHz ac magnetic field signal in the
time domain.
96
Figure 4.9 ME charge coefficients at quasi-static frequency range. The insert is the output
voltage of circuit in response to a 10 mHz input charge.
97
4.3.2 Charge noise model
As described before, the equivalent magnetic noise density is a very important
parameter which limits the detection sensitivity at a specific frequency. Thus, I also
characterized the noise density spectra of the extremely low frequency magnetic
sensor. Previously, the current noise model has been proposed, which considered the
noise source in both of ME composites and detection circuit as the current noise
source.64 Most recently, the charge noise model has been also developed.83,
84
Considering the charge induced by ME composites in response to incident magnetic
field, the charge noise model was applied in this research. However, the previous
models were not accurate to describe the magnetic noise for sensor units. Normally,
the literatures considered the noise sources for ME magnetic sensor were contributed
from ME composites and detection circuit. In detail, the noise sources from ME
composites were considered as dielectric loss noise and leakage resistance noise. For
the circuit part, the noise sources were considered to be dominated by the charge
preamplifier part, including the thermal noise from feedback resistor, current noise
and voltage noise in op-amp chips.64, 71, 81, 83 Thus, a total of five noise sources were
analyzed in these literatures, and the investigations show the estimated noise density
spectra were quite closed to the measured results.
However, the model presented before indicated the limitation as an extension of
the detectable frequency range of magnetic sensor down to 0.01 Hz. Figure 4.10
shows the results of one Metglas/PMN-PT with extremely low frequency circuit
with frequency range from 0.01 Hz to 10 Hz. Table 4.1 lists the parameters of the
Metglas/PMN-PT ME composites, and Table 4.2 lists the parameters of the circuit.
98
Table 4.1 ME composites properties
ME composites
C (pF)
R (GΩ)
Tanδ
[email protected] 1 kHz
Metglas/PMN-PT
175
195
1.2%
1.930×10-5 C/T
Table 4.2 Circuit components used for charge amplifier
Op-amp
LMC6042 a)
en,1Hz
en,1kHz
Rf
Cf
R1
(nV/√Hz) (nV/√Hz) (fA/√Hz)
(GΩ)
(pF)
(MΩ) (MΩ)
230
50
1000
10
83
in
0.2
a) Cited from LMC 6042 Operational Amplifier, Texas Instruments
99
R2
2000
Figure 4.10 Estimated and measured equivalent magnetic noise of the magnetic sensor based
on previous noise model.
100
From Figure 4.10, one can see that the estimated magnetic noise is much lower
than that of measured values, especially at frequency range of f > 1Hz. Below
frequency of 0.07 Hz, the measured noise was higher than estimated due to the low
frequency vibration that wasn’t being rejected clearly by floating table. That would
be investigated in the following study. However, it was hard to explain the frequency
above 1 Hz. At frequency of f > 10 Hz, the measured values were almost consistent
larger than predicted by a factor of 6×. I considered the proposed model has some
limitation that could not describe the sensors’ noise for the magnetic sensor unit.
Thus, more detailed investigations were performed to optimize the charge noise
model.
In this modulated noise model, I still considered five noise sources which have
main contributions to the total noise density. For ME composites, there are dielectric
loss noise (Nloss), thermal noise of the leakage resistor (NR).65 The current (Ni),
voltage (Ne) noises from op-amp and thermal noise (NRf) from feedback resistor
were the main noise sources in electronic part.
The noise charge density in (C/√Hz) for the preamplifier part can be expressed
as:
NR 
1
2 f
NRf 
1
2 f
4kbT
4kbTC tan 
; N loss 
;
R
2 f
4kbT
1
Z
; Ni1 
in ; N v1  en (1  ) / H1 ( s) ;
Rf
2 f
Zf
en  (en ,1Hz  en ,1kHz ) / f  en ,1kHz ;
101
(4.8)
where kb is the Boltzmann constant, T is the absolute temperature, tanδ and R is the
dielectric loss factor and leakage resistance of the ME composites, in is the current
noise density and vn is the voltage noise density of the amplifier.
Besides the preamplifier part, the noise sources from bandpass filter part were
also considered to have the contributions to the total noise as well, including thermal
noise from feedback resistors of R1 and R2, current and voltage noises in op-amp
chips, as shown in Figure 4.11 (a). The noise charge density in (C/√Hz) for this stage
can be written as:
N R1 
4kbTR1
H1 ( s )
; N R2 
4kbTR2
H1 ( s )  H 2 ( s )
;
Z1  Z 2
)
in  Z 2
Z1
Ni 2 
; Nv 2 
;
H1 ( s )  H 2 ( s )
H1 ( s )  H 2 ( s )
en (
(4.9)
en  (en ,1Hz  en ,1kHz ) / f  en ,1kHz .
Thus, the total noise density in (T/√Hz) can be written as:
NT 
1
 me
2
N R2  Nloss
 N R2 f  Ni21  Nv21  N R21  N R22  Ni22  Nv22 .
(4.10)
The parameters given in Table 4.2 were then used to calculate the equivalent
magnetic noise using equation (4.10).
Figure 4.11 (b) shows the equivalent magnetic noise density. This figure shows
both the measured data and the predicted values. One can see that the experimental
results matched the predicted ones by modulated charge noise model quite closely
over the frequency range of 0.07 Hz < f < 100 Hz. However, below 0.07 Hz, the
measured value increased more rapidly with decreasing frequency than the predicted
102
one due to the environmental noise in nature. The equivalent magnetic noise density
at 10 mHz was around 3 nT/√Hz, which decreased significantly with increasing
frequency to around 30 pT/√Hz at 1 Hz.
103
Figure 4.11 (a) Theoretical model for noise sources in our ME magnetic sensor; and
(b) estimated and measured equivalent magnetic noise of the sensor.
104
4.3.3 ELF magnetic sensor optimization
In the previous section, an ELF magnetic sensor which can work down to 0.01
Hz was proposed. Moreover, a more accurate charge noise circuit model was also
established which can predict the sensors’ performances much more precisely.
However, the noise floor at low frequency range is still much higher than estimated
values, which indicated there were still some external noise sources as placed the
sensor inside chamber on top of vibration shielding table. In order to confirm this
assumption, one pair of sensors were setup inside of chamber to analyze the common
external noise.85 The fundamental signal processing can be found in Ref.85. Through
analysis of coherency between two sensors, one can see if there is a common noise
inside the chamber. First of all, the transfer function of the sensors was measured to
eliminate the influence from circuits. Figure 4.12 (a) shows the transfer function of
two sensors as function of frequency. In this measurement, two low frequency
circuits were used which had the uniform gain factors over frequency range from 1
to 10 Hz. The transfer functions at 1 Hz were very identical with the amplitudes of
over 7×106 V/T. During the test, the output signals from sensors were collected by
digitizer SR 1000 and then the signal processing was applied to analyze the
coherence between them at frequency domain, as shown in Figure 4.12 (b).
105
Figure 4.12 (a) Transfer function of two sensors, and (b) coherency between two
sensors.
106
Figure 4.12 (b) shows the coherency analysis between two sensors at frequency
domain. From the result, one can see that the amplitude of coherence above 7 Hz
shows very low values which were quite closed to 0. This means the external noise
at this frequency range was very limited, so the influence from external noise could
be neglectful. However, the strong coherence was observed at frequency of f <7 Hz.
The amplitudes of two sensors at this range were closed to 1, and phase shift was
closed to 0. Considering the intrinsic noise in the detection unit was random, it was
not impossible to result in high coherence between two sensors. So, the results can
demonstrate that there is still external noise inside chamber, even if placed on top of
vibration shielding table.
Inspired by the wafer-level MEMS magnetic devices installed in a vacuum
chamber,86 it is possible to utilize the vacuum chamber to isolate the acoustic noise.
During the test, the magnetic sensor was placed in a vacuum chamber and the
installment was pumped to high vacuum condition. The equivalent magnetic noise of
the sensor was characterized at high vacuum condition.
Figure 4.13 shows the results of magnetic sensors at vacuum condition and
compared to the noise floor without vacuum. From the figure, one can see that the
equivalent magnetic noise for magnetic sensor at vacuum condition shows much
lower noise floor compared to the test results at normal condition. Simply installing
the sensor at vacuum chamber can reduce the noise floor by a factor of over 8× at
relative low frequency range which is dominated by external noise. Moreover, the
estimated noise floor was quite closed to the values measured at high vacuum
condition.
107
Figure 4.13 Comparisons of equivalent magnetic noise with and without high
vacuum conditions.
108
Moreover, the vacuum chamber can work for the ELF magnetic sensor as well,
which can reduce the external noise down to 10 mHz. During this demonstration, the
ELF magnetic sensor with bandwidth from 0.01 Hz to 10 Hz has been placed in the
vacuum chamber and pumped to high vacuum condition. The whole installment was
then put in the magnetic shielding chamber. The equivalent magnetic noise spectra at
high vacuum and normal conditions were measured, respectively. Figure 4.14
present the comparisons of the noise floors at two different measuring conditions.
Clearly, the noise floor at high vacuum conditions shows much smaller noise
density at frequencies below 0.3 Hz. The noise floor was about 2 nT/√Hz at 0.008
Hz, which was 3 times smaller than the value tested at normal condition. Meanwhile,
at high frequency range, the noise density spectra for two measurements were
overlapped perfectly. This test was also confirmed that the influence of external
noise inside chamber was occurred at relative low frequency range, and can be
eliminated by vacuum chamber greatly.
Besides that, the investigations on the reduction of electronic noise have been
also performed. According to the noise charge model proposed in section 4.2.2, noise
contributions from nine sources were identified, including two intrinsic sources in
the ME laminates and 7 sources from the electronic components in the detection
circuit. Good agreement was reported between predicted and measured equivalent
magnetic noise floors for Metglas/PMN-PT ME composites based on magnetic
sensor, as illustrated in Figure 4.15. The red line represents the noise from the
electronic portion and the black line shows the total noise of the sensor unit.
109
Figure 4.14 Comparison of equivalent magnetic noise spectra at normal and high
vacuum conditions for ELF magnetic sensors.
110
Figure 4.15 Estimated and measured equivalent magnetic noise of the ELF magnetic
sensor based on Metglas/PMN-PT ME composites. The insert is a schematic
illustration of the ME composites.
111
From Figure 4.15, it can be clearly observed that the dominant noise source was
the electronic contribution, which means the noise floor could potentially be reduced
if a charge amplifier detection circuit with reduced noise was identified. First of all,
the alternative op-amp chips were changed with lower voltage noise density, without
increasing current noise density. Op-amp LMC6042 (Texas Instruments) was used in
previous design which actually was suitable for wide band frequency range. A
different op-amp chip of LMC6442 was much better candidate for low frequency
applications which have lower voltage noise density. Table 4.3 summarizes the
comparisons of these two op-amps.
Table 4.3 Comparisons of op-amp chips
Op-amp
en,1Hz (nV/√Hz)
230
190
en,100 Hz (nV/√Hz)
90
180
in (fA/√Hz)
0.2
0.2
LMC6042 a)
LMC6442 b)
a) Cited from LMC 6042 Operational Amplifier, Texas Instruments
b) Cited from LMC 6442 Operational Amplifier, Texas Instruments
In this table, the LMC 6442 has a lower voltage noise at 1 Hz, and a similar
current noise compared to that of LMC 6042. Based on the data in Table 4.3, the
electronic contribution to the voltage noise density as a function of frequency was
determined, as shown in Figure 4.16 (a). From this figure, one can see that
LMC6442 has much lower voltage noise density below frequency of 1.5 Hz.
However, LMC6042 has better performance at frequency of f > 1.5 Hz. In detail, the
LMC6442 has voltage density of 1.2×103 nV/√Hz at 0.01 Hz, which is 10× smaller
than that of LMC6042. Thus, the LMC6442 based circuit was expected to have
112
lower noise floor at extremely low frequency range. In addition, some of the other
passive components used in the detection circuit were changed, in order to further
reduce the voltage noise: for example, the feedback resistor was increased from 50
Gohm to 500 Gohm. Thus, the corresponding voltage noise was reduced by a factor
of √10 according to the Johnson noise equation.60
Table 4.4 summarizes the
electrical parameters of the modified detection circuit design.
Table 4.4 Components used for circuit design
Op-amp
Rf (GΩ)
Cf (pF)
R1 (MΩ)
R2 (MΩ)
LMC6442
500
100
10
100
Figure 4.16 (b) gives the predicted equivalent magnetic noise power density for
our ME sensor and modified detection circuit which was based on the previously
reported noise model. It can be seen that the equivalent magnetic noise density of the
new detection unit was dramatically reduced for 10-2 Hz < f < 1 Hz, approaching that
of the dielectric loss and dc resistance contributions from the laminates. In this figure,
the black dashed line represents the total equivalent magnetic noise of the sensor unit
using LMC 6442 and the blue solid line shows that of the sensor unit using LMC
6042. Clearly, the total equivalent magnetic was reduced by a factor of about 5-10×
for 10-2 Hz < f < 1 Hz compared to previous reports.
113
Figure 4.16 (a) Calculated voltage noise densities for LMC6042 and LMC6442
operational amplifiers, and (b) comparisons of calculated magnetic noise spectra for
magnetic sensors based on optimized and previously reported detection circuits.
114
According to this prediction, a modified charge amplifier circuit was fabricated
and the transfer function of the circuit characterized. During measurements, a 440 pF
capacitor was connected to the charge amplifier circuit. An ac signal with amplitude
of 10 mVrms was applied to the capacitor at various frequencies, and the output
voltage from the circuit was monitored by a dynamic signal analyzer (SR-785). The
transfer function was calculated by using the output voltage divided by the input
charge. Figure 4.17 (a) shows the predicted and experimental values for the transfer
function of the detection unit. In this figure, it can be seen that the predicted and
measured values matched well. The transfer function was nearly constant for 10-2 Hz
< f < 7 Hz.
Finally, the ME composites and modified charge amplifier circuits were
assembled together into a battery operated magnetic sensor detection unit. The
equivalent magnetic noise floor was measured for 10-2 Hz <f < 10 Hz using a
dynamic signal analyzer (SR-785). In order to characterize the intrinsic noise, the
sensor unit was placed in a high mu-metal shielding chamber to reject the influence
of electromagnetic interference (EMI). Figure 4.17 (b) shows the equivalent
magnetic noise density spectra. It can be seen that the experimental results and the
predicted values are in good agreement over the entire frequency range. The
equivalent magnetic noise density was around 0.3 nT/√Hz at 10 mHz, which was
almost 10 times smaller than that previously reported.82 Furthermore, the noise
density was also reduced by a factor of 5× to 8 pT/√Hz at f = 1 Hz. So, the
equivalent magnetic noise density of ELF magnetic sensors based on
Metglas/PMN-PT ME composites was reduced by optimizing the detection circuit.
115
Figure 4.17 (a) Predicted and measured transfer functions of the new detection
circuit; and (b) estimated and measured equivalent magnetic noise floors of an
optimized magnetic sensor.
116
Meanwhile, the circuit was redesigned to work down to frequency as low as
0.001 Hz in order to apply the sensor for medical treatment application. The design
was based on the similar layout, and the cutoff frequency was calculated through the
equations 4.3-4.8. The feedback resistor Rf and capacitor Cf were used for 500 Gohm
and 1000 pF, respectively. Accordingly, the resistors used in bandpass part were
setup at 100 Meg and 2 Gohm, respectively. So, the approaching gain factor for this
circuit can be calculated by the following equation:
H ( s)  H1 ( s)  H 2 ( s) 
1
V
 20  0.02 (
).
1000 p
pC
(4.11)
After fabricating the circuit, the gain factor in unit of V/pC was characterized
firstly. The characterization process was followed the above process, and the gain
factor at frequency from 0.007 Hz to 1 Hz was shown in Figure 4.16. From the
figure, one can see the transfer function is homogenous from 0.007 Hz to 1 Hz
which was not attenuated below 0.01 Hz. The circuit can work down to extremely
low frequency. However, the gain below 0.07 Hz is really hard to characterize due to
the quite long measuring time required.
117
Figure 4.18 Transfer functions of the 0.001 Hz detection circuit.
118
As discussed in the previous section, the equivalent magnetic noise density
spectrum for a 0.001 Hz magnetic sensor was also measured. However, a dynamic
signal analyzer is not a good choice since the whole instrument requires a low noise
condition. Otherwise, it would be saturated easily. In order to characterize the
magnetic noise for this sensor, the digitizer CR 1000 was used during the test. The
magnetic sensor was placed inside the vacuum chamber and the whole package was
then installed in magnetic shielding chamber. In order to measure the noise down to
0.001 Hz and to have the sufficient data points to do the further signal processing,
the datalogger was operated for over 3 hours with the sample rate of 100 Hz. During
the whole process, an AC magnetic field at frequency 1 Hz was applied to the
magnetic sensor by one pair of H-coils. Figure 4.19 (a) shows the waveform of
magnetic sensor in time domain. One can see the strong output signal can be
observed with slight variation. After collecting the raw data, MATLAB was used to
perform the signal processing to convert the raw data in time domain to power
density in frequency domain. In order to enhance the frequency resolution closed to
0.001 Hz, all the 1,200,000 data points were used. After processing, the noise density
spectra are shown in Figure 4.19 (b). From this figure, one can see the measured
noise floor is very close to estimated values over the whole frequency range except
the frequency below 0.0015 Hz, and strong spike at 1 Hz due to the incident
magnetic field. The blue line shows larger variations at frequency of f > 0.05 Hz
which is a direct result of high frequency resolution. Moreover, the magnetic noise
density below 0.0015 Hz is higher than predicated one, which is probably limited by
insufficient data points. So, the ELF magnetic sensor based on ME composites has
119
been successfully proposed which can work at frequency down to 0.001 Hz. The
noise density is around 2 nT√Hz below 0.002 Hz.
120
Figure 4.19 (a) Waveform of magnetic sensor in time domain, and (b) magnetic
power spectra of magnetic sensor. The red dash line indicates the theoretical
prediction result.
121
4.4 Active magnetic sensor unit
In addition to developing a passive magnetic sensor, an alternative AC magnetic
sensor was also designed based on the nonlinearity of ME composites.87, 88 The
modulation technique was utilized in order to modulate the low frequency magnetic
signal to the relatively high frequency range which has a lower noise floor.
Accordingly, the signal-to-noise ratio was expected to be enhanced in this way.87
4.4.1 Sensor design and characterization
The modulation processing of an active mode ME sensor is shown in Figure
4.20. First, a solenoid coil was wrapped around an ME composites to work as
driving coil in order to carry the high frequency (f0) magnetic field B0, after which
the incident magnetic field B1 at low frequency (f1) was applied through the external
H-coils (not shown in this figure). As a result of the nonlinear ME effect, the induced
output from the ME composites would contain signals at a frequency of (f0 +/- f1).
This process represents how one can modulate a low frequency incident magnetic
field to relatively high frequency range.
The origin of the nonlinear ME effect stems from the fact that the
magnetostriction of Metglas is non-linear to the applied magnetic field, as described
by equation (4.11):
  B2
(4.11)
where λ is the magnetostrictive coefficient, and B is the applied magnetic field.
Considering the sine wave signals used to drive the carrier magnetic field and the
incident magnetic field, the induced magnetic field can be expressed as:
122
B0  A0 sin(2 f 0t  0 );
B1  A1 sin(2 f1t  1 ).
(4.12)
where A0, A1 correspond to the amplitudes of the driving magnetic field and incident
magnetic field, respectively; θ0, θ1 represent the phase angles of the two fields. So,
the λ under two magnetic fields can be presented as:
  ( B0  B1 ) 2  B02  B12  2 B0  B1 ;
1 2
A0 (1  cos(4 f 0t  2 0 ));
2
B0  B1  A0 A1 sin(2 f 0t   0 )  sin(2 f1t  1 )
B02 =A0 2 sin 2 (2 f 0t   0 ) 
(4.13)
1
 - A0 A1[cos(2 ( f 0  f1 )t   0  1 )  cos(2 ( f 0  f1 )t   0  1 )];
2
1
B12 =A12 sin 2 (2 f1t  1 )  A12 (1  cos(4 f1t  21 )).
2
Clearly, under two AC magnetic fields, the magnetostrition was influenced by
both the applied fields, as well as the the cross-modulation between two AC fields.
By adjusting the relative amplitudes of B0 and B1, λ can show strong a relationship
with the magnetic field at frequencies of (f0 +/- f1). Considering that the output signal
from piezo-fiber was directly related to the strain transferred from Metglas, the
induced voltage from ME composites displayed the cross modulation elements under
two AC magnetic field conditions.
123
Figure 4.20 Modulation process of active mode ME sensor.
124
In order to characterize nonlinear ME effects, the nonlinear ME voltage
coefficient was defined as:
nonlinear
 ME

E f1  f0
B0  B1
.
(4.14)
where E is the induced electric field at frequencies of (f0 +/- f1). Theoretically, these
two values should be equal.
Nonlinear coefficients as a function of DC magnetic bias have been reported in
previous literature. Specifically, it was realized that nonlinear ME coefficients show
a completely different trend under a DC magnetic field compared to linear or
primary ME coefficients. Typically, the primary ME coefficients display the smallest
values at a zero DC bias, but increase to optimized values at a DC bias of 8 Oe. In
contrast, the nonlinear ME coefficients show the largest values at approximately zero
DC bias, but decrease with increasing DC magnetic bias. Therefore, in order to
observe the maximum nonlinear ME effect, the active sensor was placed inside the
magnetic shielding chamber, which was considered to be zero magnetic field.
Normally, most prior investigations have used the induced signal at frequencies
of f0 +/- f1 to indicate the response to the incident magnetic field under a consistent
driving magnetic field. This approach was also considered to be a reasonable
characterization method according to Equation 4.14 which indicates that the output
signal was proportional to the incident magnetic field as fixing the amplitude of the
driving field. However, this method does not elucidate the relationship between
output signal and incident magnetic field in any direct way. Accordingly, the
demodulation process was required to convert signals in the high frequency range
back to the low frequency area, which then can be used to accurately represent the
125
sensors’ response to the incident magnetic field. In fact, by using a demodulator, one
is able to fully decode the signal process, which unrelated to the nature of the
materials. Specifically, during this process, the signal from the sensor and one
reference signal with the same frequency as the driving signal are applied to the
demodulator. By comparing the output signal and the driving signal, essential
information at low frequency range can be obtained. Most of previous investigations
have concluded by using a commercial lock-in amplifier to drive the sensor and
perform the demodulation process. However, due to the large size and significant
power consumption of demodulator, this method tends to be feasible only for certain
fundamental research applications or for demonstration purposes. In other words, it
is impossible to propose one alternative magnetic sensor based on this process; thus,
one analog circuit with similar functions was determined to be sufficient.
For this investigation, therefore, I proposed one simple analog circuit apparatus
that was easily-operated by two 4.5 V batteries packs with differential mode input.
The schematic illustration of the signal process in the circuit is shown in Figure 4.21,
where, one oscillator is designed to generate a consistent sine wave driving signal at
a frequency of 10 kHz, which is an adjustable gain through the buffer stage. This
high frequency signal was applied to the excitation coil to drive the sensor.
Meanwhile, it served as the reference signal for the demodulation process. It should
also be noted that the circuit was integrated with a voltage amplifier to collect the
induced voltage from the ME sensor, after which the signal went to the demodulator.
Once the process performed by the demodulator and the low pass filter occurs, the
low frequency signal can be observed by oscilloscope or other instruments.
126
Figure 4.21 (a) Schematic of our custom-built lock-in circuit; and (b) photo of a
lock-in circuit.
127
For the present investigation, the commercial multiplier AD835 (Analog
Devices) was used to perform the demodulation process, which basically can achieve
the function of multiplying the signals applied to the X and Y input ports. I tested
three high frequency signals in this study: f0 - f1, f0, and f0 - f1. Assuming these three
induced signals and reference signal can be expressed as:
V f0  f1  A1 sin(2 ( f 0  f1 )t );
V f0  A2 sin(2 f 0t );
V f0  f1  A1 sin(2 ( f 0  f1 )t );
(4.15)
Vref  A3 sin(2 f 0t ).
where A1, A2, A3 correspond to the amplitude of the signals. To simplify the
calculation, the phase shift for each signal is neglected.
According to this expression, the signals through the AD835 demodulator can
be transferred to the low frequency signal as:
Vout  (V f0  f1  V f0  V f0  f1 ) Vref ;
1
V f0  f1 Vref   A1 A3[cos(2 (2 f 0  f1 )t )  cos(2 f1t )];
2
1
V f0 Vref   A2 A3[cos(4 f 0t )  1];
2
1
V f0  f1 Vref   A1 A3[cos(2 (2 f 0  f1 )t )  cos(2 f1t )].
2
(4.16)
Clearly, the signal processed by the AD835 contained signals at the incident
frequency f1 and at the double-frequency range. The low pass filter after the
modulator stage was able to reject signals at high frequency range; thus, only low
frequency signal could be detected. Typically, the low pass filter is designed to have
cutoff frequency around 1.6 Hz. However, it can be extended to higher frequency in
order to obtain a broader detectable frequency range.
128
Figure 4.21 (b) shows the prototype of our custom-built lock-in circuit, which
features small battery packs power supply. Given that the complete lock-in circuit
was relatively compact (12 cm × 9 cm × 6 cm), it was quite portable. This size factor
has positive implications for developing an active magnetic sensor based on the
nonlinear ME effect that is easily transportable.
Similar to a passive magnetic sensor, the sensitivity and noise floors remain two
important parameters to evaluate for an active magnetic sensor as well. Here, the
sensitivity in units of μV/nT for the active magnetic sensor was defined as overall
output signal divided by input magnetic field; in other words, we did not take into
account the complicated circuit process. The experimental setup for sensitivity
characterization is shown in Figure 4.22 (a). For this test, the ME sensor was
wrapped with 100 turn coils and placed inside the big H-coils which was used to
apply the incident magnetic field with small amplitude.
The H-coils was first characterized using a commercially available fluxgate,
which had a known sensitivity. During the calibration, the driving signal applied to
the big H-coils was generated by dynamic signal analyzer. Subsequently, the induced
output signal from the fluxgate was also monitored by the dynamic signal analyzer.
In order to reduce system noise, the results were averaged 12 times, after which the
recorded data was converted to magnetic field results according to the sensitivity of
the fluxgate. Figure 4.22 (b) presents H-coils calibration results, which indicate the
relationship between induced magnetic field and applied voltage. In order to study
the performance of the active sensor down to extremely low frequencies, the
calibrations were conducted at 1 Hz and 7.875 mHz. Form this figure it can be seen
129
that the amplitudes of the generated magnetic fields excited by an arbitrary voltage
at 1 Hz and 7.875 mHz overlapped each other perfectly. Thus, we were able to
demonstrate that the magnetic fields generated by the H-coils were consistent at
varying frequencies.
The performance of active sensor was then characterized, including linearity to
the magnetic field, sensitivity and noise floor. First of all, the linearity of the sensor
was measured. This was accomplished by generating the driving voltage by dynamic
signal analyzer at different amplitudes and at a frequency of 1 Hz, after which the
induced output signal from the sensor was monitored. According to the H-coils
characterization results, the driving voltage was then converted to the magnetic field.
Figure 4.23 (a) illustrates the output signals from the sensor as a function of incident
magnetic field at a frequency of 1 Hz. From the figure it can be seen that the sensor’s
output was fairly linear to the amplitude of the incident magnetic field. The slope of
the fitting curve was 12.09 μV/nT, which indicated sensitivity at 1 Hz. Using similar
methods, sensitivity over frequencies ranging from 7.8125 mHz to 2 Hz were then
characterized (Figure 4.23 (b)).
One can see from the figure that the sensitivity for the active magnetic sensor
was consistent at a value of 12 μV/nT at a frequency as low 7.8125 mHz, and up to 1
Hz. After that upper limit, the sensitivity was attenuated as a direct result of the low
pass filter, which has a cutoff frequency of 1.6 Hz. These findings indicate that the
sensor was able to detect magnetic fields in an extremely low frequency range or DC
up to 1 Hz.
130
Figure 4.22 (a) Experimental setup for the active sensor test; and (b) H-coils
calibration results at 1 Hz and 7.875 mHz.
131
Figure 4.23 (a) Output signal from the active sensor as function of incident magnetic
field; and (b) sensitivity of the sensor at a frequency range from 7.8125 mHz to 1
Hz.
132
Finally, the equivalent magnetic noise of the active sensor was measured via the
following protocol. First, the active sensor was placed inside the chamber in order to
reduce any electromagnetic interference. Then, the H-coil was activated by an AC
signal with amplitude of 8 mV at frequency of 7.8125 mHz to check the sensor’s
response. Figure 4.24 graphically illustrates the noise density spectra of the magnetic
sensor. The noise density at 2 mHz was around 18 nT/√Hz, and decreased gradually
with increasing frequency. The noise density was reduced to around 0.4 nT/√Hz at a
frequency of 0.78125 Hz. Moreover, the sharp spike observed at a frequency of
7.8125 mHz was attributed to the incident magnetic field.
Figure 4.24 Equivalent magnetic noise density spectra of the active magnetic sensor.
133
4.4.2 Optimization of active magnetic sensor
Although the present active sensor can work only from DC to 1 Hz, the
bandwidth of the sensor can be extended by changing the low pass filter during the
final stage. Additionally, the noise floor can be reduced by enhancing the gain factor
of the circuit. By simply changing the resistor or capacitor components during the
filter stage, the bandwidth can be modulated. Figure 4.25 shows the bandwidth
extended to 10 Hz and the noise density spectra. According to gain factor test results,
one can see that the gain factor displayed consistent values of about 6.8 μV/nT from
0.004 Hz to 4 Hz, while the 3-dB cutoff frequency was around 12 Hz. Based on
noise spectra density comparisons, the extended bandwidth of the magnetic sensor
had a similar noise floor as the original sensor. This finding indicates that the
modulated sensor was not influenced by changing the bandwidth at a specific
frequency range. Furthermore, the detectable frequency range was extended up to
100 Hz.
Figure 4.26 shows the detectable frequency range of a magnetic sensor that was
designed to work up to 100 Hz. From Panel (a), one notes that the 3-dB cutoff
frequency point was around 120 Hz. However, the noise density spectra of the sensor
were increased significantly compared to the previous sensors. One possible reason
for the inferior noise spectra could be reduced gain factor which limits the
signal-to-noise ratio. Considering this limitation, the gain factor was increased while
maintaining the 100 Hz bandwidth.
134
Figure 4.25 Equivalent magnetic noise density spectra of active magnetic sensor.
135
Figure 4.26 (a) Sensitivity of the modulated sensor in the frequency range of 6 mHz
to 200 Hz; and (b) equivalent magnetic noise density spectra of the active magnetic
sensor.
136
Figure 4.27 illustrates the modulated 100 Hz magnetic sensor. In this assay, the
gain factor was increased from 1.2 μV/nT to 110 μV/nT. Accordingly, the noise
density spectra were decreased from over 100 nT/√Hz to around 10 nT/√Hz, which
was closed to the values of the previous sensors.
137
Figure 4.27 (a) Sensitivity of the modulated sensor in the frequency range of 6 mHz
to 200 Hz; and (b) equivalent magnetic noise density spectra of the active magnetic
sensor.
138
In addition to modifying the bandwidth, the driving signal was also optimized
for the specific ME sensor due to the fact that driving signal played an important role
in this active sensor design. From the Figure 4.21 (a), one notes that the driving
signal was not only applied to the excitation coils to drive the ME sensor, but also
served as the reference signal during the demodulation process. For this study, the
frequency of the driving signal was fixed at 10 kHz. Another parameter that needs to
be studied is the amplitude of the signal. From Equation 4.14 and 4.16, we can see
that the amplitude of the signal affects the nonlinear output and the output through
the demodulator.
To obtain the desired measurements, I adjusted the rheostat in the circuit, which
caused the amplitude of the driving signals to vary from 0.57 V to 1.45 V.
Meanwhile, a 100 nT incident magnetic field at a frequency of 1 Hz was applied to
the active sensor through the H-coils, after which the output signals from the sensor
and the noise floor were monitored by dynamic signal analyzer under each driving
signal, as shown in Figure 4.28.
As clearly indicated, the output voltage from the sensor was enhanced by
increasing the amplitude of the driving signal. However, it should be noted that the
relationship between these two factors was not linear. Specifically, the output signal
shows saturated values when the driving signal was over 1.20 V. Meanwhile, voltage
noise tests were also conducted in the absence of incident magnetic field conditions;
results showed that the noise level of the sensor increased when the amplitude of the
driving signal was increased. On the basis of these two findings, we were able to
confirm the driving signal should have an optimized value for the active sensor.
139
Figure 4.28 (a) Induced output signals in response to the incident magnetic field; and
(b) noise spectra of the sensor at various driving signals.
140
Based on prior results, the equivalent magnetic noise density spectra for each
condition were also calculated. As shown in Figure 4.29, the largest driving signal
resulted in the highest noise level. Moreover, noise floor results for the sensor driven
by the signals with amplitudes of 0.69 V, 0.84 V, 0.97 V and 1.08 V had the similar
noise levels form 0.4 Hz to 100 Hz.
Figure 4.29 Equivalent magnetic noise density spectra for the sensors under different
driving signals.
141
I also calculated results for sensitivity, voltage noise and equivalent magnetic
noise at 1 Hz as a function of driving signal amplitudes, as shown in Figure 4.30.
With respect to sensitivity, this parameter increased by increasing the amplitude of
the driving signal, reaching maximum value at 1.20 V. Past this driving signal level,
however, the value became smaller. Similarly, the output voltage noise also increased
when the amplitude of the driving signal was elevated, which was somewhat
analogous to our findings for magnetic noise. Finally, taking into account both
sensitivity and voltage noise, the equivalent magnetic noise at 1Hz was calculated.
We can see that the equivalent magnetic noise first decreased and then increased.
Moreover, in reviewing my findings for noise density at levels of at 0.69 V, 0.84 V,
0.97 V and 1.08 V, I confirmed that the lowest values were at approximately 0.4
nT/√Hz at 1 Hz. This means that, in principle, the highest resolution results for these
conditions should be in keeping with SNR = 1. However, by driving the sensor with
1.08 V, we were able to generate the largest output signal which was much more
convenient for practical detection methods using other instruments. Therefore,
results from this study confirmed the effective methods for optimizing the active
sensor. Additionally, driving the sensor under optimal conditions can significantly
decrease the equivalent magnetic noise.
142
Figure 4.30 Sensitivity, voltage noise density and equivalent magnetic noise density
results at 1Hz for the active sensor as a function of driving signal.
143
The biggest advantage of an active sensor in comparison to a passive one is that
there is no need for an external dc bias. So, it allows us to directly measure the
geomagnetic field noise without considering the interactions between the field and
the dc bias. The photo insert in Figure 4.31 shows the experimental setup. Initially,
the sensor was placed along the magnetic north direction, but was then rotated to the
east direction. The results are shown in Figure 4.31 (a). Clearly, one can observe the
geomagnetic noise along different directions. In detail, the noise level for north
direction was higher than the noise along east direction. It should be noted that both
of the sensors presented the strong 60 Hz magnetic noise due to the EMI in the open
environment. In addition to the spikes observed at around 60 Hz, there were also
several strong spikes at a frequency range of 20 Hz. To confirm the noise source
from this range, the fluxgate was used to measure the geomagnetic field along the
north direction as well, and subsequent data were used to compare the two sensors.
Figure 4.31 (b) shows the comparison of both sensors. As depicted, the active
sensor had a similar noise level compared to the fluxgate along north direction.
Moreover, the fluxgate also presented strong spikes at 20 Hz range, which may be
used to confirm that the noise was not a result of vibration since it had little response
to vibration. Instead, the strong spikes at 20 Hz were probably the result of
electromagnetic noise induced by the AC power.
These measurements confirm that the active sensor has the ability to measure
geomagnetic field noise precisely. Additionally, our results also imply that one needs
to consider environmental magnetic noise along different orientations when
performing research involving magnetic field testing.
144
Figure 4.31 (a) Local geomagnetic field noise measurements along different
directions; and (b) comparisons of noise spectra measured by active sensor and
fluxgate. The photo insert of in upper portion of this figure depicts the experimental
setup.
145
4.5 Summary of this section
In summary, two types of AC magnetic sensors based on ME composites were
developed and optimized, including both passive and active modes. Moreover, the
charge noise circuit model has been established to analyze the passive magnet
sensors with more reasonable simulation results. Additional, detailed results are
summarized as follows:
(i) A passive magnetic sensor based on ME composites was assembled into one
battery-operated detection unit. Considering its practical applications, different
bandwidth circuits were designed for the ME sensor. For example, a wide
bandwidth circuit can help the sensor detect a magnetic field from 1 Hz up to
1.6 kHz. In order to reduce the 60 Hz EMI, a specific notch filter was integrated
into the circuit as well, which can work effectively for obtaining practical
measurements. Additionally, one low frequency circuit was designed for a
specific low frequency field test, which was conducted at 0.6 Hz to 10 Hz. The
advantage of the low frequency circuit is that it can significantly reduce output
noise.
(ii) A more accurate charge noise model for the passive sensor was developed,
which can predict noise density for the magnetic sensor more precisely.
Moreover, a magnetic sensor capable of functioning at extremely low frequency
range (< 1 mHz) has been successfully proposed. Using data from my noise
model, some optimization results have been achieved that reduce the equivalent
magnetic noise density by a factor of 10.
146
(iii) Based on the nonlinear ME effect, an active magnetic sensor has also been
developed that can work from DC to 100 Hz. Instead of using direct
measurement,
an
active
sensor
was
designed
according
to
modulation-demodulation processes, which were investigated mathematically
and described in this section. Furthermore, the detection bandwidth of the active
sensors has been successfully modulated, which confirmed that the sensors can
be used for different applications. Finally, by adjusting the amplitude of the
driving signal, I determined that the circuit can reduce the equivalent magnetic
noise effectively, which offers one good method for optimizing the sensor.
147
5.
DC magnetic sensor
5.1 Introduction
Previous investigations have also confirmed that ME composites can be used to
detect DC magnetic fields by using an active method. In fact, reports have indicated
that the sensitivity can reach the ~nT level. One of the main applications for a DC
magnetic sensor is to detect the geomagnetic field. For example, this type of sensor
could be used in an underwater positioning system that is based on a geomagnetic
field or a local magnetic field. Interestingly, the motivation for such application was
inspired by bio-behaviors in nature and, in particular, the sea turtle, which is able to
sense geomagnetic fields and use them to navigate vast underwater distances.
Research has shown that sea turtles can detect subtle variations of intensity and
inclination angle of geomagnetic field, as shown in Figure 5.1. This finding, in part,
led us to develop a new guidance system based on geomagnetic fields.
Based on this idea, prior members of our research group attempted to use a DC
sensor to sense magnetic fields under laboratory conditions. Although their results
confirmed that the sensor was able to detect changes in magnetic field intensity
along different rotation planes (Figure 1.10), there were four critical shortcomings
that need to be addressed, as follows:
(i) Improve sensitivity to small DC magnetic fields.
149
Higher sensitivity allows a sensor to detect smaller changes in a geomagnetic
field. Considering that the geomagnetic field gradient is, on average, around 0.02
nT/m in the Virginia area, a highly sensitive sensor could improve spatial resolution.
(ii) New detection device
Although previous studies have demonstrated the ability to detect a
geomagnetic field with some accuracy, those measurements tend to be based on the
lock-in amplifier detection method. This process requires one commercial lock-in
amplifier to drive the sensor, as well as detect the induced signals. However, it is not
feasible to use this instrument in outside conditions for testing guidance devices of
the future. It is highly desirable, therefore, to develop a new detection circuit that has
the similar ability of commercial lock-in amplifier.
(iii) Multi-axial detection sensor
A multi-axial detection sensor allows us to acquire geomagnetic field
information along different directions quickly. The quick response is essential for
localization and navigation.
(iv) Applications for geomagnetic field sensor
Since no prior reports have described the real-world applications for
geomagnetic sensors based on the magnetoelectric effect, one challenge for the
current study was to perform and outside field test to sense a geomagnetic field,
including magnetic field mapping and subsequent motion monitoring based on the
detected field.
150
Figure 5.1 Geomagnetic sensing by sea turtles.
151
5.2 Improvement of sensitivity
The detection principle associated with DC testing is quite different in
comparison to AC testing. For the AC sensor, the goal is to improve optimum ME
voltage coefficients that can increase the output signal in response to an incident
magnetic field. In contrast, a DC sensor requires larger voltage changes to detect the
larger DC magnetic field variations under geomagnetic field range (-0.65 gauss to
0.65 gauss). Take one αME-Hdc curve as an example: Figure 5.2 presents the typical
curve for Metglas/PZT composites. The optimum αME at the magnetic bias of 8 Oe is
related to AC detection sensitivity, while the slope value of the linear part affects DC
detection sensitivity.
30
ME(V/cm-Oe)
20
Optimum ME
Metglas/PZT
10
dV/dH
0
-10
-20
-30
-15 -10
-5
0
5
10
15
dc magnetic field (gauss)
Figure 5.2 αME-Hdc for Metglas/PZT composites.
152
5.2.1 Different piezo-fibers
In this section, I compared highly orientated Metglas/Pb(Mg1/3Nb2/3)O3-PbTiO3
(PMN-PT) fibers with PZT fibers based sensor’s sensitivity. I used PZT (Smart
Materials, Sarasota, FL) and PMN-PT (Ceracomp Co., Ltd., Korea) fibers to make
different ME composites. The fabrication process and the geometry for each
composite was exactly the same. The piezoelectric properties for these PZT and
PMN-PT fibers are provided in Table 5.1. Higher g33 and k33 coefficients for
PMN-PT fibers were expected to improve the ME effect. However, as previously
indicated, that is not the only factors for DC sensitivity; detailed characterizations
were required.
Table 5.1 The critical piezoelectric properties for PZT and PMN-PT fibers
PZTa)
d33,p
g33,p
k33
440pC/N
25.5mV.m/N
0.72
PMN-PTb) 2000pC/N 32.4mV.m/N
0.93
a) Cited from Smart Material Corp., USA
b) Cited from Ceracomp Co., Ltd., Korea
Figure 5.3 (a) shows ME as a function of Hdc for Metglas/PMN-PT and
Metglas/PZT laminates. From this figure, we can see that ME for the two ME
laminates had similar trends with Hdc; however, the values of ME for the
Metglas/PMN-PT laminate were notably higher in comparison to those for
Metglas/PZT. In particular, the maximum value of ME for the Metglas/PMN-PT
laminate was 45 V/cm-Oe, which was about 3 times larger than that for the PZT
based one of similar size (i.e., 15 V/cm-Oe). This represents the highest value of ME
reported to date for any ME composite, by a factor of 2×.
153
Figure 5.3 ME voltage coefficient of Metglas/PZT and Metglas/PMN-PT laminates:
(a) ME as the function of dc bias Hdc at f = 1 kHz, and (b) ME as a function of ac
magnetic drive frequency.
154
Figure 5.3 (b) shows the ME voltage coefficient for Metglas/PZT and
Metglas/PMN-PT laminates as a function of AC magnetic field frequency, while
sweeping through the electromechanical resonance (EMR). The fundamental
resonant frequencies for the PZT and PMN-PT based sensors were 31.5 kHz and
27.8 kHz, respectively. In this figure, we can see (i) a strong EMR enhancement in
ME that was previously reported; and (ii) that values of ME > 1100 V/cm-Oe can be
achieved for PMN-PT laminates, which was about 3× larger than that for PZT ones.
The DC magnetic field sensitivity was characterized for both sensors using an
active method: a 100 turns coil was wrapped around the sensor which carried a small
AC current provided by the lock-in amplifier to drive the ME sensors. Voltages were
then induced in the piezoelectric layer by small changes in Hdc, which were
measured by the amplifier. Figure 5.4 presents the comparison of the DC magnetic
field sensitivity of two ME composites.
Figures 5.4 (a) shows the induced output voltages from
the Metglas/PZT
laminates in response to small changes in Hdc at driving frequencies of f=1 kHz. It
can be seen that DC magnetic field variations as small as Hdc=15 nT can be detected.
Figures 5.4 (b) shows similar sensitivity measurements to small changes in Hdc for
Metglas/PMN-PT laminates. In this figure, one can see that the sensitivity for the
Metglas/PMN-PT laminates was significantly enhanced relative to that for the
Metglas/PZT ones. The sensitivity to DC magnetic field changes for PMN-PT
lamiantes can be seen to be 5 nT at 1 kHz and Hac=0.1 Oe: which was 3 times higher
than that for PZT based ones.
155
Figure 5.4 DC magnetic field sensitivities for (a) PZT based; (b) PMN-PT based
composites.
156
Finally,
the
sensitivity
to
small
DC
magnetic
field
changes
for
Metglas/PMN-PT laminates was studied under the EMR conditions (f =27.8 kHz).
Since ME is extremely high in this case (see Figure 5.3 (b)), it was believed that the
sensitivity could be improved even further under EMR driving condition. During the
test, the ME sensor was placed in a magnetically shielded chamber to reduce
exposure to environmental noise. Figure 5.5 shows the induced output voltage to
small step changes in DC magnetic field. Clearly, the Metglas/PMN-PT laminates
can detect changes of Hdc≤1 nT. This represents a notable improvement in DC field
sensitivity relative to lower frequencies.
However, the principal limitation for driving the sensor under resonant
frequency is the unstable response outside of the chamber. A small level of magnetic
field bias could affect the output signal. That is the reason we put the above test in
the chamber. Moreover, the resonant frequencies for different sensors are quite
various that require different driving frequency for individual one. It is definitely not
convenience for practical applications considering more driving sources are required.
Therefore, I am able to achieve a significant enhancement in ME (by 3×) and
the DC magnetic field sensitivity (by up to 10×) by using PMN-PT fibers in
heterostructured composites, relative to the analogous values for the PZT fibers. The
ME voltage coefficient for Metglas/PMN-PT laminates reached values of 45
V/cm-Oe at f=1 kHz, and of 1100 V/cm-Oe at the EMR. The DC field sensitivity of
these Metglas/PMN-PT laminates was then found to be 4 nT under a constant drive
of Hac=0.1 Oe at f =10 kHz. Even smaller DC field changes of ≤1 nT were also
detected at the EMR.
157
Figure 5.5 Sensitivity of MEtglas/PMN-PT laminate to small DC magnetic field
changes under ac drive field of Hac = 0.1 Oe at the resonant frequency.
158
5.2.2 Magnetic flux concentration
This study was based in part on the assumption that the flux concentration
associated with a DC magnetic field measurement is quite important. Therefore, any
method that could improve this factor would be able to increase induced signal
changes at the same DC field variations. In response, I developed a magnetostatic
finite element model to study the effects of in-plane magnetostrictive phase
geometry on the magnetic flux concentration within high-mu layers. According to
subsequent simulation results, we then redesigned the geometry of the sensors.
Magnetostatic modeling was performed using a commercial finite element
modeling (FEM) package (Ansoft’s Maxwell 3D). A uniform DC magnetic field
was simulated by using a pair of neodymium permanent magnets separated by 25 cm
at either end of the axial direction of the Metglas ribbons, as illustrated in Figure 5.6
(a). The strength of the neodymium magnets was adjusted to provide a sufficiently
small H field, so as not to reach saturation (Hsat) within the high mu material.
A1
cm wide by 25 um thick ribbon of high-mu material was placed between the bias
magnets, and then the length was changed for various laminates between 80 and 100
mm. The mu-metal was assigned a non-linear B-H curve (see insert in Figure 4.6)
from the Ansoft materials library file to approximate the real behavior of the Metglas.
An automatic 1000 point mesh was generated within a control volume with
appropriate boundary conditions, located sufficiently far from regions of interest
within the material. The simulation was completed to within 0.5% accuracy after 100
iterations of the code.
159
Figure 5.6 (a) Schematic representation of 3-D Mangetostatic model layout
including large, permanent magnetic HDC bias generators, and (b) vector map of the
y-z (axial-height) component of the H field in the presence of the high-mu Metglas.
Insert: non-ideal B-H relationship used to define magnetostatic behavior of high mu
Metglas in FEM.
160
The magnetic flux in the space close to the Metglas was found to be
dramatically influenced by the high permeability of the foils.
A planar
representation of the H field in the space surrounding the Metglas is shown in Figure
5.6 (b). The magnetizing field (and corresponding flux density) was distorted in
regions of close proximity to the Metglas in the Y-Z plane. The flux density was
similarly distorted in all three dimensions surrounding the Metglas, although only a
single plane is shown in Figure 5.6 (b) for illustration. The net effect of the flux
concentration of the high-mu material was evidenced by a relative change in the
internal field characteristics.
As shown in Figure 5.7 (a), the in-plane magnetic field strength for longer
Metglas foils was larger than that of shorter ones, especially in the center portion of
the foil. Line scans along the axial center-line of the Metglas foils (See Figure 5.7
(b)) with increasing length of the foil from 80 to 100 mm resulted in a 36% increase
in field strength at the center of the Metglas ribbon. While the model has not been
configured to allow for accurate determination of the absolute value of the flux
density within the material, we believe that the relative increase in field strength is
physically correct, and supportive of the experimental results to be shown below.
161
Figure 5.7 (a) In-plane magnetic field strength along center plane of Metglas foils in
response to arbitrarily low DC bias field, as simulated by Maxwell 3D, and (b) line
scan traces of magnetic flux density along the axially centerline of Metglas foils for
80mm and 100mm geometries.
162
Based on these simulation results, we fabricated composites with different
lengths (8 cm and 10 cm) of Metglas foils for comparison. Figure 5.8 present the
values of ME for ME laminates of different length that exhibited similar trends with
Hdc. In both cases, ME increased from roughly 0 V/cm-Oe at zero bias to a
maximum value at an optimum bias condition, and subsequently decreased as Hdc
was increased further. The value of ME for the laminates with the longer Metglas
foils was notably higher than that for shorter ones, while also requiring smaller
magnetic biases. For example, under Hdc =2.5 Oe, the value of ME was 10 V/cm-Oe
for 100 mm long Metglas laminates, relative to 5 V/cm-Oe for 80 mm Metglas ones.
Following the above magnetostatic modeling results, the enhancement of ME for
longer Metglas directly results from higher magnetic flux concentration.
Moreover, the DC magnetic field sensitivity for both composites was
characterized. Figure 5.9 shows the measured result: DC magnetic field variations as
small as Hdc=15 nT could be detected under a 0.1 Oe, 1 kHz drive for the sensor with
Metglas foils of 80 mm in length. However, the DC magnetic field changes as small
as 6 nT were detectable by using a ME sensor with longer Metglas foils (100 mm):
please note that similar drive conditions were used. This represents a 250% increase
in the DC field sensitivity.
In summary, we found that lengthening the Metglas layer increases the magnetic
flux density over the central portion of the sensor that contains the core piezoelectric
layer. A redesign of the Metglas/PZT sensor was notably enhanced over the bias
range of -2.5 Oe<Hdc<2.5 Oe. This resulted in a 250% increase in the detection
threshold (from 15 nT to 6 nT), measured under a constant SNR=10.
163
Figure 5.8 ME voltage coefficient of laminate sensor with different Metglas lengths
as a function of DC bias Hdc in response to a 1Oe, 1 kHz AC magnetic excitation.
164
Figure 5.9 Comparison of the sensitivity for Metglas/PZT laminates to small DC
magnetic field changes under AC drive conditions of at f =1 kHz and Hac=0.1 Oe: (a)
ME sensor with 8 cm long Metlgas, and (b) ME sensor with 10 cm long Metglas.
165
5.3 Man portable magnetic sensor
5.3.1 Lock-in detection circuit
In addition to working on improvements in sensitivity, we also designed a new
circuit detection unit to replace the commercial lock-in amplifier. Figure 5.10 (a)
shows a lay-out for the custom designed lock-in circuit. An analog sine wave
oscillator (OSC) provided a modulation AC signal at frequency of 1 kHz to drive
ME composites. The sensor output signals firstly passed a high-pass filter (HPF),
and then were amplified by an instrumentation amplifier (InA). The amplified
signals were demodulated by a demodulator with the help of a reference signal
provided by the oscillator. A low pass filter (LPF) was used to provide a stable
output. A second-order low pass filter (LPF) was used to filter out high frequency
components of the demodulator output signal.
Figure 5.10 (b) provides a photo of single axis lock-in circuit prototype. In this
prototype, two 4.8-V batteries were used as the power supply. The dimensions of the
circuitry were 9 cm × 6 cm × 12 cm, while the power consumption was only 96 mW.
The OSC provided a 1 kHz sine wave, while the corner frequency of the
second-order LPF was set at 1.6 Hz. Bottom, left and right BNC connectors were
used for the modulation signal, sensor outputs and detected signal, respectively. A
switch was also used to turn off the lock-in circuit to save power.
166
Figure 5.10 (a) Schematic of our custom-built lock-in circuit;
prototype lock-in circuit.
167
(b) photo of a
After fabricated the circuit, we checked the function of each part to make sure
the circuit works well. First, we tested the oscillator, which is used to generate the
driving signals and reference signals for the demodulation process. If this part did
not work well, the circuit would not perform the expected functions. To examine the
oscillator, we simply connected the driving signal port to the oscilloscope using a
BNC cable. Figure 5.11 shows the output signals in time domain. One can see that a
perfect sine wave signal can be generated by the circuit. Moreover, by adjusting a
couple of components in the circuit, the frequency of the AC signal can be tuned
from 1 kHz to over 30 kHz. This means we can drive the sensor under off resonant
and resonant conditions depending on application requirements.
After this inspection, we compared the detection sensitivity of our fabricated
lock-in circuit and the commercial lock-in amplifier using the same ME composites.
Figure 5.12 (a) and (b) shows the DC magnetic field sensitivity detected by using the
lock-in amplifier and lock-in circuit, respectively. From this measurement, one can
see that the lab-made circuit has quite similar detection sensitivity as the lock-in
amplifier. This outcome confirmed that we would be able to assemble the
composites and the circuit in a relatively compact unit.
168
Figure 5.11 Waveforms of driving signal generated by oscillator in time domain: (a)
1 kHz; and (b) 32.7 kHz.
169
Figure 5.12 Sensitivity of composites to small DC magnetic field changes under AC
driving conditions at f=1 kHz and Hac=0.1 Oe generated by (a) lock-in amplifier
(SR-850); and (b) lock-in circuit.
170
5.3.2 Sensor performance
As a DC magnetic sensor, our detection unit can be used for DC magnetic target
localization, magnetic field mapping, and so on. The following section summarizes
the process I utilized to obtain the essential measurements need to demonstrate the
function of our DC magnetic sensors.
Firstly, I performed magnetic dipole localization. Figure 5.13(a) shows the
schematic of experimental setup. In this test, a magnetic dipole was placed at an
“unknown” position along y-axis, and the 1-axis DC magnetometer was placed 10
cm away and moved around the dipole over a 2-D grid of 50 cm by 20 cm. Since the
magnetometer was quite sensitive to Hdc along the longitudinal direction but
essentially, insensitive along the transverse direction, the detected magnetic field was
mainly along the y direction. By detecting the magnetic field generated by the
magnetic dipole, we were able to localize its position along the y-axis. Figure 5.13 (b)
shows the magnetic field distribution of the dipole simulated by Vizimag software.
Along the center, one can see that the symmetric magnetic flux lines flowed from the
north pole to the south pole, and that the magnetic intensity reached its maximum
vale around the two edges. Moreover, the magnetic flux direction was reversed over
the center of dipole. Figure 5.13 (c) shows magnetic field data obtained from the
magnetometer, which confirmed that the output signal from the magnetometer
became larger when it was moved towards the dipole due to higher magnetic field
intensity closer to the dipole. Since the magnetometer was quite sensitive to the
orientation of the magnetic field, the output signal changed quickly from positive
maximum to negative maximum values as it passed by the dipole source. All of these
171
characteristics matched the model results perfectly; in other words, there should be
no magnetic field along the y direction at the middle of dipole. In Figure 5.13 (c), the
“zero” point was located at 36.9 cm along the y axis. In order to reference this data,
the actual distance between the mid-point and the initial position was measured by a
ruler. The measured result shows the dipole was placed at 37.0 cm. Clearly, my DC
magnetometer was able to localize the dipole with little error.
Furthermore, I used the DC magnetometer to measure the DC magnetic field
distribution in real space. Figure 5.14 (a) shows the location where the field
distributions were mapped using the portable DC magnetometer. It should be noted
that this particular location had some iron pipes in vicinity, which could have
distorted the magnetic field distribution, as indicated by the arrows in the figure. The
test was performed over a spatial area of 1.2 m by 6.0 m. As shown in Figure 5.14(b),
the results verified that a magnetic field distribution could be mapped by moving the
magnetometer over this area. As expected, maximum values were detected at places
closest to the pipes at (0.3m, 4.5m). Using our portable DC magnetometer, the
maximum magnetic field change detected over this range was about 4800 nT, and
the magnetic field was increased from 0 m to 6 m.
172
Figure 5.13 Illustration of capability of our DC magnetometer to localize a magnetic
dipole: (a) schematic of experimental setup, (b) magnetic flux distribution of the
magnetic dipole, and (c) real position measurement.
173
Figure 5.14 Real space DC magnetic field test: (a) photo of test location, and (b)
output signal from DC magnetometer over spatial grid about test location.
174
5.4 Geomagnetic field detection
An important aspect of this study involved using the newly-developed and
highly-sensitive DC magnetic sensor to detect a geomagnetic field, and then use
resulting data to understand how to use this information to improve guidance
functions. As previously indicated, in order to achieve geomagnetic field intensity
along different directions, I have developed multi-axial detection unit, as shown in
Figure 5.15. Specifically, 2-axial sensors were found to be useful for the horizontal
plane test, while a 3-axial sensor was better for the 3-D space test.
Figure 5.15 Multi-axial detection magnetic sensor: (a) 2-axis; and (b) 3-axis.
175
5.4.1 2-axial magnetic sensor
As shown in Figure 5.15, one 2-axial magnetic sensor was designed.
Fundamentally, a magnetic sensor can monitor a magnetic field in the horizontal
plane. According to the detected magnetic field, the sensor can be used for an
orientation-based monitoring in a vehicle. In a 2-D plane, the geomagnetic field can
be considered as the constant vector field in the absence of any external magnetic
field interference, as shown in this figure. Ideally, when one rotates the 2-axial
sensor along the Z-axis, the output signal of one sensor would show the sine
waveform, while the other would show the cosine waveform. So, according to the
output signal for each individual component, the orientation can be obtained.
For my measurement, the magnetic sensor was placed in a tripod which has two
inclinometers to control the sensor along the horizontal plane without tilting. Initially,
the y-axis sensor was positioned along the north direction and the angle between the
y-axis sensor and the north direction was defined as θ, as shown in Figure 5.16 (a).
To evaluate performance, the sensor was orientated in a gradual motion along north,
northeast, east, southeast, south, southwest, west and northwest directions. During
the process, the output signals from 2-axial sensor were recorded individually, and
the angle θ and orientation was determined.
Figure 5.16 (b) shows the results according to the detected signals. Ideally, the
angle should be equal to 45 degrees. And indeed, one can see that we were able to
calculate the orientation from the geomagnetic field with relatively high accuracy.
The observed deviations may have resulted from the measurement system, and/or the
influence of any external magnetic field.
176
Figure 5.16 (a) Experimental setup for 2-axial geomagnetic sensor; and (b)
orientation determined based on geomagnetic field.
177
5.4.2 3-axial magnetic sensor
Next, I utilized my 3-axial detection unit to do some exterior testing of
geomagnetic fields in two locations around Blacksburg, Virginia. Figure 5.17 shows
the detection locations and the sensor used in the test. The raw data for each position
is listed in Table 5.2.
Table 5.2 Geomagnetic field measurements at two positions using the 3-axial sensor.
Location N
W
Elevation Earth’s North
A
37˚14.52’ 80˚24.72’ 2173 ft
1.1874 V
B
37˚12.99’ 80˚24.99’ 2105 ft
1.1916 V
Vertical Component
2.5882 V
2.5871 V
By using the calibrated sensitivity of 55.56 uV/nT, I was able to convert the raw
into magnetic field components. Meanwhile, the inclination angle could be
calculated as well. Tables 5.3-5.5 summarize the comparisons and errors between
test results and database values. From the test, it was able to confirm that my
magnetic sensor could sense geomagnetic fields with small errors. Thus, such a
system has potential for application in guidance systems based on geomagnetic field.
Table 5.3 Geomagnetic field intensity along North direction
Location
A
B
Earth’s North
21,371.5 nT
21,447.1 nT
Database Value*
21,446.9 nT
21,457.9 nT
Error
0.35%
0.05%
Table 5.4 Geomagnetic field intensity along Vertical direction
Location
A
B
Earth’s North
46,583.9 nT
46,564.1 nT
Database Value*
46,748.2 nT
46,728.9 nT
Error
0.35%
0.05%
Table 5.5 Comparisons of inclination Angle
Location
A
B
Earth’s North
65˚21’
65˚18’
Database Value*
65˚21’
65˚20’
Error
0.35%
0.05%
* Cited from World magnetic model 2010-2015, National Geophysical Data center
178
Figure 5.17 Geomagnetic field measurements around Blacksburg area. The insert
shows the 3-axial magnetic sensor used in the test.
179
5.4.3 Mobile magnetic sensor unit
Due to the fact that prior measurements represent “static” data, they cannot be
applied in ay reliable way to a real-time monitoring system for real-world
applications. In order to overcome this limitation, a rigid, yet mobile, sensor package
is highly desirable. Moreover, any “smart” data collection system needs to be
developed for monitoring output signals continuously.
For this research phase, the 3-axial sensor was assembled in one box which can
protect the sensor in an open environment and reject any electromagnetic
interference, as shown in Figure 5.18 (a). The positive direction for each sensor is
described in this figure as well. First, the sensitivity for each sensor was
characterized by using one H-coils pair. During the characterization, the magnetic
coil was driven by the DC output port from a lock-in amplifier. By adjusting the
output signal, the DC field was controlled within the range from -0.11 Oe to 0.11 Oe.
Then, the magnetic field was changed incrementally in measurement units as small
as 0.01 Oe in the measurements. The results are shown in Figure 5.18 (b).
From the figure, one can see that the output signals from all 3 sensors are linear
to the external magnetic field in the measured range. However, the sensitivities for
the sensors were not exactly the same: there were small variations between each
other. In detail, the sensitivities for x-axis, y-axis and z-axis were 51.45 μV/nT,
45.37 μV/nT, and 61.56 μV/nT, respectively. These magnetic sensor values were
used to convert the measured voltage to the equivalent magnetic field.
180
Figure 5.18 (a) Rigid package for 3-axial magnetic senor; and (b) characterization of
sensitivity for each axis sensor.
181
5.4.4 Demonstrations for geomagnetic field sensor
First of all, a 3-D orientation monitoring system was proposed based on
geomagnetic field. For this measurement, the 3-axial magnetic sensor was placed on
the tripod described in the prior section. Meanwhile, the Labview code was compiled
to monitor the orientation along different axes. The front panel of program is shown
in Figure 5.19 (a). In detail, the graph displays the original data obtained directly
from the sensors. And the three panels at the bottom shows the rotation angles which
are defined as Yaw, Pitch, Roll angles corresponding to the rotating along Z, Y, and
X axes, respectively.
Initially, the y-axis of the sensor was fixed along the north direction, so that the
x-axis and z-axis were situated along the east and up directions, respectively. From
this first panel, one can see that the angle is 0, which corresponds to prior
assumptions. In other words, this finding directly resulted from the sensor being
placed along the magnetic north direction. However, the second panel indicates a
huge shift which means that the local magnetic field was not exactly along the
up-down direction. By checking the parameters of the local magnetic field from the
website, one can find that the geomagnetic field showed an inclination angle of
around 65 degrees, which corresponds to the angle between the magnetic field and
the horizontal direction. In my system, the second panel should display the magnetic
field with respect to the vertical direction, which means the angle should be around
25 degrees. That can be corroborated by the data shown in Figure 5.19 (b). Moreover,
by using the Labview, I was able to collect the data as the sensor rotated, so that I
could monitor the rotation of the sensor in real time.
182
Figure 5.19 (a) Labview program for rotation monitor; and (b) experimental setup
for monitoring the orientation in 3-D space.
183
In addition to capturing orientation measurements, I also developed a mobile
magnetic sensor that enabled us to do wide range magnetic field sensing. For this
design, a multi-axial magnetic sensor, detection circuit and one wireless digitizer
were assembled in a rigid alumina bar. In terms of function, the digitizer was able to
collect the data from the magnetic sensor and then send it to a laptop through a
wireless network. With the help of this digitizer, this hand-held device can be used
for magnetic field detection over 100 m. Moreover, all of the devices can be
powered by a simple battery pack, thus eliminating the need for an external power.
A demonstration trail for magnetic field mapping was initially performed in a
parking lot over 200 m2. Figure 5.20 (a) shows a schematic illustration of magnetic
field mapping test. The sensor was taken along the path lane from a starting point to
an ending point, and then repeated in an adjacent lane location. During the
measurement, there were 4 vehicles parked in the lot and their relative positions are
shown in Figure 5.20 (a). The data was recorded with a laptop, after which the
magnetic field could be calculated.
Figure 5.20 (b)-(d) show the magnetic field mapping results for x, y and z
directions. From the figures, we can see that the magnetic fields along 3 directions
were almost homogenous for the area furthest away from the vehicles, and the
background magnetic fields measured by sensors varied. However, for the results
associated with the path lane closed to the vehicles, the magnetic fields were
influenced greatly. That was direct a result of high permeability materials which
induced the magnetic field distortion.89,90
184
Figure 5.20 (a) magnetic field mapping demonstration performed at parking lot; and
(b)-(d) magnetic field mapping results measured by the sensors.
185
In addition to the field mapping test, the geomagnetic sensor can be also used
for field sensing in large area. For this assay, the sensor was taken to a soccer field
in an open environment in order to reduce the influence of other noise sources. As
shown in Figure 5.21 (a), the sensor was moved around along the penalty area,
According to the previous results, the sensor was expected to be able to sense the
motion of turning.
Figure 5.21 (b) shows the magnetic field changes for the whole process. One
can see that the magnetic fields along all three directions did not change
significantly at the very beginning since the motion was just along the straight path
lane. Moreover, the magnetic field values varied due to the different geomagnetic
fields along x, y and z directions. Noticeable changes emerged with the first left
turn motion. Since this motion involved 90-degree turn, the y-direction changed to
–x, and the x-direction changed to y. Thus, the amplitude of the y-axis was changed
to the value of –x, and the amplitude of the x-axis was equaled to the value of y.
The motions in the whole process could be observed from the measured signals.
This resulting data indicates that the sensor was highly sensitive to presence of
the geomagnetic fields, as well as to turning motions. Potentially, if installed in a
vehicle, this geomagnetic sensor would be useful for magnetic field mapping and
for controlling the orientation of a vehicle, especially in case where no strong GPS
signals were available.
186
Figure 5.21 (a) Geomagnetic field sensing in an open environment; and (b) magnetic
fields for the process.
187
5.5 Summary of this section
A highly-sensitive, man-portable DC magnetic sensor was developed that
displayed the sensitivity in the range of 10 nT. This DC magnetic sensor has
potential for use in magnetic target localization, magnetic field mapping etc. An
important result from this study is that we were able to detect geomagnetic field with
high accuracy using the DC magnetic sensor. Moreover, a multi-axial geomagnetic
field device was shown to be able to monitor the orientation, magnetic field mapping
and motion control based on the presence of the geomagnetic field.
188
6. Other devices based on ME effect
6.1 Introduction
Previous chapters have chiefly described the development and use of a magnetic
sensor based on Metglas/piezo-fibers with multi-push pull configurations. Since ME
composites can be designed with different structures, this section will investigate the
use of unsymmetrical bi-layered ME composites, which have been shown to display
markedly different resonant effect compared to conventional multi-push pull
configurations. The inherent characteristics of bi-layered ME composites make them
applicable for the design of a magnetic resonator at various frequencies. Moreover,
the resonant frequency can be tuned to a significant degree by altering the layers of
the Metglas or by applying an active tip mass. In short, the wide-ranging tenability
of bi-layered ME composites makes them promising for practical applications at
various frequency ranges.
Although they can be used in magnetic sensor applications, there are several
other devices can be developed based on these functional composites, including
energy harvesters, magnetic memory devices, etc. In this section, I will further
investigate their use in magnetic energy harvesters. Based on conditional structures,
highly effective harvesters have been demonstrated to power battery with great
efficiency. Moreover, the 60 Hz harvester was also designed based on bi-layered ME
composites, which can be used to capture the magnetic energy generated by
189
instruments. Finally, the frequency multiplication effect that can be tuned by the
geomagnetic field in Metglas/piezo-fibers composites has also been investigated.
Such effects show promise for applications in frequency multiplier and geomagnetic
guidance devices.
6.2 Bi-layered ME composites
Recently, a number of scholars have investigated the development of
multifunctional devices based on ME composites,81, 91 as well as the influences of
various environmental conditions on the performances of these devices.85,
92
However, one of the biggest challenges for the practical application of such devices
has been the ME coefficient ME, which limits the performance of the ME devices.
Thus, it is highly desirable to enhance the value of ME in order to optimize the
property of ME devices. Recent investigations have reported that driving ME
composites under a resonance frequency (fr) can improve ME by up to a factor of
100×,93 and improve the sensitivity of ME magnetic sensor dramatically.29 However,
such EMR gains in L-L mode structures are only possible at high frequencies of
fr≈30 kHz over narrow bandwidths. Therefore, it would be desirable to shift this
gain in ME to lower frequency, while limiting the compromise in bandwidth.
In this section, we have investigated bending mode structures for bi-layer
Metglas/PZT laminates. Near a fundamental bending frequency (FBR) of 210 Hz,
the value of ME was enhanced by a factor of >10×, compared to a corresponding
L-L mode of the same size. Using a charge amplifier detection method, magnetic
noise floors of ≤ 0.3pT/√Hz were achieved near the FBR, which was about 100×
190
lower than at 1 Hz and about 10× lower than that of L-L mode at the same
frequency.
6.2.1 Design of bi-layered ME composites
We obtained PZT fibers (Smart Materials, Sarasota, FL) and Metglas foils
(Vitrovac Inc., Hanau, Germany) to fabricate the laminates. Five pieces of 180 um
thick piezoelectric fibers were oriented along the long axes to form a layer that was
in total 10 mm wide and 40 mm long. Two interdigited Kapton®-based electrodes
were then bonded to the top and bottom surfaces of the piezoelectric layer in a multi
push-pull mode configuration. To fabricate symmetrical longitudinal mode sensors,
three Metglas foils of 80 mm in length and 10 mm in width were first laminated to
each other, and subsequently laminated to both the top and bottom surfaces of the
PZT fiber layer. To fabricate an asymmetrical bending mode, six Metglas foils of the
same size were bonded together, and subsequently laminated to only the bottom
surface of the PZT fiber layer. A schematic comparison of the symmetrical L-L and
asymmetrical bending modes can be seen in Figure 6.1. Due to the symmetric
structure of the L-L mode, strains generated by the top and bottom layers of the
Metglas are identical under magnetic field: thus, the L-L mode elongates or shrinks
along the horizontal plane. However, the asymmetrical structure undergoes a flexural
deformation under magnetic field.
191
Figure 6.1 Schematics of Metglas/PZT ME laminate sensors: (a) L-L mode sensor,
and (b) bending mode.
192
First, ME for both L-L and bending mode structures was measured as a function
of dc magnetic bias Hdc, as shown in Figure 6.2(a). A lock-in amplifier (SR-850) was
used to drive a pair of Helmholtz coils to generate an ac magnetic field of Hac=1 Oe
at a frequency of f=1 kHz. The dc magnetic bias Hdc was applied along the long axis
of the ME laminates. As can be seen in Figure 6.2(a), ME for both modes exhibited
similar trends with increasing Hdc. At a frequency of 1 kHz, the maximum value of
ME for the bending mode was 24 V/cm-Oe, which was a little larger than the 20
V/cm-Oe for the L-L mode. We were surprised by these results, since the L-L
multi-push pull mode has been believed to have the highest ME coefficient.27
Figure 6.2(b) shows ME as a function of the ac magnetic field frequency. In this
figure, we can see a notable difference in ME between the L-L and bending modes
over the frequency range of 102 Hz<f<103 Hz. The value of ME for the L-L mode
was nearly constant over this frequency range at 20 V/cm-Oe. However, the bending
mode exhibited a strong EMR enhancement at 210 Hz, achieving values of ME=400
V/cm-Oe. This demonstrates that ME for the bending mode can be improved by a
factor of 20× at the FBR relative to the value for the L-L mode at the same frequency.
The insert in Figure 2(b) shows ME for the L-L mode sensor as a function of
frequency: where the EMR frequency can be seen to be about 30 kHz, as previously
reported.27
193
Figure 6.2 ME voltage coefficients of L-L and bending mode ME laminates: (a) ME
as a function of dc magnetic bias Hdc at f = 1 kHz, and (b) ME as a function of ac
magnetic drive frequency. The insert shows ME for the L-L mode for 103 <f<105
Hz.
194
Second, the ac magnetic sensitivity was measured using an operational amplifier
based detection circuit.45 Helmholtz coils were used to apply a small ac magnetic
field along the long axis of the laminates by inputting an ac signal generated by the
lock-in amplifier at f=210 Hz. Small permanent dc magnets were attached to the ME
laminates along the long axis, in order to bias the laminates to the maximum value of
ME, as identified in the ME- Hdc data of Figure 6.2(a). Details about the detection
unit can be found in Ref
79
. The noise levels of the detection units and induced ac
voltage from the laminates were monitored in the time domain using an oscilloscope
(Agilent 54624A). Details of the setup and measurement can be found in Ref
94
.
Figure 6.3 (a) shows the noise levels of the L-L and bending mode ME sensors under
Hac=0 Oe. In this figure, one can see that the peak-to-peak value of the noise for the
L-L mode sensor was about 25 mV, which was smaller than that of the bending value
of 80 mV. An applied Hac was then modulated to keep the peak-to-peak value of the
output voltage constant at about 50 mV for the L-L and 160 mV for the bending
mode sensors: which corresponded in both cases to a constant signal-to-noise ratio of
SNR=2. This was done in order to compare the ac magnetic field sensitivities for
different laminates under the same condition. Figure 6.3 (b) shows the ac magnetic
sensitivity at 210 Hz. In this figure, one can see that the ac magnetic field sensitivity
for the bending mode was about 0.05 nT at 210 Hz, which was about a factor of 10×
lower than that of the L-L mode at the same frequency.
195
Figure 6.3 (a) Noise levels for the L-L and bending mode sensors; and (b) ME output
voltage as a function of time for the L-L and bending mode sensors. The
corresponding peak-to-peak ac field sensitivities are listed in the figures.
196
Finally, the equivalent magnetic noise floors for both types of ME laminate
sensors were measured over the frequency range of 102<f<103 Hz. During the tests,
the ME sensors were placed in a magnetically shielded chamber in order to reject
environmental magnetic noise. A dynamic signal analyzer (SR-785) was used to
measure the noise power density of the ME sensors in V/√Hz. We then used the
following sensor transfer function to convert the noise floor in V/√Hz to that in
T/√Hz:
Conversion factor (V / T ) =
 ME ( pC /104 T )
gain of amplifier ( pC / V )
;
(6.1)
Noise floor (V / Hz )
Noise floor (T / Hz ) =
.
Conversion factor (V / T )
Over the frequency range of 102<f<103 Hz, the gain factor of the amplifier in V/pC
was 1 V/pC.79
Figure 6.4 shows the equivalent magnetic noise floor spectra for both L-L and
bending modes. In this figure, we can observe that the noise floor for the L-L mode
sensor was constant at about 5 pT/√Hz over the frequency range of 100 to 1000 Hz:
the constancy was due to the frequency independence of ME. In this same figure,
the magnetic noise floor for the bending mode sensor can be seen to depend
dramatically on frequency. In particular, near the FBR at 210 Hz, the noise floor was
decreased to 0.3 pT/√Hz: which was a direct consequence of the FBR enhanced ME.
Comparisons of the data in Fig.4 will show the magnetic noise floor of the bending
was decreased by (i) a factor ~100× at 210 Hz, relative to that of 1 Hz; and (ii) a
factor of ~20× at 210Hz, relative to the of the L-L mode at the same frequency. At
frequencies below the FBR, the noise floor of the bending mode was higher that of
197
the L-L by a factor of 4-5×. But at frequencies greater than the FBR, the noise floors
were nearly equivalent at a value of 5 pT/√Hz. These results may indicate that the
bending mode laminates are more sensitive to low frequency vibrations than the L-L
ones which are environmental noise sources. Nonetheless, due to the dramatic
increase in ME near the FBR, the signal-to-noise ratio was enhanced.
Figure 6.4 Equivalent magnetic noise spectra for the L-L and bending mode sensors
for 102< f <103 Hz.
198
6.2.2 Tunability of resonant frequency
The previous section described the dramatic low resonant frequency for
bi-layered ME composites, as well as how the sensitivity of ME magnetic sensor can
be improved by incorporating these composites.29 The benefit, however, is only
useful for a very narrow responsive frequency bandwidth, which limits their
potential applications. In order to apply resonant ME effect at various frequencies, a
number of approaches have been studied to tune the resonant frequency of ME
composites.32, 95, 96 In prior investigations, however, centain restrictive experimental
conditions were imposed in these studies, such as the use of double-side clamped
edges. Otherwise, the resonant ME coefficients may not be impressive and may limit
the performance of related device. Thus, strong resonant ME effect that can be easily
tuned is highly desirable.
In this section, we present a simple approach for tuning the resonant frequency
(fr) of Metglas/PZT bi-layer composites without losing the value of ME in any
significant way. Investigations show that bi-layered Metglas/PZT composites with
multi-push pull configuration have giant resonant ME coefficients of > 400 V/cm-Oe.
Moreover, by loading tip mass on two edges of the composites, the resonant
frequency of fr was shifted from 70 Hz to 220 Hz easily, which will enable the
design of devices working at various frequencies. A theoretical model for bi-layered
ME composites was developed to describe the resonant frequency tunability with tip
mass. The predicted results match the experimental data well.
Bi-layered ME composites have been fabricated following the similar process
described in the previous section. First, the shift in fr with tip mass weight was
199
measured using an impedance analyzer (Agilent 4294 A). Tip masses were added to
the two edges of the bi-layered composites, as shown in the insert of Figure 6.5 (a).
Commercial permanent magnets D41 with mass of 0.377 gram from K&J Magnetics
(USA) were used as the tip mass. Using small magnets can provide the tip mass and
the DC bias at the same time. Thus, there is no necessary to apply an external DC
magnetic field during measurement. Accordingly, the resonant frequency measured
by the impedance analyzer was a compositive effect of magnetomechanical
resonance (MMR) in Metglas and electromechanical resonance (EMR) in the
piezo-layers, as shown in Figure 6.5(a). One can see that the fundamental resonant
frequency was observed at f =215 Hz without loading of a tip mass. The value of fr
was then decreased to about 74 Hz by continuously adding more tip mass.
Next, the ME voltage coefficient ME for the bi-layered ME composites was
measured as a function of frequency. A lock-in amplifier was used to drive a pair of
Helmholtz coils, generating an ac magnetic field of Hac=0.1 Oe over a frequency
range of 1 Hz < f < 300 Hz. The induced voltage from the ME composites was
measured by the lock-in amplifier as well. In Figure 6.5 (b), one can see that the ME
resonant peak positions were well matched to those of the impedance peaks (Figure
6.5 (a)). The ME voltage coefficients reached values of ME ≥ 400 V/cm-Oe at fr =
215 Hz without tip mass, consistent with previous reports.29 The resonant peak
positions then exhibited significant tunability on loading with tip mass: shifting from
75 Hz to 215 Hz. Furthermore, ME was increased to 500 V/cm-Oe with 2 magnets
load, but decreased to 380 V/cm-Oe and 260 V/cm-Oe with 4 and 6 magnets load.
However, the values were still much larger than described in prior reports.95, 96
200
Figure 6.5 (a) Impedance spectra of Metglass/PZT bending laminates with various
tip masses; and (b) ME voltage coefficients for Metglas/PZT laminates as a function
of frequency with various tip masses. The insert is a schematic of the bending mode
laminates.
201
A theoretical model for ME bending mode laminates was then developed to
predict the behavior of the laminates. Figure 6.6 describes the model of the
bi-layered structure. To simplify the model, a 2-D bar was used to describe the
mechanical performance of the ME bi-layer structure. The x1-axis in Cartesian
coordinates is along the length direction of the bar, the x2-axis is directed across the
width, and the x3-axis is orthogonal to them. It was assumed that the piezoelectric
layers were polarized in the x1 direction and that a magnetic field was incident along
the same orientation. During the calculations, only small-amplitude oscillations of
the bi-layer were considered.
In our theoretical analysis, the following assumptions were made: (i) the length of
composites was notably larger than the thickness; (ii) the boundary conditions
between the two layers were ideal; (iii) linear elasticity could describe each layer; (iv)
the stains and displacements were small; and (v) the transverse shear stresses on the
top and bottom surfaces were zero. In addition, we assumed that Kirchoff’s
hypothesis was valid for all layers, i.e., the displacements in
and
directions
can be represented as:
w

u1 ( x1 , x3 )  u ( x1 )  x3
x1

u ( x , x )  w( x )
.
1
 3 1 3
(6.2)
The equations for the strain tensor S1m in the magnetostrictive layer (cubic
symmetry) and the strain tensor S1p in the piezoelectric one (  m symmetry) under a
magnetic field H1 and an electric field E1 were expressed as:
 S1m  m s11 mT1  m q11 m H1


p
p
p
p

 S1 p  s11 T1  d11 E1 ;
202
(6.3)
m
where
s11 and
p
s11 are the elastic compliance tensor components of the
magnetostrictive and piezoelectric layers, respectively; and
m
q11 and pd11 are the
piezomagnetic and piezoelectric coefficients.
Under the above mentioned assumptions, equations and free-free boundary
conditions with a concentrated mass on both ends of the bi-layer, we determined all
relevant fields: i.e., stress, strain, magnetic and electric fields. Finally, under the
open circuit condition of
L
D
1p
dx1  0 ;
(6.4)
L
where, D1p is the electric displacement. The ME voltage coefficient was determined
to be:
 ME 
m
hp
 tan(T L) 3  1
E1
q pd
sin h(B L)sin(B L)
  p 11 11
{ 0

}
H1
s1111 hp  hm  0  1 T L
2  2  1 B L[sin h(B L) cos(B L)  sin(B L) cos h(B L)]
 {1  K12  K12
sin h(B L)sin(B L)
1 tan(T L) 3 1
 (6.5)
}1
 0  1 T L
2  2  1 B L[sin h(B L) cos(B L)  sin(B L) cos h(B L)]
where, hm and hp are the thicknesses of the magnetostrictive and piezoelectric layers;
ρm and
ρp are the densities of these two layers. The other notations in (4) are given
by the following expressions:
 2
T 
A
; B 
 2
p
p
s11 hm
s h
; 0  m
;  1  m 11 ( m ) 2 ;
D
s11 hp
s11 hp
3
hp
hm
hm3
s11 hm 3
1 hp
 2  m ( ) ; A  p  m ; D  ( p  m );
s11 hp
s11
s11
3 s11
s11
p
  (  p hp   m hm )(1  m0 ); K12 
p
m
d112
; m0  c .
p
s11   0
mt
where, ω is angular frequency, mc is the tip mass and mt is the mass of ME
composites. The material parameters for Metglas and PZT are listed in Table 6.1.
203
,
Table 6.1 Materials parameters for Metglas, PZT used for theoretical modeling
m
ε11/ ε0
hp or hp
(10-6m)
2L
(m)
Width
(m)
ρm or ρp
(kg/m3)
50.3
…
66
0.06
0.01
7180
…
1750
180
0.06
0.01
5675
s11 or ps11
(10-12m2/N)
p
(10 C/N)
(10 m/A)
Metglasa)
10
…
PZTb)
15.3
400
Materials
d11
-12
m
q11
-9
a) Cited from Ref.97
b) Cited from Ref.98
The theoretical ME voltage coefficients for bi-layered Metglas/PZT composites
as function of frequency can be established using material parameters given in Table
6.1. Figure 6.6 (b) shows the simulation results of αME versus frequency for various
tip mass loadings. From this figure, one can see that the predictions from the model
were in very good agreement with the experimental observations in Figure 6.5 (b).
The value of fr was about 210 Hz without tip mass, which was quite closed to the
observed one. Furthermore, a huge resonant peak shift was predicted by the model,
whose values were comparable to the experimental data. Thus, our model can
provide reasonable estimated values and a sound basis for predicting further shifts
with additional increasing tip masses.
In summary, the resonant magnetoelectric (ME) effect in an unsymmetrical
bi-layered ME composites can be tuned simply by applying the active permanents:
Moreover, the actual measured and predicted results present similar resonant
frequency shifting behaviors for ME composites. Such greatly-tunable resonant
effect facilitate the design of ME composites for practical applications at various
frequency ranges.
204
Figure 6.6 (a) Theoretical model for magnetoelectric bi-layer laminates, and (b)
estimated ME voltage coefficients as a function of frequency.
205
6.3 Energy harvester
The use of ME composites can assist the establishing the relationship between
the magnetic field and the electric field. Therefore, they have potential in
applications designed to capture magnetic energy for electronic devices. In response,
this section describes the possible development of magnetic energy harvesters using
composites.
6.3.1 Multi-push pull ME harvester
Since ME composites can be used to harvest magnetic energy, ME-based sensor
units could be designed to be self-powered systems capable of very long deployment
times. Based on this relationship, the following investigation was conducted.
First, the harvested output power and voltage were measured. A lock-in
amplifier was used to generate a driving signal to a pair of Helmholtz coils that
generated a magnetic field at a frequency of f =25.5 kHz, which was the fundamental
longitudinal resonance frequency. A resistance decade box was directly connected to
the ME laminates as an electrical load, and the voltage across it was then measured
by an oscilloscope. Figure 6.7 shows the induced voltage as a function of load
resistance. It can be seen that the normalized voltage reached ~42 Vp.p./Oe at the
optimum Rload. Correspondingly, the maximum harvested power output was 8
mW/Oe under a 11 kohm load resistance.
206
Figure 6.7 Output voltage and power as a function of load resistance load for
Metglas/PMN-PT laminates at their fundamental resonance frequency.
207
Using this ME magnetic energy harvester, a circuit was setup to charge Nickel
Metal Hydride (NiMH) batteries which had a capacity of 330 mAh, as shown in
Figure 6.8(a). The charging circuit consisted of a full wave rectifier, capacitor and
battery to be charged. The voltage from the Metglas/PMN-PT laminate was first
converted to a DC output and subsequently stored on a super-capacitor. The voltage
used to charge the battery was in parallel with the capacitor.
At the beginning of the measurement, the battery was initially discharged by
connecting it to a resistor for 8 hours until the remaining voltage was below 1 volt,
and then was subsequently connected to the charging circuit. During the
measurements, an ac magnetic field (f =25.5 kHz) was generated by the H-coils
driven by a lock-in. The induced voltage from the ME laminates was rectified and
then used to power the batteries. The charging cycle is shown in Figure 4(b). From
this figure, one can see that it took 1.5 hours to charge the battery from <1 V to 3.2 V:
i.e., a 90% charging was achieved. These results demonstrate that Metglas/PMN-PT
laminates can be used in magnetic energy harvesters at their resonance frequency
range; these harvesters can then charge batteries to power the charge amplifier
detection circuits for low frequency ME magnetic sensors.
208
Figure 6.8 Illustration of ability to charge batteries of ME detection units by
magnetic energy harvesting: (a) experimental setup, and (b) testing results.
209
6.3.2 Bi-layered ME harvester
Based on this tunability of fr for bending mode laminates, a 60 Hz magnetic
field energy harvester was designed with a suitable tip mass. The ME voltage
coefficient was found to reach 274 V/cm-Oe at f = 60 Hz, as shown in Figure 6.9 (a).
The high coupling effect made it possible to more efficiently harvest stray 60 Hz
magnetic energy. The output power of the energy harvester was characterized. A
lock-in amplifier (SR 850) was used to generate a driving signal for a pair of
Helmholtz coils that generated a magnetic field at a frequency of f =60 Hz. A
resistance decade box was then directly connected to the ME laminates as an
electrical load, and the voltage across it was measured by an oscilloscope. Figure
6.9(b) shows the output voltage and power as a function of load resistance Rload. It
can be seen that the normalized voltage reached ~13 Vrms/Oe at an optimum Rload.
Correspondingly, the maximum harvested power output was 16×10-6 W/Oe under
Rload =6 Mohm.
210
Figure 6.9 (a) ME voltage coefficient of 60 Hz magnetic energy harvester as a
function of AC magnetic drive frequency; and (b) output voltage and power as a
function of resistance load at the bending mode resonance frequency.
211
Finally, we used our energy harvester to capture 60 Hz magnetic energy in an
open laboratory setting. Figure 6.10 (a) shows a photo of the harvesting system and
source. A power cable was placed across the harvester which generated a 60 Hz
magnetic field due to a flowing current. Figure 6.10 (b) shows the output voltage
from the harvester in the time domain when current was flowing through the cable.
The output voltage reached 80 mV under open circuit conditions. The period of the
signal can be seen to be 16.7 ms, corresponding to 60 Hz. Thus, this test confirmed
that the harvester was able to capture 60 Hz magnetic energy from an ambient
environment and convert it to useable electric energy.
The bi-layered laminated composites have been demonstrated to be used to
harvest 60 Hz electromagnetic energy. Presently, the optimized output power for this
harvester can reach 16 μW/Oe with a 6 Mohm resistance load, with the power
density of ≥ 200 μW/cm3. The power density was found to be limited by the high
internal impedance of the ME laminates; however, it can be reduced by using a ME
laminates array configuration.66 Since ME harvesters could be integrated into power
source cables or instruments, they could have important applications for harvesting
60 Hz magnetic energy.
212
Figure 6.10 Demonstration of ability to capture 60 Hz electromagnetic energy by
using ME magnetic harvester: (a) photo of experimental setup, and (b) output
voltage signal in the time domain.
213
6.4 Frequency multiplier
ME composites with giant ME coefficients have been developed for potential
devices, such as magnetic sensors,71,
92
and data memory devices.37 Moreover,
potential frequency doubling devices based on ME composites have recently been
proposed.53, 54 We obtained PZT fibers from Smart Materials (Sarasota, FL) and
Metglas foils from Vitrovac Inc. (Hanau, Germany) to fabricate ME composites with
a multi-push pull configuration.94 The detailed process can be found in Ref
75
.
Finally, a 100-turn driving coil was wrapped around the composites directly, as
shown in the insert of Figure 1 (a).
To observe frequency multiplication, a commercial lock-in amplifier (SR-850)
was used to generate an ac input signal to the driving coils wrapped around the ME
composites, generating an ac magnetic field of Hac=0.2 Oe at a frequency of f =1
kHz. The amplitude of the Hac and the induced signal Vout from the ME composites
were then monitored by an oscilloscope (Agilent 54624A). It should be noted that
during this measurement, a dc magnetic bias was not applied to the composites. Thus,
the strain generated by Metglas was completely influenced by Hac. On applying a
sine wave signal of frequency f = 1 kHz to our ME composite frequency multiplier, a
steady output signal at a frequency of f = 2 kHz was monitored in the time domain,
as shown in Figure 6.11 (a). The results demonstrated that the frequency
multiplication in Metglas/PZT composites was significant as absence of dc magnetic
bias. Moreover, we characterized the influence of dc magnetic bias on frequency
multiplying behaviors. During measurements, the same ac magnetic field was
generated. Meanwhile, a dc magnetic bias Hdc was applied along the longitudinal
214
axis of the multiplier, and the induced voltage at a frequency of 2 kHz from the
composites was then measured by the lock-in amplifier. The results are shown in
Figure 6.11 (b), which indicates that the amplitude of Vout was affected by dc biases
greatly: reaching maximum values for Hdc ≈0 Oe, decreasing sharply at small dc
biases (-4 Oe< Hdc < 4 Oe), and subsequently increasing with further increasing. The
results indicated that even small dc biases can effectively tune the frequency
multiplication. In fact, by applying Hdc=1 Oe, no obvious frequency doubling effect
was observed in time domain, as shown in the insert of Figure 6.11 (b).
215
Figure 6.11 (a) Waveforms of driving ac magnetic field and output signal in time
domain; and (b) induced frequency doubling signal as a function of dc magnetic bias
Hdc. The insert shows schematic of frequency multiplier based on Metglas/PZT ME
composites.
216
Furthermore, frequency multiplication can be achieved over a wide bandwidth
below the electromechanical resonant frequency (fr ≈ 28 kHz), since the ME
coefficient is frequency independent.29 Considering the inductance of driving coils
changed at various frequencies, the modulated ac signals were applied to the coils to
generate the consistent ac magnetic fields of Hac=0.2 Oe. Figure 6.12 presents the
waveforms in the time domain of the output signal in response to an input signal of
various frequencies between 100 Hz and 2000 Hz. Frequency doubling of near
constant amplitude was found at all frequencies studied.
217
Figure 6.12 Waveforms of driving ac magnetic field and output signal in the time
domain at various frequencies: (a) 100 Hz, (b) 1 kHz, and (c) 2 kHz.
218
Prior studies have found that the frequency doubling can be turned off by
applying Hdc = 62 Oe.53 However, the physical means required to apply an external
field is not convenient with regards to packaging considerations. By improving
magnetic flux concentration, much smaller required dc biases can be achieved,
allowing adjustments in these important considerations.89 Here, our frequency
multiplier was designed to be modulated by the geomagnetic fields. Table 6.2
presents the parameters for local geomagnetic fields. It can be seen that the magnetic
field intensities along different directions have significant differences, which provide
an easy and natural switch for the frequency multiplier devices.
Table 6.2 Geomagnetic field intensity a) in the Virginia Tech area
Location
Lat: 37°13' 55''
North Component
East Component
Vertical Component
+North -South
+East -West
+Down -Up
21,240.4 nT
-3048.4 nT
46,756.1 nT
Lon: - 80°25' 17''
a) Cited from National Oceanic and Atmospheric Administration, United
State
Figure 6.13 shows the geomagnetic field operated as an on-off switch for
frequency multiplication. Part (a) presents a photo of the experimental setup, and the
insert shows the 3-D coordinate system for the test: the east direction is along the
x-axis, the north direction is along the y-axis, and the up direction is along the z-axis.
We characterized the frequency multiplication along different directions, including
the horizontal and vertical planes. In the horizontal plane, we defined the angle
between device and north direction as θ. And we defined the angle between device
and east direction as φ in vertical plane. During the test, an input Hac = 0.2 Oe at f =
219
1 kHz was applied to the device. The output signals at frequency of 1 kHz and 2 kHz
from multiplier were then monitored by dynamic signal analyzer (SR-785). Figures 3
(b) and 3 (c) show the results of the ratio of V2f/Vf as function of θ and φ,
respectively. In Figure 3 (b), one can see the ratio of V2f/Vf along east (θ=90˚) or
west (θ=270˚) directions reached maximum values (V2f/Vf >8). Thus, the waveform
in time domain shows the frequency multiplication, as shown in the insert of Figure
3 (b). This is the “ON” state. However, when the device was oriented along the north
or south direction, the ratio of the second to first harmonics V2f/Vf was approaching
1. Thus, there was no obvious frequency doubling behavior, which is the “OFF” state.
Accordingly, it can be seen that the device performed in the “OFF” state as
orientating at the range of -30˚ <θ < 30˚ and -150˚ <θ < 210˚, and performed in the
“ON” state as placing along rest of directions in the horizontal plane. Similarly, the
geomagnetic field effect in vertical plane (θ = 90˚) was also studied, as shown in
Figure 3 (c). Since the magnitude of geomagnetic field in vertical direction was
larger than the value in horizontal plane, the device was switched to “ON” state
along east (φ=0˚) or west (φ=180˚) direction. The slight tilt can tune it to the “OFF”
state. The insert shows the waveforms in time domain as φ=90˚. Thus, it can achieve
a transition from “ON” to “OFF” just by using the geomagnetic field bias. One could
simply develop logic between “ON” and “OFF” states by using a stage whose
orientation could be rotated by an actuator. Furthermore, a simple guidance device
based on frequency multiplication might be enabled which could lock onto the
largest component of Earth’s field, or to an object with the highest local magnetic
fields.
220
Figure 6.13 (a) Schematics of frequency multiplier under geomagnetic field; the ratio
of the induced second to first harmonic signals V2f/Vf along various directions: (b) in
horizontal plane, and (c) in vertical plane. The inserts show the waveforms in the
time domain.
221
Finally, the origin of frequency multiplication was studied. Previous
investigations have shown the ME effect in composites was achieved through a
magneto-elasto-electric interaction mediated at the interlayer boundaries.9 Thus,
induced voltage from PZT layer was directly dependent on strain transferred from
Metglas layer.53,
99
To understand the frequency multiplication in Metglas/PZT
composites, we studied the effective magnetostriction coefficient (λ) as function of
dc magnetic field (Hdc). The magnetostriction influenced by Hdc was characterized
by a bridge module BCM-1 (Omega: Stamford, CT, USA). Figure 6.14 shows the
magnetostriction and effective linear piezomagnetic coefficients. One can see that
the magnetostriction was independent on the direction of the applied Hdc but
dependent on its amplitude. During the above measurements, for Hdc = 0 Oe, the
magnetostriction was affected by the applied Hac. In response to a sine wave, both
positive and negative input signals generated a strain with the same direction: thus,
the induced strain had a doubled frequency multiplication. Accordingly, the output
signal from the PZT layer affected by this strain has a significant second harmonic
component. This can explain why the device when oriented along the east direction
had significant frequency multiplication. On the other hand, the geomagnetic field
intensity along the up direction is able to reach 46,000 nT (0.46 Oe): at which the
effective linear piezomagnetic coefficient begins to become larger. Thus, when
oriented along the north direction, the first harmonic was increased; however, the
waveform exhibited significant distortion from a sine wave (see insert in Figure6.13
(c)).
222
In summary, a geomagnetic field tuned frequency multiplication has been
studied based on Metglas/PZT tri-layered ME composites. The steady frequency
multiplication arises when operated under low dc magnetic biases. The geomagnetic
field can serve as a switch to control this multiplication between “ON” and “OFF”
thresholds. Thus, there are potential unique applications with respect to guidance and
logic.
Figure 6.14 Magnetostriction and effective linear piezomagnetic coefficient for the
Metglas/PZT ME composites.
223
6.5 Summary of this section
In this section, one bi-layered bending mode structure was proposed for
Metglas/Piezo-fiber ME composites. The completely different resonant effect
associated with these materials allows us to design sensors capable of working in
much lower frequency ranges with higher sensitivity compared to conventional
structures. Meanwhile, the resonant frequency can be tuned by simply applying the
active tip mass.
In addition to the magnetic sensor, two other devices were investigated: (1) a
magnetic energy harvester capable of charging a battery under resonant frequency;
(2) one 60 Hz magnetic sensor designed to harvest the magnetic energy from
instruments; and (3) frequency multiplication effect in ME composites is greatly
dependent on the geomagnetic field. Based on these results, possible applications
include the development of a frequency multiplier and/or geomagnetic guidance
devices can be developed.
224
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CCXXVIII
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