northeastern university graduate school of engineering1297/... · northeastern university ....

Approval Record

NORTHEASTERN UNIVERSITY

Graduate School of Engineering

Thesis Title: Dynamic Magnetostrictive Response of Heterostructural

Magnetoelectric Magnetic Field Sensors. Author: Scott Matthew Gillette Department: Electrical and Computer Engineering Approved for Thesis Requirement of the Master of Science Degree _______________________________________ _________ Thesis Adviser: Vincent Harris Date _______________________________________ _________ Thesis Reader: Carmine Vittoria Date _______________________________________ _________ Thesis Reader: Yajie Chen Date _______________________________________ _________ Thesis Reader: Anton Geiler Date _______________________________________ _________ Department Chair: Date Graduate School Notified of Acceptance: _______________________________________ _________ Director of the Graduate School: Yaman Yener Date

Dynamic Magnetostrictive Response of Heterostructural Magnetoelectric Magnetic Field Sensors.

A Thesis Presented

by

Scott Matthew Gillette

to

The Department of Electrical and Computer Engineering

in partial fulfillment of the requirements for the degree of

Master of Science

in

Electrical Engineering

in the field of

Electromagnetics, Plasma, and Optics

Northeastern University Boston, Massachusetts

April, 2011

Abstract

Magnetoelectric (ME) heterostructural laminate composites have recently demonstrated

high sensitivity room temperature operation in magnetic field sensing applications.

Traditionally, a static (dc) magnetic field is applied to these sensors to enable peak

magnetostriction. In this thesis, the non-linear nature of the magnetostrictive response of a ME

heterostructure is utilized, by applying a modulation magnetic field, to demonstrate a peak

improvement by a factor of 11.62x in sensitivity and by 57.43 dB in 0-Hz signal-to-noise ratio of

a sensor consisting of a longitudinally magnetized and transversely poled lamination of

Metglas/PZT/Metglas layers in comparison with a conventional dc biased configuration. The ME

sensor modulated by an AC magnetic field tuned to stimulate an electro-magneto-mechanical

resonance further exhibits enhanced environmental noise immunity, 1/f noise mitigation, and

does not require a dc magnetic bias field. Combined, these advantages hold promise for the

development of miniature ME sensor elements for size- and weight-sensitive applications.

i

Acknowledgements

I begin by thanking my advisor, Professor Vince Harris, for giving me the opportunity to

work at Northeastern University’s Center for Microwave Magnetic Materials and Integrated

Circuits for the past two years. He has generously shared his time and knowledge to guide me

through a challenging, invaluably rewarding M.S. program. Thank you!

I extend a thank you to Carmine Vittoria and Yajie Chen for their help and

encouragement during the past two years.

I thank Anton Geiler for acting as a mentor and for providing his expertise on numerous

research efforts.

I thank Carmine Carosella and Dwight Viehland for providing the magnetoelectric

magnetic field sensors.

Finally, I thank all of my colleagues, my family, friends and my fiancée, Steph, for their

support and encouragement. Thank you all very much.

ii

Table of Contents

Abstract ............................................................................................................................................ i

Acknowledgements ......................................................................................................................... ii

Table of Contents ........................................................................................................................... iii

Table of Figures .............................................................................................................................. v

Table of Tables .............................................................................................................................. ix

Chapter 1. Introduction ................................................................................................................... 1

1.1. Introduction to Thesis ................................................................................................................... 1

1.2. Phenomena Background ............................................................................................................... 2

1.3. The Magnetoelectric Effect ......................................................................................................... 11

1.4. Strain Coupled Magnetoelectric Composites .............................................................................. 14

1.5. ME Laminate Composites as Magnetic Field Sensors ................................................................ 21

Chapter 2. Conventional DC Operation ........................................................................................ 27

2.1. Introduction and Theory.................................................................................................................. 27

2.2. Experimental Setup ......................................................................................................................... 29

2.2.1. DC Biasing Method Equipment List ........................................................................................ 29

2.2.2. DC Biasing Method Block Diagram and Equipment Overview .............................................. 30

2.2.3. DC Biasing Method Experimental Procedure .......................................................................... 35

2.3. Results and Analysis ....................................................................................................................... 37

2.3.1. Sensor 1 Results ....................................................................................................................... 39

2.3.2. Sensor 2 Results ....................................................................................................................... 43

2.4. Conclusion ...................................................................................................................................... 47

Chapter 3. Modulation Sensing Technique ................................................................................... 48

3.1. Introduction and Theory.................................................................................................................. 48

3.1.1. Motivation ................................................................................................................................ 48

3.1.2. Relationship Between Strain and Applied Magnetic Field. ..................................................... 49

3.1.3. Mathematical Theory of Modulation Sensing Technique. ....................................................... 53

3.2. Experimental Setup ......................................................................................................................... 59

3.2.1. Modulated Sensing Technique Equipment List ....................................................................... 59

iii

3.2.2. Modulated Sensing Technique Block Diagram and Equipment Overview ............................. 61

3.2.3. Modulated Sensing Technique Experimental Procedure ......................................................... 64

3.2.4. Noise Study and Resulting Experimental Setup Modifications ............................................... 68

3.3. Results and Analysis ....................................................................................................................... 74

3.3.1. Sensor 1 Results ....................................................................................................................... 75

3.3.2. Sensor 2 Results ....................................................................................................................... 80

3.4. Conclusion ...................................................................................................................................... 84

Chapter 4. Conclusion ................................................................................................................... 85

4.1. Future Research Plans ..................................................................................................................... 87

Appendix ....................................................................................................................................... 89

A.1. Example Data File ........................................................................................................................... 89

A.2. Matlab Code – DC Biasing Method ................................................................................................ 90

A.3. Matlab Code – Modulated Sensing Technique ............................................................................... 95

References ................................................................................................................................... 101

iv

Table of Figures

Figure 1: Magnetic field density vs. applied magnetic field hysteresis loop for a polycrystalline slab of ferromagnetic Yttrium Iron Garnet measured at room temperature using CM3IC’s vibrating sample magnetometer. .................................................................... 3

Figure 2: Charge, representing polarization vs. electric field hysteresis loop for a ferroelectric Rochelle salt crystal at 23º C and a relative humidity of 30%. This P-E loop2 demonstrates the first measurement of ferroelectricity and proved the existence of the ferroelectric phenomenon............................................................................................... 5

Figure 3: Piezoelectric strain response as a function of applied electric field for two different aspect ratios of thin film Lead Zirconate Titanate (PZT) substrates. ε33 indicates that both applied electric field and measured strain were in the Z-axis of the substrate. ..... 7

Figure 4: Magnetization and strain for TERFENOL-D as a function of applied magnetic field. The derivative of magnetostriction is plotted with the dashed line. .............................. 8

Figure 5: a) A commercial piezoelectric microphone guitar pickup fabricated by Artec. b) A commercial piezoelectric precision actuator capable of micron resolution manufactured by Physik Instruments. .......................................................................... 10

Figure 6: a) A magnetostrictive audio transducer that allows a surface, such as a table, wall, or window, to act as a speaker. This commercially available device uses the magnetostrictive material TERFENOL-D and is fabricated by FeONIC. b) A commercial magnetostrictive linear position sensor, with micron resolution, produced by MTS Sensors. .......................................................................................................... 10

Figure 7: Direct interactions between stress (σ) and strain ( ), electric field (E) and polarization (P), and magnetic field (H) and magnetization (M), are illustrated with the red, yellow, and blue arrows, respectively. In a single phase multiferroic magnetoelectric material (green arrows), electric field is directly coupled to magnetic field. In many multiferroic magnetoelectric devices, strain-coupling (black arrows) between magnetostrictive and piezoelectric phases provides the magnetoelectric effect. ......... 11

Figure 8: a) A PZT/Metglas multiferroic magnetostrictive composite, mounted to a Mylar slab, fabricated by Bolin Hu at Northeastern University's CM3IC. This image shows the leads attached for measuring the magnetoelectric effect. b) Cross-sectional view of the PZT/Metglas composite fabricated through pulse laser deposition of a PZT target onto a polished Metglas sheet. Not drawn to scale. ..................................................... 14

Figure 9: a) A Metglas/PZT/Metglas multiferroic magnetostrictive laminate provided by Carmine Carousella, mounted to a Teflon slab. The dime is provided for size reference. b) Cross-sectional view of the Metglas/PZT/Metglas heterostructure. The

v

Metglas strains under an applied magnetic field causing a strain-induced electric field transverse to the PZT. Not drawn to scale. ................................................................. 15

Figure 10: Magnetoelectric multilayer fabricated through epitaxial growth of NiFe2O4 (NFO) on BaTiO3 (BTO) on a SrTiO3 (STO) substrate. The interfaces are emphasized using horizontal lines. ............................................................................................................ 16

Figure 11: ME coupling coefficient of a heterostructural Metglas/polyvinylidene-flouride magnetoelectric laminate composite magnetic field sensor. ........................................ 20

Figure 12: Metglas/PZT/Metglas laminated heterostructural composite, provided by Carmine Carousella, held by tweezers to enable resonance bending modes during testing. Length, height, and thickness dimensions are indicated. ............................................. 23

Figure 13: Metglas/Poled-PZT/Metglas laminated heterostructural composite with interdigitated electrodes, provided by Dwight Viehland. Length, height, and thickness (at two locations along the length) dimensions are indicated. ................................................. 24

Figure 14: D31 and D33 mode operation of piezoelectric PZT. For the D31 mode, a longitudinally applied strain results in a transversely generated voltage response. For the D33 mode, a longitudinally applied strain results in a longitudinally generated voltage response. Directions 3 and 1 are denoted on the axis. ..................................... 25

Figure 15: Example of an interdigitated electrode geometry. Interdigitated electrodes are typically used in ME laminates where the piezoelectric phase is to be operated in a D33 mode, as exemplified by Sensor 2. ....................................................................... 26

Figure 16: Magnetostriction of Metglas shown on +-1000 Oe scale (left) and a +-75 Oe scale (right) to exhibit a peak magnetostriction of approximately 27.5 ppm and a maximum in slope (dλ/dH) at 40 Oe. ............................................................................................ 28

Figure 17: Slope of Metglas magnetostriction curve exhibiting a maximum at approximately 40 Oe. ................................................................................................................................ 28

Figure 18: DC biasing method experimental setup. The numbers correspond to the numbered items in the equipment list. The BNC coaxial cables, clip leads, 3.5” floppy disk, and the LakeShore Model 4060 Zero Gauss Chamber are not numbered in figure. .......... 30

Figure 19: Block diagram of the experimental setup for the DC biasing method. ....................... 31

Figure 20: The sensor mounting apparatus consists of a table top vice grip and a set of tweezers fabricated from non-magnetic materials. It is shown positioning a sensor inside the dual Helmholtz coils. ................................................................................................... 34

Figure 21: Signal-to-noise ratio as a function of applied magnetic field for Sensor 1. ............... 39

Figure 22: Sensitivity as a function of applied magnetic field for Sensor 1. ................................ 39

Figure 23: 0-Hz noise floor as a function of applied magnetic field for Sensor 1. ....................... 40

vi

Figure 24: Magnetic Spectral Density with respect to applied field for Sensor 1. X-axis is of log scale. ............................................................................................................................. 41

Figure 25: Magnetic Spectral Density with respect to applied field for Sensor 1. X-axis is of linear scale. ................................................................................................................... 42

Figure 26: Signal-to-noise ratio as a function of applied magnetic field for Sensor 2. ................ 43

Figure 27: Sensitivity as a function of applied magnetic field for Sensor 2. ................................ 43

Figure 28: 0-Hz noise floor as a function of applied magnetic field for Sensor 2. ....................... 44

Figure 29: Magnetic Spectral Density with respect to applied field for Sensor 2. X-axis is of log scale. ............................................................................................................................. 45

Figure 30: Magnetic Spectral Density with respect to applied field for Sensor 2. X-axis is of linear scale. ................................................................................................................... 46

Figure 31: (a) Magnetostriction in Metglas. (b) Slope of magnetostriction (dλ/dH). (c) Overlay of Livingston's model of coherent rotation of magnetization with the magnetostriction of Metglas for low amplitudes of applied magnetic field. ............................................... 51

Figure 32: (a) 58 KHz reference modulation magnetic field as sensed by Sensor 1. (b) 200 Hz test field modulated with the 58 KHz reference modulation field as sensed by Sensor 1. Part (b) indicates that the total applied H term is indeed squared. .......................... 52

Figure 33: Amplitude of the modulation field as a function of the detected 25 Hz test signal amplitude. This plot demonstrates that Hmod acts as a linear gain factor. ................. 59

Figure 34: Modulated sensing technique experimental setup. The numbers correspond to the numbered items in the equipment list. The BNC coaxial cables, clip leads, 3.5” floppy disk, LakeShore Model 4060 Zero Gauss Chamber, and variable capacitor bank are not numbered in figure. ................................................................................................ 61

Figure 35: Block diagram of the experimental setup for the modulated sensing technique. ....... 62

Figure 36: Voltage spectral density measurements captured of the lock-in amplifier output, representing the instruments electronic noise, compared with VSD measurements of Sensor 2. Numbers 1-4 represent capture number where each capture consists of 500 linearly averaged sweeps.............................................................................................. 70

Figure 37: Voltage spectral density measurements captured of the lock-in amplifier output, representing the instruments electronic noise, compared with VSD measurements of Sensor 1. Numbers 1-4 represent capture number where each capture consists of 500 linearly averaged sweeps.............................................................................................. 71

Figure 38: Voltage spectral density measurements of 4 configurations showing contributions to the noise floor. The output of the lock-in amplifier is transmitted to the digital spectrum analyzer for each configuration. The modulated sensing technique with a 5

vii

KHz modulation frequency and 200 Hz test signal is shown in blue. The green trace was measured from a setup with 5 KHz modulation field and no test field. The red trace was measured from a setup with no modulation field and a 200 KHz test field. The teal trace was measured from a setup with no input and represents the lock-in amplifiers instrumental electronic noise floor. ............................................................. 73

Figure 39: Signal-to-noise ratio as a function of modulation frequency for Sensor 1. ................. 75

Figure 40: Sensitivity ratio as a function of modulation frequency for Sensor 1. ........................ 76

Figure 41: 0-Hz noise floor as a function of modulation frequency for Sensor 1. ....................... 76

Figure 42: Magnetic Spectral Density with respect to modulation frequency. X-axis is of log scale. ............................................................................................................................. 78

Figure 43: Magnetic Spectral Density with respect to modulation frequency. X-axis is of linear scale. ............................................................................................................................. 79

Figure 44: Signal-to-noise ratio as a function of modulation frequency for Sensor 2. ................. 80

Figure 45: Sensitivity as a function of modulation frequency for Sensor 2. ................................ 80

Figure 46: 0-Hz noise floor as a function of modulation frequency for Sensor 2. ....................... 81

Figure 47: Magnetic Spectral Density with respect to modulation frequency. X-axis is of log scale. ............................................................................................................................. 82

Figure 48: Magnetic Spectral Density with respect to modulation frequency. X-axis is of linear scale. ............................................................................................................................. 83

Figure 49: Full comparison between DC biasing method and modulation sensing technique. ... 85

viii

ix

Table of Tables

Table 1: Piezoelectric Material Properties. ................................................................................... 18

Table 2: Magnetostrictive Material Properties. ............................................................................ 19

Table 3: DC Biasing Method: Peak Values of SNR, Sensitivity and Noise Floor for Sensor 1... 40

Table 4: DC Biasing Method: Peak Values of SNR, Sensitivity and Noise Floor for Sensor 2... 44

Table 5: Modulation Sensing Technique: Peak Values of SNR, Sensitivity and Noise Floor for Sensor 1. ....................................................................................................................... 77

Table 6: Modulation Sensing Technique: Peak Values of SNR, Sensitivity and Noise Floor for Sensor 2. ....................................................................................................................... 81

Table 7: Comparison of DC Biasing Method to Modulated Sensing Technique. ........................ 86

Chapter 1. Introduction

1.1. Introduction to Thesis

The research presented in this thesis focuses on the use of multiferroic magnetoelectric

laminates as magnetic field sensors with a strong focus on the development of a modulation

sensing technique for use with these sensors. The newly developed modulation sensing

technique exhibits greater signal-to-noise ratio (SNR), higher sensitivity, and a reduction in noise

floor compared to measurements made using the conventional static magnetic field biasing

method for experimentally identical environments. The modulated sensing technique also offers

improvements over the conventional static magnetic field biasing technique, herein referred to as

the “DC biasing method”, by providing superior noise mitigation and a reduction in low-

frequency 1/f noise. Presentation, results, analysis, and discussion of the modulated sensing

technique developed at Northeastern University’s Center for Microwave Magnetic Materials and

Integrated Circuits (CM3IC) are the primary topics being reported.

This thesis consists of four chapters that discuss the following topics. In Chapter 1 the

origin, operational phenomena, fabrication techniques, and applications of multiferroic (MF)

magnetoelectric (ME) devices are explained. In addition, a description of two state of the art

prototypes, used for making measurements in this thesis, is provided. In Chapter 2, the

conventional DC biasing method of MF ME laminates in a magnetic field sensing application is

explained and presented with measurements using this method captured at CM3IC. Chapter 3

explains the modulated sensing technique designed for use with MF ME laminates in a magnetic

field sensing application and presents its theory, development, and performance. Being the

1

primary focus of this thesis and offering the most value to the scientific community, Chapter 3

includes discussion of the evolution of the modulated sensing technique by detailing a noise floor

study and resulting modifications made to the experimental setup. Chapter 4 concludes this

thesis with a general overview of the research, its implications, and future work.

1.2. Phenomena Background

The phenomenon of ferromagnetism, which is described as the ability of a material to

exhibit net magnetic moment under the influence of an applied magnetic field, and its analogue

phenomenon of ferroelectricity, which is described as the ability of a material to exhibit electric

polarization under the influence of an applied electric field, have been widely investigated since

their discoveries in ancient times1 and in 19202, respectively. According to Chikazumi,

ferromagnetism was first discovered when a shepherd’s staff, containing iron, experienced an

attractive force when placed nearby a certain type of stone. This discovery, representing

mankind’s initial conscious encounter with a magnetic force was believed to occur in Asia

Minor, in either Magnesia, Macedonia or in Magnesia, Ionia whose location is speculated to lend

its name to the origin of the word “magnetism”. One of the first applications utilizing

magnetism came in the form of a compass where splinters of the magnetic stone, known at the

time as loadstones, were used to determine direction due to the stone’s ability to align itself with

Earth’s magnetic poles1. In present day, the phenomenon of ferromagnetism is a widely studied

topic in academia3,4,5,6 and numerous applications utilizing ferromagnetic materials, such as

electronic motors, generators, inductors, transformers, hard drives, etc. surround our daily life.

2

Ferromagnetic materials (and ferrimagnetic materials) possess long range magnetic

ordering where magnetic domains are aligned in a manner such that the bulk material exhibits a

net magnetic moment. Ferromagnetic materials are typically quantified in the form of a B-H

loop, as shown in Figure 1, where magnetism (magnetic flux density) is plotted as a function of

applied magnetic field.

Figure 1: Magnetic field density vs. applied magnetic field hysteresis loop for a polycrystalline slab of ferromagnetic Yttrium Iron Garnet measured at room temperature using CM3IC’s vibrating sample magnetometer.

As the applied magnetic field amplitude increases, magnetic domains increasingly align

until they become fully oriented resulting in saturation of the magnetic field density. The

permeability of a ferromagnetic material is responsible for this nonlinear dependence to applied

3

magnetic field H. Equation (1.1) describes the relationship between magnetic field density B,

permeability μ, magnetic field H, and magnetization M7.

(1.1)

For materials with weak magnetic ordering, permeability will linearly relate B to H.

However, for ferromagnetic materials, permeability is a complex non-linear relationship. Many

ferromagnetic materials are characterized by non-linear permeability exhibiting time-dependence

resulting in a B H loop with hysteretic nature as seen in Figure 1.

Ferromagnetic materials may sometimes be known as “hard” magnetic materials where a

very large applied magnetic field is required to fully magnetize or saturate the material. Hard

magnetic materials exhibit high coercivity and high remanence, making them useful in

permanent magnet applications, among many. Ferrimagnetic materials may be known as “soft”

magnetic materials due to their ability to be magnetically saturated under low applied magnetic

fields. Soft magnets exhibit low coercivity, and are useful in switched electromagnet

applications, among many. Metglas is an example of a soft magnetic material and is used in the

sensors that are investigated in this thesis due to the material’s ability to become magnetically

saturated under relatively low applied magnetic fields.

The theorized phenomenon of ferroelectricity was proven to exist by J. Valasek at the

University of Minnesota in 1920 when he demonstrated that, like the hysteretic nature of

magnetization in iron, a hysteretic electric polarization exists in Rochelle salt crystals under

switched values of applied electric field2 as shown in

4

Figure 2. Permittivity in a ferroelectric material exhibits a nonlinear dependence on

applied electric field, E, and time, resulting in hysteretic behavior.

Figure 2: Charge, representing polarization vs. electric field hysteresis loop for a ferroelectric Rochelle salt crystal at 23º C and a relative humidity of 30%. This P-E loop2 demonstrates the first measurement of ferroelectricity and proved the existence of the ferroelectric phenomenon.

This discovery has spurred vast new fields of research including tunable ferroelectric

capacitors8, where the permittivity of the dielectric spacing in a capacitor can be tuned by

applying a DC voltage, and ferroelectric tunnel field effect transistors capable of unpowered

memory state-retention up to a few minutes9.

5

Ferroelectric materials behave in an analogous manner to ferromagnetic materials in that

electric dipoles will align under the influence of an applied electric field. Ferroelectrics will also

exhibit continuously increasing dipole alignment under increasing amplitudes of applied electric

field until the dipoles become fully aligned, representing a state of saturation. The relationship

between applied electric field E, electric flux density D, and polarization P is described through

equation (1.2)7.

(1.2)

Ferroelectricity and ferromagnetism enable the manipulation of polarization and

magnetization, through the application of respective E and H fields. There also exist the

phenomena of piezoelectricity and magnetostriction in which polarization and magnetization,

respectively, are tightly coupled to the material’s atomic lattice. Atomic lattice coupling with

polarization and magnetization also exists in the forms of electrostriction and piezomagnetism;

however, these phenomena are not discussed in this thesis.

Piezoelectricity is defined as the ability of a material to exhibit coupling between

polarization and strain, therefore enabling a coupling between strain and applied electric field. A

piezoelectric material will undergo bulk dimensional deformation correlating to an applied

electric field as demonstrated by the butterfly-shaped piezoelectric response curve of thin film

lead zircon titanate (PZT) in Figure 3.

6

Figure 3: Piezoelectric strain response as a function of applied electric field for two different aspect ratios of thin film Lead Zirconate Titanate (PZT) substrates10. ε33 indicates that both applied electric field and measured strain were in the Z-axis of the substrate.

The general constitutive equations for a piezoelectric material, (1.3) and (1.4),

mathematically describe strain and electric displacement, respectively11.

(1.3)

(1.4)

7

The strain, is defined as the axial change in length divided by original length ∆ ⁄ .

The magnetic flux density is denoted by D and E is the applied electric field. Variables, and

represent the material’s remnant strain and polarization, respectively. The elastic compliance

tensor , the piezoelectric tensor , and the dielectric permittivity tensor are defined by

the material’s properties11.

Magnetostriction describes ferromagnetic materials with the ability to exhibit coupling

between magnetization and strain, thus providing a coupling of strain to applied magnetic field.

A magnetostrictive material will undergo bulk dimensional deformation correlating to an applied

magnetic field6 as demonstrated by the magnetostriction curve in Figure 4.

Figure 4: Magnetization and strain for TERFENOL-D as a function of applied magnetic field. The derivative of magnetostriction is plotted with the dashed line12.

8

The general constitutive equations for a magnetostrictive material, (1.5) and (1.6),

mathematically describe strain and magnetization, respectively13.

(1.5)

(1.6)

Here, strain equals the axial change in length divided by length ∆ ⁄ . The compliance

tensor is denoted by . The applied stress T is in units of force per unit area. The

magnetostrictive strain constant is d. The permeability tensor is denoted by . H is the applied

magnetic field and B is the magnetic flux density.

The strain coupling in both piezoelectric and magnetostrictive materials operates in a reverse

manner such that an applied strain will generate net polarization or magnetization, respectively.

The ability to manipulate the dimensions of a piezoelectric material by an applied electric field

and a magnetostrictive material by an applied magnetic field, or to generate respective electric

and magnetic fields by applying strain, has proven useful in numerous applications.

Piezoelectric materials are currently used in commercial devices such as instrument microphone

pickups or precision electrostatic actuators as shown in Figure 5. Magnetostrictive materials

may be found in commercial devices such as audio transducers and linear position sensors as

shown in Figure 6.

9

Figure 5: a) A commercial piezoelectric microphone guitar pickup fabricated by Artec14. b) A commercial piezoelectric precision actuator capable of micron resolution manufactured by Physik Instruments15.

Figure 6: a) A magnetostrictive audio transducer that allows a surface, such as a table, wall, or window, to act as a speaker. This commercially available device uses the magnetostrictive material TERFENOL-D and is fabricated by FeONIC16. b) A commercial magnetostrictive linear position sensor, with micron resolution, produced by MTS Sensors17.

10

1.3. The Magnetoelectric Effect

The magnetoelectric effect is defined as the ability to induce magnetization through an

applied electric field and/or to induce polarization through an applied magnetic field6. This effect

can be enabled due to direct coupling of electric field to magnetization, magnetic field to

polarization, polarization to magnetization, or indirectly via strain as illustrated in Figure 7.

Figure 7: Direct interactions between stress (σ) and strain ( ), electric field (E) and polarization (P), and magnetic field (H) and magnetization (M), are illustrated with the red, yellow, and blue arrows, respectively. In a single phase multiferroic magnetoelectric material (green arrows), electric field is directly coupled to magnetic field. In many multiferroic magnetoelectric devices, strain-coupling (black arrows) between magnetostrictive and piezoelectric phases provides the magnetoelectric effect18.

11

The direct magnetoelectric effect (DME) describes magnetic field induced polarization as

shown in equation (1.7).

(1.7)

The converse magnetoelectric effect (CME) describes electric field induced

magnetization as shown in equation (1.8)19.

(1.8)

The direct magnetoelectric coupling coefficient α, defined in units of ,

serves as the conventional figure of merit for quantifying the magnitude of the magnetoelectric

effect present in a magnetoelectric device.

The magnetoelectric effect may exist in single phase multiferroic materials that can be

both electrically and magnetically polarized, where the term “multiferroic” denotes a material

that exhibits two or more combinations of ferroic orders, such as ferroelectric and ferromagnetic

ordering19. The magnetoelectric effect may also be enabled by fabricating bulk combinations of

piezoelectric and magnetostrictive materials together in a strain-coupled manner, illustrated by

the black arrows in Figure 7. Few single phase multiferroic magnetoelectric materials exist that

exhibit useful magnitudes of magnetoelectric coupling, and if so, the coupling is typically

exhibited at very low temperatures making these materials impractical for engineering

problems20. Currently, strain-coupled magnetoelectric composites consisting of a bulk single

phase magnetostrictive material with a bulk single phase piezoelectric material have

demonstrated direct magnetoelectric coupling coefficients on the order of 100 ⁄ ,

12

which is several orders of magnitude higher than reported coefficients of single phase

multiferroic magnetoelectrics19. For this reason, strain-coupled magnetoelectric composites,

exhibiting large magnetoelectric coupling coefficients at room temperature hold great potential

for the development of applications utilizing magnetoelectric effect.

In composites of magnetostrictive and piezoelectric materials the direct magnetoelectric

effect is the result of the product of the respective magnetomechanical and electromechanical

strain interaction as described in equation (1.9)19.

(1.9)

Similarly, the converse magnetoelectric effect is the product of each phase’s strain

interact s d in equation (1ion as de cribe .10).

1.10

Equations (1.9) and (1.10) indicate that strain transfer is responsible for the generation of

either the DME or CME. For instance, if a magnetoelectric composite is exposed to a magnetic

field represented by the numerator in the first term of (1.9), the magnetostrictive phase will

deform due to induced strain, represented by the denominator of the first term in (1.9). The

magnetostrictively induced strain will transfer to the piezoelectric phase, causing a mechanical

deformation, represented by the numerator of the second term in (1.9), and generate a separation

of charge resulting in polarization, as represented by the denominator of the second term in (1.9).

13

This research presented in this thesis utilizes laminated composites that obtain the

magnetoelectric effect through strain coupling between separate bulk magnetostrictive and

piezoelectric materials. For more information on single phase multiferroic magnetoelectric

materials that exhibit direct coupling between constituents, the reader is encouraged to seek out

related literature6, 21, 22, 23, 24.

1.4. Strain Coupled Magnetoelectric Composites

Optimal strain coupling requires intimate contact between the magnetostrictive and

piezoelectric phases which is typically achieved through direct deposition, lamination, or

epitaxial growth fabrication techniques as shown by the examples in Figure 8, Figure 9, and Figure

10, respectively.

Figure 8: a) A PZT/Metglas multiferroic magnetostrictive composite, mounted to a Mylar slab, fabricated by Bolin Hu at Northeastern University's CM3IC. This image shows the leads attached for measuring the magnetoelectric effect. b) Cross-sectional view of the PZT/Metglas composite fabricated through pulse laser deposition of a PZT target onto a polished Metglas sheet. Not drawn to scale.

14

Direct deposition magnetoelectric composite devices exhibit a distinct interface between

piezoelectric and magnetostrictive phases which enables direct strain coupling. These

composites are typically made through chemical vapor deposition or pulsed laser deposition of a

magnetostrictive phase onto a piezoelectric phase (or vice-versa) and exhibit a thin-film on

substrate topology.

Figure 9: a) A Metglas/PZT/Metglas multiferroic magnetostrictive laminate provided by Carmine Carousella, mounted to a Teflon slab. The dime is provided for size reference. b) Cross-sectional view of the Metglas/PZT/Metglas heterostructure. The Metglas strains under an applied magnetic field causing a strain-induced electric field transverse to the PZT. Not drawn to scale.

A magnetoelectric laminate consists of two or more magnetostrictive and piezoelectric

phases bonded together using an adhesive that enables strain coupling. The adhesive plays an

important role in transferring strain between ferroic phases and its mechanical properties must be

considered. In addition, certain laminate topologies such as the one in Figure 9, require that the

15

adhesive is conductive, allowing the Metglas to serve the dual purposes of magnetostrictive

phase and electrodes. Magnetoelectric laminate composites are abundant in literature due to ease

of fabrication.

Figure 10: Magnetoelectric multilayer fabricated through epitaxial growth of NiFe2O4 (NFO) on BaTiO3 (BTO) on a SrTiO3 (STO) substrate25. The interfaces are emphasized using horizontal lines.

A magnetoelectric composite fabricated using epitaxial growth techniques exhibits

atomic lattice matching of magnetostrictive and piezoelectric phases. This intimate

crystallographic interface between phases results in favorable strain coupling. Epitaxially-grown

magnetoelectrics are not as common as laminates due to the complex fabrication process which

requires that each phase exhibits similarly sized crystal lattices. This requirement also limits the

combinations of compatible magnetostrictive and piezoelectric materials.

16

Strain coupled magnetoelectric composites can be described using the following

constituent equations, (1.11), (1.12), and (1.13), that relate magnetoelectric and piezoelectric

phases through elastic interaction19.

(1.11)

(1.12)

(1.13)

For equations (1.11), (1.12), and (1.13), σ, D, and B represent stress, electric

displacement, and magnetic induction, respectively. S, E, and H are the strain, electric field, and

magnetic field, respectively. Tensors c, e, q, ε, α, and μ, are the stiffness, piezoelectric

coefficient, piezomagnetic coefficient, dielectric constant, magnetoelectric coefficient, and

permeability, respectively, are determined by the choice of materials used in the composite. The

superscript T denotes the transpose of the tensor19.

Properties of several common piezoelectric and magnetostrictive materials used in

magnetoelectric composites are shown in Table 1, and Table 2, respectively26.

For Table 1, d31 and d33 represent piezoelectric constants, ε is the permittivity, Tc is the

Curie temperature, ρ is density, Qm is the mechanical quality factor, and k33 is the

electromechanical coupling factor.

17

The piezoelectric material PZT and magnetostrictive material Metglas have been widely

investigated in a heterostructural laminate composite topology26. PZT exhibits a relatively high

piezoelectric constant, resulting in higher polarization per input strain than BTO and PVDF. In

addition, PZT is abundant and inexpensive. Metglas exhibits relatively low magnetostriction,

however, it is easily saturated by low amplitude applied magnetic fields due to high permeability.

Unlike Terfenol-D that has a magnetostriction of 1400 parts per million and requires bias fields

on the order of 2500 Oe, Metglas exhibits 40 ppm magnetostriction at less than 10 Oe applied

bias magnetic field. The magnetoelectric laminate composites investigated in this thesis consist

of Metglas and PZT phases.

Table 1: Piezoelectric Material Properties.

BaTiO3 PZT-5 PZT-4 PZNPT PMNPT PVDF

d31(pC/N) -90 -175 -109 N/A 700 16.5

d33(pC/N) 191 400 300 N/A 2000 -33

ε 1700 1750 1350 7200 5000 10

Tc(ºC) 152 360 320 163 80 129

ρ(g/cm3) 6 7.7 7.6 8.2 7.8 1.78

Qm N/A 80 500 N/A N/A 4

k33 0.63 0.72 0.68 0.94 0.9-0.94 0.19

18

For Table 1, d31 and d33 represent piezoelectric constants, ε is the permittivity, Tc is the

Curie temperature, ρ is density, Qm is the mechanical quality factor, and k33 is the

electromechanical coupling factor.

Table 2: Magnetostrictive Material Properties.

NiFe2O4 Terfenol-D Fe-Ga Metglas 2605

λ(ppm) 27 -1400 200 40

μ 20 6-10 20 >40000

k33 N/A 0.44 N/A 0.37

Qm N/A N/A N/A 1000

ρ(g/cm3) 5.37 7.8 7.7 7.18

R(Ω-m) 1e6 5.8e-7 6e-7 1.3e-6

Tc(ºC) 535 N/A N/A 395

For Table 2, λ is the saturation magnetostriction, μ is the permeability, k33 is the

electromechanical coupling factor, Qm is the mechanical quality factor, ρ is density, R is

resistivity, and Tc is the Curie temperature26.

Of the three methods for fabricating strain coupled magnetoelectric devices, laminate

composites exhibit the largest sensitivity. Currently, Dr. Dwight Viehland, from the Department

of Material Science and Engineering at Virginia Polytechnic Institute, has demonstrated the

19

highest magnetoelectric coupling coefficient in a device fabricated by laminating together thin

layers of Metglas (25 microns) to polyvinylidene-flouride (28 microns)27. This device exhibits

an off-resonance ME sensitivity coefficient of approximately 7 V/cm-Oe corresponding to a 1

KHz AC input magnetic field and an 8 Oe magnetic bias field as shown in Figure 11 a). In Figure

11 b), an on-resonance ME sensitivity coefficient of 310 V/cm-Oe, corresponding to an electro-

magneto-mechanical mode stimulation frequency of approximately 50 KHz, is shown for an

applied static magnetic field of 8 Oe.

Figure 11: ME coupling coefficient of a heterostructural Metglas/polyvinylidene-flouride magnetoelectric laminate composite magnetic field sensor.

Although no commercial applications utilizing the magnetoelectric effect yet exist,

several proposed applications utilizing the relatively large magnetoelectric effect associated with

ME laminate composites are currently in research and development phases. These applications

20

include the development of tunable microwave devices, transformers, and magnetic field

sensors19. Presented in this thesis is an investigation of the use of magnetoelectric laminate

composites as magnetic field sensors.

1.5. ME Laminate Composites as Magnetic Field Sensors

Strain-coupled magnetoelectric laminate composites that exhibit large ME coupling

coefficients have emerged as promising candidates for the development of highly-sensitive

magnetic field sensors in recent years27. Key advantages of this technology include operation at

room temperature, low cost, and simple fabrication requirements. In addition, steadily increasing

magnetoelectric coefficient values potentially enable these devices to target highly-sensitive

magnetometer markets that include optically pumped cesium vapor magnetometers, spin-

exchange relaxation-free (SERF) atomic magnetometers, and superconducting quantum

interference devices (SQUID)28. As previously described, ME laminate composite magnetic

field sensors rely on a stress-mediated coupling between magnetostrictive and piezoelectric

phases in order to produce an output voltage in response to an applied magnetic field.

Magnetostrictive phases that have been utilized in the construction of ME sensors include

Terfenol-D, Metglas, and Galfenol intermetallic alloys, as referenced in Table 2, whereas the

piezoelectric phase is typically lead zirconate titanate (PZT) or lead magnesium niobate - lead

titanate (PMN-PT), as referenced in Table 1. The magnetoelectric effect is obtained through

laminating the aforementioned materials together such that under the influence of an applied

magnetic field, the magnetic phase is then either longitudinally or transversely magnetized and

the piezoelectric phase is longitudinally or transversely poled.

21

Two magnetoelectric laminated composite magnetic field sensors were provided for the

testing and comparison of conventional static applied magnetic field biasing with the novel

modulated sensing technique that employs an applied time varying magnetic field. The first

sensor, shown in Figure 12, is a laminated composite tri-layer heterostructure consisting of a

piezoelectric PZT film bonded between two magnetostrictive Metglas ribbons in a

Metglas/PZT/Metglas configuration, provided by Carmine Carousella. The

Metglas/PZT/Metglas topology allows for the Metglas to act as both magnetostrictive phase and

electrodes where charge can accumulate as the PZT phase undergoes strain. Leads were attached

to each Metglas ribbon allowing for voltage measurements. The dimensions of this

magnetoelectric laminate were measured to be 28.3 mm long by 2.0 mm wide by 0.2 mm thick.

Metglas ribbons are manufactured to be 1 mil thick, equal to 0.0254 millimeters. Therefore the

PZT film including the thickness of the lamination adhesive is calculated to be approximately

0.1492 mm thick, equal to 149.2 microns. This device is categorized as a longitudinally

magnetized, transversely poled magnetoelectric magnetic field sensor and is designed to exhibit

peak performance for sensing magnetic fields that interact parallel to its length. The magnetic

field sensor, pictured in Figure 12, is herein referred to as “Sensor 1”.

22

Figure 12: Metglas/PZT/Metglas laminated heterostructural composite, provided by Carmine Carousella, held by tweezers to enable resonance bending modes during testing. Length, height, and thickness dimensions are indicated.

The second sensor, shown in Figure 13, is a laminated composite tri-layer heterostructure

consisting of a poled piezoelectric PZT film bonded between two magnetostrictive Metglas

ribbons in a Metglas/Poled-PZT/Metglas topology. Instead of utilizing the Metglas phase as an

electrode, this sensor exhibits internal patterned interdigitated electrodes in contact with the

poled-PZT film separated by a distance of approximately 1mm. This magnetoelectric magnetic

field sensor is categorized as a longitudinally magnetized, longitudinally poled device and is

designed to exhibit peak performance for sensing magnetic fields that interact parallel to its

length. The dimensions of this magnetoelectric laminate were measured to be 80.4 mm long by

10.4 mm wide and exhibited a thickness of 0.4mm where PZT was sandwiched between

Metglas, and a thickness of 0.2 mm in the absence of a PZT layer at either end. This indicates

that four layers of Metglas (two layers laminated together per side of PZT) were used in total.

The approximate thickness of PZT, including lamination adhesive, is calculated to be 0.2 mm.

The Metglas layers were purposefully constructed to exhibit a length longer than that of the PZT

phase in order to maximize the magnetoelectric coefficient by straining the PZT in a more

23

uniform manner. Extensive optimization regarding number of Metglas layers, Metglas length,

and additional factors have been investigated29. This device was generously provided by Dwight

Viehland’s Materials Science group at Virginia Polytechnic Institute. The magnetic field sensor

pictured in Figure 13, is herein referred to as “Sensor 2”.

Figure 13: Metglas/Poled-PZT/Metglas laminated heterostructural composite with interdigitated electrodes, provided by Dwight Viehland. Length, height, and thickness (at two locations along the length) dimensions are indicated.

Sensor 1 and Sensor 2 are constructed of similar materials in the same layered laminate

topology; however, each sensor operates in a fundamentally different manner due to the

directionally dependent method of harvesting the piezoelectrically generated voltage response of

strained PZT. It is observed in Table 1 that the D33 piezoelectric coefficient is much greater

than the D31 coefficient for PZT of similar types. A diagram demonstrating the difference

between utilizing PZT in a D31 mode and a D33 mode is shown in Figure 1430.

24

Sensor 1 was fabricated to utilize the PZT in a D31 mode where a longitudinally applied

strain, coupled from magnetostrictively induced strain in the Metglas, results in a transversely

generated voltage response. Conveniently, use of a D31 mode enables Sensor 1 to utilize the

Metglas as electrodes on either side of the PZT film. Although the piezoelectric coefficient is

lower for ME sensors utilizing the D31 mode, the complexity of sensor construction is greatly

reduced.

Figure 14: D31 and D33 mode operation of piezoelectric PZT. For the D31 mode, a longitudinally applied strain results in a transversely generated voltage response. For the D33 mode, a longitudinally applied strain results in a longitudinally generated voltage response. Directions 3 and 1 are denoted on the axis.

Sensor 2 was fabricated to utilize the PZT in a D33 mode where a longitudinally applied

strain, coupled from magnetostrictively induced strain in the Metglas, results in a longitudinally

25

generated voltage response. In order to detect this voltage response an interdigitated pair of

electrodes, demonstrated by the geometry shown in Figure 15, was placed longitudinally on the

PZT, underneath the Metglas. Leads were then attached to exposed portions of the interdigitated

pair of electrodes for voltage measurements. By designing a ME magnetic field senor to utilize

the D33 sensing mode, the device benefits from a higher piezoelectric coefficient but increases

the complexity of sensor construction29.

Figure 15: Example of an interdigitated electrode geometry. Interdigitated electrodes are typically used in ME laminates where the piezoelectric phase is to be operated in a D33 mode, as exemplified by Sensor 2.

The following two chapters detail the use of both magnetoelectric laminate composites,

Sensor 1 and Sensor 2, in a magnetic field sensing application. In Chapter 2, each sensor is

characterized using the conventional method of biasing magnetoelectric magnetic field sensors

with an applied static (DC) magnetic field. In Chapter 3, each sensor is characterized using the

novel modulated sensing technique where an applied time varying (AC) magnetic field is used to

modulate each device. By using two sensors exhibiting different operational modes, dimensions,

magnetoelectric coefficient, and constructions, it is demonstrated that the modulated sensing

technique exhibits no preference to sensor type.

26

Chapter 2. Conventional DC Operation

2.1. Introduction and Theory

Strain-coupled magnetoelectric laminate composites have conventionally5,19 been biased

using an applied static magnetic field which enables optimal magnetostriction properties in the

magnetostrictive phase and provides a maximum output voltage in response to an input magnetic

field signal, herein defined as sensitivity (Volts/Oersted). Typically, these devices exhibit peak

sensitivity when the amplitude of the applied DC magnetic bias field corresponds with a

maximum in the slope (dλ/dH) of the magnetostriction curve for a magnetostrictive material.

When magnetically DC biased at this point, a superimposed magnetic field source signal will

cause the greatest percentage change in magnetostriction, and if coupled to a piezoelectric, will

induce a maximum voltage response. Static magnetic field biasing of the ME sensor can be

accomplished using permanent magnets or through the use of DC current driven electromagnets.

The term “DC”, meaning direct current, is used here to describe a static magnetic bias

field. Electromagnets, in the form of dual nesting Helmholtz coils, were utilized in the

experimental setup to generate all required magnetic fields. For generating a static magnetic

field, direct current (DC) was applied to the coils. For generating a time varying magnetic field,

alternating current (AC) was applied to the coils. This nomenclature is frequently used

throughout the thesis to describe static and time varying magnetic fields.

The provided ME laminate magnetic field sensors were both constructed using a Metglas

magnetostrictive phase. The magnetostriction in a similar sample of Metglas, shown in Figure

16, was measured to exhibit 0 ppm strain in the absence of an applied magnetic field and to non-

27

linearly saturate at a maximum strain of 27.5 ppm under a 200 Oe magnetic bias field. The

maximum dλ/dH, is observed to occur at approximately 40 Oe as demonstrated in Figure 17.

Figure 16: Magnetostriction of Metglas shown on +-1000 Oe scale (left) and a +-75 Oe scale (right) to exhibit a peak magnetostriction of approximately 27.5 ppm and a maximum in slope (dλ/dH) at 40 Oe.

Figure 17: Slope of Metglas magnetostriction curve exhibiting a maximum at approximately 40 Oe.

28

Metglas was chosen for use in these sensors due to its ability to be saturated using

relatively low amplitude DC magnetic bias fields. Both sensors were designed for potential

deployment in power-conscious applications where the generation of high amplitude magnetic

fields is impractical. Although the measured sample of Metglas differs slightly from the material

used in each ME laminate sensor, the notion of Metglas exhibiting magnetostrictive saturation

under relatively low magnetic fields is valid.

2.2. Experimental Setup

2.2.1. DC Biasing Method Equipment List

The following list of equipment was used to measure both Sensor 1 and Sensor 2 using

the conventional DC biasing method and is number coordinated with Figure 18:

1) Stanford Research Systems SR770 FFT Digital Spectrum Analyzer

2) Stanford Research Systems SR830 DSP Lock-in Amplifier

3) Sorensen DCR 80-12B Power Supply

4) LakeShore 421 Gaussmeter with MNT-4E04-VH Transverse AC Hall Probe

5) Dual nesting Helmholtz coil with 9 cm uniform field capability.

6) Non-magnetic sensor mounting apparatus

7) BNC coaxial cables and clip leads

8) 3.5 Inch Floppy Disk

9) LakeShore Model 4060 Zero Gauss Chamber

29

Figure 18: DC biasing method experimental setup. The numbers correspond to the numbered items in the equipment list. The BNC coaxial cables, clip leads, 3.5” floppy disk, and the LakeShore Model 4060 Zero Gauss Chamber are not numbered in figure.

2.2.2. DC Biasing Method Block Diagram and Equipment Overview

A block diagram of the experimental setup used to take DC biased measurements of

Sensor 1 and Sensor 2 is shown below in Figure 19. Signal flow direction is demonstrated using

red arrows.

30

Figure 19: Block diagram of the experimental setup for the DC biasing method.

The magnetoelectric sensors were connected to the input of a Stanford Research Systems

SR770 FFT digital spectrum analyzer which was configured to capture voltage spectral density

measurements (Vrms/√Hz) of sensor response to an applied magnetic test field. The magnetic

test field was generated by passing a 25 Hz alternating current signal from the SR770 source

output through Helmholtz coil set 1. The amplitude of the 25 Hz magnetic field was measured

using the MNT-4E04-VH transverse AC hall probe, which exhibits AC bandwidth from 10 Hz to

400 Hz, in conjunction with the LakeShore 421 gaussmeter set in AC Gauss RMS mode. The

31

AC magnetic test field was set to 25 Hz at 0.10 Gauss RMS, equal to 10-5 Tesla RMS in air, and

was held constant for the remainder of all measurements.

Generation of the DC biasing magnetic field was accomplished by passing a direct

current, generated by a Sorensen DCR 80-12B, through Helmholtz coil set 2. For precise,

constant control of the current, strapping of the Sorensen DCR 80-12B was reconfigured to

enable signal programming voltage mode as described in section 3.2.4 of the instrument user

manual. In this mode, the full-scale voltage output of the Sorensen DCR 80-12B can be

programmed using a 0-10VDC input signal capable of sourcing at least 1 mA. The Aux output 1

of the SR830 DSP lock-in amplifier, which can provide -10.5 VDC to +10.5 VDC at an output

current up to 10 mA, was used to control the voltage output of the Sorensen DCR 80-12B with

high precision.

The dual nesting set of Helmholtz coils was fabricated specifically for use in these

experiments. Two non-magnetic ring-shaped coil housings, fabricated from aluminum and

plastic, were wrapped with two differing sets of coil windings. The first coil set consisted of

1500 turns of 30 AWG insulated magnet wire which accommodated the low alternating current

output of the SR770 signal generator source. This coil was used in conjunction with the SR770

source output to generate the AC magnetic test field signal. The second coil consisted of 200

turns of 18 AWG insulated magnet wire and accommodated the high direct current output of the

Sorensen DCR 80-12B power supply. This coil was used to generate a DC biasing magnetic

field from 0 Gauss up to 50 Gauss.

A Helmholtz coil is defined as a pair of symmetrical electromagnet coils that are

separated by a distance equal to the radius of each coil. When current is passed through both

32

coils, separated by their radius, a uniform magnetic field is produced along a length between the

coils approximately equal to the distance of separation. A key design aspect in fabricating the

Helmholtz coil was the ability to generate uniform magnetic fields over the length of the largest

sensor. Therefore, the uniform field length was required to be at least as long as the active

element area in Sensor 2 of 40 mm, and preferably the entire length of Sensor 2 of 80.4 mm.

The dual Helmholtz coils constructed for this investigation were fabricated to exhibit a 90 mm

radius, therefore providing an approximate 90 mm uniform field length. The Helmholtz equation

(2.1) calculates magnetic flux density along a line centered through each coil as a function of

permeability , number of turns , current , and coil radius .

⁄

(2.1)

Both coils were secured to Plexiglas frames and mounted on a wood platform to provide

a stable electromagnetic Helmholtz coil test fixture promoting repeatable measurements. Two

sets of banana connectors were mounted to the wood platform where leads from both sets of

Helmholtz coils were tied. This method of interfacing with the dual Helmholtz coil provided

robust repeatable connectivity.

During testing, each ME sensor was mounted into plastic tweezers as shown in Figure 12,

and suspended by a table top vice grip fabricated from aluminum and plastic. Supporting each

sensor on either end using a clamp, instead of on a dielectric slab as shown in Figure 9a, is

theorized to promote the generation of bending modes, resulting in higher sensitivity, and to

reduce mechanical damping effects associated with attaching a sensor to a dielectric slab.

However, no study was performed to analyze the different sensor mounting methods due to the

33

scope of this thesis. For consistency, both sensors were mounted in an identical manner for

testing. As shown in Figure 20, the mounting apparatus simply positions a ME sensor inside the

dual Helmholtz coil. The use of clip leads and tweezers enable quick switching between sensors.

Clip leads were attached to the electrode leads on the sensor and connected via BNC coaxial

cables to the SR770 for measurements.

Figure 20: The sensor mounting apparatus consists of a table top vice grip and a set of tweezers fabricated from non-magnetic materials. It is shown positioning a sensor inside the dual Helmholtz coils.

34

2.2.3. DC Biasing Method Experimental Procedure

The following experimental procedure will enable a reader to accurately reproduce the

DC biasing test method used to capture measurements presented in this thesis:

1) Configure the Sorensen DCR 80-12B strapping for signal programming voltage mode:

a. Remove all strapping from current configuration.

b. Connect nodes 7 to 8.

c. Connect node 1 to + Output.

d. Connect node 2 to – Output.

e. On Front Panel, connect + Output to Ground.

f. Set Current knobs fully clockwise.

2) Configure SR830 Aux Out 1 to provide voltage programming of the DCR 80-12B:

a. Press Aux Out and set to 0.000 VDC.

b. Connect Aux Out 1 + Voltage signal to node 3 on Sorensen DCR.

c. Connect Aux Out 1 Ground to node 1 on Sorensen DCR.

3) Connect the Sorensen DCR 80-12B DC output to coil set 2.

4) Setup the SR770 using the following steps:

a. Set frequency scale from 0 to 50 Hz.

b. Set Window to BMH.

c. Set Measure to PSD.

d. Set Display to Log Mag.

e. Set Units to Volts RMS.

f. Set Input to A.

g. Set Grounding to Ground.

35

h. Set Coupling to AC.

i. Set Trigger to Continuous.

j. Set Source to Sine.

k. Configure Source to generate a 25 Hz 780 mV AC RMS signal.

l. Press Auto Scale.

m. Set Auto-Ranging On.

n. Set Averaging On.

o. Set Number Averages to 500.

p. Set Average Type to RMS.

q. Set Average Mode to Linear.

5) Connect the SR770 source out to coil set 1.

6) Place the MNT-4E04-VH Transverse AC Hall Probe inside the LakeShore Model 4060

Zero Gauss chamber.

7) On the LakeShore 421 Gauss meter press the Zero Probe button to calibrate the hall

probe in a zero gauss environment.

8) Place the MNT-4E04-VH Transverse AC Hall Probe along the central axis inside the

Helmholtz coils and confirm the LakeShore 421is measuring 0.1 Gauss RMS.

9) Connect the sensor leads to input A on the SR770 and position sensor along the central

axis inside the Helmholtz coils.

10) Set LakeShore 421 to measure DC magnetic field and verify the DC field is 0 Gauss.

11) Insert a 3.5” floppy disk into the SR770.

12) Press Store/Recall then press Format Disk on the SR770.

36

13) Press the Start key on the SR770 to begin collecting 500 linearly averaged sweeps for 0

Gauss applied field.

14) When data collection has completed, press Store/Recall, Save Data, enter a file name,

then press Save ASCII Data to write a two column (frequency, power spectral density)

text data file do the floppy disk. An example data file is provided in Appendix A.1.

15) Increment the Aux Out 1 output voltage using the rotary knob on the SR830, causing the

Sorensen to increasingly pass direct current through Coil Set 2, generating a DC magnetic

field, until the LakeShore 421 measures 1 Gauss.


Gauss applied field.

17) Using a unique filename, save the data in ASCII format to floppy disk.

18) Repeat steps 15, 16, and 17 for all desired increments of DC bias magnetic field for both

magnetoelectric sensors.

2.3. Results and Analysis

The conventional DC biasing method was used, by following the previously described

procedure, to collect Sensor 1 and Sensor 2 frequency domain voltage response data, consisting

of 500 linearly averaged sweeps from 0 to 50 Hz, of a 25 Hz 0.1 Gauss RMS test field for

varying DC bias magnetic fields. DC bias magnetic field values of 0, 1, 2.5, 5, 7.5, 10, 15, 20,

30, and 50 Gauss were chosen because both sensors exhibit peak performance within that range.

Signal-to-noise ratio (SNR), sensitivity, 0-Hz noise floor, and magnetic spectral density

measurements are presented in section 2.3.1 for Sensor 1 and section 2.3.2 for Sensor 1.

37

The SR770 digital FFT spectrum analyzer has the ability to measure from DC to 100

KHz with a dynamic range of 90 dB. This instrument enabled accurate measurements from 0 Hz

to 50 Hz and provided magnetoelectric response data corresponding to the magnetic test field,

environmental noise factors, and internal device noise factors. The convention for describing the

noise floor of magnetoelectric laminate composites involves converting voltage spectral density

measurements to magnetic spectral density in Tesla/√Hertz through the equation 2.2.

√

√ (2.2)

This calculation requires the value of inverse sensitivity where sensitivity is defined as

Volts per Oersted. Sensitivity is calculated by converting the voltage spectral density

measurement at 25 Hz to Volts RMS. The single point noise floor value of magnetoelectric

laminate composites is typically quantified by the amplitude of the 0-Hz peak28. The 0-Hz peak

has typically exhibited the largest non-signal noise floor in ME composites where the output

viewed in the time domain exhibits the largest DC noise effects. Recently, several methods of

mediating the 0-Hz noise peak associated with 1/f noise have been developed, as exhibited in

Sensor 2, however, single-point noise floor measurements continue to be taken with respect to

the 0-Hz noise floor.

The noise floor and signal-to-noise plots are calculated using the single 0-Hz noise floor

data point. Dynamic magnetic spectral density noise floor data is also presented in logarithmic

and linear scales to exhibit the environmental noise floor frequency content.

38

2.3.1. Sensor 1 Results

Data was imported and analyzed using the Matlab code shown in Appendix section A.2.

0 10 20 30 40 50

-20

-15

-10

-5

0

5SNR Vs. Applied DC H-Field

Applied DC H-Field (Oe)

SN

R (d

B)

Figure 21: Signal-to-noise ratio as a function of applied magnetic field for Sensor 1.

0 10 20 30 40 5010

-4

10-3

10-2

Sensitivity Vs. Applied DC H-Field


Sen

sitiv

ity (V

/Oe)

Figure 22: Sensitivity as a function of applied magnetic field for Sensor 1.

39

0 10 20 30 40 5010

-5

10-4

10-3 0-Hz Noise Floor Vs. Applied DC H-Field


0-H

z N

oise

Flo

or (T

/ √H

z)

Figure 23: 0-Hz noise floor as a function of applied magnetic field for Sensor 1.

Peak values of SNR, sensitivity, and noise floor from Figure 21, Figure 22, and Figure 23,

respectively, are provided in Table 3 below.

Table 3: DC Biasing Method: Peak Values of SNR, Sensitivity and Noise Floor for Sensor 1.

Property Sensor 1

Peak SNR 1.858 dB

Peak Sensitivity 2.713*10-3 V/Oe

Lowest Noise Floor 1.632*10-5 T/√Hz

40

100

101

10-9

10-8

10-7

10-6

10-5

10-4

10-3

X: 25.02Y: 2.021e-005

Frequency (Hz)

Mag

netic

Spe

ctra

l Den

sity

(T/ √

Hz)

MSD of Sensor 1 for 25 Hz 0.1 Oe Test Field

0 Oe1 Oe2.5 Oe5 Oe7.5 Oe10 Oe15 Oe20 Oe30 Oe50 Oe

Figure 24: Magnetic Spectral Density with respect to applied field for Sensor 1. X-axis is of log scale.

41

0 10 20 30 40 5010

-9

10-8

10-7

10-6

10-5

10-4

10-3

X: 25.02Y: 2.021e-005

Frequency (Hz)

Mag

netic

Spe

ctra

l Den

sity

(T/ √

Hz)



Figure 25: Magnetic Spectral Density with respect to applied field for Sensor 1. X-axis is of linear scale.

42


0 10 20 30 40 5010

20

30

40

50



SN

R (d

B)

Figure 26: Signal-to-noise ratio as a function of applied magnetic field for Sensor 2.

0 10 20 30 40 5010

-3

10-2

10-1

100

Sensitivity Vs. Applied DC H-Field


Sen

sitiv

ity (V

/Oe)

Figure 27: Sensitivity as a function of applied magnetic field for Sensor 2.

43

0 10 20 30 40 5010

20

30

40

50



SN

R (d

B)

Figure 28: 0-Hz noise floor as a function of applied magnetic field for Sensor 2.



Table 4: DC Biasing Method: Peak Values of SNR, Sensitivity and Noise Floor for Sensor 2.

Property Sensor 2

Peak SNR 58.8 dB



44

10-1

100

101

102

10-9

10-8

10-7

10-6

10-5

10-4

X: 25.02Y: 2.021e-005

Frequency (Hz)

Mag

netic

Spe

ctra

l Den

sity

(T/ √

Hz)



Figure 29: Magnetic Spectral Density with respect to applied field for Sensor 2. X-axis is of log scale.

45

0 10 20 30 40 5010

-9

10-8

10-7

10-6

10-5

10-4

X: 25.02Y: 2.021e-005

Frequency (Hz)

Mag

netic

Spe

ctra

l Den

sity

(T/ √

Hz)



Figure 30: Magnetic Spectral Density with respect to applied field for Sensor 2. X-axis is of linear scale.

46

2.4. Conclusion

Sensor 1 is shown to exhibit a 1.858 dB peak signal-to-noise ratio, a 2.713*10.3 V/Oe

sensitivity and a lowest 1.632*10-5 T/√Hz 0-Hz noise floor. Sensor 2 exhibits a much higher

peak SNR of 58.8 dB, peak sensitivity of 2.583*10-1 V/Oe and lowest 0–Hz noise floor of

2.404*10-8 T/√Hz. The differences between both sensors are to be expected due to Sensor 1

utilizing PZT in a D31 mode and Sensor 2 utilizing PZT in a D33 mode. In addition, the Sensor

2 exhibits an approximate 7x larger active surface area and an approximate 14.7x larger total

surface area than Sensor 1 enabling Sensor 2 to exhibit greater sensitivity.

The magnetic spectral density plots for Sensor 1 exhibit a significant 1/f noise

contribution in addition to several harmonic peaks resulting from the 25 Hz magnetic test field

signal. The MSD plots for Sensor 2 exhibit a unique dip in 1/f noise contribution at

approximately 1 Hz which comes as an intentional result of Virginia Tech’s design. Several

harmonic peaks resulting from the 25 Hz magnetic test field signal are exhibited.

The X and Y coordinate marker indicated on each Matlab MSD plot shows that each

trace has been normalized to a 25 Hz, 0.10 Oe magnetic test field. 2.021*10-5 corresponds to the

magnetic spectral density in Tesla/√Hz and is equal to 1*10-5 Tesla.

The data presented in this chapter represents the conventional way of biasing a

magnetoelectric laminate composite sensor to exhibit peak performance by optimizing the

amplitude of a DC magnetic bias field.

The following chapter details a new sensing technique for ME laminate composites that

requires no DC magnetic field bias.

47

Chapter 3. Modulation Sensing Technique

3.1. Introduction and Theory

3.1.1. Motivation

Sensitivity enhancement and noise floor reduction in ME magnetic field sensors has been

pursued through several different approaches. The role of laminate assembly configurations and

respective magnetic/electric poling directions on the vibrational and thermal noise rejection

capability has been investigated29. Device scaling effects and their influence on the output noise

level and signal-to-noise ratio (SNR) have also been reported. The role of Metglas/PZT

thickness ratio has been studied and optimized to achieve further sensitivity improvement

compared to single layer Metglas/PZT/Metglas heterostructures29. In these and other

experiments, it was observed that the sensitivity of the ME sensor can be enhanced and the noise

floor reduced by increasing the volume or the surface area of the active region of the device.

However, from a practical point of view, miniature, low profile, and lightweight sensing

elements that can be integrated into compact gradiometric arrays and other magnetometer

configurations are needed. There exists a strong need for methods of increasing the sensitivity

and mitigating external noise sources, especially low frequency 1/f noise, without significantly

increasing the size and weight of sensors. Anticipated applications include the deployment of

magnetoelectric sensors in a variety of payload-sensitive platforms, such as unmanned

autonomous systems, including aircraft vehicles, that can reap the full benefits of the ME sensor

technology without sacrificing the current characteristics of these systems.

48

Presented in this chapter is a sensing technique that provides a dramatic improvement in

sensitivity, an enhancement in signal-to-noise ratio, and an enhancement in noise floor over peak

values obtained using the conventional DC biasing method for magnetoelectric laminate

composite magnetic field sensors. Sensitivity enhancement is due, in part, by the use of a

modulation magnetic field that is capable of stimulating an electro-magneto-mechanical

resonance mode. It has been demonstrated26 that magnetoelectric laminate composites exhibit a

significant enhancement in sensitivity when exposed to an AC magnetic field that stimulates a

resonance mode. Here, we take advantage of provoking a resonance mode and through the use

of a lock-in demodulation scheme are able to detect off resonance magnetic field signals.

3.1.2. Relationship Between Strain and Applied Magnetic Field.

This technique, herein referred to as the modulated sensing technique, employs an AC

magnetic modulation field, instead of a DC magnetic bias field, to take advantage of the non-

linear nature of the magnetostriction constant dependence on an externally applied magnetic

field, exhibited in Metglas magnetostrictive phase of both sensors. For small amplitudes of

applied magnetic field, the magnetostrictive response can be defined using Livingston’s model of

coherent rotation of magnetization

31 shown in equation (3.1):

(3.1)

Where the saturation magnetostriction constant is , HA is the magnetic anisotropy field,

and H is the applied magnetic field. For simplification, the strain can be related to an applied

49

magnetic field using equation (3.2), where C is the magnetostrictive coefficient parameter, thus

indicating that strain is linearly proportional to C.

(3.2)

Figure 31 (a) illustrates the magnetostriction in Metglas, (b) the slope of the

magnetostriction, and (c) strong agreement of Livingston’s model of coherent rotation with

magnetostriction for low amplitudes of applied magnetic field. The modulation sensing

technique operates in the dS/dH realm as shown in Figure 31 (b) where the slope maximum is

exhibited at an applied DC magnetic field of 0 Oe. Consequently, a superimposed signal field

will cause the greatest percentage change in magnetostriction at 0 Oe, indicating that this sensing

technique requires no DC bias field.

50

Figure 31: (a) Magnetostriction in Metglas. (b) Slope of magnetostriction (dλ/dH). (c) Overlay of Livingston's model of coherent rotation of magnetization with the magnetostriction of Metglas for low amplitudes of applied magnetic field.

The H2 term shown in equation (3.2) is critical for operation of the modulated sensing

technique because it squares the applied field term which consists of the superposition of the

applied magnetic test field signal with the applied magnetic modulation field signal, resulting in

modulated frequency terms, and enables the lock-in amplifier to provide phase-locked

demodulation. Proof that the strain term squares the superposition of two applied fields is

51

demonstrated in Figure 32, where a 200 Hz test H-field and 58KHz modulation H-field are

simultaneously applied to Sensor 1. The voltage output waveform of Sensor 1 was captured

using the Tektronix TDS 520A 2 channel digitizing oscilloscope to demonstrate the

multiplication of both signals. Due to practical interest in lower frequency test signals, dynamic

range limitations in the experimental setup, and maintaining consistency between DC biasing

method and modulation sensing techniques, the test field was set to 25Hz.

Figure 32: (a) 58 KHz reference modulation magnetic field as sensed by Sensor 1. (b) 200 Hz test field modulated with the 58 KHz reference modulation field as sensed by Sensor 1. Part (b) indicates that the total applied H term is indeed squared.

52

3.1.3. Mathematical Theory of Modulation Sensing Technique.

Livingston has defined the strain in a magnetostrictive material, under low amplitudes of

applied magnetic field H to be:

3

2

Which can be simplifi e a s e coefficient parameter to: ed by using C as th m gneto trictiv

Indicating that:

The modulation sensing technique utilizes the simultaneous application of two magnetic

fields Hsig, which can be an AC or DC magnetic test field signal, and Hmod, which is the

modulation magnetic field generated by using the reference channel of a lock in amplifier and

thus sharing the same frequency.

H from (3.2) is the applied magnetic field consisting of the superposition of Hsig with

Hmod:

Calculating for H2 yields:

53

2

Where it can be now shown that stra is pro o the H2 term: in portional t expanded

2

For the modulation sensing technique, the voltage output generated by a magnetoelectric

magnetic field sensor, which is proportional to strain and thus proportional to , is passed

through a lock-in amplifier. The lock-in amplifier digitally multiplies an input signal by an

internal reference signal to perform phase sensitive detection32.

The resulting signal Vpsd is the product of an input signal Vtest with the internal reference

signal VLI wn low: ref as sho be

Expanding yields:

2

54

Traditionally, it is observed that for phase-locked detection of a test frequency

equal to the LIref frequency that the first cosine term goes to unity, yielding a DC result,

and the second cosine term goes to twice the test frequency, which can be rejected using a low-

pass filter. However, for the modulation sensing technique, Vtest consists of two modulated

signals, and use of the lock-in amplifier produces several mixing terms described in the

following.

It is important to note that for this modulation sensing technique: .

The voltage response output generated by a magnetoelectric magnetic field sensor will be

proportional to the strain:

Therefore the signal after phase sensitive detection Vpsd is proportional to the square of

the applied magne mu th ck-in signatic field ltiplied by e lo reference l VLIref:

2

55

Expanding yields:

2

The output of the SR830 lock-in amplifier contains at least an internal gain factor of 10x,

which may be compounded with user defined gain. However, these gain terms can be placed in

the proportionality constant, and the n be d cribed as: output of the lock-in amplifier VLIout ca es

2

56

Where further expanding yields:

2

12

Proper setting of the time constant on the SR830 provides rejection of all the higher order

mixing ms and the tput tter reduces ou o:

57

Using the SR830 lock-in amplifier reference output to modulate the coil, the internal

reference frequency and modulation field frequency exhibit the same value and

through phase sensitive detection can be cancelled out to yield:

1

The first cosine term goes to unity and the second cosine term goes to a frequency

twice . Due to being much greater than the test frequency, this term is removed by

properly setting the low pass filter time constant. Additionally, the term is placed in the

proportionality. The output voltage of the lock in amplifier is shown to be linearly

proportional to multiplied by :

Here, may be an AC or DC magnetic signal field and the resulting expression,

indicating that Hmod d Hsig act as linear gain ter an ms, is shown below:

cos

The amplitude of Hmod was varied to prove that it linearly scales the amplitude of the

output signal, therefore acting as a gain term as shown in Figure 33.

58

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

25 Hz Signal vs. Hmod Amplitude

Hmod (Oe)

Vde

tect

ed (m

Vrm

s)

Figure 33: Amplitude of the modulation field as a function of the detected 25 Hz test signal amplitude. This plot demonstrates that Hmod acts as a linear gain factor.

3.2. Experimental Setup

3.2.1. Modulated Sensing Technique Equipment List

The following list of equipment was used to measure both Sensor 1 and Sensor 2 using

the modulated sensing technique and is numerically coordinated with Figure 34:

59

1) Stanford Research Systems SR770 FFT Digital Spectrum Analyzer

2) Stanford Research Systems SR830 DSP Lock-in Amplifier

3) Tektronix TDS 520A 2 Channel Digitizing Oscilloscope

4) LakeShore 421 Gaussmeter with MNT-4E04-VH Transverse AC Hall Probe

5) Keithley 199 Digital Multimeter

6) Dual nesting Helmholtz coil with 9 cm uniform field capability.

7) BNC coaxial cables and clip leads

8) Non-magnetic sensor mounting apparatus

9) 3.5 Inch Floppy Disk

10) LakeShore Model 4060 Zero Gauss Chamber

11) Variable capacitor bank

12) AC amplifier with bandwidth from at least 10KHz through 70KHz

13) 1 Ohm Sense Resistor

14) Stanford Research Systems SR552 BJT Input Voltage Preamplifier

60

Figure 34: Modulated sensing technique experimental setup. The numbers correspond to the numbered items in the equipment list. The BNC coaxial cables, clip leads, 3.5” floppy disk, LakeShore Model 4060 Zero Gauss Chamber, and variable capacitor bank are not numbered in figure.

3.2.2. Modulated Sensing Technique Block Diagram and Equipment Overview

A block diagram of the experimental setup used to take DC biased measurements of

Sensor 1 and Sensor 2 is shown below in Figure 35. Signal flow direction is demonstrated using

red arrows.

61

Figure 35: Block diagram of the experimental setup for the modulated sensing technique.

The magnetoelectric sensors were connected to the input of a Stanford Research Systems

SR830 DSP lock-in amplifier. The SR830 provides phase sensitive detection and demodulation

of the signal field from the modulation reference field as described in section 3.2.1, low-pass

filtering of higher ordered frequency terms, and passes the output signal, via X output, to the

62

input of the SR770 FFT spectrum analyzer. The SR552 BJT preamplifier was used to combat

the high instrument noise floor of the lock-in amplifier. A discussion on the noise floor

evaluation is presented in section 3.2.4. The magnetic test field was generated by passing a 25

Hz alternating current signal from the SR770 source output through Helmholtz coil set 1. The

amplitude of the 25 Hz magnetic field was measured using the MNT-4E04-VH transverse AC

hall probe in conjunction with the LakeShore 421 gaussmeter set in AC Gauss RMS mode. The

AC magnetic test field was set to 25 Hz at 0.10 Gauss RMS, equal to 10-5 Tesla RMS in air, and

was held constant for all measurements.

The reference output of the SR830 drove an AC power amplifier capable of sourcing

higher current and was used to generate the reference modulation field at varying frequencies

from 10 KHz to 70 KHz in the Helmholtz coil. Generating high frequency alternating magnetic

fields is a tricky task and required the use of a variable capacitor bank, placed in series with the

circuit, to abate the high impedance associated with passing high frequency current through an

inductive element. Applied modulation field frequencies of 10 KHz, 20 KHz, 30 KHz, 40 KHz,

50 KHz, 60 KHz, and 70 KHz were used and, as expected, the variable capacitor required

retuning at every frequency interval. Due to the LakeShore 421 gaussmeter’s limited bandwidth

max of 400 Hz, a Keithley 199 DMM in VAC mode, exhibiting bandwidth from DC to 100 KHz,

was used to monitor the current passing through a 1 Ohm sense resistor placed in series with the

circuit. The coil was calibrated to generate a 0.25 Gauss RMS magnetic field at a frequency

within the range of the LakeShore 421 gaussmeter which corresponded to an approximate 7

mVAC RMS reading on the Keithley 199 across the sense resistor. When driving the Helmholtz

coil at higher frequencies, the capacitor bank was used to tune the resonator circuit to generate

63

7mVAC RMS across the sense resistor, thus corresponding to a 0.25 Gauss RMS magnetic

modulation field.

Descriptions of the dual nesting Helmholtz coil can be found in section 2.1.2 as no

modifications to this device were performed. In addition, use of the sensor mounting apparatus

is identical to that of section 2.1.2 and no further description of its use is required here.

Proper setup of the Stanford Research Systems SR830 lock-in amplifier is required to

produce an optimal X output and the setup procedure is described in the following section.

3.2.3. Modulated Sensing Technique Experimental Procedure

The following experimental procedure will enable a reader to accurately reproduce the

modulated sensing technique used to capture measurements presented in this thesis:


a. Set frequency scale from 0 to 50 Hz.

b. Set Window to BMH.

c. Set Measure to PSD.

d. Set Display to Log Mag.

e. Set Units to Volts RMS.

f. Set Input to A.

g. Set Grounding to Ground.

h. Set Coupling to AC.

i. Set Trigger to Continuous.

64

j. Set Source to Sine.

k. Configure Source to generate a 25 Hz 780 mV AC RMS signal.

l. Press Auto Scale.

m. Set Auto-Ranging On.

n. Set Averaging On.

o. Set Number Averages to 500.

p. Set Average Type to RMS.

q. Set Average Mode to Linear.

2) Connect the SR770 source out to coil set 1.

3) Place the MNT-4E04-VH Transverse AC Hall Probe inside the LakeShore Model 4060

Zero Gauss chamber.

4) On the LakeShore 421 Gauss meter press the Zero Probe button to calibrate the hall

probe in a zero gauss environment.

5) Place the MNT-4E04-VH Transverse AC Hall Probe along the central axis inside the

Helmholtz coils and confirm the LakeShore 421is measuring 0.10 Gauss RMS.

6) Temporarily turn off the SR770 Source in order to calibrate the SR830 modulation field,

the probe should now read 0.00 Gauss RMS.


a. Set time constant to 1 millisecond.

b. Set Slope to 6 dB per octave.

c. Set input to single ended voltage connection A.

d. Set Coupling to AC.

e. Set Ground to Ground.

65

f. Set notch filter to both 60 Hz and 120 Hz.

g. Set Reserve to Low Noise.

h. Set Display to X.

i. Set Output to X.

j. Set Sine Out to Internal.

8) Connect the SR830 reference Sine Out to the AC power amplifier.

9) Connect the AC power amplifier out to the sense resistor, variable capacitor bank, and

Helmholtz coil set 2 in a series circuit.

10) Set the variable cap bank to a relatively large capacitance (~100’s of mF).

11) Connect the Keithley 199 DMM across sense resistor, set to mVAC RMS, press Zero to

remove any instrument bias.

12) Set the Frequency of the SR830 reference to 350 Hz and increase the voltage output until

the LakeShore 421 reads 0.25 Gauss RMS.

13) Take note of the corresponding voltage produced across the sense resistor as measured

by the Keithley 199 DMM. For instance, the voltage corresponding to 0.25 Gauss RMS

equals Vsense.

14) Remove the MNT-4E04-VH Transverse AC Hall Probe from the Helmholtz coils.

15) Position sensor along the central axis inside the Helmholtz coils.

16) Connect the sensor leads to the SR552.

17) Connect the SR552 to the SR830 single ended voltage input A.

18) Connect the SR830 X output to input A on the SR770.

19) Turn on the SR770 Source.

20) Increase the SR830 modulation frequency to 10 KHz.

66

21) Tune the variable capacitor and increase the modulation signal amplitude (if needed) to

obtain a reading of Vsense on the Keithley 199 DMM.

22) On the SR770 press Marker Max/Min and use the scroll wheel (if needed) to center the

marker on the 25 Hz signal peak.

23) Turn off averaging on the SR770 and press start.

24) Manually adjust the phase of the SR830 using the scroll wheel until the 25 Hz signal

exhibits a maximum value. Note: The value of this peak will change depending on phase.

For a perfectly matched lock-in phase the 25 Hz signal will exhibit a maximum value. It

is up to the user to match the phase as the auto phase function on the SR830 does not

work in this scenario.

25) Insert a 3.5” floppy disk into the SR770.

26) Press Store/Recall then press Format Disk on the SR770.

27) Turn on averaging on the SR770.


KHz applied modulation field.

29) When data collection has completed, press Store/Recall, Save Data, enter a file name,

then press Save ASCII Data to write a two column (frequency, power spectral density)

text data file do the floppy disk. An example data file is provided in Appendix A.1.

30) Increase the modulation frequency on the SR830 to the next increment (20 KHz).

31) Retune the variable capacitor and signal amplitude so that the Keithley 199 DMM reads

Vsense.

32) Turn off SR770 averaging and press start.

67

33) Maximize 25 Hz detected signal by manually adjusting the reference phase on the

SR830.

34) Turn on SR770 averaging.

35) Press the Start key on the SR770 to begin collecting 500 linearly averaged sweeps.

36) Using a unique filename, save the data in ASCII format to floppy disk.

37) Repeat steps 29 through 35 for all desired frequency increments of reference modulation

magnetic field for both magnetoelectric sensors.

3.2.4. Noise Study and Resulting Experimental Setup Modifications

Extensive noise measurements of the modulated sensing technique experimental setup

were performed. The goal during this study was to identify the sources of noise within detection

electronics and quantify their contributions to the overall sensor noise floor. Initial experiments

indicated that the modulated sensing technique exhibited an enhancement in SNR, sensitivity,

and noise floor over the standard DC biasing method when using Sensor 1. However, when a

lower noise floor optimized Metglas/PZT-fiber/Metglas heterostructure (Sensor 2) was used; a

comparable improvement in SNR, sensitivity, and noise floor was not observed. It was

hypothesized that this effect was the result of measurements being limited by electronic noise in

the experimental setup. In other words, the noise floor of the detection electronics was above the

noise floor of the sensor causing erroneous sensor noise floor measurements. An early version of

the experimental setup of the modulated sensing technique employed a QSC MX 3000a audio

power amplifier to drive the modulation coils. It was demonstrated that by eliminating the audio

amplifier used to drive the modulation coil an enhancement to SNR, sensitivity, and noise floor

was achieved, thus confirming the hypothesis. In light of that finding, a comprehensive noise

68

floor study was undertaken to identify additional potential limiting factors in the modulated

sensing technique experimental setup.

A comparison between the noise floor levels of the lock-in amplifier and Sensor 2 is

given in Figure 36.Sensor noise floor measurements were performed without the application of

either test or modulation fields while the lock-in amplifier noise floor measurements were

performed with the input terminated using a short. Data was collected and presented in

logarithmic scale from 0 to 400 Hz. It was observed that the lock-in amplifier exhibits a higher

noise floor than that of Sensor 2. Seeing as this would cause modulated sensing technique

measurements of Sensor 2 to be dominated by the SR830 instrument noise, it also seems to be

the cause of a negligible enhancement to noise floor measurements when using the modulated

technique. It was known at the time that Sensor 2 exhibited a relatively high sensitivity, at least

much greater than the sensitivity of Sensor 1; however, it was not anticipated to exhibit a noise

floor below that of the scientific instruments. This realization resulted in having to modify the

modulation sensing technique test method.

Prior to devising a new testing method, Sensor 1 was put through the same test. Figure 37

shows the same voltage spectral density measurements of the lock-in amplifier in comparison to

Sensor 1 noise voltage spectral density measurements under no test or modulated fields. It is

observed that at low frequencies Sensor 1 exhibits a higher noise floor than the lock-in amplifier,

and is not limited by the lock-in noise floor but rather by the sensor itself. As previously

mentioned, noise floor measurements were taken with respect to the 0-Hz frequency point which

is where Sensor 1 exhibits a higher noise floor than the lock-in amplifier’s electronic noise. Since

the modulation sensing technique has the ability to reject environmental drift and noise, as

evident from the relatively frequency-independent noise voltage spectral density spectra we can

69

expect to see an enhancement in the ability of Sensor 1 to sense low frequency magnetic fields

when utilizing the modulation sensing technique.

100

101

102

10-8

10-7

10-6

10-5

10-4

10-3

Frequency (Hz)

Vol

tage

Spe

ctra

l Den

sity

(Vrm

s/ √H

z)

Lock-In Amplifier and Sensor Noise Floor

LI1LI2LI3LI4S21

S22S23

S24

Figure 36: Voltage spectral density measurements captured of the lock-in amplifier output, representing the instruments electronic noise, compared with VSD measurements of Sensor 2. Numbers 1-4 represent capture number where each capture consists of 500 linearly averaged sweeps.

70

100

101

102

10-8

10-7

10-6

10-5

10-4

10-3

Frequency (Hz)

Vol

tage

Spe

ctra

l Den

sity

(Vrm

s/ √H

z)Lock-In Amplifier and Sensor Noise Floor

LI1LI2LI3LI4S11

S12S13

S14

Figure 37: Voltage spectral density measurements captured of the lock-in amplifier output, representing the instruments electronic noise, compared with VSD measurements of Sensor 1. Numbers 1-4 represent capture number where each capture consists of 500 linearly averaged sweeps.

71

Noise contributions from components of the modulated sensing technique’s experimental

setup are shown in Figure 38. For this experiment, the SR830 lock-in amplifier was connected to

the SR770 spectrum analyzer and left in a steady state. Measurements of four different

configurations were captured to understand which components introduced noise. A modulated

sensing technique measurement, of 5 KHz 1 Oe modulation field and 200 Hz 1 Oe test field is

shown in blue to exhibit a 0Hz noise floor of 0.3 mVrms/√Hz. This measurement is shown to

exhibit the highest noise floor of the remaining four configurations. The 200 Hz 1 Oe test field

was removed resulting in the green trace which shows a 0 Hz noise floor of 0.4 mVrms/√Hz. The

elimination of this test field shows negligible effect on low frequency noise floor. The 200 Hz 1

Oe test field was reapplied and the 5 KHz 1 Oe modulation field removed for the measurement

shown in red. A reduction of the 0 Hz noise floor by a factor of 3.33 is observed indicating that

the modulation field is responsible for increasing the measurement noise floor, which is expected

as because the amplitude of the modulation field should serve as a gain factor. The last

configuration, shown in teal, is a measurement of the instrumental noise of lock-in amplifier. By

removing the 200 Hz 1 Oe test field and the sensor, a reduction of the 0 Hz noise floor by a

factor of 7.6 is observed. This indicates that the test signal is causing a higher noise floor, but it

is not as significant as the effect of modulation signal.

72

100

101

102

10-6

10-5

10-4

10-3

10-2

10-1

100

Frequency (Hz)

Vol

tage

Spe

ctra

l Den

sity

(Vrm

s/ √H

z)Lock-in to DSA Instrument Noise

Standard 5KHzMod 200HzTest5KHz Mod NO TEST200Hz Test NO MODLockIn NO INPUT Instrument Noise

Figure 38: Voltage spectral density measurements of 4 configurations showing contributions to the noise floor. The output of the lock-in amplifier is transmitted to the digital spectrum analyzer for each configuration. The modulated sensing technique with a 5 KHz modulation frequency and 200 Hz test signal is shown in blue. The green trace was measured from a setup with 5 KHz modulation field and no test field. The red trace was measured from a setup with no modulation field and a 200 KHz test field. The teal trace was measured from a setup with no input and represents the lock-in amplifiers instrumental electronic noise floor.

73

It was observed that electronic noise of the lock-in amplifier is, in the case of highly

sensitive Sensor 2, limiting the sensitivity of the measurement setup. Thus, to take advantage of

the low noise floor of the sensing element and still realize the sensitivity enhancement using a

modulation drive, one of two options needed to be pursued: either the noise floor of detection

electronics had to be reduced or the noise floor of the sensor had to be increased. For

practicality, increasing the noise floor of the sensor by using the SR552 BJT preamplifier which

contains a gain factor of 100, was pursued. However, this resulted in having to reduce the

original magnetic test field from 1 Oe to 0.10 Oe and the magnetic modulation field from 1 Oe to

0.25 Oe in order to comply with the dynamic range of both the lock-in amplifier and spectrum

analyzer. The resulting modulation testing setup is that which is described in section 3.2.1.

3.3. Results and Analysis

The modulated sensing method was used, by following the previously described

procedure, to collect Sensor 1 and Sensor 2 frequency domain voltage response data, consisting

of 500 linearly averaged sweeps from 0 to 50 Hz, of a 25 Hz 0.1 Gauss RMS test field for

varying modulation field frequency. As previously mentioned, modulation frequencies of 10

KHz, 20 KHz, 30 KHz, 40 KHz, 50 KHz, 60 KHz, and 70 KHz were used to demonstrate the

dynamic magnetostrictive response of the magnetoelectric laminate composites. Signal-to-noise

ratio (SNR), sensitivity, 0-Hz noise floor, and magnetic spectral density measurements are

presented in section 3.4.1 for Sensor 1 and section 3.4.2 for Sensor 2.

The signal-to-noise ratio, sensitivity, and 0-Hz noise floor values are calculated and

presented in the following sections for Sensor 1 and Sensor 2. These values are calculated the

74

same way as described in the DC biasing section except that additional gain factors due to the

lock-in amplifier and SR552 are factored out. In addition, dynamic magnetic spectral density

noise floor data is also presented in logarithmic and linear scales to demonstrate the ability of the

modulated sensing technique to mitigate environmental noise.


Data was imported and analyzed using the Matlab code shown in Appendix section A.3.

10 20 30 40 50 60 7035

40

45

50

55

60SNR Vs. Modulation Frequency

Mod. Freq. (KHz)

SN

R (d

B)

Figure 39: Signal-to-noise ratio as a function of modulation frequency for Sensor 1.

75

10 20 30 40 50 60 7010

-4

10-3

10-2

10-1 Sensitivity Vs. Modulation Frequency

Mod. Freq. (KHz)

Sen

sitiv

ity (V

/oe)

Figure 40: Sensitivity ratio as a function of modulation frequency for Sensor 1.

10 20 30 40 50 60 7010

-8

10-7

10-6 0-Hz Noise Floor Vs. Modulation Frequency

Mod. Freq. (KHz)

0-H

z N

oise

Flo

or (T

/ √H

z)

Figure 41: 0-Hz noise floor as a function of modulation frequency for Sensor 1.

76



Table 5: Modulation Sensing Technique: Peak Values of SNR, Sensitivity and Noise Floor for Sensor 1.

Property Sensor 1

Peak SNR 59.29 dB



77

100

101

10-9

10-8

10-7

10-6

10-5

10-4

X: 25.02Y: 2.021e-005

Frequency (Hz)

Mag

netic

Spe

ctra

l Den

sity

(T/ √

Hz)

Sensor 1 MSD

10KHz20KHz30KHz40KHz50KHz60KHz70KHz

Figure 42: Magnetic Spectral Density with respect to modulation frequency. X-axis is of log scale.

78

0 10 20 30 40 5010

-9

10-8

10-7

10-6

10-5

10-4

X: 25.02Y: 2.021e-005

Frequency (Hz)

Mag

netic

Spe

ctra

l Den

sity

(T/ √

Hz)

Sensor 1 MSD


Figure 43: Magnetic Spectral Density with respect to modulation frequency. X-axis is of linear scale.

79


10 20 30 40 50 60 7045

50

55

60

65SNR Vs. Modulation Frequency

Mod. Freq. (KHz)

SN

R (d

B)

Figure 44: Signal-to-noise ratio as a function of modulation frequency for Sensor 2.

10 20 30 40 50 60 7010

-3

10-2

10-1

100

101 Sensitivity Vs. Modulation Frequency

Mod. Freq. (KHz)

Sen

sitiv

ity (V

/oe)

Figure 45: Sensitivity as a function of modulation frequency for Sensor 2.

80

10 20 30 40 50 60 7010

-8

10-7

10-6 0-Hz Noise Floor Vs. Modulation Frequency

Mod. Freq. (KHz)

0-H

z N

oise

Flo

or (T

/ √H

z)

Figure 46: 0-Hz noise floor as a function of modulation frequency for Sensor 2.

Peak values of SNR, sensitivity, and noise floor from Figure 44, Figure 45, and Figure

46, respectively, are provided in Table 6 below.

Table 6: Modulation Sensing Technique: Peak Values of SNR, Sensitivity and Noise Floor for Sensor 2.

Property Sensor 2

Peak SNR 63.18 dB

Peak Sensitivity 1.273 V/Oe


81

100

101

10-10

10-9

10-8

10-7

10-6

10-5

10-4

X: 25.02Y: 2.021e-005

Frequency (Hz)

Mag

netic

Spe

ctra

l Den

sity

(T/ √

Hz)

Sensor 2 MSD


Figure 47: Magnetic Spectral Density with respect to modulation frequency. X-axis is of log scale.

82

0 10 20 30 40 5010

-10

10-9

10-8

10-7

10-6

10-5

10-4

X: 25.02Y: 2.021e-005

Frequency (Hz)

Mag

netic

Spe

ctra

l Den

sity

(T/ √

Hz)

Sensor 2 MSD


Figure 48: Magnetic Spectral Density with respect to modulation frequency. X-axis is of linear scale.

83

3.4. Conclusion

Sensor 1 is shown to exhibit a 59.29 dB peak signal-to-noise ratio, a 3.154*10-2 V/Oe

sensitivity and a lowest 2.194*10-8 T/√Hz 0-Hz noise floor. Sensor 2 exhibits a peak SNR of

63.18 dB, peak sensitivity of 1.273 V/Oe and lowest 0-Hz noise floor of 1.401*10-8 T/√Hz.

Unlike the large performance gap in SNR, sensitivity, and 0-Hz noise floor exhibited between

Sensor 1 and Sensor 2 for the DC biasing case, both sensors offer relatively close performance

characteristics.

The magnetic spectral density plots are provided in full page view to emphasize the

ability of the modulated sensing technique to mitigate environmental noise and harmonic noise

for both sensors compared to the DC biasing method. It is also observed that this technique has

provided a significant reduction in the 1/f noise for Sensor 1, and has slightly reduced the effect

of 1/f noise in Sensor 2.

The X and Y coordinate marker indicated on each Matlab MSD plot shows that each

trace has been normalized to a 25 Hz, 0.10 Oe magnetic test field. 2.021*10-5 corresponds to the

magnetic spectral density in Tesla/√Hz and is equal to 1*10-5 Tesla.

The data presented in this chapter demonstrates that the novel modulated sensing

technique applied to magnetoelectric laminate composite sensors has the ability to stimulate

electro-magneto-mechanical resonance modes to provide an enhancement of SNR, sensitivity,

and noise floor.

84

Chapter 4. Conclusion

A full comparison between both sensing approaches, shown in Figure 49 and Table 7,

demonstrates that the modulation sensing technique can provide a significant enhancement to the

sensing ability of a magnetoelectric laminate composite magnetic field sensor.

0 20 40-20

0

20

40

60DC SNR

SN

R (d

B)

0 20 40

100

DC Sensitivity

Sen

sitiv

ity (V

/Oe)

0 20 40

10-5

DC 0-Hz Noise Floor


0-H

z N

oise

Flo

or (T

/ √H

z)

20 40 60-20

0

20

40

60Modulation SNR

Sensor 1Sensor 2

20 40 60

100

Modulation Sensitivity

20 40 60

10-5

Modulation 0-Hz Noise Floor

Mod. Freq. (KHz)

Figure 49: Full comparison between DC biasing method and modulation sensing technique.

85

Table 7: Comparison of DC Biasing Method to Modulated Sensing Technique.

Peak Parameter

DC Biasing Method

Modulated Sensing

Technique

Mod. Sensing Technique

Improvement Sensor 1

SNR 1.858 dB 59.29 dB + 57.43 dB

Sensor 1 Sensitivity

2.713*10-3 V/Oe

3.154*10-2 V/Oe 11.62 x

Sensor 1 0-Hz Noise

Floor

1.632*10-5 T/√Hz

2.194*10-8 T/√Hz 743.85 x

Sensor 2 SNR 58.8 dB 63.18 dB + 4.38 dB

Sensor 2 Sensitivity

2.583*10-1 V/Oe 1.273 V/Oe 4.93 x

Sensor 2 0-Hz Noise

Floor

2.404*10-8 T/√Hz

1.401*10-8 T/√Hz 1.72 x

The modulated sensing technique, applied to magnetoelectric laminate composite

magnetic field sensors, demonstrates an enhancement in signal-to-noise ratio, sensitivity, and 0-

Hz noise floor over the conventional DC biasing method for both Sensor 1 and Sensor 2. In

addition, the modulated technique exhibits excellent environmental, harmonic, and 1/f noise

suppression. This novel approach eliminates the previous requirement of a DC magnetic bias

field thus eliminating the need to use heavy permanent magnets or drive relatively large DC

86

currents through electromagnets. The significant enhancements to magnetoelectric laminate

composite characteristics provided by the development of this novel modulation sensing

technique and presented in this thesis bring such magnetic field sensors one step closer to

deployment in commercial applications.

4.1. Future Research Plans

The following steps will be taken to improve upon the reported modulated sensing

technique in order to establish further improvements in the merit of this design:

1) Increase gain for measurements made with Sensor 2 to bring up 0-Hz noise floor.

The issue of applying the correct amount of gain to this ultra-sensitive magnetoelectric

heterostructure in order to bring the sensor noise floor level above that of the lock-in amplifier

while remaining within the limits of the SR830 and SR770 dynamic range has become

increasingly challenging, especially when operating the sensor directly at its resonance mode.

Neither sensor was operated directly at a resonance mode, but rather slightly off

resonance, due to using uniform modulation frequency intervals. This leads to the second

improvement:

2) Capture modulation measurements of both sensors at smaller steps of modulation

frequency increments, and at corresponding resonance stimulation frequencies.

87

Limitations of the dynamic range of the SR830 and SR770 prevented taking on-

resonance measurements of Sensor 2. Plans to accurately reduce magnetic signal and

modulation field amplitude should enable on-resonance measurements of both sensors to be

made and result in higher modulation sensing technique figures of merit.

88

Appendix

A.1. Example Data File

Shown below is a sample data file exhibiting the comma separated, two column structure

of an output ASCII data file produced by the Stanford Research Systems SR770 FFT Digital

Spectrum Analyzer. All data was saved in this format on a 3.5” floppy disk and transferred to a

host PC for processing using Matlab.

To conserve space, a sample of only ten data points are provided below.

Ten points from an ASCII data file:

0.0000000e+000, 5.4847847e-006,

1.2207031e-001, 5.5033786e-006,

2.4414063e-001, 4.6560494e-006,

3.6621094e-001, 4.3307424e-006,

4.8828125e-001, 5.3418847e-006,

6.1035156e-001, 7.3627243e-006,

7.3242188e-001, 5.8490748e-006,

8.5449219e-001, 4.6876737e-006,

9.7656250e-001, 4.0009887e-006,

1.0986328e+000, 2.0429158e-006,

89

A.2. Matlab Code – DC Biasing Method

% DC Biasing Importer & Analyzer

% Scott Gillette

%===================================================================

%=============================DATAIMPORT===========================

%===================================================================

% Raw data is in the form of Vrms/sqrt(Hz)

TestFieldAmplitude = 0.1; %in Oe RMS

% Test Field of 0.10 Oe at 25 Hz

% NU_DC

NU_DC_0 = importdata('11D'); NU_DC_1 = importdata('12D');

NU_DC_2p5 = importdata('13D'); NU_DC_5 = importdata('14D');

NU_DC_7p5 = importdata('15D'); NU_DC_10 = importdata('16D');



% VT_DC

VT_DC_0 = importdata('1D'); VT_DC_1 = importdata('2D');

VT_DC_2p5 = importdata('3D'); VT_DC_5 = importdata('4D');

VT_DC_7p5 = importdata('5D'); VT_DC_10 = importdata('6D');



% Conversion factor from Vrms/sqrt(Hz) -> to Vrms.

VrmsConversionFactor = 0.494701;

%===================================================================

%===============================ANALYSIS===========================

%===================================================================

% XXDC is a matrix of [A B C]

90

% Where A is DC bias in Oe

% B is a Peak Amplitude column at 25 Hz in Vrms/sqrt(Hz)

% and C is the DC Noise Amplitude Column in Vrms/sqrt(Hz)

VT_DC = [

0 VT_DC_0(206,2) VT_DC_0(1,2)

1 VT_DC_1(206,2) VT_DC_1(1,2)

2.5 VT_DC_2p5(206,2) VT_DC_2p5(1,2)

5 VT_DC_5(206,2) VT_DC_5(1,2)

7.5 VT_DC_7p5(206,2) VT_DC_7p5(1,2)

10 VT_DC_10(206,2) VT_DC_10(1,2)

15 VT_DC_15(206,2) VT_DC_15(1,2)

20 VT_DC_20(206,2) VT_DC_20(1,2)

30 VT_DC_30(206,2) VT_DC_30(1,2)

50 VT_DC_50(206,2) VT_DC_50(1,2)

];

NU_DC = [

0 NU_DC_0(206,2) NU_DC_0(1,2)

1 NU_DC_1(206,2) NU_DC_1(1,2)

2.5 NU_DC_2p5(206,2) NU_DC_2p5(1,2)

5 NU_DC_5(206,2) NU_DC_5(1,2)

7.5 NU_DC_7p5(206,2) NU_DC_7p5(1,2)

10 NU_DC_10(206,2) NU_DC_10(1,2)

15 NU_DC_15(206,2) NU_DC_15(1,2)

20 NU_DC_20(206,2) NU_DC_20(1,2)

30 NU_DC_30(206,2) NU_DC_30(1,2)

50 NU_DC_50(206,2) NU_DC_50(1,2)

];

91

VTDCSNR = 20*log10(VT_DC(:,2))-20*log10(VT_DC(:,3));

NUDCSNR = 20*log10(NU_DC(:,2))-20*log10(NU_DC(:,3));

figure(1)

hold on

plot(NU_DC(:,1),NUDCSNR,'-.m','LineWidth',2)

plot(VT_DC(:,1),VTDCSNR,'r','LineWidth',2)

title('SNR Vs. Applied DC H-Field','FontSize',16)

xlabel('Applied DC H-Field (Oe)','FontSize',12)

ylabel('SNR (dB)','FontSize',12)

legend('Sensor 1','Sensor 2','Location','Southeast')

box on

VTDCSensitivity = (VT_DC(:,2).*VrmsConversionFactor)./TestFieldAmplitude;

NUDCSensitivity = (NU_DC(:,2).*VrmsConversionFactor)./TestFieldAmplitude;

figure(2)

hold on

semilogy(NU_DC(:,1),NUDCSensitivity,'-.g','LineWidth',2)

semilogy(VT_DC(:,1),VTDCSensitivity,'b','LineWidth',2)

title('Sensitivity Vs. Applied DC H-Field','FontSize',16)


ylabel('Sensitivity (V/Oe)','FontSize',12)


VTCDNF = (VT_DC(:,3))./(VTDCSensitivity.*(10^4));

NUDCNF = (NU_DC(:,3))./(NUDCSensitivity.*(10^4));

figure(3)

hold on

semilogy(VT_DC(:,1),NUDCNF,'-.g','LineWidth',2)

semilogy(VT_DC(:,1),VTCDNF,'b','LineWidth',2)

title('0-Hz Noise Floor Vs. Applied DC H-Field','FontSize',16)

92


ylabel('0-Hz Noise Floor (T/ \surdHz)','FontSize',12)


%===============================================================

VD0 = VT_DC_0(:,2)./(VTDCSensitivity(1)*10^4);


VD2p5 = VT_DC_2p5(:,2)./(VTDCSensitivity(3)*10^4);


VD7p5 = VT_DC_7p5(:,2)./(VTDCSensitivity(5)*10^4);






ND0 = NU_DC_0(:,2)./(NUDCSensitivity(1)*10^4);


ND2p5 = NU_DC_2p5(:,2)./(NUDCSensitivity(3)*10^4);


ND7p5 = NU_DC_7p5(:,2)./(NUDCSensitivity(5)*10^4);






f = VT_DC_0(:,1);

figure(4)

loglog(f,VD0,f,VD1,f,VD2p5,f,VD5,f,VD7p5,f,VD10,f,VD15,f,VD20,f,VD30,f,VD50)

93

%axis([0 390 10^-10 10^-5])

legend('0 Oe','1 Oe','2.5 Oe','5 Oe','7.5 Oe','10 Oe','15 Oe','20 Oe','30 Oe','50 Oe','Location','best')

title('MSD of Sensor 2 for 25 Hz 0.1 Oe Test Field','FontSize',14)

xlabel('Frequency (Hz)','FontSize',12)

ylabel('Magnetic Spectral Density (T/ \surdHz)','FontSize',12)

figure(5)

semilogy(f,VD0,f,VD1,f,VD2p5,f,VD5,f,VD7p5,f,VD10,f,VD15,f,VD20,f,VD30,f,VD50)

%axis([0 390 10^-10 10^-5])





figure(6)

%subplot(1,2,2)

loglog(f,ND0,f,ND1,f,ND2p5,f,ND5,f,ND7p5,f,ND10,f,ND15,f,ND20,f,ND30,f,ND50)

%axis([0 390 10^-10 10^-5])





figure(7)

%subplot(1,2,2)

semilogy(f,ND0,f,ND1,f,ND2p5,f,ND5,f,ND7p5,f,ND10,f,ND15,f,ND20,f,ND30,f,ND50)

%axis([0 390 10^-10 10^-5])




94


%================================================================

A.3. Matlab Code – Modulated Sensing Technique

% Modulated Data Importer & Analyzer

% Scott Gillette

%=================================================================

%=============================DATA IMPORT========================

%=================================================================

% Raw data is in the form of Vrms/sqrt(Hz)

RefFieldAmplitude = 0.25; %in Oe

TestFieldAmplitude = 0.1; %in Oe

% NU_Mod_#KHz were taken using:

% Modulation Reference Field of 0.25 Oe


NU_Mod_10KHz = importdata('1'); NU_Mod_20KHz = importdata('2');



NU_Mod_70KHz = importdata('7');

% This step accounts for the lock in amplifier gain of 10,

% and the modulation reference field amplitude of 0.25 Oe,

NU_Mod_10KHz(:,2) = NU_Mod_10KHz(:,2)./( 100*10*RefFieldAmplitude);




95




% VT_Mod_#KHz were taken using:

% Modulation Reference Field of 0.25 Oe.


VT_Mod_10KHz = importdata('11'); VT_Mod_20KHz = importdata('12');



VT_Mod_70KHz = importdata('17');

% This step accounts for the lock in amplifier gain of 10,

% and the modulation reference field amplitude of 0.25 Oe,

% and the test field amplitude of 0.1 Oe.

VT_Mod_10KHz(:,2) = VT_Mod_10KHz(:,2)./(100*10*RefFieldAmplitude);

VT_Mod_20KHz(:,2) = VT_Mod_20KHz(:,2)./( 100*10*RefFieldAmplitude);






%===================================================================

%===============================ANALYSIS===========================

%===================================================================

96

% XXDC is a matrix of [A B C]

% Where A is Modulation Frequency in KHz

% B is a Peak Amplitude column in Vrms/sqrt(Hz)

% and C is the DC Noise Amplitude Column in Vrms/sqrt(Hz)

NUMod = [

10 NU_Mod_10KHz(206,2) NU_Mod_10KHz(1,2)







];

NUModSNR = 20*log10(NUMod(:,2))-20*log10(NUMod(:,3));

VTMod = [

10 VT_Mod_10KHz(206,2) VT_Mod_10KHz(1,2)







];

VTModSNR = 20*log10(VTMod(:,2))-20*log10(VTMod(:,3));

figure(1)

hold on

plot(NUMod(:,1),NUModSNR,'r','LineWidth',2)

plot(VTMod(:,1),VTModSNR,'-.b','LineWidth',2)

97

title('SNR Vs. Modulation Frequency','FontSize',8)

xlabel('Mod. Freq. (KHz)','FontSize',10)

ylabel('SNR (dB)','FontSize',10)

legend('Sensor 1','Sensor 2','Location','Northeast')

box on

Conversiondata = [

746.6 369.3

6.941 3.433

2.135 1.057

];

VrmsRtHzTOVrms = sum(Conversiondata(:,2)./Conversiondata(:,1))/3

NUModSensitivity = (NUMod(:,2).*VrmsRtHzTOVrms)./(TestFieldAmplitude);

VTModSensitivity = (VTMod(:,2).*VrmsRtHzTOVrms)./(TestFieldAmplitude);

figure(2)

semilogy(NUMod(:,1),NUModSensitivity,'r','LineWidth',2)

hold on

semilogy(VTMod(:,1),VTModSensitivity,'-.b','LineWidth',2)

title('Sensitivity Vs. Modulation Frequency','FontSize',8)


ylabel('Sensitivity (V/oe)','FontSize',10)


NUModNF = (NUMod(:,3))./(NUModSensitivity*10^4);

VTModNF = (VTMod(:,3))./(VTModSensitivity*10^4);

figure(3)

semilogy(NUMod(:,1),NUModNF,'r','LineWidth',2)

hold on

98

semilogy(VTMod(:,1),VTModNF,'-.b','LineWidth',2)

title('Noisefloor Vs. Modulation Frequency','FontSize',8)


ylabel('Noise Floor (T/ \surdHz)','FontSize',10)


NU10 = NU_Mod_10KHz(:,2)./(NUModSensitivity(1)*10^4);







VM10 = VT_Mod_10KHz(:,2)./(VTModSensitivity(1)*10^4);







f = VT_Mod_10KHz(:,1);

figure(4)

loglog(f,NU10,f,NU20,f,NU30,f,NU40,f,NU50,f,NU60,f,NU70)

legend('10KHz','20KHz','30KHz','40KHz','50KHz','60KHz','70KHz','Location','best')

title('Sensor 1 MSD','FontSize',16)



99

figure(5)

semilogy(f,NU10,f,NU20,f,NU30,f,NU40,f,NU50,f,NU60,f,NU70)





figure(6)

loglog(f,VM10,f,VM20,f,VM30,f,VM40,f,VM50,f,VM60,f,VM70)





figure(7)

semilogy(f,VM10,f,VM20,f,VM30,f,VM40,f,VM50,f,VM60,f,VM70)





%================================================================

100

101

References

1 Chikazumi, S. (1997). Physics of Ferromagnetism. New York: Oxford University Press Inc. 2 Valasek, J. (1921). Piezo-Electric and Allied Phenomena in Rochelle Salt. Physical Review 17 ,

475-481. 3 H. Ohno, D. C. (2000). Electric-field control of ferromagnetism. Nature 408 , 944-964. 4 Guoxi Liu, X. C. (2010). A tunable ring-type magnetoelectric inductor. Journal of Applied

Physics , DOI:10.1063/1.3504218. 5 Fiebig, M. (20005). Revival of the magnetoelectric effect. Journal of Applied Physics , 123-

152. 6 W. Eerenstein, N. D. (2006). Multiferroic and Magnetoelectric Materials. Nature , 759-765. 7 Balanis, C. A. (1989). Advanced Engineering Electromagnetics. Hoboken, NJ: John Wiley &

Sons, Inc. 8 Yong-Kyu Yoon, D. K. (2003). A reduced intermodulation distortion tunable ferroelectric

capacitor-architecture and demonstration. IEEE Transactions on Microwave Theory and

Techniques , 2568 - 2576. 9 A.M. Ionescu, L. L. (2010). The Hysteretic Ferroelectric Tunnel FET. IEEE Transactions on

Electron Devices , 3518 - 3524 . 10 J. X. Zhang, G. S. (March 2010). Large electric field induced strains in ferroelectric islands.

Applied Physics Letters 96 , doi:10.1063/1.3373915. 11 Landis, C. M. (January 2004). Non-linear constitutive modeling of ferroelectrics. Current

Opinion in Solid State and Materials Science, Volume 8 , 59-69. 12 Engdahl, G. (2000). Handbook of Giant Magnetostrictive Materials. San Diego: Academic

Press. 13 M. Bailoni, Y. L. (2008). Mathematical Modelling and Simulation of Magnetostrictive

Materials. Comsol Conference 2008 Worldwide. Hannover. 14 Surface-Adhesive Piezo Pickup. (n.d.). Retrieved 2 16, 2011, from Artec:

http://www.artecsound.com/acou/index.html 15 P-855 Miniature Piezo Actuator. (n.d.). Retrieved 2 16, 2011, from PI:

http://www.physikinstrumente.com/en/products/prdetail.php?sortnr=100650

102

16 FeONIC F1.3 DML AUDIO DRIVE. (n.d.). Retrieved 2 16, 2011, from FeONIC:

http://www.feonic.com/#f13Info 17 Linear-Position Sensors. (n.d.). Retrieved 2 16, 2011, from MTS Sensors:

http://www.mtssensors.com/products/linear-position-sensors/index.html 18 Nicola A. Spaldin, Manfred Fiebig. The Renaissance of Magnetoelectric Multiferroics, Science, July

2005, DOI: 10.1126/science.1113357 19 Ce-Wen Nan, M. B. (Feb. 2008). Multiferroic magnetoelectric composites: Historical

perspective, status, and future directions. Journal of Applied Physics - Applied Physics Reviews -

Focused Review , doi:10.1063/1.2836410. 20 Yutaro Kitagawa, Y. H. (August 2010). Low-field magnetoelectric effect at room temperature.

Nature Materials , DOI: 10.1038/NMAT2826. 21 E. Ascher, H. R. (1966). Some properties of ferromagnetic nickel-iodine boracite,

Ni13B7O13I. Journal of Applied Physics , 37, 1404-1405. 22 Astrov, D. (1960). The magnetoelectric effect in antiferromagnetics. Sov. Phys. JETP 11 , 708-

709. 23 V.J. Folen, G. R. (1961). Anisotropy of the magnetoelectric effect in Cr2O3. . Phys. Rev. Lett.

6 , 607-608. 24 T. Kimura, G. L. (2005). Electric polarization rotation in a hexaferrite with long-wavelength

magnetic structures. Phys. Rev. Lett. 94 , 137201. 25 Chaoyong Deng, Y. Z.-W. (October 2007). Magnetic-electric properties of epitaxial

multiferroic NiFe2O4–BaTiO3 heterostructure. Journal of Applied Physics 102 ,

doi:10.1063/1.2785818. 26 Junyi Zhai, Z. X. (2008). Magnetoelectric Laminate Composites: An Overview. Journal of the

American Ceramics Society , DOI: 10.1111/j.1551-2916.2008.02259.x. 27 Junyi Zhai, S. D. (August 2006). Giant magnetoelectric effect in Metglas/polyvinylidene-

fluoride laminates. APPLIED PHYSICS LETTERS 89 , DOI: 10.1063/1.2337996. 28 S. M. Gillette, A. L. (n.d.). Low frequency sensitivity enhancement and environmental noise

mitigation of unbiased magnetoelectric magnetic field sensors using modulated ac

magnetostrictive response. Unpublished . 29 J. Das, J. G. (August 2009). Enhancement in the field sensitivity of magnetoelectric laminate.

Applied Physics Letters , DOI: 10.1063/1.3222914.

103

30 Park, G. (2005). Overview of Energy Harvesting Systems. The First Engineering Institute

Workshop . Los Alamos National Laboratory: Engineering Institute of Engineering Sciences &

Applications. 31 Livingston, J. D. (1982). Magnetomechanical properties of amorphous metals. Physica Status Solidi -

Applied research , 591-596. 32 ThinkSRS. (n.d.). About Lock-In Amplifiers: Application Note#3. Retrieved 3 15, 2011, from

ThinkSRS: http://www.thinksrs.com/downloads/PDFs/ApplicationNotes/AboutLIAs.pdf

northeastern university graduate school of engineering1297/... · northeastern university ....

Documents