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Passive Wireless Wall Shear Stress Sensors

Permanent Link: http://ufdc.ufl.edu/UFE0042524/00001

Material Information

Title: Passive Wireless Wall Shear Stress Sensors
Physical Description: 1 online resource (192 p.)
Language: english
Creator: SELLS,JEREMY
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: CAPACITIVE -- DRAG -- FLOW -- MEMS -- PASSIVE -- RESONANT -- SENSORS -- SHEAR -- WIRELESS
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The design and realization of the first ever passive wireless wall shear stress sensors are presented. The sensors are capable of directly measuring shear forces, 4 mPa to 4 Pa, created at the solid-fluid boundary of a flow. To capture the spatially small structures of a turbulent flow, a micromachined, variable-capacitor floating element sensor is designed. Passive wireless capability is achieved with the addition of an inductive coil and interrogating antenna. These sensors will enable characterization of complex flow phenomena. The primary benefit of the system is that the sensors operate without the need of a direct electrical connection. This simplifies installation of the sensors and enables their placement in locations where the rest of the system either will not fit or cannot survive. By using a passive wireless technique, a power source is not required, extending the life of the sensor and simplifying fabrication. The system makes use of frequency separation, allowing one interrogating antenna to query multiple sensors configured as an array simultaneously. Two generations of the wireless sensor are presented. The design, fabrication, packaging, and characterization of two first-generation sensors have dynamic ranges of 37 and 52 dB. Following this work, specific design improvements were identified and integrated into a second generation sensor design, resulting in an improvement to 62 dB dynamic range and an order of magnitude reduction in parasitic capacitance and humidity sensitivity. Ideas for a third generation are presented, but realization of this design is left for future work.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by JEREMY SELLS.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Arnold, David.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-10-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0042524:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042524/00001

Material Information

Title: Passive Wireless Wall Shear Stress Sensors
Physical Description: 1 online resource (192 p.)
Language: english
Creator: SELLS,JEREMY
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: CAPACITIVE -- DRAG -- FLOW -- MEMS -- PASSIVE -- RESONANT -- SENSORS -- SHEAR -- WIRELESS
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The design and realization of the first ever passive wireless wall shear stress sensors are presented. The sensors are capable of directly measuring shear forces, 4 mPa to 4 Pa, created at the solid-fluid boundary of a flow. To capture the spatially small structures of a turbulent flow, a micromachined, variable-capacitor floating element sensor is designed. Passive wireless capability is achieved with the addition of an inductive coil and interrogating antenna. These sensors will enable characterization of complex flow phenomena. The primary benefit of the system is that the sensors operate without the need of a direct electrical connection. This simplifies installation of the sensors and enables their placement in locations where the rest of the system either will not fit or cannot survive. By using a passive wireless technique, a power source is not required, extending the life of the sensor and simplifying fabrication. The system makes use of frequency separation, allowing one interrogating antenna to query multiple sensors configured as an array simultaneously. Two generations of the wireless sensor are presented. The design, fabrication, packaging, and characterization of two first-generation sensors have dynamic ranges of 37 and 52 dB. Following this work, specific design improvements were identified and integrated into a second generation sensor design, resulting in an improvement to 62 dB dynamic range and an order of magnitude reduction in parasitic capacitance and humidity sensitivity. Ideas for a third generation are presented, but realization of this design is left for future work.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by JEREMY SELLS.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Arnold, David.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-10-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0042524:00001


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1 PASSIVE WIRELESS WALL SHEAR STRESS SENSOR S By JEREMY SELLS A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2011

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2 2011 Jeremy Sells

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3 To my loving wife, Keri, who supported me through all the late nights and long hours

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4 ACKNOWLEDGMENTS I would like to start by acknowledging my chairman, Dr. David P. Arnold. He has been a great teacher, mentor, and professional advisor. He has provided me with the many opportunities that have propelled me to this point in my career. This w ork would not have been possible without his guidance I would also like to thank the rest of my committee: Dr. Mark Sheplak whose work in the field of shear stress sensors is the basis of much of this work, Dr. Henry Zmuda who is one of my professors and technical advisors in the area of electromagnetic field theory, and Dr. Louis Cattafesta whose tutelage resulted in much of my experimental and data analysis knowledge. I would like to thank my technical mentors at the National Aeronautics and Space Admin istration (NASA) Langley Research Center: Catherine McGinley and George Beeler who helped to coordinate my two summer internships in 2008 and 2009. These experiences provided me with the expertise, skills, and confidence to excel in both an academic and pr ofessional work place. Most of all, I have to thank all of my colleagues and peers in the Interdisciplinary Microsystems Group (IMG). More than any other source, the hours of discussion in front of a white board have produced the seeds of ideas presented i n this work. Specifically, I have to thank Dr. Vijay Chandrasekharan who was my partner on the NASA project. His dissertation work on the wired version of the first generation sensors paved the way for the wireless sensor's success. My newest partner on the NASA project has been Jess Meloy, who has replaced Vijay on the wired sensors since his graduation. I also have to thank my undergraduate assistant, Zach ary Kaufman, who collected a lot of the data presented in this dissertation and who built the circuit ry for the electrostatic actuation test. TaiAn Chen gave me my first introduction and training on microfabrication in the cleanroom. I also received fabrication and characterization help from

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5 Niagong Wang, Sheetal Shetye, and Janhavi Agashe. I had many ac ademic discussions with officemates, Alex Phipps Drew Wetzel and Matt Williams where I learned things from other fields that I was able to use for my own work. Two sensor generations were fabricated and packaged entirely in house here in the Nanoscale Res earch Facility (NRF) at the U niversity of Florida. I would like to thank all of the support staff at NRF and especially the cleanroom techs, Al Ogden Bill Lewis David Hays, and Ivan Kravchenko. Packaging and testing of th e sensor s would not have been pos sible without Ken Reed at TMR Engineering. I have to thank NASA for the financial support of this work. This project was supported by NRA Grant NNX07AB27A under the Subsonic Fixed Wing Project, which is a part of the Aeronautics Research Mission Directorat e. Personal funding was supplied by a NASA GSRP fellowship and ARMD scholarship under Grant NNXO7AT43H. Anthony Springer at NASA headquarters and Angela Medyk with the University of Florida Grants Office went above and beyond to help me with my fellowship. There are many people that I have to thank for help in editing this dissertation. My advisor, Dr. David Arnold, went above and beyond in helping me edit this document, both for grammar and language as well as for technical accuracy. Dr. Zmuda, Dr. Catafest a, and Dr. Sheplak of my committee contributed technical edits toward the completion of this work. The copy editing of this dissertation was performed by Dr. Victoria of www.Edit911.com. I owe both Dr. Victoria and Dr. Baldwin, the Editor in Chief of Edit911, a huge debt of gratitude for coming through for me when my deadlines were looming. I also had help with individual chapter edits from some of my colleagues at IMG, specifically Dr. Vijay Chandrasekharan, Jess Meloy, Brandon Bertolucci, and Erin Patrick .

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...............................................................................................................4 LIST OF TABLES ...........................................................................................................................9 LIST OF FIGURES .......................................................................................................................11 ABSTRACT ...................................................................................................................................18 CHAPTER 1 INTRODUCTION ..................................................................................................................19 1.1 Basic Sensor Operation .................................................................................................22 1.2 Sp ecific Applications ....................................................................................................24 1.3 Dissertation Organization ..............................................................................................28 2 BACKGROUND ....................................................................................................................29 2.1 Wireless Sensor History ................................................................................................29 2.2 Passive Wireless Literature Review ..............................................................................31 2.2.1 Review of Work Done at the Institute for Visual Sciences ..............................32 2.2.2 Review of Work Done at Uppsala University in Sweden ................................33 2.2.3 Review of Work Done at the Korean Institute of Science and Technology .....34 2.2.4 Review of Work Done at Pennsylvania State University .................................36 2.2.5 Review of Work Done at the University of Michigan ......................................37 2.2.6 Review of Work Done at the University of Minnesota ....................................38 2.2.7 Review of Work Done at the Georgia Institute of Technology ........................39 2.2.8 Review of Work Done at the C alifornia Institute of Technology ....................40 2.3 Summary .......................................................................................................................40 3 SENSOR MODELING ...........................................................................................................44 3.1 Coil and Antenna Models .............................................................................................44 3.1.1 Sensor Coil and Antenna Inductance ................................................................45 3.1.2 Mutual Inductance ............................................................................................50 3.1.3 Parasitics ...........................................................................................................52 3.2 Capacitive S hear Stress Sensor .....................................................................................55 3.2.1 Mechanical Model ............................................................................................55 3.2.2 Capacitance Model ...........................................................................................57 3.2.3 Pa rasitics ...........................................................................................................62 3.3 Full Sensor Model .........................................................................................................69 3.3.1 Single Sensor Model .........................................................................................70 3.3.2 Coupled Resonators ..........................................................................................72 3.3.3 Quality Factor at Resonance .............................................................................76

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7 3.3.4 Multiple Sensor Array Model ...........................................................................77 4 EXPERIMENTAL SETUPS ..................................................................................................80 4.1 Die Level Testing ..........................................................................................................80 4.1.1 Electrical Impedance Testing ...........................................................................80 4.1.2 Electrostatic Actuation Testing ........................................................................82 4.2 Wireless Sensor Testing ................................................................................................84 4.2.1 Network Analyzer Resonance Tracking ...........................................................84 4.2.2 Noise Floor and Frequency Stability Testing ...................................................86 4.2.3 Humidity Sensitivity Testing ............................................................................87 4.2.4 Static Calibration Testing .................................................................................89 4.2.5 Wind Tunnel Testing ........................................................................................91 5 FIRST GENERATION DEVICES ........................................................................................97 5.1 Device Overview ...........................................................................................................97 5.1.1 Coil and Antenna Modeling Results .................................................................98 5.1.2 Capacitive Sensor Modeling Results ..............................................................103 5.1.3 Completed Model Results ..............................................................................107 5.2 Fabrication and Packaging ..........................................................................................108 5.2.1 Process Flow ...................................................................................................109 5.2.2 Hybrid Packaging ...........................................................................................111 5.3 Experimental Results ..................................................................................................113 5.3.1 Impedance Characterization ...........................................................................114 5.3.2 Electrostatic Actuation Test ............................................................................117 5.3.3 Wireless Resonant Frequency, Stability, and Noise Floor .............................118 5.3.4 Static Shear Flow Calibrations .......................................................................122 5.3.5 Wireless Range Test for Design 1 ..................................................................124 5.3.6 Wireless Humidity Test for Design 1 .............................................................126 5.3.7 NASA 20 x 28 Wind Tunnel Test of Design 2 ...............................................127 6 SECONDGENERATION DEVICES .................................................................................131 6.1 Design Improvements .................................................................................................132 6.1.1 Sensor Structure ..............................................................................................132 6.1.2 Parasitics .........................................................................................................134 6.1.3 Humidity S ensitivity .......................................................................................134 6.2 Device Overview .........................................................................................................136 6.2.1 Coil and Antenna Modeling Results ...............................................................136 6.2.2 Capacitive Sensor Modeling Results ..............................................................137 6.2.3 Completed Model Results ..............................................................................140 6.3 Fabrication And Packaging .........................................................................................142 6.4 Experimental Results ..................................................................................................144 6.4.1 Impedance Characterization ...........................................................................145 6.4.2 Wireless Resonance Stability .........................................................................146 6.4.3 Wireless Humidity Tests ................................................................................147

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8 6.4.4 Static Shear Flow Calibrations .......................................................................148 7 CONCLUSIONS AND FUTURE WORK ...........................................................................152 7.1 Summary .....................................................................................................................152 7.2 Research Contributions ...............................................................................................154 7.3 Future Work ................................................................................................................154 7.3.1 Future Gen erations .........................................................................................155 7.3.2 Additional Testing ..........................................................................................157 7.3.3 System Optimization ......................................................................................159 APPENDIX A LINEARITY DERIVATIONS .............................................................................................161 A.1 Mechanical Nonlinearity .............................................................................................161 A.2 Capacitive Nonlinearity ..............................................................................................162 A.3 Resonant Nonlinearity .................................................................................................163 A.4 Cascaded Results .........................................................................................................165 B IMPEDANCE DERIVATIONS ...........................................................................................166 B.1 Single Sensor ...............................................................................................................166 B.2 Array of Sensors With No Inter Sensor Coupling ......................................................167 B.3 Array of Sensor With InterSensor Coupling .............................................................168 C COUPLED RESONATOR FREQUENCY DEPENDANCE ..............................................170 C.1 Same Resonant Frequencies ........................................................................................170 C. 2 Different Resonant Frequencies ..................................................................................172 D QUALITY FACTOR DERIVATIONS ................................................................................175 D.1 Inductors and Capacitors .............................................................................................175 D.2 Simple RLC Resonant Circuits ...................................................................................177 D.3 Wireless Shear Stress Sensor Quality Factor ..............................................................178 E COMB FINGER ELECTROSTATIC PULL IN DERIVATIONS ......................................180 E.1 Parallel Plates ..............................................................................................................180 E.2 Comb Fingers ..............................................................................................................182 LIST OF REFERENCES .............................................................................................................184 BIOGRAPHICAL SKETCH .......................................................................................................192

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9 LIST OF TABLES Table page 21 Passive wireless sensor quantities from literature review ..................................................41 41 Agilent E4991A material property analyzer settings. ........................................................81 42 HP 4294A impedance analyzer settings. ...........................................................................82 43 Agilent 8719D network analyzer settings. .........................................................................86 44 NASA tunnel test configuration settings and conditions ...................................................93 51 Geometric parameters used for the spiral coil inductors and loop antenna in the first generation wireless design. ................................................................................................99 52 Parameter values extracted numerically, analytically, and experimentally for the coupled inductor model. ...................................................................................................103 53 Geometric parameters from the two capacitive MEMS sensors used for the first generation wireless tests. .................................................................................................104 54 Analytical modeling results for the MEMS capacitive sensors. ......................................105 55 Geometries of parasitic capacitive structures in the capacitive MEMS sensors. .............106 56 Parasitic results for the MEMS sensor derived using analytical, numerical and experimental models. .......................................................................................................106 57 Full wireless system resonance and sensitivity results. ...................................................108 58 Electrostatic pullin parameters for the first generation designs. ....................................118 59 Results predicted by the model. .......................................................................................121 510 Final experimental sensitivity, minimum detectable signal and dynamic range. ............124 511 Flat plate turbulent boundary layer test results ................................................................129 61 Parameter values ext racted numerically, analytically, and experimentally for the coupled inductor model. ...................................................................................................136 62 Geometric parameters for the second generation capacitive sensor. ...............................139 63 Analytical modeling results for the second generation capacitive sensor. ......................139 64 Geometries of parasitic capacitive structures in the second generation capacitive sensors. .............................................................................................................................140

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10 65 Parasitic results for the second generation capacitive sensor derived using numerical and experimental models. ................................................................................................140 66 Full wireless system resonance and sensitivity results for the second generation wireless sensor. ................................................................................................................141 67 Results predicted by the model for the second generation device. ..................................147 68 Final experimental sensitivity, minimum detectable signal, and dynamic range for the second generation sensor. ..........................................................................................149 71 Performance summary and comparison with previous work from the literature. ............154

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11 LIST OF FIGURES Figure page 11 Simplified aerodynamic geometries in two dimensional flow. .........................................20 12 General concept for a passive wireless shear stress sensor. ...............................................23 13 Gener al concept for a wireless array. ................................................................................24 14 Sensor cabling requirement comparison. ...........................................................................25 15 Basic diagram of flow over an airfoil with laminar and turbulent regions. .......................25 16 Illustration of a separated boundary layer on an airfoil. ....................................................27 17 Illustration of the sensor being used for nonintrusive wireless measurement of the flow rate inside a pipe. .......................................................................................................27 21 Wireless sensor categories, with the LC resonant passive wireless sensor technique used in this research highlighted. .......................................................................................30 22 Reprint of Figure 2 from Carter Collins, "Miniature passive pressure transensor for implanting in the eye," 1967, IEEE Transactions on Biomedical Engineering, reprinted with permission from IEEE. ...............................................................................33 23 Reprint of Figure 1a from Lars Rosengren, "A system for passive implantable pressure sensors," 1994, Sensors and Actuators A: Physical reprinted with permission from Elsevier. ..................................................................................................34 24 Reprint of Figure 1 from Park, E .C., "Hermetically sealed inductor capacitor (LC) resonator for remote pressure monitoring," 1998, Japanese Journal of Applied Physics reprinted with permission from the Japan Society of Applied Physics. ..............35 25 Reprint of Figure 1b from Keat Ong, "Design and application of a wireless, passive, resonant circuit environmental monitoring sensor," 2001, Sensors and Act uators A: Physical reprinted with permission from Elsevier. ...........................................................36 26 Reprint of Figure 1 from Orhan Akar, "A wireless batch sealed ab solute capacitive pressure sensor," 2001, Sensors and Actuators A: Physical reprinted with permission from Elsevier. ..................................................................................................38 27 Reprin t of Figure 1a from Antonio Baldi, "A self resonant frequency modulated micromachined passive pressure transensor," 2003, IEEE Sensors Journal reprinted with permission from IEEE. ..............................................................................................39

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12 28 Reprints of figures from Michael A. Fonseca, "Flexible wireless passive pressure sensors for biomedical applications," 2006 Hilton Head Workshop on Sensors and Actuators, reprinted with the permission of the author and the Transducer Research Foundation. A) A reprint of Figure 3b. B) A reprint of Figure 4b. ...................................39 29 Reprint of Figure 3 from PoJui Chen, "Wireless intraocular pressure sensing using microfabricated minimally invasive flexible coiled LC sensor implant," 2010, Journal of Microelectromechanical Systems reprinted with permission from IEEE. ......41 31 Basic circuit model for the wireless shear stress sensor. ...................................................44 32 A 3D diagram of a single layer 2 turn spiral coil. .............................................................46 33 Cross sections of spiral coil from Figure 3 2 with geometric parameters indicated. ........46 34 Skin depth effect on current density inside a conductor. ...................................................48 35 Discretization of wire segments for high frequency compensation. ..................................49 36 Qualitative current density distributions in various wire be nd configurations. .................50 37 Equivalent transformer model circuits for coupled coils. ..................................................52 38 Non ideal circuit model for the sensor coil. .......................................................................52 39 Non ideal circuit model for the antenna. ...........................................................................52 310 Cross section side view showing two wires of the coil. ....................................................55 311 Mechanical diagram of the floating element sensor structure. ..........................................56 312 Simplified clamped clamped beam mechanical model of sensor with force vectors. .......56 313 A 3D graphic of the sensor with variable capacitive structures indicated (not to scale). .................................................................................................................................58 314 Zoomed in 3D graphic showing capacitive comb fingers (not to scale). ...........................60 315 Zoomed in 3D graphic showing element end capacitance (not to scale). ..........................61 316 Zoomed in 3D graphic showing tether capacitance (not to scale). ....................................61 317 Non ideal circuit model for capacitive shear stress sensor. ...............................................62 318 Two 3D pad structures showing dimensions for parasitic calculations. ............................63 319 Finger fringe simulation results. ........................................................................................65 320 Element end fringe field simulation results. ......................................................................65

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13 321 Tether cross sections and fringing simulation results. .......................................................66 322 Pad gap cross section showing simulated fring ing fields and the effect of the substrate beneath the pads. .................................................................................................66 323 A 3D graphic showing the side view of the pads with overlaid circuit model of the bulk parasitic capacitive structures (not to scale). .............................................................68 324 Equivalent circuit models for padto bulk parasit ics. ........................................................68 325 A generic waterfall plot showing a resonant frequency shifting in time. ..........................69 326 Full circuit model for a single wireless shear stress sensor. ..............................................70 327 Sensor spectrum showing resonant peak and the shift due to a change in capacitance. ....71 328 Normalized sensitivity of the sensor response to 10 % variations in fabricated geometries. .........................................................................................................................73 329 Basic T circuit for magnetically coupled resonators. .........................................................74 330 Coupled resonator plot showing overlapping and separated resonances. ..........................74 331 Resonant frequency se nsitivities to electrical parameters. ................................................75 332 Resonant frequency sensitivities to electrical parameters. ................................................76 333 Plot showing MDS dependence on Q. ...............................................................................77 334 Circuit model for a 2 x 2 sensor array. ...............................................................................79 335 Array spectrum sowing individual bandwidths for four sensors. ......................................79 41 Probe station setup for impedance characterizations. ........................................................81 42 Electrostatic actuation test setup. .......................................................................................83 43 Network analyzer operation ..............................................................................................85 44 Diagram of a single sensor placed in a faraday cage to reduce external noise. .................87 45 Humidity sensitivity test setup. ..........................................................................................88 46 Static calibration flow cell. ................................................................................................89 47 NASA 20" x 28" wind tunnel setup showing the location of the sensor in the model. .....91 48 Pres sure tap readings from the ceiling of the Shear Flow Control Tunnel for all test points. .................................................................................................................................94

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14 49 Turbulent boundary layer profile for 15 m/s flow over a flat plate. ..................................95 410 Turbulent boundary layer plotted in + units to illustrate the Law of The Wall. ................95 51 Optical image showing the Design 2 capacitive shear stress sensor next to a pencil for scale. .............................................................................................................................97 52 Coil designs showing simulated and realized inductors. ...................................................98 53 Design showing both the simulated and realized loop antenna. ........................................98 54 Skin depth vs. frequency for copper. ...............................................................................100 55 Coil discretization plot looking at the cross sectio nal area of a wire trace. ....................100 56 Inductive coupling was simulated with the coil and antenna coaxially aligned with a 1.5 mm separation. ...........................................................................................................100 57 FastHenry simulation results for Design 1. ......................................................................101 58 FastHenry simulation results for Design 2. ......................................................................101 59 Parasitic capacitance due to RF connectors between the network analyzer and the loop antenna. ....................................................................................................................102 510 Optical images of the MEMS capacitive s ensors highlighting the vital components. .....104 511 Simulated capacitance and conductance factoring in the bulk layer model. ...................107 512 Resonant dips in the reflection coefficient predicted by the model for both Design 1 and Design 2. ...................................................................................................................109 513 Generation 1 MEMS sensor fabrication process flow. ....................................................110 514 Photolithography dark field mask set used to define etches in the process flow. ............110 515 Packaging concept for hybrid wireless shear stress sensors. ...........................................111 516 Process flow for hybrid wireless packaging. ...................................................................112 517 Final packaged wireless sensor shown next to a U.S. penny for perspective. .................112 518 Wireless sensor boards flush mounted in test plugs used for the flow cell calibration and wind tunnel tests. .......................................................................................................113 519 Capacitance measurement and error for Design 1 and 2. ................................................115 520 Die level high frequency impedance sweeps for six Design 1 sensors. ...........................116

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15 521 Die level high freq uency impedance sweeps for six Design 2 sensors. ...........................117 522 Video frame from electrostatic forcing test. ....................................................................118 523 Displacement results processed by MATLAB. ...............................................................119 524 Resonant dips showing the accuracy of the model.. ........................................................120 525 Sensor resonance drift. .....................................................................................................121 526 Noise plot. ........................................................................................................................122 527 Linear static calibration for sensor Design 1. ..................................................................122 528 Static shear stress calibration for Design 2. .....................................................................123 529 Repeatability shear stress calibrations for Design 2. .......................................................124 530 Frequency sweeps showing resonant frequency dip height reduction with increasing coil antenna separation. ....................................................................................................125 531 Range test results showing the maximum separation within which re sonance can be determined. .......................................................................................................................126 532 Wireless sensor response to humidity. .............................................................................127 533 Boundary layer profiles for all test cases. ........................................................................128 534 Wind tunnel calibration for Design 2. ..............................................................................129 61 Optical image showing the second generation capacitive shear stress sensor next to a pencil for scale. ................................................................................................................131 62 Representations of the sensor structures shown out of scale. .........................................133 63 Pressure driven flow diagrams. ........................................................................................133 64 Illustration of secondgeneration sensor bond pad. .........................................................134 65 Backlit photograph of the secondgeneration wireless sensor showing a 6turn coil with a 3.5 mm inner diameter and diamonddesign capacitive sensor. ...........................137 66 SEM image of the second generation sensor die highlighting the vital components. .....138 67 Second generation frequency response showing the accuracy of the model and a comparison to the first generation. ...................................................................................141 68 Fabrication process flow for second generation device. ..................................................143

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16 69 Mask set used for phot olithography in steps 3 and 9. ......................................................144 610 Capacitance and conductance impedance sweeps for second generation sensor. ...........146 611 Measured second generation device drift. .......................................................................147 612 Second generation sensor response to humidity. .............................................................148 613 Linear static calibration for the second generation sensor. .............................................149 614 Second generation hysteresis test results showing two full cycles. .................................150 615 Rotation test illustration. ..................................................................................................151 616 Rotation test results showing directional response of the sensor. ....................................151 71 Back side of the third generation concept sensors. ..........................................................155 72 Fabrication technologies required to realize third generation integrated wireless shear stress sensors. .........................................................................................................156 73 Wireless arrays realized by dicing devices in blocks. ......................................................157 74 Basic concept for RF circuitry that would enable dynamic shear stress testing. .............158 75 Diagram of the plane wave tube used for dynamic shear stress characterization. ...........159 76 General system optimization loop. ..................................................................................160 A 1 Capacitive shear stress sensor mechanical nonlinearity plot. ..........................................164 A 2 Capacitive shear stress sensor capacitive nonlinearity plot. ............................................164 A 3 Capacitive shear stress sensor resonant nonlinearity plot. ...............................................165 A 4 Capacitive shear stress sensor cascaded nonlinearity plot. ..............................................165 B 1 Full single wireless sensor mode l for impedance derivations. ........................................167 B 2 Wireless sensor array model for impedance derivations with no inter sensor coupling. ...........................................................................................................................168 B 3 Wireless sensor array for impedance derivations with full coupling model. ...................169 B 4 Multiport impedance model. ............................................................................................169 C 1 Simple coupled resonator circuit. ....................................................................................172 C 2 Coupled resonator circuit. ................................................................................................174

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17 D 1 Simple RL and GC circuits. .............................................................................................175 D 2 Simple RLC and GLC resonant circuits. ..........................................................................177 D 3 Wireless shear stress sensor circuit including parasitics. .................................................178 E 1 Basic parallel plate diagram for electrostatic pullin derivation. .....................................181 E 2 Comb finger diagram for electrostatic pullin derivation. ...............................................183

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18 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PASSIVE WIRELESS WALL SHEAR STRESS SENSOR S By Jeremy Sells ABSTRACT M a y 2011 Cha ir: David P. Arnold Major: Electrical and Computer Engineering The design and realization of the first ever passive wireless wall shear stress sensors are presented The sensors are capable of directly measuring shear forces 4 mPa to 4 Pa, created at the solid fluid boundary of a flow. To capture the spatially small structures of a turbulent flow, a micromachined, variable capacitor floating element sensor is designed. Passive wireless capability is achieved with the addition of an inductive coil and inte rrogating antenna. These sensors will enable characterization of complex flow phenomena. The primary benefit of the system is that the sensors operate without the need of a direct electrical connection. This simplifies installation of the sensors and enables their placement in locations where the rest of the system either will not fit or cannot survive. By using a passive wireless technique, a power source is not required, extending the life of the sensor and simplifying fabrication. The system makes use of frequency separation, allowing one interrogating antenna to query multiple sensors configured as an array simultaneously. Two generations of the wireless sensor are presented The design, fabrication, packaging, and characterization of two first generation sensors have dynamic ranges of 37 and 52 dB Following this work, specific design improvements were identified and integrated into a second generation sensor design, resulting in a n improvement to 62 dB dynamic range and an order of magni tude reduction in parasitic capacitance and humidity sensitivity Ideas for a third generation are presented, but realization of this design is left for future work.

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19 CHAPTER 1 1 INTRODUCTION Transportation of people and goods is essential to modern society. We use cars to travel back and forth from work or school every day, and aircraft allow us to cross continents and oceans. Trucks deliver goods to our local stores, and trains transport huge quantities of cargo across the county. Nearly every individual and business depends on some form of transportation. With rising fuel prices and enormous demand, technologies that can help to imp rove the performance (speed, safety, efficiency, etc.) of these vehicles are needed. The growing green economy is also creating a greater demand for more fuel efficient vehicles. All terrestrial vehicles must travel through a fluidic medium, air for cars a nd planes to get from point A to point B. Like gravity, many of us forget about the air around us until we are hit by a large gust of wind. However, a moving vehicle must constantly overcome forces imposed on it by the air to accelerate or maintain a cons tant velocity. This resistance to motion is referred to as drag and includes any force on the outer surface of the vehicle body that is opposite to the direction of travel. For subsonic and transonic vehicles, the total drag includes two primary components pressure drag and friction drag. The dominant source depends on the geometry of the body and the direction of the airflow [1] as illustrated in Figure 1 1. The lowest total drag is achieved with aerodynamic geometries and the more aerodynamic the structure is the greater the influence of friction drag. Reduction of friction drag is t herefore a vital objective in improving the efficiency of future aircraft and other vehicles. Aerodynamic geometries used in modern vehicle designs are often dominated by friction drag. For a modern business jet, the friction drag accounts for up to 53% of the total drag [2] For m odern high speed trains the ratio of the friction drag to the pressure drag depends on the length of the train [3] The pressure drag is related to the effective frontal area of the train while the

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20 friction drag is related to the total surface area of the train assuming the flow is attached all the way to the trailing edge For a single standard car 60' long x 9' wide x 11' tall the friction drag will only be about 5% of the total drag. F or a passenger train with 9 cars the friction drag approaches 52% of the total aerodynamic drag. As the train gets longer the contribution from friction drag rises higher still. A B C D Figure 11. Simplified aerodynamic geometries in two dimensional flow. A) Infinitely thin plate parallel to the flow. B) Infinitely thin plate perpendicular to the flow. C) Teardrop airfoil geometry. D) Cylinder. Reducing friction drag in future aerodynamic vehicles requires ongoing effort by the scientific and engineering community. Numerical modeling using computational fluid dynamics (CFD) has been advancing rapidly, enabled by the huge growth of computational power over the last few decades [4] CFD can be very beneficial in studying how structures interact with flows, and even for predicting skin friction. However, no matter how advanced computers get, the accuracy of these simulations is only as good as the underlying physical models, so experimental measurement and validation of fundamental physical phenomena including shear stress is needed. FlowPressure Drag 0% Friction Drag 100% FlowPressure Drag 100% Friction Drag 0% FlowPressure Drag ~10% Friction Drag ~90% FlowPressure Drag ~90% Friction Drag ~10%

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21 Unfortunately, there are very few viable sensors for measuring friction drag. This is largely due to the technical challenges involved in making these measurements [5 7] Shear stress is the fundamental physica l quantity associated with friction drag. Shear stress is defined as force per unit area (areal force density) acting tangential to the body's surface and has units of Pa = N/m2. To quantify the flow over a body, the sensors have to be exposed to the flow. This makes packaging very difficult and leaves the sensor s vulnerable to other changes in the environment, such as temperature, humidity, vibrations, etc. The shear forces are very small compared to the pressure forces which make it difficult to isolate them from each other. Also the shear stress levels can vary greatly across a surface, making it necessary to make measurements at multiple locations. The lack of suitable measurement technologies is a primary motivation for the work presented in this dissertation. The development of a sensor capable of providing accurate, time resolved, directional shear data with high spatial resolution will present a major advancement for aerodynamic testing. In addition to meeting the requirements to accurately meas ure shear stress, the sensors will be capable of being tested wirelessly. This allows the sensor to be separated from the electronics and multiple sensors grouped into arrays to be monitored with a single antenna. A passive wireless detection scheme both p owers the sensors and allows the response to be tracked by an external antenna. The design is an elegantly simple extension of a wired sensor design[8] that does not require any complex tr ansceiver circuitry for the wireless link. The sensor and wireless capability are combined into a single device as described in the following section.

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22 1.1 Basic Sensor Operation Shear stress will be measured directly with a microelectromechanical (MEMS) sensor A floating element structure on the surface of the sensor is suspended by flexible tethers and located at the solid/fluid interface. The tangential drag force on the surface area of the floating element causes it to move in the same direction as the flow The physical displacement of the plate is then detected electrically by choosing a suitable transduction scheme. There are many transduction methods, such as optical [9 11] piezoresistive [12,13] and capacitive [8,1416] that have been used in previous shear stress sensors. Capacitive transduction offers advant ages in sensitivity, noise and packaging simplicity over the other techniques [17] More importantly, it is essential for the passive wireless readout technique being proposed here. A capacitor is a device consisting of two electrically isolated conductors. Capacitance is a function of the geometry of the conductors, the distance between them, and the dielectric material in between. The edge of the moving, floating element serves as one co nductor, while an adjacent fixed surface serves as the second conductor. Displacement of the floating element changes the separation, resulting in a change in capacitance. The proposed wireless detection scheme is shown in Figure 12. It relies on tracking the resonant frequency of an LC tank circuit. A LC tank circuit is an electrical second order resonator consisting of a capacitor and an inductor. T he natural frequency in Hz is given by 01 2 f LC, ( 11) where L is inductance in Henrys and C is capacitance in Farads. The MEMS shear stress sensor provides the capacitance for the tank circuit. A spiral coil connected across the terminals of the sensor provides the inductance and completes the tank. An input shear f orce will change the sensor capacitance, changing the resonant frequency of the tank circuit.

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23 Figure 12. General concept for a passive wireless shear stress sensor. A single sensor along with the interrogation setup and a basic circuit representation are shown. Wireless detection of the resonant frequency is achieved by placing a loop antenna in proximity to the sensor's induct or. The loop antenna and the sensor inductor become magnetically coupled, and a drop in the reflection coefficient of the antenna identifies the resonance of the tank circuit Changes in the sensors capacitance show up as frequency shifts in the resonant dip generated by the sensor. One advantage of this passive wireless approach is that the resonant frequency tracking technique makes the measurement less susceptible to electromagnetic interference (EMI) induced amplitude noise. EMI can be especially problematic for high impedance devices, such as capacitive sensors. High impedance devices pick up EMI from the environment. The LC circuit will naturally filter out EMI and any remaining signals will show up in the output as noise in the output spectrum. This may make determining the resonant frequency more difficult and raise the noise floor but it will not mimic a frequency shift from an input shear stress Another key advantage of the passive wireless approach is that more than one sensor can be interrogat ed by the same antenna, lending this technique to an array of sensors, as shown in Figure 13. For this to work, each sensor in the array must operate in a different frequency bandwidth. The frequency range of the spectrum can be set to include all of the sensors in the array, and sensors can be designed to operate within separate bands. This can be accomplished in

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24 two ways. First, identical shear stress sensors can be used, and different coils can be designed for each sensor, such that L is different for each. Alternatively, sensors with differing capacit ances can be designed T hen identical inductors can be used for each sensor, again resulting in each sensor occupying a different band. Figure 13. General concept for a wireless array. A 2 x 2 array is represented along with the spectrum indicating four resonances. A significant problem for any experimentalist that uses sensor arrays is the mass of wires or other connections that have to be routed between each individual sensor and the detection circuitry. Working these webs of wires into a wind tunnel test model whi le preventing things, such as cross talk between adjacent channels, can be a big problem. By using different frequencies for all of the sensors in the array, a single antenna with only one set of wires can be used to interrogate the entire array of sensors A comparison is illustrated in Figure 14. Using wireless arrays can greatly simplify model construction/wiring and increase flexibility for sensor c onfigurations within the array. 1.2 Specific Applications Aerospace engineers are in terested in the development of shear stress sensor s for fundamental flow studies of airfoils [6] The knowledge gained from these studies can be applied to improving the designs of future airfoils. A basic diagram for external flow over an airfoil is shown in Figure 15. Streamlines are shown to represent the velocity field and the boundary

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25 layer is highlighted. Flow velocity u(y) at the surface of the airfoil is zero due to the no slip boundary condition and increases to the free stream velocity U. The boundary layer is the region bounded by the surface and extends to where the local velocity reaches 99% of the free stream value. Boundary layers originate at the stagnation point (the point at the leading edge where the flow velocity is zero) and grow until they are shed at the trailing edge or when a separation condition is reached. A B Figure 14. Sensor cabling requirement comparison. A) The mess associated with a wired sensor array. B) Simplified to a single wire with the wireless sensor array. Figure 15. Basic diagram of flow over a n airfoil with laminar and turbulent regions There are three flow regimes in a boundary layer [1] ; laminar, transitional and turbulent. Laminar flow is steady and organized with no mixing in any direction and is characterized by a constant shear stress at the surface. When the flow is either tripped or the inertial forces in the flow overcome the viscous forces, eddies that break up the orderly flow form in the boundary

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26 layer. At first there will be both laminar and turbulent regions in the boundary layer, which is referred to as a transitional flow. Once these eddies permeate the entire boundary layer, the flow is referred to as turbulent. Turbulence is stochastic and contributes both mean and dynamic shear stress at the surface. A shear stress sensor capable of mean measurements can be used t o measure the characteristics of all three regimes, while a dynamic sensor is only useful for turbulence studies. The ultimate goal is a sensor capable of measuring both mean and fluctuating shear stress at the same time. Under certain conditions, often at high angle of attack the boundary layer can separate before the trailing edge of the wing. This phenomenon is known as separation and can cause a vehicle to stall if it progresses too far up the wing. When the adverse pressure gradient in a two dimensional flow becomes too large, it can retard the flow to the point where the reduced momentum is enough to cause a separation of the boundary layer as shown in Figure 16. The shear stress at the point of separation is zero, while further downstream from the separation point recirculation can cause a small shear in the opposite direction. A mean measurement of shear stress can detect the onset of separation, and the spatial location can be found by using a 1 x N array oriented along the stream wise direction. The onset detection and location of separation forms another important application area, which may be useful for active flow control strategie s [18,19] In addition to aerospace applications, the sensor could be used to measure the flow rate inside pipes. The wireless readout of the sensors would be particularly useful in this application, because it would enable measurement without any holes in the sidewall s A wired sensor would require a port for the wires to exit, which could compromise the integrity of the pipe walls. Fifty percent of all modern pipelines, including natural gas pipelines, are made of plastic [20]

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27 The nonconductive plastic construction enables a sensor mounted on the inner sidewall to be interrogat ed by an antenna located just outside the pipe, as shown in Figure 17. A velocity profile can be determined by m easuring the mean shear stress at the pipe wall under certain conditions [1] The pipe must contain a Newtonian fluid, and the flow must be fully developed. Once the velocity profile is inferred volumetric flow rate can be f ound by multiplying the average velocity by the cross sectional area of the pipe. The result is a sensor capable of wirelessly measuring the flow rate without adding any head loss to the pipe. Figure 16. Illustration of a separated boundary layer on an airfoil Figure 17. Illustration of the sensor being used for non intrusive wireless measurement of the flow rate inside a pipe. Boundary Layer Air Foil Separation Air Flow u(y) Pipeline Sensor Detection Circuitry Antenna Uavg

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28 1.3 Dissertation Organization This dissertation is organized as follows : C hapter 2 presents an in depth literature review of passive wireless sensors, including the current state of the art. Chapter 3 provide s a comprehensive model of the sensor and wireless detection strategy The sensor system is first segmented into mechanical, electrostatic, and magnetostatic models, each of which is described in detail. At the end of C hapter 3, these sub models are combined into a complete system model to predict the sensor s behavior. Chapter 4 gives details of the experimental setups used to characterize the wireless shear stress sensors. A first generation of the sensor, including design, fabrication, and experimental results, is presented in Chapter 5. Chapter 6 addresses shortcomings of the first generation devices, and presents an improved secondgeneration design, including the fabrication and test results. The final chapter gives concl uding remarks, including future work for the existing sensors and suggestions for the next generation of the sensor

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29 CHAPTER 2 2 BACKGROUND This chapter provide s a review of the relevant literature for wireless sensors. A shear stress sensor that is the first of its kind is presented so there are no precedents to compare it to. To give adequate background for comparison with previous work, a brief history of wireless sensors is given followed by an indepth review of eight passive wireless pressure force sensors. A summary is provided at the end with a table of relevant metrics for com parison. The emphasis here is more on the wireless sensing, particularly passive wireless sensing, and less on the design/optimization of the shear stress sensor itself. For a detailed review of the previous work on shear stress sensors see the review papers by Sheplak et al., Naughton et al. and Etabari [5 7] and the background chapters of dissertations by V. Chandrasekharan [21] and Y. Li [22] 2.1 Wireless Sensor History Early miniaturization of w ireless sensors was proposed t o enable the monitoring of biological processes inside the body without the need for wires protruding through the skin. In 1957 three separate groups, Mackay [23] in Sweden, Farrar [24] in the U .S ., and Sprung [25] in Germany reported on wireless sensors, referred to as endoradiosondes. These devices took the form of a pill with the sensor electronics and battery all sealed in a biocompatible casing. The internal battery power source enabled the devices to transmit the digitized sensor data to base units worn on the patients or carried by the physicians. These devices were intended to interrogate intestinal processes. The pill was to be swallowed and then disposed of, so the limited lifetime of the battery was not a restrictive issue. M any battery powered wireless sensors [2630] have been developed since these first works but a need existed for longer lasting wireless sensors that could be powered and

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30 interrogated by an external antenna. The idea for passive wireless sensors was mentioned in Mackays work [23] but it was not realized until 1967 by another researcher, Collins [31] w ho had collaborated with Mackay. There are two categories of devices described in the literature as passive wireless sensors. Figure 21 shows the classification of wireless sensors used here. Both digital and analog wireless sensors are passive, meaning neither type requires an integrated power source. Digital wireless sensors are similar to radio frequency identification (RFID), in which the interroga ting antenna is used both to power the device and receive the data [3234] Like their battery powered cou nterparts, they have the added benefit of using digital coding to improve the signal to noise ratio. However, they require integrated RF to dc power conversion and encoding circuits, making them more complicated to design and fabricate. Figure 21. Wireless sensor categories, with the LC resonant passive wireless sensor technique used in this research highlighted. Analog passive wireless sensors can be further separated into surface acoustic wave (SAW), magnetic resonance, or LC resonant devices. SAW devices rely on a change in the mechanical resonance of the sensor structure to detect changes in their environment [3537] An Wireless Sensors Passive (RF powered) Active (battery powered) Digital (RF-DC, IC, Sensors) Analog LC Resonant (frequency domain) SAW (time domain) Magnetic Resonance (frequency domain)

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31 RF pulse is sent to the sensor, where it generates a traveling acoustic wave. This wave propaga tes down the length of the sensor and is converted back to an RF electrical signal. Time domain analysis is used to track these echo pulses and identify any perturbations. Magnetic resonance devices [3840] operate based on the principles of magnetostriction, where a magnetic field causes a mechanical strain in certain materials. Similar to the SAW devices, an RF pulse is sent that causes mechanical changes in the material. These perturbations are selective to the mechanical resonant frequency, which will change depending on the sensors environment. Magnetostriction is reciprocal, so the mechanical strains pro duce an RF tone at the mechanical resonant frequency. Lastly, LC resonant sensors operate by tracking a change in electrical resonance in order to sense changes in their environment. Changes in either the inductance, L or the capacitance, C cause the reson ant frequency to shift. The resonant frequency changes are detected via an external antenna, which is inductively coupled to the inductor in the LC tank. To maintain consistent terminology, "passive wireless" will be used in the rest of this document to re fer to the LC resonant category highlighted in Figure 2 1. 2.2 Passive Wireless Literature Review There are many passive wireless devices reported in the literature from as far back as 1967 with the first work by Collins [31] Devices targeting pressure [31] humidity [41] temperature [42] pH [43] glucose [44] biological pathogens [45] and chemical agents [46] are all realizable using this technique. The pressure sensors are the most relevant for comparison to this work because they measure forces, so they are chosen for this review. The following reviews are placed in chronological order starting with Collins [31] Many of these papers use mmHg, psi, kPa, or bar for pressure, so in order to simplify comparison all pressure values have been c onverted to Pa.

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32 2.2.1 Review of Work Done at the Institute for Visual Sciences Carter C. Collins, of the Institute for Visual Sciences, San Francisco, California, presented the first passive wireless sensor in 1967 [31] The primary purpose of the device was for testing intraocular pressure in the eye, but was presented as an absolute pressure sensor viable for any part of the body within a few cm of the ski n. His design took the same plastic encapsulated pill form as the devices made by Mackay, Farrar and Sprung [2325] The device was handfabricated but it ha d dimensi ons (2 mm diameter, 1 mm thick, 62.5 The cross section of the basic device is shown in Figure 22. The pill had a sealed chamber with a compliant polymer film stretched over the top and bottom. Coils were attached to the top and bottom films and were fr ee to move with them. This created an absolute pressure sensor that could detect the compression or expansion of the pill from changes in the external pressure relative to the internal pressure. The sensor inductance was from the wire coils and the capacit ance from between the coils. As the pill contracted, the coils got closer together, and both the mutual inductance and the capacitance increased, decreasing the self resonant frequency of the device. The coils were configured so that they had a positive mutual coupling and were connected at the outer diameter of the winding. The device operated at a resonant frequency of 120 MHz and had a quality factor ( Q ) of 80. This is the highest Q reported to date. The response of the device was predicted up to 133 kPa but the calibration test was only performed up to 13 kPa. The sensitivity reported was 0.75 kHz/Pa. The discrepancy came from the fact that several different devices were reported. Drift, frequency sensitivity to coil coupling, and acceleration sensitivi ties were all tested and combined to find the precision of the device. The minimum detectible pressure was 67 Pa, which corresponds to a 167.5 kHz shift in frequency.

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33 Figure 22. R ep rint of Figure 2 from Carter Collins Miniature passive pressure trans ensor for implanting in the eye ," 1967, IEEE Transactions on Biomedical Engineering, reprinted with permission from IEEE. The electronics used for Collins research were referred to as a grid dip oscillator absorption detector. The electronics were based on a voltagecontrolled oscillator (VCO) and a phase detector. The VCO was fed a triangle wave input to sweep through a range of frequencies. At resonan ce, a phase dip detector output the voltage of the trian gle wave, which corresponded to a specific frequency in the VCO. Using this circuitry, the sensor was successfully tested both in vitro and in vivo in rabbit eyes. 2.2.2 Review of Work Done at Uppsala University in Sweden There is a large gap in time before the next significant work was presented in this area. There are several articles in the medical literature on clinical trials [47,48] of devices simi lar to Collins, but no new sensors were presented until the early 90s. Backlund and Rosengren, from Sweden presented a sensor for measuring the absolute pressure of the eye [49,50] in 1994. This was also the first work to use microfabrication technologies to build the capacitive sensor. The sensor shown in Figure 23 was made by attaching a coil to a silicon capacitive pressure sensor. The coil was wound around a form that housed the sensor chip and was then coated in a silicon rubber. The size of the entire device was 5 mm in diameter by 2 mm thick. and back side of a silicon wafer. This wafer was then bonded to another silicon wafer with a

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34 1 Figure 23. R ep rint of Fi gure 1a from Lars Rosengren A system for passive implantable pressure sensors ," 1994, Sensors and Actuators A: Physical reprinted with permission from Elsevier. The device operated at 43.6 MHz and used a griddip oscillator, similar to the circuit used by Collins [31] to detect the resonant frequency. In the first generation [49] a low Q of 5.5 was obtained, which li mited the performance of the device. The problem was attributed to parasitics within the silicon, but careful doping of the wafers brought the Q up to around 30 in the secondgeneration [50] The sensitivity of this circuit was 4 mV/kHz, and the sensitivity of the sensor was 7.5 Hz/Pa. The sensor was tested from zero to 10.7 kPa in 1.3 kPa steps. The minimum shift detected in this work was 9.75 kHz. Rosengren alluded to significant drift a nd coupling sensitivity but did not quantify the problems or isolate their sources. 2.2.3 Review of Work Done at the Korean Institute of Science and Technology The next logical step was to integrate the inductor into the MEMS design, thus simplifying the packagi ng. Figure 2 4 shows the sensor developed in Korea by Park et al. [51] which incorporates a copper coil into the sensor. An anodic wafer bonding technique was used to form the cavity. The bottom substrate was glass instead of silicon, which reduces the coils substrate parasitic capacitance and conduction losses. The bottom plate was formed by a gold liftoff process, and the coil ran from this plate out to the doped silicon cap. Electroplating copper up photoresist mold formed the square spiral coil. Instead of using a timed KOH

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35 etch for the membrane, an electrochemical etch stop was used in which the silicon left behind was defined by a doped region. This gave better control of the diaphragm thickness, which was r packaging was required. The device measured 3mm x 3mm x 0.6 mm. Figure 24. R ep rint of Figure 1 from Park, E.C., Hermetically sealed inductor capacitor ( LC ) resonator for remote pressure monitoring ," 1998, Japanese Journal of Applied Physics reprinted with permission from t he Japan Society of Applied Physics The inductor was well designed and characterized in the work as having an inductance of 220 nH, resistance of ly 380 fF. The sensor capacitance, nominally 3 pF, was also characterized and measured under pressure loading of up to 13 kPa. The data showed obvious nonlinearity with a 9x change in capacitance. The diaphragm was poorly designed for these pressures. The over compliant diaphragm was collapsing onto the bottom electrode. The grid dip oscillator was used again in this work and displayed a self resonant frequency of 120 MHz with no loading. This did not correspond with the inductor and capacitor values given and likely pointed to problems with the sensors. No pressure data was given as a result of these problems. Despite the outcome of this design, the inclusion of the coil into the fabrication was a significant contribution that was repeated in more recent wo rk by other groups.

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36 2.2.4 Review of Work Done at Pennsylvania State University All of the devices presented thus far are absolute pressure sensors for biological applications. In 2000, Keat Ong et al., part of Craig Grimes group at Pennsylvania State University published their work on a passive wireless sensor platform [52] that could, with slight modifications, be used for sensing pressure, humidity, temperature [42] relative permittivity changes, bacterial growth [45] and chemical gasses [4 6] The pressure sensor is shown in Figure 25 and was very similar to the previous designs, in which a cavity was formed separating two conductive plates that are attached to a coil. In contrast to most of the other sensors in this revie w, the devices here were very large, ranging from 3 cm x 3 cm to 6 cm x 6 cm. The increased size, along with different interrogation techniques enabled monitoring from up to 1.5 m away for the larger sensors. These sensors were similar in size and construc tion to the RF anti theft tags, which also work up to a few meters away, used in retail stores. Figure 25. R ep rint of Figure 1b from K eat Ong D esign and application of a wireless, passive, resonant circuit environmental monitoring sensor ," 2001, Sensors and Actuators A: Physical reprinted with permission from Elsevier. Two monitoring techniques were characterized and used for these sensors. The first was an impedance analyzer used with a si ngle antenna to measure impedance spectra. The second technique employed two antennas. A single frequency tone was applied to the input of the first

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37 antenna and resulted in a voltage appearing at the terminals of the second. This voltage changed as the ton e frequency was swept across a range of frequencies believed to contain the resonance. The resulting spectra traces out a curve very much like the impedance spectra from which the resonance is determined. This measurement scheme was used to increase the separation between the sensor and the detector coils, but the sensor had to be between the two coils for this approach to work. Antenna characterization was also presented, giving detection ranges as a function of number of turns and turn radius. Ong showed the potential of the wireless LC sensor techniques for many different applications and presented an analysis of the coil and antenna interactions. Due to the wide breadth of his work, little detail was given for any one sensor. The resonant frequency of t he pressure sensor was 57 MHz, and a frequency shift of 6.4 MHz was shown to be linear with an input pressure from 0 to 34 kPa. No inductance, capacitance, Q resolution, or drift data was given. 2.2.5 Review of Work Done at the University of Michigan Orhan Aka r, part of Khalil Najafi and Kendsall Wises group at the University of Michigan, took the design from Parks [51] sensor and improved upon it to create a working device [53] The same fabrication procedure was used to make the device shown in Figure 26. The first and most important change was a thicker, less compliant diaphragm that limited the maximum deflection to 400 nm. This corresponded to a capacitance change of 14% full scale with 13 kPa e possible by using more closely spaced turns. The overall dimensions of the device were smaller at 2.6 mm x 1.6 mm. The measured Q of this device was 8 and required a network analyzer to be used as the detection electronics. The network analyzer was used to obtain impedance spectra from which

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38 the resonant frequency was determined. It was slower and did not give a voltage output as did the grid dip detector, but it was much more sensitive and was capable of detecting sensors with poor Q This sensor operat ed at 76 MHz and had a full scale shift of 6 MHz for a 13 kPa input. This corresponded to a sensitivity of 900 Hz/Pa. The response was measured in 3.3 kPa steps, so the smallest detected shift was 3 MHz. Figure 26. R ep rint of Figure 1 from Orhan Akar A wireless batch sealed absolute capacitive pressure sensor ," 2001, Sensors and Actuators A: Physical reprinted with permission from Elsevier. 2.2.6 Review of Work Done at the University of Minnesota A new idea fo r a passive wireless pressure sensor was explored at the University of Minnesota. Antonio Baldi published a paper in 2003 [54] in which, instead of having a variable capacitive sensor, he attached a ferrite core to the diaphragm making it a variable inductor sensor. The capacitance was supplied by the coils intrinsic capacitance. The device was 3 mm x 3 mm overall and used a 0.95 mm diameter, 0.5 mm thick ferrite disk. The device was fabr icated in two pieces and glued together, creating the sealed cavity shown in Figure 27. The coil was electroplated on oxide coated Si, which causes the device to have a poor Q of only 5.4. The device displayed a linear range of 60 kPa before the ferrite hit the bottom of the cavity. The cavity was 1 mm deep with a 2 mm diameter. This meant that the deflection of the diaphragm was 0.5 mm at the upper limit. This sensor was collapsing similar to the sensor in Park et al. [51] and would also have benefited from a stiffer diaphragm. The linear sensitivity measured with an impedance analyzer was 9.6 Hz/Pa with a nominal resonance of 31.8 MHz.

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39 Figure 27. R ep rint of Figure 1a from Antonio Baldi A self resonant frequency modulated micromachined passive pressure transensor ," 2003, IEEE Sensors Journal reprinted with permission from IEEE. 2.2.7 Review of Work Done at the Georgia Institute of Technology A sensor for measuring aortic pressure was commercialized by CardioMEMS. This sensor w as presented in papers by English [55,56] and Fonseca [57,58] who were part of Mark Allens [59] group at the Georgia Institute of Technology. The device is shown in two configurations in Figure 28 consisted of two round spiral coils surrounding a sealed chamber with conductive plates on its top and bottom. The devices were made from Cuclad polymers and, in the second design, a ceramic chamber. They were roughly 10 mm in diameter and could be folded during implantation into the subject. B Figure 28. Reprints of figures from Michael A. Fonseca, Flexible wireless passive pressure s ensors for biomedical applicat i ons," 2006 Hilton Head Workshop on Sensors and Actuators reprinted with the permission of the author and the Transducer Research Foundation. A) A rep rint of Figure 3b. B) A rep rint of Figure 4b. The devices made use of the circular coil design used by Collins [31] and the lack of a conductive substrate to achieve Q values of up to 77, the highest reported since Collins [31] The impedance phase dip was used to characterize the system, but for clinical trials a new system was A

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40 used. Little detail is given in the technical literature, but the basic idea is as follows: An RF burst is sent to the sensor to charge the tank circuit. At the end of the burst, a decaying sine wave in the sensors resonant frequency is detected. The dynamic requirement of the system is set by the heart rate, which is at a maximum 200 beats per minute or 3.33 Hz. This sy stem tracked the resonance at 35.7 MHz with a sensitivity of 43 Hz/Pa for the stiffer ceramic chamber device. Frequency shifts of 120 kHz were detected at a 2 Hz heart rate. The sensor was successful in animal testing with a range of up to 20 cm coil separ ation. This was a very successful device that proved that this technology could be commercially viable. 2.2.8 Review of Work Done at the California Institute of Technology Po Jui Chen et al. of the California Institute of Technology presented in 20 10 the most recent passive wireless sensor found [60] They reported a new generation of wireless intraocular pressure sensors that were previously published in 2008 [61] The updated design is shown in Figure 29. They achieved much higher quality factors by removing the silicon substrate from beneath the coils. This also allowed the device to be folded for implantation, as are the CardioMEMS sensors. This group use d impedance spectra from a network analyzer for resonance detection. The device had a radius of 4 mm and wa s 4 mm x 1 .5 mm when folded for implantation The device was characterized from 0 to 13.3 kPa with 1.33 kPa resolution. This correspond ed to a detected frequency shift of 1.6 MHz They also determined the range of the sensor to be 2 cm. The sensors were te sted in vivo in rabbit eyes. 2.3 Summary A summary of metrics is presented in Table 21. The nominal static capacitance of the device is listed as Co, and static inductance is listed as L The nominal resonant frequency, quality factor and full scale shift are listed under fo, Q and ffs, respectively. The sensitivity of the sensors to changes in pressure is given as S with units of kHz/Pa. All of the sensors reviewed

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41 operate at different frequencies, so it is useful to compare a normalized sensitivity given by dividing the sensitivity S by the resonant frequency fo. The resulting normalized sensitivity, Sn is reported in ppm/Pa. To account for the variation in diaphragm size this is further normalized by the area to give the normalized force sensitivity SF in 1/N. Values inferred from the data presented in the paper are italicized All pressure units are converted to Pa for ease of comparison. Figure 29. R ep rint of Figure 3 from Po Jui Chen, W ireless intraocular pressure sensing using microfabricated minimally invasive flexible coiled LC sensor implant ," 2010, Journal of Microelectromechanical Systems reprinted with permission from IEEE. Table 21. Passive wireless sensor quantities from literature review Citation Interrogati on Circuit C o [pF] L [H] Q f o [MHz] fs [MHz] S [kHz/Pa] S n [ppm/Pa] S F [ 1/N] Collins Grid Dip 0.16 2.5 80 120 32.5 0.75 6.25 0.079 Rosengren Grid Dip 30 43.6 0.08 0.007 0.161 0.049 Park Grid Dip 3 0.22 120 15.0* 125* 500.0* Ong Z Spectra 57 6.4 0.18 3.15 0.004 Akar Z Spectra 3.65 1.2 8 76 6 0.9 11.9 12.87 Baldi Z Spectra 1.7 5.4 31.8 0.19 0.009 0.283 0.022 Fonseca Z Spectra 77 35.7 0.043 1.21 0.091 Chen Z Spectra 3.6 0.057 30 350 16 1.20 3.41 1.085 *Predicted

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42 All of the reviewed papers have a few things in common. They all used frequency sweep methods to characterize the sensor. Regardless of whether a grid dip oscillator, network analyzer, or impedance analyzer was used, they captured data from a sweep of frequencies before the exact resonant frequency was determined. They all used a loop antenna to monitor the sensors, and close proximity was required between the sensor and antenna. All of the authors modeled this link as a pair of magnetically coupled coils w ith a mutual inductance M This near field magnetostatic analysis assumed that the sensor and the antenna were not moving with respect to each other. This is an important consideration for packaging and testing passive wireless sensors. The biggest conclusion that can be taken away from these works is the critical importance of Q The Q determines the sharpness of the detected peaks that are used to determine the resonant frequency of these devices. In the case of the grid dip oscillator, there is a minimum Q for the circuit to lock onto the resonance. For values below this, the circuit will not work. For the other measurement techniques, the sharper the peak the more precisely the shift can be quantified. This means that the resolution, or minimum detectable signal ( MDS ) is directly related to the Q An important lesson can be learned by comparing the sensors above that achieved Q s of 30 or more with those that had Q s of less than 10. The comm on difference between them was the location of the coil and its surrounding medium. All of the high Q devices had coils encased in polymers rather than on the conductive silicon die. This important knowledge led to the development of a new packaging techni que for the wireless shear stress sensor with the coils embedded in the dielectric package around the capacitive sensor. There is another issue that deserves mentioning for adaptation of this passive wireless technique for use in shear stress measurements. The force sensitivities seen in all of these devices are too small for this application In general forces that are normal to the surface ( pressure) are

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43 several orders of magnitude larger than the forces that are tangential to the sur face ( s hear). The reviewed works focused on environments where the pressure forces were between 10 to 60 kPa, so these sensitivities were adequate for detection. The target shear stress levels for the sensors presented in this dissertation are around 5 Pa. In Chen's work [60] for example, w ith a sensitivity of 1.2 kHz/Pa, a 5 Pa shear stress (considering only the magnitude of the force and ignoring the direction) would give only a 6 kHz f ullscale shift. To achieve even a meager 40 dB of dynamic range require s a resolution of 60 Hz and a Q of over 600. A similar comparison made with any of the reviewed device parameters would arrive at the same conclusion. The sensitivity of the wireless s hear stress sensor must be improved by several orders of magnitude in order to reach a practical detection level.

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44 CHAPTER 3 3 SENSOR MODELING A comprehensive electromagnetic model for the wireless shear stress sensor is presented in this chapter. The sensor is separated into discrete circuit components. Models for the coils and antenna are first explained, after which the capacit ive shear stress sensor is described in detail. At the end of the chapter, the submodels are consolidated and used to predict the overall response of the system to an input shear stress. A complete model is presented for both a single sensor as well as an array. The most simplistic circuit model for the wireless sensor is shown in Figure 31. The capacitive shear stress sensor is represented by the var iable capacitance, Cs whose value is a function of the input shear. The inductor Lc connected to the sensor capacitance is referred to as the sensor coil and is used to establish the primar y resonance in the system. The second inductor La represents th e loop antenna. Inductive coupling of the two is represented b y the mutual coupling M Note that throughout the remainder of the dissertation the term coil is often used to refer to the inductor coil and its associated inductance, whereas the term ante nna is used to refer to the antenna (also technically a coil) and its inductance. Figure 31. Basic circuit model for the wireless shear stress sensor. 3.1 Coil and Antenna Models In this section t he inductances of the sensor coil and antenna are presented. The wireless link is achieved through mutual coupling of these two coils The simplistic model shown in Figure 31 represents the ideal behavior. In reality, however, there are both reactive and resistive LaLcM Cs

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45 parasitics present. The major sources of these parasitics and their incorporation into the model are presented at the end of the section. 3.1.1 Senso r Coil and Antenna Inductance There is a wide range of inductive geometries and materials that can be used for the coil and the antenna. For this work, space and fabrication complexity are considered in order to choose appropriate coil and antenna designs. First consider the LC tank. The sensor capacitance is expected to be in the low pF range, so an inductance on the order of a few hundred nH is required to achieve the desired MHz resonant frequency range. This relatively high inductance level rules out meander line inductors [62] Fabrication complexities rule out solenoid or multilayer coils, at least for the initial design. Instead, planar spiral coils are used, which facilitate high inductance and simple, single layer construction. The inductance of a planar spiral is proportional to the area bounded by the coil and the number of turns. The capacitive shear stress sensors are made using a wafer level microfabrication process and are cut from silicon wafers into square die. With this consideration, the bounded area and number of turns can be maximizedthereby maximizing inductance by using square coils. A 3D schematic of a square spiral coil is shown in Figure 32. A coils inductance is defined by both geometric and material parameters. As a general rule, inductance is proportional to the permeability of the surrounding medium, the area bounded by the turns, and the square of the number of turns N Closedform approximations exist for simplified geometries, such as long solenoids and filamentary loops, but not for planar spiral coils. There are also empirical approximations [6366] but these models are inaccurate for spirals of fewer than 10 turns and for f requencies above the kHz range.

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46 Figure 32. A 3D diagram of a single layer 2 turn spiral coil. The xy and yz planes are indicated for reference to Figure 3 3. Figure 33. Cross sections of spiral coil from Figure 32 with geometric parameters indicated. A) A yz plane side view showing crosscut coil lines. B) A xy plane top view showing the spiral pattern. A common technique [67] to calculate the inductance for square spiral coils is to break them up into sections, as shown in Figure 33 B Considering each section separately, the system will have an inductance matrix of 1121 212 1 n mnLMM ML ML ( 31) The self inductance Ln for a straight wire segment is xy-plane yz-plane 9 5 1 3 h b p Di 7 9 8 7 6 5 4 3 2 1N Di p b A B

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47 21 ln 22o nll L bh ( 32) where l is the length, b is the width, and h is the height of the segment. Assuming parallel, straight wire filaments the mutualinductance Mnm is given by 22 22ln11 2o nmllllp M pl pp ( 33) in which l is the length of the filaments and p is the distance between them. Consider a twoturn square spiral as shown in Figure 33. This structure will contain 9 segments giving self inductances ( L1, L2, L9) and 72 mutual inductances ( M12, M13, M89, M98, ... M31, M21). The inductance matrix is reciprocal so Mnm = Mmn, and the total number of unique mutual inductances is reduced to 36 ( M12, M13, M89). The sign of the mutual inductance depends on the current direction in the wires positive for wires with c urrent in the same direction and negative for wires with current in opposite directions. Wires at 90o angles do not contribute any mutual inductance so 121416182325272934360 MMMMMMMMMM ( 34) and 384547495658676978890 MMMMMMMMMM ( 35) The total inductance 22totselfLLMM ( 36) is the sum of the self inductances of each segment 123456789 selfLLLLLLLLLL ( 37) plus the positive coupling terms 1519263748MMMMMM ( 38)

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48 minus the negative coupling terms ( 39) The procedure outlined above is more accurate than the empirical approximations, but it assume s uniform current density in each wire segment. This simplifying assumption does not account for high frequency current distribution effects, where the current in the conductors travels primarily through the outer skin of the conductor, as shown in Figure 34. This phenomenon is known as the skin effect, and the characteristic skin depth can be calculated by ( 310) where is the resistivity of the conductor and f is the frequency. To account for this effect, each of the nine wire segments must be further discretized, as shown in Figure 3 5. Filaments can then replace these wire segments, and the inductance can be calculated as outlined above. An appropriate scali ng factor is assigned to each filament to account for the current density in the location of the wire segment. The frequency dependent scaling factor is found based on the 3D solution to Maxwell's Equations on all of the filaments. Figure 34. Skin depth effect on current density inside a conductor. Using this technique to account for frequency, the number of filaments in the system and thus the number of elements in the matrix are drastically increased. The total number of filaments Nfil is given by ( 311)

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49 where N is the number of turns, Nh is the discretization of the height and Nb is the discretization of the base. Take for example a basic 5 turn coil with 7 height and 9 base discretization s This results in a huge 1323 x 1323 matrix with 1,750,329 inductance terms. An ideal technique used in computational electromagnetics for dealing with very large matrices is the method of moments (MoM). FastHenry is part of the Fast Field Solver software package, written at the Massachusetts Institute of Technology, and is a free MoM code for finding the inductances of 3D geometries. It is a text based code, so a MATLAB code was written to convert the inductor geometry into appropriate input files for use by the FastHenry solver. Figure 35. Discretization of wire segments for high frequency compensation. An additional advantage of the FastHenry code is that the wire segments are not limited to the parallel and perpendicular segments shown in Figure 33 B so more advanced features like rounded corners can be integrated into the simulation. Rounded corners offer significant advantages in the current distribution of the coil without giving up a significant area that would reduce the total inductance. The current distribution in the lengths of the wires is changed at higher frequencies as described by the skin depth. The current density at the corners however is dominated by the geometry. A finite element simulation (using COMSOL Multiphysics) of four different coil corner geometries is shown in Figure 36. The areas of hig h current density are b h NbNh

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50 shown in red, and low current density in blue. Low current density concentrations are desirable to reduce resistive losses. For this reason, the second rounded geometry (Rounded 2) is selected, which actually shows a decrease in the current density around the bend. Figure 36. Qualitative current density distributions in various wire bend configurations. Red indicates high curre nt density; blue indicates low current density. After solving for the inductance of the sensor coil, the antenna inductance is simple. The same model shown in Figure 33 can be used by setting the number of turns to one and the pitch to zero. The antenna inductance is solved in the same way using the FastHenry MoM solver. With the self inductances of both the sensor coil and the antenna, the next step is to determine the mutual coupling between the coil and antenna. 3.1.2 Mutual Inductance The sensor coil and loop antenna are placed in close proximity and are treated as mutually coupled coils. The coupling factor acM k LL ( 312) is a ratio of the mutualinductance, M to the root product of the self inductances La and Lc. A transformer is a special case of coupled coils where the windi ngs share nearly all of their flux. A Squared Mitered Rounded 1 Rounded 2

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51 transformer often uses a soft magnetic core to direct the flux and achieve a near perfect coupling k For the wireless sensor, a common core is not possible, so only a fraction of the total flux is shared by the loop antenna and the sensor coil. T he mutual inductance M can be determined by simulating both the antenna and the sensor coil in a single FastHenry model The two coils are identified by separate input ports, Port 1 and Port 2, and the software gener ates a 2 x 2 matrix specifying the mutualinductances and the self inductances, 1112 2122LM ML ( 313) The mutual inductance from the antenna to the coil is equal to the mutual inductance from the coil to the antenna, that is 1221MMM ( 314) The antenna is identified as Port 1 so 11 aLL ( 315) and the sensor coil is identified as Port 2 22 cLL ( 316) To represent the nonideal coupling, two equivalent twoport circuit representations are possible, as shown in Figure 37. The first uses an ideal transformer with a turns ratio of aL a M ( 317) a shunt inductor on the input side, and a series inductor on the sensor side. Alternatively, a T circuit can be used, as shown in the second circuit. To simplify the circuit analysis, the T circuit is used for the wireless sensor model.

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52 Figure 37. Equivalent transformer model circuits for coupled coils. A) Ideal transformer model with shunt and series inductors. B) T circuit model. 3.1.3 Parasitics There are both reactive and resistive parasitics that have to be accounted for in the models of both the sensor coil and the antenna. These parasitics are inherent in any real system and can be reduced by careful design, but not eliminated entirely. The equivalent circuits shown in Figure 38 and Figure 39 include the parasitic components for the inductor coil and loop antenna respectively. Figure 38. Nonideal circuit model for the sensor coil. Figure 39. Nonideal circuit model for the antenna. The resistive components, Rc a nd Ra respectively, account for the energy loss in the circuits. There are several sources of energy loss, including far field radiation, eddy current generation, conduction in the substrate, and I2R conductive heating in the winding. Electrically conducti ve surfaces must be kept at a distance from the wireless link, so that eddy current generation is minimized. The coils are made on FR4 substrates w ith reasonably low loss tangent so the conduction losses should not be a major factor. The coil lengths are much less than the 1:a La(1-k2)Lc M (La-M) (Lc-M) Lc LcRcCc La LaRaCa A B

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53 wavelengths around 100 MHz, so the radiation losses should also be minimized. This leaves I2R heating as the dominant resistive parasitic source for both the a ntenna and inductor coil. For long, thin conductors, the resistance is given by totl R A ( 318) where is the resistivity, ltot is the total length, and A is the cross sectional area. For a spiral coil, where the length of each turn gets progressively smaller toward the center, the length can be calculated given the number of turns N the turn to turn pitch p, the base width b, and the inner diameter Di, by 1421N tot i nlNDbpn ( 319) The effective area of current flow through the wire is a function of frequency. At dc, current flows through the entire cross section, and given the height h, the area is simply dcAbh ( 320) As the frequency increases, however, the skin effect shown in Figure 3 4, restricts the current to the outer shell of the wire. To account for this, the center of the conductor is removed for the ac effective area given by 22dc s sAAbh ( 321) The resistance for the sensor coil is found by combining Equations 318, 319 and 321 to get 1 2221 2N i n c ssNDbpn R bh ( 322) For the single tur n loop antenna, N = 1, p = 0 and the resistance simplifies to

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54 22 2i a ssDb R bh ( 323) The inductors are intended to operate as reactive components, but there are still undesirable reactive parasitics that can limit the performance of the inductor. Any structure or mechanism that stores energy in a magnetic field adds to the inductance of th e coil, while any structure or mechanism that stores energy in an electric field acts as a capacitance and degrades the inductance. The parasitic reactance can be modeled as parallel capacitor s, Cc and Ca, as shown in Figure 38 and Figure 39. The parasitic capacitance subtracts from the total reactance of the inductor and sets up a self resonant situation at a specific frequency where the total reactance is effectively zero. Inductors must be used below their self resonant frequency, and so the parasitic capacitance parameters are of vital concern. The primary parasitic capacitance in the coil arises from inter winding capacitances, as illustrated in Figure 310. To calculate the inter winding capacitance, some approximations must be made. First the coil is unwrapped, and segments 1 through 4 and 5 through 8 from Figure 33 are placed in parallel, separated by a gap of p b. A well known equation for the capacitance of two parallel wires on a substrate [6870] is 22 ln 1oPCB cC pp l bhbh ( 324) where PCB = FR4 Mask 3 and l is the length of the segments. For more than two turns, the same procedure is used with the capacitance of each successive loop being added in series to give 1 11 22 1 ln 1 421oPCB c N n iC pp bhbh Dbpn ( 325)

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55 Figure 310. Cross section side view showing two wires of the coil. For the antenna parasitic capacitance, a oneturn coil is undefined according to Equations 324 and 325. Looking at the geometry, the wire elements are now separated by Di, which is much larger than p b. Thus, the resulting ca pacitance is negligible for a single turn loop antenna. The dominant source of parasitic capacitance for the antenna comes from the RF coaxial adapters that connect the antenna to the external circuitry. The parasitic capacitance of the adapters is the sam e for all of the tests and is simply measured prior to attaching the antenna. 3.2 Capacitive Shear Stress Sensor The first step in defining the relationship between the input shear and the resulting capacitance change is to determine the displacement of the sensor resulting from the shear stress input. The displacement is then used with a variable gap capacitive transduction derivation to find the change in capacitance. Sources of parasitics are identified at the end of the sensor capacitance section, since the y are inherent to the sensor and affect its sensitivity. 3.2.1 Mechanical Model Figure 311 shows the floating element structure of the sensor. The checkered area in the figure indicates the floating element ; this is the primary surface area that the in plane shearing forces will act on to cause a displacement. The four tethers attached to the sensing area hold the sensing structure suspended and act as restor ing springs to return the sensor to its neutral position when the input force is reduced back to zero. The deflection equation for the sensor is vital to the rest of the modeling, because it relates shear input to deflection used in the capacitive transduc tion equations in Section 3.2.2. For a more detailed treatment of the sensor mechanics, Cc h p b FR4Mask

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56 including dynamics and nonlinear deflection, the reader may refer to the previous floating element shear stress sensor literature [21,22,71,72] Figure 311. Mechanical diagram of the floating element sensor structure. The deflection of the floating element is obtained by solving the Euler Bernoulli beam equation on a simplified mechanical model. The floating element is pre sumed to be perfectly rigi d and can be replaced by a point load. The sensor is also assumed to be perfectly symmetric, so each of the two pairs of tethers should support half of the floating element load This reduces the point load by a factor of two and simplifies the system to a single clamped clamped beam shown in Figure 312. Shear stress will also act on the surfaces of the tethers and is represented by a distributed load a cross the beam. Figure 312. Simplified clamped clamped beam mechanical model of sensor with force vectors. The deflection at the center of the beam in the simplified model will be the same as the floating element displacement needed for the sensor model. The resulting equation modified from the derivation in [21] is LeWeNf Wf Lf h Lt Wt P Q Lt Wt x=0

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57 32 () 1 4ett teALA w EhWA ( 326) where is the input shear stress; E is the Youngs modulus; and h, Lt, and Wt are the thickness, length, and width of the tethers. This equation and the nonlinear equation [21] for deflection are given in the discussion of nonlinearity in Appendix A The area of the tethers At is given by tttAWL ( 327) The area of the floating element Ae is given by eeefffAWLNWL ( 328) where Le and We are the length and width of the floating element and Lf, Wf, and Nf are the length, width, and number of comb fingers on the floating element. The linear mechanical shear to displacement sensitivity Sw in nm/Pa is purely a function of geometry and material properties and can be written as 32 1 4ett w tewALA S EhWA ( 329) 3.2.2 Capacitance Model A c apacitive transduction model is used to find the change in capacitance when the sensor 's floating element is displaced by an input shear as found in Section 3.2.1. This section presents the capacitive structures used to develop the model. Only the variable capacitive structures that contribute to the transduction are considered. All other fixed capacitive structures are addressed in the next section and are considered parasitic. A s shown in Figure 3 13, t here are three electrically isolated regions on the sensor, which form two sets of variable capacitors. The capacitive structures were designed in complementary pairs red blue and green blue, for a wired differen tial readout. For the wireless technique, only a

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58 sin gle variable capacitor is needed In this example, red blue is chosen and green is left floating. The primary structure is the comb finger C1 at the edge of the floating element. The sensor also leverages the gaps between the fixed sidewalls and the free end of the floating element C2 and the moving tethers C3. Figure 313. A 3D graphic of the sensor with variable capacitive structures indicated (not to scale). The parallel plate capacitance assumption is us ed defining the capacitance as A C g ( 330) in which, = o is the permittivity of free space, since the medium in the gaps is air. A is the area of the sidewalls, and g is the gap The three variable capacitors are in parallel so their capacitances are simply summed The total capacitance is then 123 sCCCC ( 331) Each of the three capacitors can be represented by a nominal capacitance and a change in capacitance and defined by ()ioiiCCCw ( 332) C1C2C3

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59 The nominal capacitance Coi is a constant and is simply given by the parallel plate equation for the respective geometry. The change in capacitance Ci is the amount the sensor capacitance changes and is a function of the displacement of the floating element w given by Equation 326. To simplify the fabrication an asymmetric comb with primary gap go1 and secondary gap go 2 is used, as shown in Figure 3 14. This enables the use of the more sensitive variable gap for sensing without needing to isolate and run overlapping traces to each finger. The number of fingers Nf includes all of the fingers attached to the floating element, so when using only one set of fingers, this value must be halved. The number of fingers that will fit on the floating element is given by 122 2 2et f fooWW N Wgg ( 333) rounded down to the nearest even number. The distance xo is the nominal overlap of the fingers, and h is the height. The nominal capaci tance for this structure is 1 122 2f f oo o ooN N xh C gg ( 334) and the change in capacitance is 1 121222 () 2ff ff oo ooooNN NN xh Cw gwgwgg ( 335) The next capacitive structure is the sidewall of the floating element, as shown in Figure 315. The nominal capacitance for this structure is simply 2 1 oe o oLh C g ( 336)

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60 and the change in capacitance is 2 1111 ()oe ooCwLh gwg ( 337) The tether shown in Figure 316 uses the asymmetric gap as well, but there is a further complication. When the sensor moves, the tethers bend, and the separation is no longer uniform. At the clamped end the deflection is zero, while at the floating element it is w To compensate for this, a piston equivalent area is used. With this approximation, half of the tether is included in the variable capacitance and the other half is left as a fixed capacitance [ 21] The fixed capacitance adds to the parasitics of the sensor but the added sensitivity offsets this negative effect. In addition to the two gaps shown in Figure 316, there are two more narrow gaps indicated by the arrows in Figure 313. The nominal capacitance for this structure is 3 1231 2ot o ooLh C gg ( 338) and the change in capacitance is 3 12123131 () 2ot ooooLh Cw gwgwgg ( 339) Figure 314. Zoomed in 3D graphic showing ca pacitive comb fingers (not to scale). WfLfh xogo1go2

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61 Figure 315. Zoomed in 3D graphic showing element end capacitance (not to scale). Figure 316. Zoomed in 3D graphic showing tether capacitance (not to scale). Adding Equations 334, 336, and 338, the nominal capacitance, which is only a function of the sensor geometry, is 122 23 2fot foet o os ooNxL NxLL h C gg ( 340) The total change in capacitance is inherently nonlinear given by 121222 23 23 () 2fot fot foet foet o s ooooNxL NxL NxLL NxLL h Cw gwgwg g ,( 341) but using a linear approximation as derived in Appendix A the equation is reduced to 22 122 23 () 2fot foet o s ooNxL NxLL hw Cw gg ( 342) Leh go1 go1go2h WtLt

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62 The displacement to change in capacitance sensitivity Swc in fF / nm is purely a function of geometry and can be written as 22 122 23 2fot foet so wc ooNxL NxLL Ch S wgg ( 343) 3.2.3 Parasitics As with the coils, there are both resistive and reactive parasitics on the capacitive shear stress sensor. The three conductive regions on the sensor shown in Figure 3 13 are electrically isolated, so at dc the conduction between them will be zero. However, as the frequency is increased, there will be finite ac losses in the conductive layers of the device. For a capacitor, this can be represented by a conductance term G between the capacitive terminals as shown in Figure 317. Also shown is the reactive parasitic component Cp which represents all of the fixed capacitance. It is considered parasitic, because it adds to the total cap acitance without contributing to the change in capacitance. In the next section, this will be shown to effectively decrease the overall sensitivity. First, the major sources of parasitic capacitance will be identified, and then the primary conductance sour ce will be explained. Figure 317. Nonideal circuit model for capacitive shear stress sensor. There are three sources of fixed or parasitic capacitance in the sensor. The first source, Cp1 consists of all the gaps in the sensor that must be included in the design for isolation purposes but that do not vary with an input shear. This includes the trenches around the pads that the tethers are anchored to as shown in Figure 318. There is two of each type on the die. These trenches are Cs Cs Cp Gs

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63 required to isolate the floating element from the rest of the die to form the three isolated conductors shown in Figure 313. Figure 318. Two 3D pad structures showing dimensions for parasitic c alculations. A) Type one, large pad used to electrically connect to and anchor the floating element. B) Type two, small pad used to anchor the tether. The total capacitance of the pads is 1212222o pads pppph CWWLL g ( 344) where g is the trench gap, Wp1 and Lp1 are the width and length of the first pad, and Wp 2 and Lp 2 are the width and length of the second pad. The gap is maximized in the design to minimize the contribution of this source of fixed capacitance. The pads have differing lengths, so that type one can extend all the way to the edge of the die, isolating the two major regions. In contrast, type two is thin enough to provide a conduction path that connects in parallel the three variable capacitances, described in Section 3.2.2. The equivalent model for the variable tether capacitance in Equations 338 and 339 includes only half of the tether to account for the difference in displacement along the length of the tether. The other half is effectively unchanging and must be added to this first parasitic capacitanc e term, such that 13 ppadsoCCC ( 345) Lp1Wp1 g h Lp2Wp2 g h A B

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64 The second source Cp2 of parasitic capacitance comes from the fringing fields of all the gaps in the sensor. A parallel plate assumption was used to derive all of the equations for capacitance thus far. This only accounts for the electric fields directly between the structure sidewalls and also assumes that those fields are all perpendicular to the sidewalls. All capacitors have fringing fields at the edges. The contribution of these fields to the total capacitance are dependent on the relative permittivity of the dielectric in the gap and the ratio of the height to the gap width. In the shear stress sensor, the plates must be free to move, so the dielectric in the gap field guidance in the gap. The sidewall height and gap widths are chosen to maximize sensitivity to shear while minimizing sensitivity to other forces, so there is a limit to this ratio. The analysis and quantification of these fringing fields form a complex problem, so 2D finite element analysis (FEA) simulations using COMSOL Multiphysics is used. All of the different capacitive geometries discussed are analyzed in COMSOL to quantify the contribution to the total capacitance by the fringing fields. First, the variable gap capacitive structures are simulated. The fingers are shown in Figure 319 with both a vertical cross section to show the top and bottom fringe fields and a horizontal cross section to show the fringing fields at the tips of the fingers. To simplify the simulation, a single set of fingers was drawn with periodic boundary conditions to account for the surrounding sets of fingers. Next, the end of the ele ment capacitance is shown in Figure 320, which again shows a vertical cross section to illustrate the top and bottom fringes. There will not be any e nd fringes as the element gaps end where the tethers begin with no geometry change. There are two types of capacitive configurations for the tethers, as shown in Figure 3 21. The first type has a small gap on both sides and effectively separates the two large conducting surfaces. As such, it

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65 consists of three separate conductors with only two being used for the wireless sensor. This simulation is perfo rmed by floating the third structure with the source and ground on the other two. The second tether has one large gap and one small gap and is surrounded by a common electrode. For all three of these variable capacitive structures, the fringing field adds an additional 30% of static parasitic capacitance. Figure 319. Finger fringe simulation results A) Cross section cutting through fingers to show top and bottom fringe patterns. B) Top view of fingers showing tip fringes. Figure 320. Element end fringe field simulation results The final gap structure to be analyzed for fringing fields is the gap between the pads described as part of the first s ource of parasitic capacitance. In this case, there is a change in dielectric permittivity between the gap and the medium occupied by the fringe fields. The gap and the area above the gap is still air, but beneath the pads is an oxide (r = 3.9) layer and the go2go1 h Wf Lf Wfgo2go1 go1 h A B

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66 bulk silicon (r = 11.6) layer. As shown in Figure 322, this actually has the effect of preferentially pulling the electric field towards this med ium, which completely invalidates the parallel plate approximation. The resulting capacitance is an order of magnitude larger than estimated by Equation 344. Figure 321. Tether cross sections and fringing simulation results. A) Smallsmall gap tether with one side floating. B) Smalllarge gap tether with both sides grounded. Figure 322. Pad gap cross section showing simulated fringing fields and the effect of the substrate beneath the pads. The third source of parasitic capacitance Cp3 comes from the electrodeto bulk capacitance. At dc, this is the largest source of parasitic capacitance, but it has a frequency dependence that minimizes its effect at the RF frequencies of operation for the wireless sensor. The areas that make up the electrodes in this sensor are f ar larger than most other sensors, as shown in Figure 3 13. This simplified the fabrication allowing all of the trenches to be etched in one step, forming go1 h Wtgo1 go2go1 h Wt h g A B

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67 the sensor structures and the pads at once. This creates a problem, in that the pads are separated from the bulk by a thin oxide layer of thickness tox with a relative permittivity of 3.9. The large area, small gap, and increased permittivity make fo r a very large parasitic capacitance. Figure 323 shows the electrode pads with a cross section of the sensor to illustrate the circuit connections. The two capacitances Cs each represent the combined trench parasitic and variable sensor capacitance. The center pad to bulk capacitance is 1 oxpads b oxA C t ( 346) where the area is defined as 112222padsppppAWLWL ( 347) The larger surrounding pads have a capacitance of 2 oxsur b oxA C t ( 348) where the area is defined as () 2diepadselement surAAA A ( 349) The electrical conductivity of the underlying bulk silicon is represented by a conductance Gb and will be determined experimentally in Chapter 5 by fitting measured impedance vs. frequency data using calculated values for Cs, Cb1 and Cb2. The circuit shown in Figure 323 can be simplified at high a nd low frequencies. At low frequencies (<1 MHz), the high impedances of the capacitors Cb1 and Cb2 dominate over the conductance Gb. Replacing the conductances with shorts, the series combination of Cs and Cb2 is added in parallel with Cb1, all of which ar e combined in series with Cb2. Due to the magnitudes of these capacitances, the effective capacitance combination reduces to approximately Cb1 As the

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68 frequency increases, the impedances of the capacitors are reduced, and at very high frequencies the conductance terms dominate. In this case, all that is left is Gb across the terminals of the sensor capacitance. These results are summed up by the followin g four equations: 313,0high lowf f pbpCCC ( 350) and 0,high lowf f bGGG ( 351) The frequency at which this transition occurs is determined experimentally along with the value of Gb. The c ircuit in Figure 323 reduces to one of the two shown in Figure 324, depending on the frequency range. Figure 323. A 3D graphic showing the side view of the pads with overlaid circuit model of the bulk parasitic capacitive structures (not to scale). Figure 324. Eq uivalent circuit models for padto bulk parasitics. A) Low frequency equivalent circuit valid when capacitance dominates. B) High frequency equivalent circuit valid when conductance dominates. The final parasitic values to be used in the final model are the parallel combination of all three parasitic capacitan ces given by Cs Gb Gb CsCb2Cb1Cb2h Wp tox Cs Cb1 Gb Cs A B

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69 123 ppppCCCC ( 352) The primary source of conduction at high frequency is given by bGG ( 353) Using these parameters along with those from the pr eceding sections, a full model is described in the next section. 3.3 Full Sensor Model All of the components discussed thus far are put together in this section to describe the full sensor system. First, the complete electrical equivalent circuit is given. The output resonant frequency of the sensor is determined from this circuit. In operation, the resonance is tracked to determine the input shear stress. This is best illustrated as a waterfall plot in Figure 325 where the frequency shift can be seen in time. Next, a general theory of coupled resonators is presented to analyze the effect of coupling on the resonant frequency. The quality factor Q will be defined and related to the minimum detectable signal ( MDS ). At the end of the section, assumptions are given to extend this model to an array of sensors. Figure 325. A generic w aterfall plot showing a resonant frequency shift ing in time. S11

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70 3.3.1 Single Sensor Model The full circuit model is given in Figure 326. This model is made up of quantities determined analytically, numerically, and experimentally. The sensor parasitic conductance, G variable capacitance, Cs and parasitic capacitance Cp were described in Section 3.2. The self inductances for the coil Lc, the antenna La, and the mutual inductance M from Section 3.1.1 are represented in the T circuit given in Section 3.1.2 Cc, Ca, Rc and Ra represen t the parasitics of the coils given in Section 3.1.1. Figure 326. Full circuit model for a single wireless shear stress sensor. To analyze this model and determine the resonant frequency of the sensor, the impedance at the input to the device ZL is derived by standard circuit analysis (see Appendix B ). 22 11L aa a cccpsM Z RjL jC RjLjCCCG ( 354) Since a network analyzer is ultimately used to measure the sensor response, this impedance is then transformed into a reflection coefficient Lo LoZZ ZZ ( 355) using the standard characteristic impedance 50oZ ( 356) The reflection coefficient, also known as the scattering parameter S11, is the value measured by the network analyzer that will be connected to the output of the antenna. The resonance of the M (La-M) (Lc-M) Cp Cs CaRaRc G Cc ZL

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71 sensor shows up as a dip in the magnitude of the reflection coefficient, as shown in Figure 327. The frequency is given by 1 2o cspcf LCCC ( 357) As the capacitance of the sensor Cs changes with input shear, the resonant dip shifts in frequency. Figure 327. Sensor spectrum showing resonant peak and the shift due to a change in capacitance. The relationship between change in capacitan ce Cs and change in frequency f is inherently nonlinear, but assuming sospcCCCC the local slope (and hence sensitivity) can be obtained by taking the derivative of Equation 357 with respect to Cs. See Appendix A for a detailed derivation. The resulting equation i s related to the static resonance and the ratio of the change in capacitance over the total static capacitance, () 2os s ospcfC fC CCC ( 358) The change in capacitance to change in frequency sensitivity in kHz/fF can then be written as Frequency |Reflection| fo f(Cs)

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72 2o cf s ospcff S C CCC ( 359) and the total shear stress to change in frequency sensitivity in kHz/Pa can then be written as 3 22 12 122 23 2 1 16 2 23 2fot foet oeot t teo o f fot foet o pc ooNxL NxLL fALA EWAg g S NxL NxLL h CC gg ( 360) where Sf = SwSwcScf A more important metric for wireless sensors, whose static resonances tend to span a wide range of frequencies, is the normalized sensitivity expressed in ppm/Pa as 3 22 12 122 23 2 1 16 2 23 2fot foet eot t teo o f n o fot foet o pc ooNxL NxLL ALA EWAg g S S f NxL NxLL h CC gg ( 361) The normalized force sensitivity is given by 3 22 12 122 23 2 1 16 2 23 2fot foet ott teo o n F e fot foet o pc ooNxL NxLL LA EWAg g S S A NxL NxLL h CC gg ( 362) The independent geometric variables in this equation are We, Le, Wt, Lt, h, Wf, Lf, go1 and go2. B y changing each variable independently the sensitivity of Equation 362 to fabrication uncertainties is shown in Figure 328. It is clear that the most important quantities are Wt, Lt, go1 and go2. 3.3.2 Coupled Resonators The full model presented is a pair of mutually coupled resonators. Theory for these types of systems is used in electroacoustics [73] The most relevant aspect for this work is the effect that coupled resonators have on each others resonant frequencies. This poses a potential

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73 problem, since the resonance of the sensor is s ensitive to a change in the coupling or the resonance of the antenna. This is interpreted as a change in shear stress, giving a false output. This effect is minimized through careful design of the system. Figure 328. Normalized sensitivity of the sensor response to 10 % variations in fabricated geometries. Two situations are described for a general pair of coupled resonators shown in Figure 329. First, the capacitances and inductances are set equal ( L1 = L2 = L and C1 = C2 = C ) so that both have the same resonant frequency 1,21o oof f k ( 363) where 1 2of LC ( 364) would be the resonance of both sides in the absence of one another, and 12M k LL ( 365) 0.9 0.95 1 1.05 1.1 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 Normalized Change in Variable Normalized Change in SF We Le Wt Lt h Wf Lf go2 go1

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74 is the coupling coefficient. For zero coupling, both resonators resonate at a frequency described by the standard second order equation and given by Equation 364. As soon as they couple, they interact with each other, resulting in a splitting of the resonance as shown in Figure 330. Two peaks appear at frequencies defined by Equation 363. A sensitivity analysis shown in Figure 331A,B is performed at around 100 MHz by varying the five parameters and quantifying the resonance shift that results. These plots show that the resonant frequency is highly sensitive to changes in all capacitive and inductive parameters. It also shows that the variation is highly nonlinear which invalidates the models developed in Section 3.3.1.Another problem is that an antenna is most sensitive to noise from EMI at its self resonant frequency. This noise affects the sensor output if it is resonating at the same frequency as the antenna. Figure 329. Basic T circuit for magnetically coupled resonators. Figure 330. Coupled resonator plot showing overlapping and separated resonances M (L1-M) C1(L2-M) C2 102 103 0 10 20 30 40 50 60 70 80 90 100 Frequency (MHz) |Z| (dB) fo1 = fo2 fo1 fo2

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75 Figure 331. Resonant frequency sensitivities to electrical parameters. A) Sensitivity for fo1 with fo1 = fo2. B) Sensitivity for fo2 with fo1 = fo2. To reduce the sensors sensitivity to the coupling k antenna parasitics, and EMI, separated resonances are used. When L1 L2 and C1 C2, 1,2 2 1212 2222 2 1122112212121 21 2 24oof CCLLk CLCLCLCLCCLLk ( 366) gives the two separated resonant frequencies derived in Appendix C By choosing the first resonance as the sensor resonance, the effect of changes in M is reduced. To confirm this assumption, a sensitivity analysis shown in Figure 332A ,B is also performed for the two resonances in the hundreds of MHz range and separated by 0 and 500 MHz. The most advantageous resonance for the sensor is the first resonance where changes in M are minimized. Using a fixed inductance L2 the sensitivity analysis in Figure 332A shows the ideal situation with the resonant frequency being sensitive to only changes in the variable capaciti ve shear stress sensor. 0.9 0.95 1 1.05 1.1 0.95 1 1.05 Normalized Change in Variable Normalized Change in fo1 L1 C1 M L2 C2 0.9 0.95 1 1.05 1.1 0.95 1 1.05 Normalized Change in Variable Normalized Change in fo2 L1 C1 M L2 C2 A B

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76 Figure 332. Resonant frequency sensitivities to electrical parameters. A) Sensitivity for fo1 with fo1 fo2. B ) Sensitivity for fo2 with fo1 fo2. 3.3.3 Quality Factor at Resonance The quality factor of a resonator is a unitless quantity that relates the maximum energy stored to the total energy lost in one cycle of resonance. The effect of Q on the output of the sensor is shown in F igure 333 where the higher the Q the narrower the resonant dip. The sensor resonance has energy storage elements Lc, Cc, Cp and Cs and energy dissipative terms Rc, and G As derived in Appendix D at resonance, the quality factor of the sensor is given by 2 2 11 cps c cps c cQ G CCC R G CCC L G L ( 367) It is desirable to maximize the quality factor to achieve the sharpest dip. The sharper the dip, the lower the noise floor and the smaller the MDS will be. Additionally for arrays, the sharper the dip, the less bandwidth it will occupy, enabling more sensors to fit in the bandwidth below the antenna resonance. The noise floor of the sensor is given by 2oa ffn n Q [74] ( 368) 0.9 0.95 1 1.05 1.1 0.95 1 1.05 Normalized Change in Variable Normalized Change in fo1 L1 C1 M L2 C2 0.9 0.95 1 1.05 1.1 0.95 1 1.05 Normalized Change in Variable Normalized Change in fo2 L1 C1 M L2 C2 A B

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77 as shown in Figure 3 33. The MDS in Pa is obtained using the standard definition 12 3 22 122 23 2 23 2 1 4fot foet a pc oo f f fot foet ett teo oNxL NxLL n CC gg n MDS S NxL NxLL ALA Q EhWAg g ( 369) From Equation 367, we see that to increase the quality factor and minimize the MDS the parasitics Cc, Cp, Rc, and G must be minimized and the self inductance Lc must be maximized. There is a trade off in the sensor capacitance between quality factor and sensitivity that will affect the MDS This will be balanced in the final design by maximizing the ratio Cs/Cos. Figure 333. Plot showing MDS dependence on Q. For the same amplitude noise in both spectrums, a higher Q results i n a smaller MDS. 3.3.4 Multiple Sensor Array Model T o apply the single sensor model to an array of sensors, superposition must be valid. It is desired that the frequency shift of each sensor s resonance be related to an input shear stress on that sensor. For this to be true, the sensors must not have strong coupling between their individual coils. If this is the case then the resonant frequency, quality factor, sensitivity and Frequency |Reflection| Peak 1, Q = 10 Peak 2, Q = 50 fMDS fMDSna

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78 noise floor will all be given for each of the individual sensors by the equations developed for the single wireless sensors. The total impedance and reflection spectra will be different and requires more development that is presented in Appendix B for a generic number of sensors in the array. The parasitics are removed from this discussion for simplicity but they can easily be added the same way they were added to the single sensor equations. For the case of four wireless sensor s each with mutual inductances to each other and to the antenna. If the sensor to sensor coupling is negligible then 1213142324340 MMMMMM ( 370) The circuit diagram in Figure 334 shows the case where only coupling between the sensors and the antennas are present. The full coupling model is also derived in Appendix B For this circuit the four sensors will be defined by 1iii iZRjL C ( 371) The total input impedance is given by 22222222 1234 1234 aaaa LaaMMMM ZRjL ZZZZ ( 372) The spacing between the sensors and their orientation should minimize the inter sensor coupling enough t o satisfy this requirement. The simulated spectrum in Figure 3 35 show s a single peak for each sensor located at 1 2oi iif LC ( 373) The bandwidths shown in the figure are limited by the Q of the sensors and given by

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79 oi i if BW Q ( 374) The spacing between the resonances must satisfy the R ayleigh C riterion in order to be distinguishable as separate peaks. This minimum spacing is given by min2iBW f ( 375) Provided the design of the sensors meets these criteria the array can be interrogated with each spatial location in the array corresponding to the frequency shifts in the assigned bandwidth. Figure 334. Circuit model for a 2 x 2 sensor array. Figure 335. Array spectrum sowing individual bandwidths for four sensors. Ra La Ma1Ma2Ma4Ma3R2R1R3R4L2L1L3L4C2C1C3C4ZL Frequency |Reflection| fo1fo2fo3fo4BW1 BW2BW3BW4

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80 CHAPTER 4 4 EXPERIMENTAL SETUPS The experimental setups and methods used to characterize the wireless shear stress sensor s are described in this chapter. Before packaging, the individual capacitive shear stress sensors are visually inspected to sort out clearly damaged die. I mpedance measurements are then made using die level electrical probing to extract relevant electrical model parameters Electrostatic actuation of the comb fingers ensures that there are no mechanical obstructions to the free floating structures on the sensors. After packaging dies to form t he wireless sensor packages, the inherent noise floor and stability are determined with zero input Humidity testing is also conducted to explore the sensors sensitivity to humidity. Next, t he static (dc) shear stress sensitivity is determined by performi ng device calibration in a flow cell The fi nal test setup described in this chapter is a wind tunnel at NASA Langley in V irginia Subsequent chapters will present the actual data and results from these tests on first generation and secondgeneration devic es. 4.1 Die Level Testing Before packaging the capacitive shear stress sensors, dielevel characterization is performed to identify the best candidates as well as to extract parameters and confirm model predictions from Section 3.2. The finished wafers are diced into 5 mm x 5 mm die and sorted by sensor design. Visual inspections of each die are performed under an optical microscope (100x 1000x magnifi cation) to check for defects. Die that pass the visual inspection undergo impedance testing and actuation testing before being packaged and tested wirelessly. 4.1.1 Electrical Impedance Testing After the die are individually inspected, a full electrical characte rization is performed on the good die The setup for these test s is shown in Figure 41. T wo impedance analyzers are used to cover the broad frequency range necessary for fully evaluating the model parameters. First the

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81 HP 4294A is used to test the devices at low frequencies fro m 100 Hz to 100 MHz. Next, t he E 4991A is used to cover the high frequency testing from 1 MHz to 1 GHz. A Cascade M150 measurement platform is used to perform the required die level tests. The probe tips are observed under a microscope, while the manipulators are used to land them on the contact pads of the sensors. A rising stage and movable chuck are used to maintain probe orientation from test to test. Figure 41. Probe station setup for impedance characterizations. For the HP 4294A, a set of Cascade Microtech DCP 150R coaxial shielded probes are used with four 3' SMAA to BNC cables that connect directly to the instrument. First, a four point probe (4TP 1M) cable phase correction is performed to remove the effect of the cable length on the measurement. Next, a GGB Industries impedance standard substrate ( ISS ) model 40A GS 150C is used to perform open, short, and load compensation tests All of the testing parameters for the E4991A are given in Table 41. Table 41. Agilent E4991A material property analyzer settings. Parameter Sett ing Number of points 801 Oscillation level 100 mV Start 1 MHz Stop 1 GHz Scale log C alibration Open, Short, Load Microscope Stage Chuck Manipulators Probes DUT E4991a HP4294a

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82 For the E 4991A, a single GGB Industries 40A GS 150C RF probe is used, which again is calibrated using the ISS. The RF probe is connected to an Agilent E4991A Opt 010 test box, mounted to a single specialized Cascade Microtech probe manipulator with a short semirigid SMA cable. This reduces test variation and improves repeatabil ity. All of the testing parameters for the HP 4294A are given in Table 42. Table 42. HP 4294A impedance analyzer settings. Parameter Setting Number of points 801 Oscillation level 500 mV Bandwidth 5 Start 100 Hz Stop 100 MHz Scale log Compensation 4TP 1M C alibration Open,Short,Load 4.1.2 Electrostatic Actuation Testing To ensure that the sensors are ready for packaging, an electrostatic test is also performed on each sensor. For a sensor to work properly, it must be free and clear of any materials that could restrict the free motion of the floating element structures. Th ese obstructions can be difficult to detect visually even with the aid of a high power microscope, and if an obstruction is nonconductive, it may not show up in the electrical impedance tests described in Section 4.1.1. However, an electrostatic force applied to the sensors will result in an observable, predictable, and repeatable displacement if the sensor is fully released and free of obstructions. The setup used for this test is shown in Figure 4 2. A square wave voltage signal is applied to the sensor die via needle probes. At the same time, a camera mounted to a 500x microscope is

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83 used to collect video of the s ensor as it is actuated. Video processing is then used to measure the resulting displacement. Figure 42. Electrostatic actuation test setup. The voltages used to actuate the sensors must be determined based on the geometry of the comb fingers and tethers. The voltage level used to actuate the comb fingers needs to be large enough so that the displacement is visible under a 500x microscope. However, if the displacement becomes too large, the attractive g ap closing electrostatic force may overcome the restoring spring forces, and the fingers will clamp shut. This phenomenon is referred to as pull in and ultimately results in the destruction of the sensor, because the fingers become welded together from t he current spike when the sensor shorts out. To prevent this pull in, the forcing voltage is limited to 80% of the calculated pullin voltage. The pull in voltage is a function of the finger geometry and the spring constant, in this case, the tethers. From previous work on H Bar structures [21,22,75,76] the spring c onstant of the tethers is given by 3 2 24 64 1 12 4 15t t t e t e t eW Eh L AA k A A A A ( 41) where the geometric and material properties are defined in Section 3.2.1 and illustrated in Figure 311. The pull in voltage, derived in Appendix E is given by Camera Waveform Generator Probes DUT Comb Fingers At 500xVmax

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84 33 121pi ff oo opiopik V NN xh gxgx ( 42) where the geometric and material properties are defined in Section 3.2.2 and illustrated in Figure 314. The pull in displacement pix is determined from the nonlinear equation 12 33 12(3)() 1opi opi opi opigxgx N N gxgx ( 43) and must be solved numerically (see Appendix E ). MATLAB is used to solve for pix and piV for each design. This is then used to set 0.8maxpiVV on the waveform generator. 4.2 Wireless Sensor Testing Once a good capacitive sensor die is identified it is flush mounted in a printed circuit board (PCB) and wire bonded to the onboard coil. On the backside of the PCB, an RF connector is soldered to the loop antenna to complete the wireless shear stress sensors. Next, a set of tests is performed to cha racterize the wireless devices. For all of the tests described in this section, a LabVIEW control program is used to automate and allow continuous monitoring of the test progress. 4.2.1 Network Analyzer Resonance Tracking A network analyzer is used to track the resonant frequency of the wireless shear stress sensor in all of the experimental tests. An HP8719D [77] with an operational frequency range from 50 MHz to 13.5 GHz is used. A network ana lyzer measures the scattering parameters of a DUT (device under test). For a single port device, such as the wireless shear stress sensor, all that is required to electrically characterize the DUT is the scattering parameter S11. This is also

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85 referred to a s the "reflection coefficient" or It is a complex nondimensional parameter relating the reflected to the incident voltage by 11A S R ( 44) in which A is the incident voltage and R is the reflected voltage. As shown in Figure 43, the source voltage Voc is split, and half is sent to the DUT while the other half is measured at A The reflected voltage is separated by a directional coupler and measured at R A single frequency tone is used as the input voltage Voc. To obtain a spectrum, the frequency is swept through a user defined set of frequencies, and 11S is measured at each tone. If the frequency range includes the resonance of the wireless sensor, there will be a dip in the magnitude of the reflection coefficient as shown in Figure 3 27. The resonance shifts of the sensor are determined by tracking this dip. Figure 43. Network analyzer operation. The DUT includes the antenna and the wireless sensor. Fo r all tests, a full one port calibration is preformed using the Agilent 85050B 7 mm calibration kit. This includes measuring open, short, and 50 load terminations. A 7 mm SMB adapter is used to connect the antenna to the network analyzer after the calibr ation is complete. Frequency sweeps consisting of 1601 points are taken with an IF BW of 300 Hz and a source level of 125 mV. The frequency sweep center and range depend on the sensor being tested. The V V D U T R A Voc Directional Coupler Power Splitter

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86 center point is always set to the resonant frequency of the sensor, but the span depends on the purpose of the sweep. A wide bandwidth search span of 1 GHz is used to identify the resonant frequency of the sensor. The frequency resolution at 1601 points is inadequate for resonance tracking, so a narrow bandwi dth test span from 1.6 to 16 MHz, depending on the Q of the sensor is used. The setup parameters for the network analyzer are given in Table 4 3. Tabl e 43. Agilent 8719D network analyzer settings. Parameter Setting Number of points 1601 Oscillation level 125 mV IF BW 300 Hz Sweep Time 6 seconds Center fo Search Span 1 GHz Test Span 1.6 16 MHz Scale lin ear C ompens ation Open, Short, Load 4.2.2 Noise Floor and Frequency Stability Testing The noise floor of the sensor determines the minimum detectable input shear, which is then used to determine the dynamic range of the sensor. For the wireless sensor, the noise floor is related to the quality factor Q the resonant frequency fo and the amplitude noise na in the frequency sweep of the network analyzer by Equation 368. The Q and the resonant frequency can be determined by taking a wideband sweep to capture the entire resonant dip, and the amplitude noise is determined at the narrow bandwidth that the resonant frequency will be tracked. The inherent noise floor of the device includes only sources within the sensor and measurement system, so to remove outside source like electromagnetic interference (EMI), these tests are performed in a grounded faraday cage ( Figure 44).

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87 Figure 44. Diagram of a single sensor placed in a faraday cage to reduce external noise. This setup will be used to determine the noise floor and stability of the device. In addition to the noise floor testing, the faraday cage is used for lon gterm stability tests to measure the drift of the resonant frequency. Frequency drift is a phenomenon that has been shown to affect previous wireless sensors [31,41,58,60,78] and must be explored to eliminate false readings of input shear. The sensor is tested in the faraday cage with zero input shear. Ideally, the resonant frequency should remain constant in time. Frequency sweeps are taken every six seconds with the same settings as the noise floor tests. T his process is repeated for three hours to get an esti mate of the long term drift 4.2.3 Humidity Sensitivity Testing During the course of this research, while performing static calibrations in the flow cell, a change in sensor sensitivity was observed at the start of the test. If the same test was repeated immedia tely, this phenomenon disappeared. After a detailed analysis of the problem, humidity was identified as the root cause of the sensitivity variation. The compressed air used to drive the flow in the flow cell was drier than the air in the room due to treatment at the compressor and inline desiccants. Once this phenomenon was identified, it was easily avoided by setting a constant low flow condition until the humidity stabilized, after which the static sensor calibrations were performed to determine the sensi tivity to shear stress. This testing procedure did nothing to quantify or improve the root problem though. Antenna Sensor Network Analyzer Faraday Cage

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88 The sensitivity to humidity is an undesirable effect of the capacitive structures responding to a change in permittivity [79 85] rather than the change in the comb finger gaps due to input shear stress, as described in Section 3.2.2. This happens when water molecules adhere to the sidewalls of the fingers and can be estimated by 2HO effA C g ( 45) To characterize this phenomenon and investigate future improvements to reduce this undesirable sensitivity, a dedicated test setup is required. A simple humidity test chamber is devised wherein the sensor performance is measured with va rying relative humidity (zero shear stress). The construction included a sealed chamber with a Lascar USB t emp/ humidity data l ogger ( EL USB 2) and a desiccant, as shown in Figure 4 5. The data logger is synchronized with the time stamp of the computer controlling the network analyzer for post test comparison of the frequency shifts to the humidity changes. Figure 45. Humidity sensitivity test setup. For testing, the sample rate of the data logger and the sensor are set to 0.1 Hz, which is the highest available rate for the data logger used. At the beginning of the test, the shear stress sensor and humidity sensor are subjected to room humidity (50 %RH). This establishes a stable baseline. Next, both sensors are sealed in the chamber with fresh desiccant causing the humidity to drop from 50% RH to 5 % RH. Once the humidity stabilizes, the chamber is opened and the humidity settles back to room humidity. Variations in humidity are very slow, with time Humidity Data Logger Network Analyzer Sensor Sealed Chamber Desiccant

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89 constants on the order of approximately 20 minutes in comparison to electrical and mechanical time constants for this device, which are on the order of milliseconds or less. This experiment enables reasonable characterization of the humidity sensitivity. Improvements to the sensors through hydrophobic treatments are evaluated with this test setup. 4.2.4 Static Calibration Testing The static (dc) shear stress sensitivity is characterized using a calibration flow cell as shown in Figure 46. The flow cell operates on the assumption of Poiseuille flow between stationary infinite parallel plates. The flow cell duct is 330 mm x 100 mm x 1 mm, so the duct height is two orders of magnitude smaller than the length or width, validating the infinite parallel plate assumption. Two taps measu re the pressure drop along the flow direction in the flow cell. The sensor is placed 240 m m from the flow entrance, ensuring that the flow is fully developed by the time it reaches the sensor. A dielectric plug is located in the back plate directly opposite to the sensor that constrains the size of the antenna and coil windings. Figure 46. Static calibration flow cell. The 2D fully developed Poiseuille flow [1] is given by 2()2 P uyhyy x ( 46) wher e h is the height of the chamber is the viscosity of the fluid, P is the differential pressure between the taps, and x is the distance between the taps. To find the shear stress at the wall, the velocity gradient at y = 0 is determined by Sensor Input h 2D Flow Pressure Taps x Plug P

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90 02yduhP dyx ( 47) Using the relationship between the velocity profile and shear stress at the wall, 0 ydu dy ( 48) the shear can be calculated, resulting in 2 hP x ( 49) The pressure differen ce P is measured across the sensor at two pressure taps, 76.2 mm apart, on the opposite wall of the flow cell. The height of the channel h is set by a shim ( 1 mm for the first generation or 0.5 mm for the second generation) placed between the top and bottom plates. A smaller channel height result s in higher flow rates and higher maximum shear stress levels. A Heise pressure meter with a 50 in H2O (12.5 kPa) pressure module is used to get the best measurement resolution without over ranging at the maximum flow rate. For calibration, the flow is stepped from 0 to 2 Pa for the first generation devices and 0 to 4 Pa (Pmax = 12.2 kPa) for the secondgeneration devices. The flow rate is increase in regular intervals, using an AALABORG mass flow controller operated by a Keithley voltage source, until the maximum shear stress is reached. After increasing the flow rate and prio r to triggering the sensor measurement, the flow is allowed to stabilize for 60 seconds. This ensures that any transients will have died out and that the flow will be fully developed for the measurement. Twenty pressure measurements are taken with the Heis e and averaged to determine the input shear stress given in Equation 49. After the 60 second dwell time, the HP 8719D network analyzer is triggered. The resonant frequency is then extracted, and a plot of resonant frequency versus shear stress is generated.

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91 Ideally, the plot should show a linear change, where the slope is the sensitivity of the device. This sensitivity Sf is divided by the resonant frequency to get a normalized sensitivity Sn, which is a better metric with which to evaluate the sensor. Using this sensitivity and the noise floor found using the test setup in Section 4.2.1, the MDS of the sensors can be determined by Equation 369. The dynamic range ( DNR ) of the devices is then calculated usi ng this MDS as 20logMaxDNR MDS ( 410) where max is the maximum input shear before the nonlinearity of the sensitivity Sf reaches 3%. 4.2.5 Wind Tunnel Testing In addition to the benchtop testing described above, one of the first generation wireless sensor designs is tested in real world flow conditions i n a functional wind tunnel. The sensor w as brought to NASA Langley in the summer of 2010 to be tested in the 20" x 28" Shear Flow Control Tunnel. This wind tunnel is a fandriven openloop tunnel with a 15foot long 20" x 28" test section. Figure 4 7 show s the tunnel with the intake on the right and the exhaust on the left Figure 47. NASA 20" x 28" wind tunnel setup showing the location of the sensor in the model. To simplify the number of variables in the test, a flat plate model with a wellknow n behavior is used and the flow conditions a re set to achieve a fully developed turbulent boundary layer The sensor is located in the third chamber of the test section, approximately 10 feet from Test Section Fan Flat Plate Model Exhaust Intake Pitot/Static Probe Temp/Humidity Trip Sensor Pitot Probe

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92 the leading edge of a flat plate model. The flat plate model extends the entire length of the test section and from wall to wall, as shown in Figure 47. A 2D trip wire is located close to the leading edge to initiate mixing and ensure the boundary layer is fully developed by the time it reaches the sensor locati on. The length scale x of the model is defined as the separation between the trip and the sensor. The ceiling of the test section is made up of adjustable plates and monitored with an array of pressure taps to control the pressure gradient in the strea m wi se direction. This i s used to set a zero pressure gradient along the model ensuring that the flow remains attached and predictable all the way to the trailing edge of the model Using equations for turbulent flow over a flat plate [8689] experimental parameters are chosen to closely match calibrations performed in the flow cell. Table 44 shows the settings and expected flow conditions for each test. Standard values are chosen for the viscosity = 17.98x106 Pa s and density = 1.218 kg/m3 of air [90] The sensor is located at x = 3.47 m from the trip, which is used as the length scale for the Reynolds number calculation given by xUx Re ( 411) in which U is the freestream velocity. For 5751010xRe the nondimensional friction coefficient [1] is given by 1 5 ,0.059fx xCRe ( 412) The y locations for the Pitot profiles are predetermined by the total thickness of the boundary layer, such that the range extends into the freestream and has sufficient resolution to capture the important regions. The boundary layer thickness is given by [1] 1 50.38xxRe ( 413)

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93 The shear stress va lues are determined by 2 ,1 2wfxCU ( 414) Table 44. NASA tunnel test configuration settings and conditions Test U [ m/s ] [ kg/m 3 ] [Pa s ] Re x C f,x [mm] w [ Pa ] 1 0 1.2 18 17 .9 8E 6 0 0 0 0 2 5 1.218 17.98E 6 1.19E6 3.59E 3 80 0.06 3 10 1.218 17.98E 6 2.39E6 3.13E 3 70 0.19 4 15 1.218 17.98E 6 3.58E6 2.88E 3 64 0.40 5 20 1.218 17.98E 6 4.77E6 2.72E 3 61 0.67 6 25 1.218 17.98E 6 5.97E6 2.60E 3 58 1.00 7 30 1.218 17.98E 6 7.16E6 2.51E 3 56 1.38 8 35 1.218 17.98E 6 8.35E6 2.44E 3 54 1.83 9 40 1.218 17.98E 6 9.54E6 2.37E 3 53 2.32 A full set of tunnel conditions are collected for all tunnel tests. This includes freestream static pressure P, freestream stagnation pressure Po, temperature T relative humidity RH streamwise tap array pressures P1 30, and the traverse location y The density and viscosity of the air are calculated as functions of f ( P, T RH ), and freestream velocity U is calculated as a function of f ( P, Po, T ). This data was used to correct for flow variations between tests. Before tes ting the wireless shear stress sensor, the boundary layer is fully characterized at each of the test conditions. The first step in characterizing the flow is to confirm the zero pressure gradient assumption. The array of pressure ports P1 30 extending from the leading edge to the trailing edge of the flat plate model are tested at each flow condition. Plotting pressure versus distance from the leading edge, the slope of the curve should be zero in the vicinity of the sensor. This is found to be the case for all test conditions, as shown in Figure 48.

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94 Figure 48. Pressure tap readings from the ceiling of the Shear Flow Control Tunnel for all test points. The sensor location is indicated in the plot around 3.5 m. The next assumption to be confirmed is the establishment of a stable, fully developed turbulent boundary layer. The boundary layer at the sensor location is tested by taking Pitot profiles at each flow condition. The probe tip is raised incrementally from the surface until it reaches the freestream. An example of a typical profile taken at a 15 m/s test condition is shown in Figure 49. Converting to wall units and plotting on a log scale gives a better indication of the state of the boundary layer. Wall units are calculated as *u yy ( 415) where the physical parameters are density and viscosity of the flow and u* is the friction velocity. The friction velocity is calculated by *2fC uU ( 416) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -0.16 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 Downstream Location (m)Pressure (psi) 5 m/s 10 m/s 15 m/s 20 m/s 25 m/s 30 m/s 35 m/s 40 m/s

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95 in which U is the freestream velocity and Cf is the friction coefficient. The nondimensional velocity defined by *U u u ( 417) is plotted versus. y+ and shown in Figure 410. Figure 49. Turbulent boundary layer profile for 15 m/s flow over a flat plate. Figure 410. Turbulent boundary layer plotted in + units to illustrate the Law of The Wall. The different regions in the boundary layer are identified in this figure. 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 0 10 20 30 40 50 60 70 80 90 100 U/U y (mm) 101 102 103 8 10 12 14 16 18 20 22 24 26 28 y+ u+ 1 ln() uyB Free Stream Outer Layer Viscous Sublayer Buffer Layer Log Layer

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96 Five distinct regions in the boundary layer are indicated in Figure 410. The freestream is where the boundary l ayer height is estimated. The buffer layer and the outer layers are transitional layers and are not scrutinized. The viscous sublayer is very thin, and due to the size of the Pitot probe tip, the number of data points is insufficient to accurately determ ine the shear stress from the gradient at the wall. Instead the log layer is used by fitting a line to this region defined by 1 ln() uyB ( 418) where = 0.41 and B = 5.0 are constants A fit is performed using a LabVIEW program from NASA Langley to implement Spalding's Law of the Wall [91] This program gives the Cf where the Law of the Wall best fits the profiles. The shear stress at the wall for each flow velocity is then calculated using Equation 414. There are many additional tests that could be performed on the sensors. Dynamic shear stress testing, pressure rejection, vibration sensitivity, stress testing and many more boundary layer studi es are a few of the possibilities. These test will all require additional resources and time that would be better invested once the technology matures. Additional generations and testing are all left to future work.

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97 CHAPTER 5 5 FIRST GENERATION DEVICES This chapter presents design, fabrication, and characterization of two first generation devices. First, the design and predicted performance is presented, using the modeling techniques presented in Chapter 3. Next, details of the fabrication and packaging are described. Last, using the experimental techniques described in Chapter 4, t he performance of each device is fully characterized. The results are then compared against the model predictions. 5.1 Device Overview The modeling of the wireless shear stress sensor consists of a combination of analytical, numerical, and empirical results. This section presents specific modeling results for two wireless sensor designs, labeled Design 1 and Design 2. First, the coil and antenna results are presented, including their associated parasitics. Next the results for the capacitive shear stress sensor shown in Figure 5 1 are presented, followed by a combination of the results into the final complete wireless sensor performance. Figure 51. Optical image showing the Design 2 capacitive shear stress sensor next to a pencil for scale.

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98 5.1.1 Coil and Antenna Modeling Results The simulated and realized geometries for the coil inductors for both designs are shown in Figure 52. The loop antenna design used for both sensors is shown in Figure 53. The design par ameters corresponding to the variables in Figure 33 are given in Table 51. The center diameters Dc are constrained by the capacitive shear stress sensor die size, which are different for the two designs. Design 1 uses a 3.5 x 3.5 mm2 die, while Design 2 uses a 5 x 5 mm2 die. The pitch p and coil wi dths b are constrained by manufacturing limits, and the height is determined by the thickness of the 1 oz copper clad FR4 used to make the coils. The number of turns is maximized within a 10 x 10 mm2 footprint defined by the dielectric window between the pressure taps, shown in Figure 4 6, in the metal flow cell used to characterize the devices. T he antenna diameter Da is similarly constrained by this window. Figure 52. Coil designs showing simulated and realized inductors. A) Design 1 is a 5turn coil with a 3.5 mm inner diameter. B) D esign 2 is a 4 turn coil with a 5 mm inner diameter. Figure 53. Design showing both the simulated and realized loop antenna. Design 1 3.5 mm Design 2 5 mm Antenna 12.5 mm A B

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99 Table 51. Geometric parameters used for the s piral coil inductors and loop antenna in the first generation wireless design Variable Design 1 Design 2 Dc [mm] 3.5 5 pc [m] 500 500 bc [m] 250 250 hc [m] 35 35 Nc 5 4 Da [mm] 12.5 12.5 ba [m] 250 250 ha [m] 35 35 The wireless sensors operate in the hundreds of MHz range. Simulations in the range of 50 MHz to 1 GHz are performed on the coil design to ensure that this full range is covered. As discussed in Section 3.1.1, the current in the coils is constrained to the outer surfaces at high frequencies. This skin depth is an important consideration for the discretization of the wire segments performed by FastHenry prior to simulation. If the filaments of the discretizatio n are larger than this depth, then the simulation results will be inaccurate. A visualization tool is created as part of a MATLAB code written to both generate the geometry input files for FastHenry and analyze the results. The skin depth for copper betwee n 50 MHz and 1 GHz is plotted in Figure 54. Considering the skin depth at 1 GHz, this plot shows that the minimum filament must be below 2 m. Figure 55 shows that the discretization input parameters produce an accurate numerical result. For the first sets of tests, the antenna is located coaxially with the coil on the backside of the board ( Figure 5 6) in order to maximize the coupling factor. This means that the separation between the antenna and the coil is defined by the thickness of the FR4, which is 1.5 mm. In later tests, the antenna is moved to a separate board, making the separation gap 3 mm or more. The coupling results for both 1.5 mm and 3 mm is reported for completeness. The FastHenry

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100 simulation results as a function of frequency for Design 1 are given in Figure 57 and for Design 2 in Figure 58. In both of these plots, the inductance drops with frequency, while the resistance rises. This indicates that the lower the operating frequency, the higher the mutual inductance and the l ower the resistive losses. Figure 54. Skin depth vs. frequency for copper. Figure 55. Coil discretization plot looking at the cross sectional area of a wire trace. Figure 56. Inductive coupling was simulated with the coil and antenna coaxially aligned with a 1.5 mm separation. 100 200 300 400 500 600 700 800 900 1000 2 3 4 5 6 7 8 9 10 qy g q q ( Frequency (MHz) Skin Depth ( m) 0 50 100 150 200 250 0 10 20 30 width (m) height (m) 1.5 mm Separation

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101 Figure 57. FastHenry simulation results for Design 1. The parameters are indicated at the resonant frequency of this device. Figure 58. FastHenry simul ation results for Design 2. The parameters are indicated at the resonant frequency of this device. 100 200 300 400 500 600 700 800 900 1000 0 50 100 150 200 250 Frequency (MHz)Simulated Inductance (nH) Antenna Resistance Coil Resistance Antenna Inductance Coil Inductance Mutual Inductance 100 200 300 400 500 600 700 800 900 1000 0.25 0.75 1.25 1.75 2.25 2.75 Simulated Resistance () 100 200 300 400 500 600 700 800 900 1000 0 50 100 150 200 250 Frequency (MHz)Simulated Inductance (nH) Antenna Resistance Coil Resistance Antenna Inductance Coil Inductance Mutual Inductance 100 200 300 400 500 600 700 800 900 1000 0 0.5 1 1.5 2 2.5 Simulated Resistance () R a L a M R c R a L a M R c L c L c

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102 The inductance values are extracted and used to determine the resonant frequency of both devices. This is then used to determine the appropriate parasitic re sistance values to use from the plots. These frequencies and their associated parameter values are indicated in the plots. All of the results from these tests are reported in Table 52. The modeling results for the two designs are comparable in inductance, resistance, and coupling. This means that differences in their performance are dominated by the capacitive shear stress sensor performance. The other two remaining parasitics are the capacitances Ca and Cc. The coil parasitic capacitance Cc is obtained analytically using Equation 325 and is also reported in Table 52. The RF connectors between the antenna and the network analyzer dominated the antenna parasitic capacitance Ca. The network analyzer has a 7 mm port, so a 7 mm to SMA connector and an SMA to SMB connector are both required to attach to the SMB terminal soldered to the antenna. The capacitances of these connectors and the terminal are measured, and the results are shown in Figure 59. The total accumulated capacitance is indicated in the plot and added to the results in Table 52. Figure 59. Parasitic capacitance due to RF connectors between the network analyzer and the loop antenna. 50 100 150 200 250 300 350 400 450 500 0 1 2 3 4 5 6 7 Frequency (MHz) Equivalent Parallel Capacitance (pF) Base Line + 7-mm Connector + SMA Connector + SMB Terminal C a

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103 Table 52. Parameter values extracted numerically, analytically, and experimentally for the coupled inductor model. Coupling values are given for 1.5 mm (3 mm) separation. Variable Design 1 Design 2 L c [nH] 228 202 R c 1.22 1.14 L a [nH] 43.2 43.2 R a 0.50 0.50 M [nH] 19.8 (14.7) 21.0 (15.2) k 0.20 (0.15) 0.22 (0.16) C c [fF] 230 377 C a [pF] 4.9 4.9 Obtained experimentally Obtained though numerical simulations 5.1.2 Capacitive Sensor Modeling Results T wo designs for the MEMS capacitive sensor, shown in Figure 51, are described in this section. The analytical models in Section 3.2 are used to predict the static sensor capacitance and part of the parasitic capacitance. The models also predict the total shear to displacement and displacement to change in capacitance sensitivities. Using these sensitivities and the maximum input shear stress, the full scale displacement and change in capacitance are determined. The sensors are both shown in magnified optical images in Figure 5 10. The tethered floating element is visible with comb fingers along either side. The capacitive sensor geometries are selected based on an optimization of this structure reporte d by V. Chandrasekharan [21] who studied a wired version of the shear stress sensor. The optimized 1 mm and 2 mm floating element designs from his work were slightly modified to obtain larger displacements by sacrificing unneeded mechanical bandwidth. The primary purpose of the wireless sensor is to make mean shear measurements, so high bandwidth is not necessary. Both devices have the same tether and finger geometries, except that the 2 mm element can hold more fingers due to the added length. All of the geometric design variables for the sensor, as illustrated in Figure 311 and Figure 314, are given in Table 53.

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104 Figure 510. Optical images of the MEMS capacitive sensors highlighting the vital components. A) Design 1 is 3.5 x 3.5 mm2 and has a 1 x 1 mm2 floating element. B) Design 2 is 5 x 5 mm2 and has a 2 x 2 mm2 floating element. Table 53. Geometric parameters from the two capacitive MEMS sensor s used for the first generation wireless tests Variable Design 1 Design 2 W e [m] 1000 2000 L e [m] 1000 2000 W t [m] 10 10 L t [m] 1000 1000 W f [m] 10 10 L f [m] 170 170 x o [m] 150 150 g o1 [m] 3.5 3.5 g o2 [m] 20 20 h [m] 45 45 N f 22 45 The capacitive modeling results are given in Table 54. The most important parameters for the complete wireless model are Co s, Cs a nd Sc. The full scale values are calculated assuming a maximum shear stress input of 2 Pa. As described in Appendix A the 3% nonlinearity point defines this limit. Because of the complex chain of events shear stress creates a displacement, Floating Element 3.5 mm Tethers Comb Fingers 3.5 mm Floating Element 5 mm Tethers Comb Fingers 5 mm A B

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105 which causes a c apacitance change that leads to a resonant frequency shift various sensitivities are reported. Sw is given by Equation 329 and relates the floating element displacement to the input shear stress. Swc is given by Equation 343 and relates the change in capacitance to the floating element displacement. Sc is the p roduct of the first two sensitivities. Table 54. Analytical modeling results for the MEMS capacitive sensors. Variable Design 1 Design 2 max [Pa] 2 2 w (max) [nm] 72.4 276 C o1 [fF] 438 900 C o2 [fF] 114 228 C o3 [fF] 181 181 C os [pF] 0.73 1.31 C1(max) [fF] 7.71 64.0 C2(max) [fF] 2.40 19.5 C3(max) [fF] 3.57 14.5 Cs(max) [fF] 13.7 98.0 Sw [nm/Pa] 36.2 138 S wc [fF/nm] 0.19 0.33 Sc [fF/Pa] 6.70 45.5 The parasitic structures of the capacitive shear stress sensor are covered in Section 3.2.3. The remaining geometries that are purely parasitic are given in Table 55. A summary of the results is tabulated in Table 56. The results of the parasitics are derived from three sources. The isolation gaps around the contact pads and the stationary end of the tethers are calculated analytically in Equation 345 and reported as Cp1. The fringing field capacitances are simulated in a COMSOL finite element model as described in Section 3.2.3 and are represented as Cp2. The pad areas coupling with the bulk substrate are separated into Cb1, Cb2 and Gb.

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106 Table 55. Geometries of parasitic capacitive structures in the capacitive MEMS sensors Variable Design 1 Design 2 L p1 [m] 250 300 L p2 [m] 250 500 W p1 [m] 430 430 W p2 [m] 500 500 g [m] 50 50 h ox [m] 2 2 Table 56. Parasitic results for the MEMS sensor derived using analytical, numerical and experimental models. Variable Design 1 Design 2 Cp1 [fF] 200 204 Cp2 [fF] 451 687 Cb1 [pF] 8.03 12.6 Cb2 [pF] 92.5 174 Gb [mS] 0.1 0.1 Cp3 [fF] 130 1000 G [mS] 0.62 1.32 Obtained experimentally. Obtained though numerical simulations. The plots in Figure 511 show the simulated total shunt capacitance Cp3 and conductance G that result from the circuit combination of Cb1, Cb2 and Gb. The high capacitance seen at low frequency is attributed to the parallel combination of the sensor capacitance Cos, the parasitic capacitances Cp1 and Cp2, and the pad to bulk capacitance Cb1. The low capacitance seen at high frequency is attributed to the parallel combination of the sensor capacitance Cos and the parasitic capacitances Cp1 and Cp2. The frequency at which the transition occurs is a function of Gb. This frequency is known from experiments and is used to determine Gb. The equivalent Cp3 and G are determined iteratively to account for slight inconsistencies. The die from the firstgeneration wafers were originally 5 x 5 mm2, but the capacitive sensor die for De sign 1 was diced down to 3.5 x 3.5 mm2 to reduce t he size of the contact pads. This corresponds to a significant reduction

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107 in Cp3 and G when compared to De sign 2. It can be seen that with this reduction, the fringe field parasitic capacitance becomes the dominant source. Figure 511. Simulated capacitance and conductance factoring in the bulk layer model. A) Shunt capacitance model. B) Shunt conductance model. 5.1.3 Completed Model Results With all of the parameters from the coils and capac itive sensor defined, the complete device performance can be predicted. The resonant frequency fo is given by Equa tion 357 and quality factor Q by Equations 367. The results for both devices are presented in Table 57. The resonant frequency of De sign 2 is lower due to the larger floating element size, which has more fingers and thus gives a higher static capacitance. The lowest resonant frequency possible is desirable to reduce coil resistances, but the reduct ion of the capacitive sensor parasitics achieved in De sign 1 had a greater effect on Q This shows that for the present designs the dominant parasitics are from the capacitive sensor. This is uncommon in LC resonators where the resistive losses of the coil usually dominate. The final device sensitivity needed to relate a change in the resonant frequency to the input shear stress is determined based on the complete wireless model shown in Figure 326. The sensitivities relating displacement to shear and change in capacitance to displacement are reported in the previous section. The final sensitivity Scf relates the resonance shift to a ch ange in 105 106 107 108 0 2 4 6 8 10 12 14 16 Frequency (Hz) Total Shunt Capacitance (pF) Design 1 Design 2 105 106 107 108 10-7 10-6 10-5 10-4 10-3 Frequency (Hz) Total Shunt Conductance (S) Design 1 Design 2 A B

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108 capacitance and is given by Equation 359. The full device sensitivity Sf is the product of Stc from Table 54 and Scf. The normalized sensitivity Sn is reported in units of parts per million [ ppm ] This normalized sensitivity is useful for comparing wireless devices that operate in different frequency bands. The predicted normalized sensitivities are over two orders of magnitude larger than previously reported wireless sensors [31,42,50,51,53,54,58,60] This improved sensitivity is necessary for the application of detecting the minute tangential shear forces in subsonic flows. Table 57. Full wireless system resonance and sensitivity results. Variable Design 1 Design 2 fo [MHz] 252 187 Q 4.58 3.59 f(max) [MHz] 0.95 2.33 Scf [kHz/fF] 70.9 25.9 Sf [kHz/Pa] 475 1167 Sn [ppm/Pa] 1885 6241 SF [ 1/ N ] 1885 1560 The reflection coefficient spectrum of the wireless sensors are used to detect and track the wireless resonance as described in Section 4.2.1. At e ach frequency, the reflection coefficient is given by Equation 355. The theoretical spectrums showing the resonant dips for both sensor designs are plotted in Figure 512. De sign 1 shows a minimum in the reflection coefficient at 252 MHz, and De sign 2 shows a minimum in the reflection coefficient at 187 MHz. As expected, the minimums are located at the resonant frequencies of the devices. 5.2 Fabrication and Packaging The system uses a hybrid packaging approach that combines the silicon capacitive MEMS sensor with an inductive coil fabricated in a PCB substrate. An alternative configuration for the devices would have been to fabricate and integrate the coils on the silicon capacitive sensor dies.

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109 Realizing such structures, however, would involve a complicated and expensive fabrication process, so a hybrid packaging approach is selected. The silicon die is flush mounted in a recess in the PCB to provide a smooth surface for exposure to the flow. In the current design, t he MEMS capacitive sens ors are connected to the inductor coil s via gold wire bonds, but future implementations may use other interconnect technologies such as through wafer vias to eliminate the wire bonds and ensure a hydraulically smooth surface. Figure 512. Resonant dips in the reflection coefficient predicted by the model for both Design 1 and Design 2. 5.2.1 Process Flow A simple two mask fabrication process is used to create the sensor. These sensors were incorporated into the m ask files with V. Chandrasekharan's designs [21] and fabricated at the same time using the same process. A more detailed description of the fabrication can be found in his dissertation An overview of the fabrication process flow is illustrated in Figure 513. A silicon on insulator ( SOI ) wafer with a highly doped device layer is etched via deep reactive ion etching (DRIE) to define the sensor structures using M ask 1 ( Figure 514A ). The highly doped silicon (Si++) is then electroplated with ni ckel (Ni). The nickel is intended to reduce conductivity 50 100 150 200 250 300 350 400 450 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 Frequency (Hz) Reflection Coefficient | | Design 1 Design 2

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110 and eliminate charge accumulation in the native oxide that naturally grows on the surfaces of the silicon. A front to back alignment is used to pattern a photoresist layer with M ask 2 ( Figure 514B ) to define the backside cavity etch underneath the floating element. To release the mechanical structures a buffered oxide etch ( BOE ) is us ed to remove the underlying oxide Figure 513. Generation 1 MEMS sensor fabrication process flow. Figure 514. Photolithography dark field mask set used to define etches in the process flow. A) Sensor structure etch. B) Back cavity etch. 1) Start with an SOI wafer. 2) DRIE topside to define sensor. (Mask 1) 3) Electroplate Ni for charge passivation. 4) DRIE backside to create a cavity. (Mask 2) 5) BOE etch to release the sensor. Si Si++ Oxide Ni Mask 1 Mask 2 A B

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111 5.2.2 Hybrid Packaging The hybrid packaging scheme enables fast turnaround time, increased flexibility, and separates testing of the sensor capacitances and coil induct ances. The coils and antennas are fabricated using a PCB milling machine. The sensor die is then mounted into a recess in the PCB and connected via gold wire bonds. A top view of this concept is illustrated in Figur e 515 for both a single device as well as an array. The dashed lines indicate the antenna, which exists on the backside of the board. More specific details are described in the following para graphs. Figure 515. Packaging concept for hybrid wireless shear stress sensors. A) Single sensor design. B) A 2 x 2 array design. The packaging process is shown in Figure 516. A c opper clad FR4 board is milled to create the inductor coil and loop antenna The coil is electroplated with Ni to enable electroless deposition of Au for wire bonding to the sensor die in the final step. A photodefinable solder mask polymer is then applied to reduce the surface roughness due to the Cu traces. Contact window openings are made in the solder mask and Au is plated to facilitate electrical connections to the inductor bond pads. A cavity is milled in the top surface of the board to accommodate the sensor die. DualBond 707 e poxy is applied to only one corner of the die to affix it in the cavity and avoid mechanical st resses on the die as the glue dries. Gold ball wedge wire bonding is used to connect the sensor to the inductor. The final device footprint for the single sensor construction is 10 mm x 10 mm in the center of a 30 mm x 30 mm x 1.5 mm board. A B

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112 The board size allows room for up to a four sensor array. Figure 517 shows the die packaged in the PCB with a U.S. penny for perspective Figure 516. Process flow for hybrid wireless packaging. Figure 517. Final packaged wireless sensor shown next to a U.S. penny for perspective. 1) Start with copper clad FR4. 2) Mill the coil on top and antenna on bottom. 3) Electroplate Ni on top coil. 4) Apply solder mask and develop coil pads. 5) Electrolessly plate Au on pads. 6) Mill recess for flush mounting of the sensor. 7) Insert MEMS sensor and epoxy in place. 8) Wirebond sensor pads to coil pads.

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113 The boards are housed in an acrylic plug, which enables mounting to calibration flow cells and installation in wind tunnel models. The topside of the plug is designed with a smooth, flush surface, and the backside has a SMB connector for electrical connect ion of the loop antenna to an interrogation circuit or network analyzer. An illustration of the front and backside of this plug with the sensor in place is shown in Figure 518. Figure 518. Wireless sensor boards flush mounted in test plugs used for the flow cell calibration and wind tunnel tests. A) Frontside showing sensor being fit into the plug. B) Backside view showing antenna and RF connector. 5.3 Experimental Results The experimental tes t results for De sign 1 and De sign 2 are presented in this section using the test setups described in Chapter 4. These tests are performed to fully characterize the performance of the sensors. First impedance characteristics are obtained on individual sensor die prior t o packaging in the wireless boards Next the die are evaluated electrostatically to ensure the free floating structures on the die were free of obstructions. T he stability, noise floor and sensitivity are obtained in a series of tests giving the minimum detectable signals ( MDS ) and dynamic ranges ( DNR ) of the devices. A simple range test is presented to evaluate the coil antenna separation limitations. During testing, an unexpected and undesirable sensitivity to humidity was found, and therefore dedicated humidity tests were also conducted to quantify this A B

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114 sensitivity. Finally baseline shear stress measurements from a real world wind tunnel are presented. 5.3.1 Impedance Characterization Two sets of impedance data are taken for the two capacitive shear stress sensor designs as described in Section 4.1.1. First, a high accuracy low f requency test is performed on an impedance analyzer to compare to the capacitive shear stress sensor model results from Section 5.1.2. The maximum frequency of the impedance analyzer is below the resonant frequencies of the devices, so a high frequency test is conducted. A material property analyzer (RF impedance analyzer) is used to extend the range of these tests and obtain values for the parasitic capacitance and conductance. 5.3.1.1 Impedance analyzer 100 kHz to 100 MHz Since each sensor design actually includes differential capacitors, both sides of the differential capacitor were measured. The resulting shunt capacitance and shunt conductance for each o f the four capacitors are plotted in Figure 519. Additionally, the measurement error is also shown; the random error is plotted using a 95% t distrib ution, and the bias error is calculated according to the impedance analyzer manual [92] For the tests, the random error is several orders of magnitude less than the bias error, indicating that the measurements are repeatable from sweep to sweep and will also be repeatable from die to die. The bias error is an inherent limitation of the analyzer and cannot be improved upon, but since it is several orders of magnitude lower than the measure d values, it is not a limiting factor in the overall wireless sensor model accuracy. Comparing the measured data in Figure 5 19 against the theory in Figure 5 11, one major discrepanc y is observed. The high frequency response never flattens out; dotted lines in Figure 519 show where the data was expected to asymptote. This effect is consistent for both devices and

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115 points to some higher order effects that are not captured in the simple model. The impedance data seems to point to an additional leakage path between the terminals of the capacitive sensor. One possibility is dust or debris that has entered the gaps and bridges between the two capacitor structures. Another possibility is a poor qual ity oxide with pinholes or other defects. Whatever the source, as the conductance climbs the quality factor Q drops. This creates a design challenge, since MDS is a function of Q Figure 519. Capacitance measurement and error for Design 1 and 2. A) Mean shunt capacitance. B) Measurement errors. C) Mean shunt conductance. D) Measurement errors. 5.3.1.2 Material property analyzer 1 MHz to 1 GHz The same test was repeated w ith the Agilent E4991A material property analyzer at a different frequency range. For these tests, the same sensor designs were tested, but more dies were tested to get a better sample population. The results for Design 1 are plotted in Figure 520, 105 106 107 108 2 4 6 8 10 12 14 16 18 20 Shunt Capacitance (pF) S1A3C2 S1A3C1 S2A6C2 S2A6C1 105 106 107 108 10-5 10-4 10-3 10-2 10-1 100 Measurement Error (pF) Random Error Bias Error 105 106 107 108 10-7 10-6 10-5 10-4 10-3 10-2 Frequency (Hz) Shunt Conductance (S) S1A3C2 S1A3C1 S2A6C2 S2A6C1 105 106 107 108 10-10 10-9 10-8 10-7 10-6 10-5 10-4 Frequency (Hz) Measurement Error (S) Random Error Bias Error A B C D

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116 and the results for Design 2 are plotted in Figure 521. These tests confirm that the shunt conductance continues to rise without leveling off, as was suspected in the first set of impedance tests. These tests provide data in the operation range of the wireless sensor that is used to estimate the shunt con ductance, G and capacitance, Cp3 for the full wireless sensor models. The bias and random errors for these tests are higher due to the reduced accuracy of the material property analyzer with respect to the impedance analyzer. The bias error s are still seve ral orders of magnitude lower than the measured values, so they will not affect the overall accuracy of the wireless model. Figure 520. Die level high frequency impedance sweeps for six Design 1 sensors. A) Mean shunt capacitance. B) Random and bias error for the capacitance measurements. C) Mean shunt conductance. D) Random and bias error for the conductance measurements. 106 107 108 109 0 2 4 6 8 10 12 14 16 18 Shunt Capacitance (pF) S2A5C2 S2A7C2 S2B3C2 S2B4C2 S2B5C2 S2C3C2 106 107 108 109 10-5 10-4 10-3 10-2 10-1 100 101 Measurement Error (pF) Random Error Bias Error 106 107 108 109 10-5 10-4 10-3 10-2 Frequency (Hz) Shunt Conductance (S) S2A5C2 S2A7C2 S2B3C2 S2B4C2 S2B5C2 S2C3C2 105 106 107 108 10-10 10-9 10-8 10-7 10-6 10-5 10-4 Frequency (Hz) Measurement Error (S) Random Error Bias Error A B C D C p3 G

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117 Figure 521. Die level high frequency impedance sweeps for six Design 2 sensors. A) Shunt capacitance. B) Random and bias error for the capacitance measurements. C) Shunt conductance. D) Random and bias error for the conductance measurements. 5.3.2 Electrostatic Actuation Test The primary purpose of this test is to provide a qualitative result to determine the best sensors for testing. Before applying an actuation voltage, the pull in characteristics have to be determined so that the maximum input voltage does not exceed these limits. The pullin displacement is given by Equation 43, and the pull in voltage is given by Equation 42 in Section 4.1.2. The geometries from Table 5 3 are used, and the results are given in Table 58. Forcing voltages of 80% of the pull in are used to induce a visible displacement. With the microscope focused on a few sets of fingers, the voltage signal is applied and video is taken of the moving fingers at 25 frames per second. The video file is processed in 106 107 108 109 2 4 6 8 10 12 14 Shunt Capacitance (pF) S1A1C2 S1A3C2 S1A5C2 S1A6C2 S1B3C2 S1B4C2 106 107 108 109 10-5 10-4 10-3 10-2 10-1 100 101 Measurement Error (pF) Random Error Bias Error 106 107 108 109 10-5 10-4 10-3 10-2 Frequency (Hz) Shunt Conductance (S) S1A1C2 S1A3C2 S1A5C2 S1A6C2 S1B3C2 S1B4C2 106 107 108 109 10-8 10-7 10-6 10-5 10-4 10-3 Frequency (Hz) Measurement Error (S) Random Error Bias Error A B C D C p3 G

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118 MATLAB to identify the fingers, as shown in Figure 522, and tracked to find the variations in the gap width. The results of 8 seconds of this test is plotted in Figure 5 23. The displacement is roughly 600 nm from the nominal 3.5 m gap of the sensor. This result is estimated using a pixel to distance calibration in the code. Table 58. Electrostatic pullin parameters for th e first generation designs. Variable Design 1 Design 2 k [N/m] 30.2 30.2 xpi [m] 1.16 1.16 Vpi [V] 17.2 12.0 Vmax [V] 14 10 Figure 522. Video frame from electrostatic forcing test. A) Raw image showing two sets of fingers. B) Formatted image used to track finger displacements. 5.3.3 Wireless Resonant Frequency, Stability, and Noise Floor After the capacitive shear stress sensor die has been characterized it is packaged with the coil and antenna to form a wireless shear stress sensor. The first test that is performed on the wireless sensor is to determine the resonant frequencies of the devices. A wideband search sw eep is performed with the network analyzer, as described in Section 4.2.1, and the resonant frequency is identified by dips in the reflection coeff icient. The results are shown in blue for De sign 1 in Figure 524 A and for De sign 2 in Figure 524 B The model spectrums from Figure 512 are A B

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119 plotted in black. As can be seen in the plots, the model is a very good approximation to the actual device responses. Figure 523. Displacement results processed by MATLAB. Plot shows 8 seconds worth of video at 25 frames/s. A common problem with passive wireless sensors is frequency drift. To quantify this effect a threehour drift test i s conducted in a Faraday cage to measure the inherent drift of the sensor. The resonant frequency is tracked using a network analyzer as described in Section 4.2.1. The results from these stability tests are plotted in Figure 525. The overall drift of the sensors is found to be 0.57 kHz/min for De sign 1 and 0.22 kHz/min for De sign 2. This corresponds to an equivalent drift in shear stress of 1.2 mPa/min and 0.19 mPa/min, using the sensitivities given in Table 57. This means that the drift can rise above the noise floor of the sensors within a matter of minutes. Extended tests will be unreliable unless a new base line frequency is updated periodic ally, which will add more complexity to the test procedure. A reduction in the frequency drift is one of the goals for future sensor generations. 20 40 60 80 100 120 140 160 180 200 2.5 3 3.5 4 4.5 Frame Gap Width (m)

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120 Figure 524. Resonant dips showing the accuracy of the model. A) Design 1. B) Design 2. The noise floor is a vital parameter required to determine the dynamic range of the sensor. The noise floor for the sensor was derived in Section 3.3.3, Equation 368. The amplitude noise in the reflection coefficient na was extracted from the plot of a resonant di p shown in Figure 526. Using this parameter, the resonant frequency, and quality factor of the devices, the frequency noise level is around 5 kHz. This value is used to determine the minimum detectable signal given by Equation 369 and dynamic range given by Equation 410 of the sensors, 50 100 150 200 250 300 350 400 450 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 Reflection Coefficient | | Data Model 50 100 150 200 250 300 350 400 450 0.88 0.9 0.92 0.94 0.96 0.98 1 Frequency (MHz) Reflection Coefficient | | Data Model A B

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121 assuming a maximum input shear Max of 2 Pa. The results are given in Table 59. These results are based on the predicted sensitivities given in Table 57. Figure 525. Sensor resonance drift. A) Design 1. B) Design 2. Table 59. Results predicted by the model. Variable Design 1 Design 2 na 0.0002 0.0002 nf [kHz] 5.97 4.37 MDS [mPa] 12.6 3.74 DNR [dB] 44.0 54.6 Drift [kHz/min] 0.56 0.22 0 20 40 60 80 100 120 140 160 180 251.8 251.85 251.9 251.95 252 252.05 252.1 252.15 Resonance (MHz) 0 20 40 60 80 100 120 140 160 180 185.9 185.95 186 186.05 186.1 186.15 186.2 186.25 186.3 Time (Minutes) Resonance (MHz) A B

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122 5.3.4 Static Shear Flow Calibrations Using the setup described in Section 4.2.4, a shear stress calibration is performed on Design 1 by monitoring the resonant frequency of the sensors while incrementing the input shear fro m 0 to 1.6 Pa The results of this test are shown in Figure 527, indicating a linear (R2 = 0.994) sensitivity of 21 9 kHz/Pa. This corresponds to a normalized sensitivity of 865 ppm/Pa. Figure 526. Noise plot. Figure 527. Linear static calibration for sensor Design 1. 244 246 248 250 252 254 256 258 0.866 0.868 0.87 0.872 0.874 0.876 0.878 0.88 0.882 Frequency (MHz) Reflection Coefficient | | 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 258.25 258.3 258.35 258.4 258.45 258.5 258.55 258.6 258.65 Shear (Pa) Resonance (MHz) Design 1 Calibration Linear Fit 219 kHz/Pa R 2 = 0.994 n a

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123 Design 2 is also tested using the same flow cell. The measurement range is increased slightly for an input shear from 0 to 2.25 Pa. The results of this test are shown in Figure 528, indicating a linear (R2 = 0.996) sensitivity of 894 kHz/Pa. This corresponds to a normalized sensitivity of 4,781 ppm/Pa which is better than Design 1, as predicted. The trade off is spatial resolution. Design 2 has a 2 x 2 mm2 floating element, which is four times the area of the 1 x 1 mm2 floating element on Design 1 A large sensitivity is very important for shear stress measurement in air where the shear forces are extremely small. To check the repeatability of the measurement, the test is repeated three times. Figure 529 shows that the results are repeatable. Figure 528. Static shear stress calibration for Design 2. The final experimental results for sensitivity, MDS and DNR are reported in Table 510. The sensitivity values do not quite match the predicted values. This could be due to a wide array of sources, but the most likely reason is reduced deflections due to higher stiffness than expected or nonlinear Duffing spring deflections. Overall, the devices performed extremely well, given the low quality factors and testing nonidealities. 0 0.5 1 1.5 2 192.5 193 193.5 194 194.5 195 Shear (Pa)Resonance (MHz) Device 2 Calibration Linear Fit 894 kHz/Pa R 2 = 0.996 Design

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124 Figure 529. Repeatability shear stress calibrations for Design 2. Table 510. Final experimental sensitivity, minimum detectable signal and dynamic range. Variable Design 1 Design 2 Predicted Realized Predicted Realized Sf [kHz/Pa] 475 218 1167 894 S n [ppm/Pa] 1885 865 6241 4781 S F [ 1 / N ] 1885 865 1560 1195 MDS [mPa] 12.6 27.4 3.74 4.89 DNR [dB] 44.0 37.3 54.6 52.2 5.3.5 Wireless Range Test for Design 1 Another metric of interest for a wireless sensor is the effective range of the device. The maximum wireless range has serious implications for the successful implementation of the device in any useful application. To test the range of the sensor, the gap between the coil and the antenna for Design 1 is incremented from the minimum of 3 mm (limited by PCB thickness) to 11 mm, where the signal disappears into the noise as seen in Figure 530. The maximum power of the 8719D, which is limited to 5 dBm (3.4 mW,125mV), is used for all measurements. 0 0.5 1 1.5 2 192.5 193 193.5 194 194.5 195 Shear (Pa)Resonance (MHz) Run 1 Run 2 Run 3

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125 Figure 530. Frequency sweeps showing resonant frequency dip height reduction with increasing coil antenna separation. At each gap, a resonant peak magnitude is measured. The peak height is normalized by the maximum peak height found with the minimum gap of 3 mm. This normalized peak height is plotted versus the gap in Figure 531. The signal strength decays exponentially with distance, as expected for electromagnetic coupling of the sensor to the antenna. Even with proper network analyzer correction performed before e ach measurement, the reflection coefficient spectrum is not perfectly flat when the wireless sensor is absent. The resonant frequency estimation becomes unreliable when the resonant peak is reduced to the same order of magnitude as the amplitude variations at around 9 mm separation. This value is defined as the noise floor for the signal strength in the range test and is indicated by the blue line in Figure 5 31. The effective range for this configuration with this specific network analyzer is around 9 mm, which should be adequate for many test applications if the airfoil skin or pipe wall is the limiting factor for sensor to antenna separation. This rang e requires that any material separating the antenna from the sensor is of a dielectric nature. max i

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126 Figure 531. Range test results showing the maximum separation within which resonance can be determined. 5.3.6 Wireless Humidity Test for De sign 1 During initial tests, a large, unexpected frequency drift was observed during the static shear stress calibrations. The source of this drift was eventually attributed to humidity differences between the ambient air and the com pressed dry air being used in the flow cell. The sensors respond to this change in humidity as described in Section 4.2.3 and the change in frequen cy from the humidity cannot be separated from the change in frequency from the input shear stress. Running a low flow in the flow cell to dry out the sensor prior to the shear calibration tests eliminates this effect. For completeness, the humidity sens itivity is further investigated. A humidity test described in Section 4.2.3 is performed on De sign 1. As shown in Figure 5 32, the resonant frequency rise is correlat ed with the humidity drop measure with a humidity sensor. The response of both signals is exponential, with a time constant of around 20 minutes. The 3 4 5 6 7 8 9 10 11 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Gap (mm) Normalized Peak Magnitude | i| / |max| Resonant Peaks Noise Floor

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127 f requency drop is ~20 kHz/% RH, which corresponds to 0.3 fF/% RH. Mitigation of this humidity effect is explored in Chapter 6 with the presentation of a second generation design. Figure 532. Wireless sensor response to humidity. 5.3.7 NASA 20 x 28 Wind Tunnel Test of De sign 2 The final sensor characterization for the first generation sensor involves measurements in a wind tunnel facility. Before the sensor is tested in the wind tunnel, the flow conditions of the tunnel must be well characterized. A flat plate turbulent boundary layer is chosen for the first "real world" test of the wireless sensors. The full test process is described in Section 4.2.5. The tunnel flow velocities are chosen to match the maximum input shear stress of the wireless sensor. The input shear stress at each flow velocity is determined by a boundary layer profile prior to testing the wireless sensor. The profiles for all velocities are given in Figure 533. The log regions used to extract the friction coefficient, and thus the shear stress, is highlighted in each of the profiles. All of the parameters from the wind tunnel characterization are presented in Table 511. The wireless sensor data is shown in Figure 5 34. 0 20 40 60 80 100 120 252 252.25 252.5 252.75 253 Time (Minutes) Resonance (MHz) Humidity Sensor Wireless Sensors 0 20 40 60 80 100 120 5 15 25 35 45 Relative Humidity (%RH)

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128 Figure 533. Boundary layer profiles for all test cases. A) 5 m/s freestream velocity. B) 10 m/s freestream velocity. C) 15 m/s freestream velocity. D) 20 m/s freestream velocity. E) 25 m/s freestream velocity. F) 30 m/s freestream velocity. G) 35 m/s freestream velocity. H) 40 m/s f reestream velocity. 101 102 103 104 10 15 20 25 u+ 101 102 103 104 10 15 20 25 u+ 101 102 103 104 10 15 20 25 u+ 101 102 103 104 10 15 20 25 u+ 101 102 103 104 10 15 20 25 u+ 101 102 103 104 10 15 20 25 u+ 101 102 103 104 10 15 20 25 y+ u+ 101 102 103 104 10 15 20 25 y+ u+ A B C D E F G H

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129 Table 511. Flat plate turbulent boundary layer test results Test U [ m/s ] [kg/m 3 ] [ Pa s] [mm] u [m/s] C f w [ Pa ] 1 0 0 2 5.12 1.19 17.97 73.90 0.24 4.30E 3 0.07 3 10.16 1.19 17.96 58.90 0.41 3.26 E 3 0.21 4 14.94 1.19 17.98 49.72 0.57 2.93E 3 0.40 5 19.67 1.19 17.95 47.51 0.74 2.84E 3 0.68 6 24.88 1.19 17.96 45.03 0.92 2.76E 3 1.05 7 30.08 1.19 17.96 44.79 1.11 2.71E 3 1.51 8 34.95 1.17 18.05 44.54 1.27 2.62E 3 1.97 9 40.54 1.17 18.08 44.31 1.45 2.56E 3 2.59 Estimated by the law of the wall Figure 534. Wind tunnel calibration for Design 2. After the flow is characterized at the preset test conditions, the sensor is inserted into the model for the wireless measurements. To determine the response of the sensor, 20 averages are taken at each test condition. The average resonance frequency of th e sensor at each condition is then plotted versus the approximated shear obtained from the flow characterizations in Table 50 0.5 1 1.5 2 2.5 3 185 185.5 186 186.5 187 187.5 188 Shear (Pa) Resonance (MHz) Tunnel Data Linear Fit 861 kHz/Pa R 2 = 0.942

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130 11. The results of the tes t are shown in Figure 534 with a maximum shear of 2.5 Pa at 40 m/s. The results show a linear trend (R2 = 0.942) with a sensitivity of 861 kHz/Pa and a normalized sensitivity of 4,599 ppm/Pa. These results are within 5% of the 894 kHz/Pa and 4,781 ppm/Pa obtained in the flow cell calibrations.

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131 CHAPTER 6 6 SECONDGENERATION DEVICES This chapter presents a second generation capacitive shear stress sensor, shown in Figure 61. As described in Chapter 5, some design flaws were identified with the firstgeneration sensors. With an understanding of the limitati ons of the first generation design, a second generation design was developed. The limitations of the first generation and the proposed design improvements are first discussed. Next, an overview of the complete wireless sensor, incorporating a re designed capacitive shear stress sensor, is given. This overview repeats the modeling for the new sensor, and provides new performance predictions. The fabrication and packaging is also presented, focusing on the new fabrication techniques used to realize the second generation capacitive shear stress sensors. Details and results from dielevel and devicelevel characterizations are presented at the end of the chapter. Figure 61. Optical image showing the second gener ation capacitive shear stress sensor next to a pencil for scale.

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132 6.1 Design Improvements The first generation capacitive shear stress sensors represent a significant leap forward in passive wireless sensing, but there are several problems and inefficiencies in the design for practical applications. The first generation sensor has very high parasitic capacitance and conductance, which limits the Q There is a significant humidity sensitivity that gives false shear stress readings and causes frequency drift. The sensor structure originally designed as a wired deviceis implemented in a differential configuration with two complementary variable capacitors. The passive wireless implementation only uses one side of this pair, so the other side is wasted. To address t hese limitations, improvements are made in the material selection and sensor geometry. These design changes are implemented into a new fabrication run for realization of second generation sensors. 6.1.1 Sensor Structure The physical layout of the floating elemen t, tethers, and comb fingers is an important consideration that affects the performance of the capacitive shear stress sensor. In the first generation die shown in Figure 62 A only one side of the floating element has fingers that are used in transduction (the sections colored red and blue). The other side is used for the differential wired shear stress sensor [21] The secondgeneration design, shown in Figure 62 B makes use of a diamondshaped flo ating element that enables all four sides of the floating element to have comb fingers. A 1.5 x 1.5 mm2 floating element is rotated 45 degrees, and 1 mm tethers are attached at the mid points, allowing a more compact design. The sensor fits on a 3.5 mm x 3.5 mm die. Another important geometrical difference is the back cavity of the floating element. In the first generation sensor, shown in Figure 63 A the back cavity depth is the total thickness of the bulk wafer. The bulk silicon is etched from the back side to fully release the floating element.

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133 The large cavity (0.5 mm in height) provides very little resistance to pressure driven flow underneath the floating element. The flow cell test setup describ ed in Section 4.2.4 has a channel height of 0.5 to 1 mm, which is on the order of backside cavity height. In contrast, the second generation cavity, shown in Figure 63 B can be set to a specific depth and thus becomes a design parameter that can be optimized. The cavity height is set to 6 m in this design and presents a very large resistance compared to any feasible test channel height. This design rejects pressure driv en flow under the element and improves confidence in the calibration procedures and the overall accuracy of the sensor. Figure 62. Representations of the sensor structures shown out of scale. A) First generation design. B) Secondgeneration design. Figure 63. Pressure driven flow diagrams. A) First generation sensor with flow under and over the floating element. B) Second generatio n sensor with flow only over the floating element. FLOWPhPl Rcav Rchannel FLOW PhPl Rcav Rchannel A B A B

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134 6.1.2 Parasitics The materials used for the second generation sensor are chosen to drastically reduce the parasitics discovered while characterizing the first generation sensors. The material properties of the b ulk silicon in the first generation causes parasitic capacitance orders of magnitude larger that the active variable capacitance. The parasitic conductance from the bulk silicon causes the capacitive sensor to be the Q limiting factor in the resonant circuit. For the second generation, the bulk silicon underneath the floating element is replaced with Pyrex (7740 equivalent). Pyrex is a borosilicate glass that provides excellent dielectric properties in addition to havin g thermal expansion properties that match Si for fabrication. In using a non conductive bulk substrate, the floating element layer is the only conductive layer. As shown in Figure 6 4, this eliminates the deviceto bulk parasitic capacitance and conductances. The only remaining parasitics are the capacitances associated with the stationary gaps around the pads (required for electrical isolation) and the fringing fields around the comb fingers. Figure 64. Illustration of second generation sensor bond pad. 6.1.3 Humidity Sensitivity Another important change in the secondgeneration design addresses the humidity sensitivity found with the first generation sensors. In the first generation process flow, Ni was Cs Csh Wp tPyrex

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135 electroplated onto the comb fingers of the capacitive sensor in an effort to e nsure a highly conductive surface and eliminate possible charge accumulation. Tests were completed on the first generation capacitive sensors with and without the Ni plating, and there was not any noticeable difference in drift. In essence, the Ni did not really seem to have an effect. Rather, the electroplating step added unnecessary complexity to the fabrication process. Moreover, it is believed that the process of applying the Ni coating contributed to the large humidity sensitivity seen in the first gen eration sensors. One of the methods for reducing the humidity sensitivity is the application of a hydrophobic coating to the surfaces of the sensors. The theory is that this coating rejects the condensation of water molecules onto the surfaces of the capa citive plates. Water has a very high dielectric permittivity of around 80, which changes the total effective permittivity in the gap. This causes a shift in resonant frequency without any movement of the fingers. Parylene C was found to have some humidity sensitivity reducing effects, but the process was never perfected for the capacitive shear stress sensors. Hydrophobic self assembled monolayers [93] were also investigated, but the capability to deposit these layers was not easily accessible. Another coating that was researched, but not systematically tested, was the Teflon like passivation layer used in the BOSCH deep reactive ion etch (DRIE) process for silicon [94,95] DRIE is already part of the fabrication process, so it is the best candidate with which to start. In the first generation process flow, after the DRIE etch and b efore the Ni plating, the wafers were dipped in a piranha (H2SO4:H2O2) etch to remove the passivation layer, followed by an HF etch to remove any oxide formed on the surfaces. This process stripped the comb finger sidewalls of the hydrophobic Teflonlike c oating and applied a hydrophilic Ni coating to replace

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136 it. For the second generation process flow, the Ni plating step is eliminated, and the DRIE passivation layer is intentionally left on the sidewalls at the end of the process. 6.2 Device Overview The model ing results of the second generation wireless sensors are determined using the same procedures as the first generation in Chapter 5. First the coil and antenna results are presented including their associated parasitics. Next, the capacitive sensor results are predicted, followed by the combination of the results into the final complete wireless sensor performance. This section presents all of these results and compares them to the first generation sensors 6.2.1 Coil and Antenna Modeling Results The same coil and antenna designs that were used for the first generation sensors are used for the second generation wireless shear stress sensors. This allows for a more accurate comparison of the first and secondgeneration capacitive shear stress sensors. Improvements in the overall performance are then directly attributable to improvements in the capacitive sensor. This wireless sensor is referred to as Design 3 in this dissertation. Using FastHenry for electromagnetic simulation, the resulting parameters are given in Table 6 1. A backlit picture of the wireless sensor with the second generation die is shown in Figure 65. Table 61. Parameter val ues extracted numerically, analytically, and experimentally for the coupled inductor model. Variable Design 3 Lc [nH] 335.7 Rc 1.77 La [nH] 43.2 Ra 0.50 M [nH] 28.3 k 0.23 Cc [fF] 198 Ca [pF] 4.9 Obtained experimentally Obtained though numerical simulations

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137 Figure 65. Backlit photograph of the secondgeneration wireless sensor showing a 6 turn coil with a 3.5 mm inner diameter and diamonddesign capacitive sensor. 6.2.2 Capacitive Sensor Modeling Results The capacitive modeling for the second generation sensor is similar to the modeling for the first generation sensors. The sensor geometry is shown in an SEM in Figure 66. The sensor still consists of a floating element area, tethers and comb fingers. The tethers and the floating element function and are analyzed in the same way as the first generation. The fingers still have th e same gap widths and overlapping areas. There are, however, a few key design changes for the model. Mechanically the tethers are made thicker to make the sensor more robust, improve yield, and push the maximum shear stress up to 5 Pa. Electrostatically the number of fingers changed by a factor of four. The only equations that have to be modified are Equations 338 and 339, which become 3 1211 2oot ooCLh gg ( 61) and 3 12121111 ()2ot ooooCwLh gwgwgg ( 62) The se equations a re different because of the single si ded capacitor configuration, and C2 = 0 since there is no floating element end in the diamond design.

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138 Figure 66. SEM image of the second generation sensor die highlighting the vital components. Using the geometric parameters given in Table 6 2 and the modeling methods described in Chapter 3 with the modifications mentioned, the predicted results are given in Table 63. The second generation sensor has a 1.5 x 1.5 mm2 floating element, which is in between the two first generation floating element areas. A direct comparison of the results without considering the floating element areas does not provide a fair assessment. Instead, a correction factor is applied to each comparison using a ratio of the floating element areas. The static capacitance for the second generation Design 3 is 180% higher than the first generation Design 1 and 26% higher than the fi rst generation Design 2. Normalizing for these areal differences, the full scale capacitance change ratio for Design 3 is 109% higher than Design 1 and 16% higher than Design 2. The parasitics of the second generation device are expected to be greatly redu ced. In addition to the elimination of the Si bulk substrate, the pads are smaller. The Design 3 geometry Floating Element Tethers Comb Fingers

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139 for the pads is given in Table 64, and the resulting parasitics are given in Table 65. The parasitic capacitance is reduced by an order of magnitude for the low frequency case and by half for the highfrequency case. Table 62. Geometric parameters for the second generation capacitive s ensor. Variable Design 3 W e [m] 1500 L e [m] 1500 W t [m] 15 L t [m] 1000 W f [m] 10 L f [m] 170 x o [m] 150 g o1 [m] 3.5 g o2 [m] 20 h [m] 45 N f 90 Table 63. Analytical modeling results for the second generation capacitive sensor. Variable Design 3 max [Pa] 5 w (max) [nm] 119 Co1 [fF] 1800 Co2 [fF] 268 Cos [pF] 2.07 C1(max) [fF] 56 C2(max) [fF] 8.3 Cs(max) [fF] 64.3 Sw [nm/Pa] 25.3 Swc [fF /nm] 0.49 Sc [fF/Pa] 12.4 The parasitic conductance of the second generation Design 3 was expected to be negligible, but experimentally it was found to still have a quantifiable degradation to the sensor's quality factor. Possible sources of this conductance are leakage paths throu gh debris left during

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140 the dicing process or links of conductive sodium from the bonding step. Later experiments show that the parasitic conductance dropped to half the value of Design 1 and 21% of the value of Design 2. Table 64. Geometries of parasitic capacitive structures in the secondgeneration capacitive sensors Variable Design 3 L p1 [m] 250 L p2 [m] 100 W p1 [m] 150 W p2 [m] 350 g [m] 50 Table 65. Parasitic results for the second generation capacitive sensor derived using numerical and experimental models. Variable Design 3 Cp1 [fF] 285 Cp2 [fF] 525 G [mS] 0.28 Obtained experimentally. Obtained though numerical simulations. 6.2.3 Completed Model Results With all of the parameters from the coils and capacitive sensor defined the complete device performance can be predicted. The resonant frequency and quality factor for the secondgeneration sensor is presented along with the full scale frequ ency shift and sensitivities in Table 66. Compared to the first generation design, the higher sensor capacitance results in a lower resonant frequency The comparison of the predicted and tested frequency response curves are shown in Figure 67. The frequency responses of Design 1 and 2 from the fir st generation sensors are plotted on the same axes for comparison. A comparison of the modeling results shows an overall improvement in the wireless sensor performance. First, the Q is doubled to 8.6 by the reduction in conductance. This results in a

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141 larger resonant dip, as shown in Figure 67. Again, the ratio of the sensors floating element areas are used as a factor to compare the three designs. The total normalized sensitivity dropped for this generation as a result of the decision to use thicker (15 m instead of 10 m), less compliant tethers. The effective compliance, given by Equation 41 for the second generation tethers is 102 which is 3.3 x higher than 30.2 N/m for the first generation. However, the overall dynamic range is predicted to increase due to the increase in maximum shear and the decreas e in minimum detectable shear from the improvement in Q Table 66. Full wireless system resonance and sensitivity results for the second generation wireless sensor. Variable Design 3 fo [MHz] 168 Q 8.6 f(max) [MHz] 1.56 Scf [kHz/fF] 25.1 Sf [kHz/Pa] 311 Sn [ppm/Pa] 2004 SF [ 1/ N ] 890 Figure 67. Secondgeneration frequency response showing the accuracy of the model and a comparison to the first generation. 50 100 150 200 250 300 350 400 450 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Frequency (MHz) Reflection Coefficient | | Gen 2 Data Model Gen 1 Design 1 Gen 1 Design 2

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142 6.3 Fabrication And Packaging The second generation sensor uses a simple twomask fabrication process as well. The replacement of the Si bulk layer with Pyrex requires a completely new fabrication process. The process employs anodic wafer bonding t o realize a silicon floating element structure on a thick Pyrex structure for mechanical support. The fabrication process is illustrated in Figure 68 It starts with a 100 mm diameter, double side polished Corning 7740 Pyrex wafer. This specific Pyrex is chosen to match the thermal expansion coefficient of Si. This reduces (ideally eliminates) thermal stresses that could destroy the bond during thermal cycles. Another important consideration required for anodic bonding of glass to Si is the sodium content of the glass. Pyrex has a 4% sodium content, which is sufficient for a successful bond. The next four steps create a cavity in the glass while leaving the bonding areas planar and clean. A Cr hard mask, defined using M ask 1 from Figure 6 9A is used to protect the Pyrex surface during the cavity etch with HF. Without the hard mask, the HF would rapidly etch between the photoresist and the Pyrex, resulting in undercuts that extend for hundreds of microns. The Cr layer acts as an adhesion prom oter between the photoresist and the glass surface, limiting the undercut. Undercut on the order of the depth of the cavity still occurs due to the isotropic nature of the HF etchant. The next steps are for anodic bonding of the Pyrex wafer and a separate SOI wafer. After the photoresist and Cr are removed from the wafer, both the Pyrex wafer and an SOI wafer are cleaned in a 3:1 H2SO4:H2O2 piranha etch, which removes any particulates that could interfere with the bond. This etch also hydrates the surfac es by growing a thin oxide on the Si, which is another important property for the formation of a good bond. The wafers are then aligned and bonded with the device layer of the SOI facing the Pyrex. An EVG 501 Anodic bonder is used with the following proces s parameters: temperature = 400 oC, force = 200 N, and voltage = 1 kV.

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143 The bond is performed in a nitrogen environment at ~ 0.5 atm. The peak current for the bond is limited to 50 mA. Figure 68. Fabricatio n process flow for secondgeneration device. After bonding, the majority of the SOI wafer is removed by KOH etching, leaving just the thin device layer. First, a thin wax is applied to the edge of the wafer stack to protect the device layer from being etch ed away from the outside in. Then, the wafer stack is inserted into a 20% KOH bath heated to 80 C for 8 hours to etch the bulk Si layer. After the silicon is removed, a buffered oxide etch (BOE) is performed to remove the buried oxide leaving only the device layer suspended across the Pyrex cavities. 1) Start with a Pyrex wafer 2) Deposit Cr hard mask layer Si Si++ Oxide Pyrex Cr 3) Etch Cr hard mask (Mask 1) 4) 1:1 HF:H2O Deep Pyrex cavity etch 5) Etch Cr and clean surface for bonding 6) Anodic bond SOI wafer to Pyrex wafer 7) KOH etch bulk Si 8) BOE etch to remove buried oxide 9) DRIE etch to define sensor structure (Mask 2)

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144 Figure 69. Mask set used for photolithography in steps 3 and 9. A) Cavity defining mask. B) Sensor structure mask. The final step in the process uses M ask 2 from Figure 69 B to define the sensor structures. Photoresist is first patterned, and DRIE is used to etch the silicon, defining the floating element, comb fingers, and bond pads. An O2 clean is performed in the DRIE chamber to remove the photoresist, and a clean finished wafer is removed from the machine ready to be diced. The wafers are diced by first applying a thermal release tape (Nitto Denko Revalpha No.3195M) to cover and protect the sensitive mechanic al structures during the dicing procedure. Pyrex has an increased hardness and a reduced thermal conductivity in comparison to Si. As a result, thicker resin bonded blades have to be used instead of the standard Ni bonded blades, and much slower cutting sp eeds are required to prevent the thermal tape from being released. After dicing and sorting, electrical testing is performed and then the hybrid packaging, described in Figure 516, is used to complete the second generation wireless sensor. 6.4 Experimental Results The experimental tes t results for the second generation wireless sensor are presented in this section using the test setups described in Chapter 4 First impedance characteristics are obtained Mask 1 Mask 2 A B

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145 on the capacitive sensor die prior to packaging After packaging, t he stability, noise floor and sensitivity are obtained in a series of tests giving the minimum detectable signal ( MDS ) and dynamic range ( DNR ) of the new sensor In addition to the standard flow calibration tests, two new tests are added. A hysteresis test and a rotation test both provide further confidence in the sensors operation. Because of time and resource limitations, no wind tunnel tests are performed with the secondgeneration device. The results for the secondgeneration Design 3 are compared with Design 1 and Design 2 from the first generation 6.4.1 Impedance Characterization Impedance measurements on the second generation die confirm the elimination of the bulk substrate capacitance. Results of the tests are presented in Figure 6 10. The measurements show that the capacitance is steady and flat at around 2.25 pF, near the theoretically predicted value. This measurement includes the parasitics from the pads and the fringing fie lds. The shift from large capacitance values at low frequency (due to the bulk capacitance) to low capacitance values at high frequency (due to the sensor's capacitance) is clearly absent. This confirms that the Si bulk layer was the source of this phenome non in the first generation devices. The plot shows a stable sensor capacitance with very little parasitics. The bias error for the capacitance shows that the measurement is not useful below 1 kHz, even though the random error is several orders of magnitud e lower than the measured values. The conductance still increases with frequency, which in turn reduces the Q factor of the wireless sensor. The exact cause for this conductance rise was not explored in detail. Moreover, the error for the conductance measurements is practically the same as the measured values, which hampers any quantitative analysis.

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146 Figure 610. Capacitance and conductance impedance sweeps for second generation sensor. A) Mean shunt capacitance. B) Measurement errors for capacitance. C) Mean shunt conductance. D) Measurement errors for conductance. 6.4.2 Wireless Resonance Stability After packaging the second generation capacitive sensor with the coil and antenna, a st ability test is performed. Figure 611 shows a stable response with resonance around 168 MHz for the entire three hour long test. The measured drift f or this test is around 60 Hz/min, which corresponds to a 9x improvement over the first generation Design 1 and a 4x improvement over Design 2. Using the predicted sensitivity, this corresponds to a drift of 190 Pa/min. The amplitude noise is dominated by the network analyzer and remains the same for the second generation sensor. Using the theoretical values from Table 66, the noise floor is 102 104 106 108 0 0.5 1 1.5 2 2.5 3 3.5 Frequency (Hz) Shunt Capacitance (pF) 102 104 106 108 10-6 10-4 10-2 100 102 Frequency (Hz) Measurment Error (pF) Random Error Bias Error 102 104 106 108 10-14 10-12 10-10 10-8 10-6 10-4 10-2 Frequency (Hz) Shunt Conductance (S) 102 104 106 108 10-12 10-10 10-8 10-6 10-4 Frequency (Hz) Measurment Error (S) Random Error Bias Error A B C D

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147 calculated to be 1.95 kHz, resulting in an MDS of 6.3 mPa. This gives a theoretical dynamic range of 58 dB. These results are tabulated in Table 67. Figure 611. Measured secondgeneration device drift. Table 67. Results predicted by the model for the secondgeneration devi ce. Variable Design 3 na 0.0002 nf [kHz] 1.95 MDS [mPa] 6.3 DNR [dB] 58 Drift [kHz/min] 0.06 6.4.3 Wireless Humidity Tests A humidity test is also conducted on the second generation sensors. A surprising result of the new fabrication process is a dramatically reduced humidity sensitivity, as seen in Figure 612. From this test, the humidity sensitivity is less than 1 kHz/%RH, which corresponds to 40 aF/% RH (essentially negligible). This test was repeated to confirm the results. Additionally, it was noted that during the flow cell calibrations, there was no longterm transient (dry out time), as observed in the first generation sensor calibrations. 0 20 40 60 80 100 120 140 160 180 167.7 167.75 167.8 167.85 167.9 167.95 168 168.05 168.1 Time (Minutes) Resonance (MHz)

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148 Figure 612. Secondgeneration sensor response to humidity. A convenient resul t of the secondgeneration process flow is that the DRIE is the last step before dicing. This means that the sidewalls of the sensors are left with a Teflonlike polymer passivation layer [9 5] This layer has good hydrophobic properties, and from the results of the humidity test, this appears to help mitigate the humidity sensitivity which is now below the nois e floor of the wireless sensor. 6.4.4 Static Shear Flow Calibrations A static shear st ress calibration is performed in the flow cell, as described in Section 4.2.4. The maximum shear stress that the second generation sensor is designed for is 5 Pa. The results of the calibration test are shown in Figure 613. Te n sweeps were taken at each flow condition and 20 shear averages were taken for each sweep. The 95% confidence error bars are shown for both the resonance and the shear. The shear stress sensitivity is around 474 kHz/Pa, determined by a linear fit (R2 = 0. 997) to the date shown in red. This is even higher than the predicted 311 kHz/Pa. The normalized sensitivity is 2729 ppm/Pa. Using the experimental sensitivity, the MDS and DNR are 4.1 mPa and 61.7 dB, respectively. Compared to the larger first generation Design 0 20 40 60 80 100 120 167 167.25 167.5 167.75 168 Time (Minutes) Resonance (MHz) Humidity Wireless Sensor 0 20 40 60 80 100 120 5 15 25 35 45 Relative Humidity (%RH)

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149 2 sensor, this secondgeneration Design 3 sensor achieved a higher dynamic range by 9.5 dB, while increasing the spatial resolution by 43 %. The secondgeneration Design 3 sensor also beat the smaller firstgeneration Design 1 sensor by 24.4 dB in d ynamic range, but with a decrease in spatial resolution by 44%. A summary of the device performance is given in Table 68. Figure 613. Linear static calibration for the second generation sensor. Table 68. Final experimental sensitivity, minimum detectable signal, and dynamic range for the second generation sensor. Variable Design 3 Predicted Realized Sf [kHz/Pa] 311 474 Sn [ppm/Pa] 2004 2729 SF [1/N] 890 1213 MDS [mPa] 6.3 4.1 DNR [dB] 58 61.7 Another set of tests are conducted to add to the confidence in the sensors performance and to explore repeatability and hysteresis effects. Using the flow cell, the shear stress (flow) is ramped up and then backed down, and this is repeated a second time. If there are any delays, 0 0.5 1 1.5 2 2.5 3 3.5 4 171.5 172 172.5 173 173.5 174 Shear (Pa)Resonance (MHz) Static Calibration Linear Fit 474 kHz/Pa R 2 = 0.997

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150 drift, or other hysteretic phenomenon in the sensor response, they would show up in this test. The test results are shown in Figure 614. With the exception of one anomaly in the second flow increase, the sensor shows no hysteresis, and the resonance tracks the shear stress repeatedly. Figure 614. Secondgeneration hysteresis test results showing two full cycles. The final set of flow tests demonstrates the flow direction ality sensitivity of the sensor. Ideally, the sensor should only be sensitive to shear when a component of shear is perpendicular to the tethers. As illustrate d in Figure 6 15, at 0o flow causes an increase in the sensor capacitance, which results in a decrease in the resonant frequency. At 90o flow causes n o change in the sensor capacitance, which results in no change in the resonant frequency. At 180o flow causes a decrease in the sensor capacitance, which results in an increase in the resonant frequency. To confirm this behavior, the sensor plug in the flow cell was rotated in three positions 0o, 90o, and 180oto test these cases. The result of the test is plotted in Figure 616, which shows good agreement with the predicted response. 0 0.5 1 1.5 2 2.5 172.4 172.6 172.8 173 173.2 173.4 173.6 173.8 Shear Stress (Pa) Resonance (MHz) Increasing Flow 1 Decreasing Flow 1 Increasing Flow 2 Decreasing Flow 2

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151 Figure 615. Rotation test illustration. A) Sensor at 0 rotation. B) Sensor at 90 rotation. C) Sensor at 180 rotation. Figure 616. Rotation test results showing directional response of the sensor. Flow Flow Flow 0 0.5 1 1.5 2 2.5 3 3.5 4 0.99 0.992 0.994 0.996 0.998 1 1.002 1.004 1.006 1.008 1.01 Shear Stress (Pa) Normalized Resonance 0 Rotation 90 Rotation 180 Rotation A B C

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152 CHAPTER 7 7 CONCLUSIONS AND FUT URE WORK The final chapter in this dissertation provides a summary of the work and key conclusions. The fundamental research contributions are then listed. The dissertation concludes by describ ing opportunities for future work 7.1 Summary This dissertation pr esented the first passive wireless shear stress sen sor ever developed. The passive wireless interrogation strategy was adapted from work dating back to the 1960s. These earlier sensors were primarily developed to detect static pressures for medical purposes where the normal forces are very large. In contrast, shear stress sensors must be capable of detecting minute tangential forces that are orders of magnitude smaller than pressure force. To achieve this level of detection, the sensor requires a much larger sensitivity. Normalized sensitivities of 0.1 to 20 ppm/Pa were demonstrated in the previous works. The normalized sensitivities for the shear stress sensors presented in this dissertation were much greater, between 865 to 4781 ppm/Pa. A detailed model was presented for the passive wireless sensor. This model included analytical calculations for the floating element mechanics and electrical capacitive transduction of the shear stress sensor. Numerical methods were used to predict the inductances and fringing field parasitic capacitances. The rest of the conductive losses were determined experimentally and can be used as empirical correction factors for future designs. A linear sensor response was predicted using these models, and this linear behavior was confirmed in later testing. Two generations of the sensor were designed, fabricated, packaged, and tested. A hybrid package was used for both generations in which the inductive coil and antenna were milled in a printed circuit board ( PCB ) and the capacitive shear stress sensor was added to complete the

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153 devices. The first generation sensor used a modified version of a previously developed wired shear stress sensor [21] For the secondgeneration devices, a completely new fabrication process was developed to improve upon the first generation designs, with the goal of reducing unwanted parasitic effects and sensitivity to humidity. Both generations were subjected to a series of tests at both the die level and as finishe d wireless sensors. Two first generation designs, with different floating element sizes, and one second generation design were characterized. The small floating element (Design 1), high spatial resolution, first generation sensor showed a MDS of 27.4 mPa, a dynamic range of 37.3 dB and a maximum coupling distance of 9 mm. The large floating element (Design 2), low spatial resolution, first generation sensor had a much better MDS of 4.89 mPa, a dynamic range of 52.2 dB, and was successfully tested in a flat plate turbulent boundary layer at NASA Langley. The second generation sensor had an improved MDS of 4.1 mPa, while the maximum input shear stress increased from 2 Pa to 5 Pa and the spatial resolution improved compared to Design 2 of the first generation sensor. The resulting dynamic range was 61.7 dB. This second generation sensor is able to test the equivalent of a turbulent flat plate boundary layer with speeds from 1 m/s to 60 m/s, which corresponds to a range from 2 mph to over 130 mph. The second gen eration sensor was also shown to have a directional response, enabling a vector flow measurement (direction and magnitude) to be determined with two perpendicular sensors positioned next to each other. Furthermore, in the second generation, the parasitics were dramatically decreased by over an order of magnitude and the humidity sensitivity was reduced to below the noise floor. These improvements make the sensor viable for realistic test environments. All of the performance parameters for the three sensors tested are summarized in Table 71, along with two of the best performing passive wireless pressure sensors from the

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154 literature for comparison. The normalized force sensitivity defined as the normalized sensitivity divided by the active area in [1\ N] shows a three order of magnitude increase over previous work. Table 71. Performance summary and comparison with previous work from the literature. Shear Stress Range [ Pa ] Dynamic Range [ dB ] Normalized Sensitivity [ ppm/Pa ] Force Sensitivity [ 1 /N ] First Gen eration Design 1 0.013 1.60 37.3 865 865.0 First Gen eration Design 2 0.004 2.25 52.2 4781 1195 Second Gen eration Design 3 0.004 3.90 61.7 2729 1213 Collins [31] 67.0 13,000* 45.7 6.25 0.079 Fonseca et al. [58] 3,800 400,000* 40 0.043 0.091 Chen et al. [60] 333 13,300* 32 1.20 1.085 Equivalent force in pressure 7.2 Research Contributions D evelop ed and demonstrated the first passive wireless shear stress sensor capable of measurement without direct electrical wire connection s Developed and validated comprehensive electromagnetic models for passive wireless sensing, which can be extended to other passive wireless sensor system s. Demonstrated silicon onpyrex microfabrication process that can be adapted to enable other high performance silicon MEMS based passive wireless transducers. Identified and reduced parasitic capacitance and humidity sensitivity which can be extended to other wired or wireless MEMS capacitive sensors 7.3 Future Work Suggested future work proposed for the sensor system focuses on two key enhancements. The first is to design and develop a new fabrication process where the inductor coil is monolithically integrated on the MEMS sensor die. The second is development of RF electronics to dynamically track the sensor resonant frequency. The new circuitry will enable the sensor to

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155 detect the dynamic variations in shear stress to fully characterize a turbulent boundary layer. Potential designs for the future generation can be optimized using the models developed in this dissertation for the mechanics, electrostatics, and magnetic coupling. The RF electronics design can also be incorporated into the optimization. 7.3.1 Future Generations The next generation for the sensor is planned wi th integration of the coil into a single chip device as the primary goal. An optimization routine can be used to decide on the geometry, and the previous fabrication work can be integrated into the process flow. Pyrex wafers with through glass vias (TGVs) may be used to enable the coil to be placed on the backside of the sensors, as shown in Figure 71. The TGVs enable connection of the coil to the capa citive sensor structure on the topside. The sensor die can still be 3.5 mm x 3.5 mm and have a spiral inductor electroplated on the backside. The integrated coil diameter would be smaller than the hybrid coils by a factor of approximately three, but the number of turns would be increased by a fa ctor of approximately three. The inductance is proportional to D, but it is also proportional to N2 so the integrated inductor can actually achieve a greater inductance L than the hybrid designs in the first two generations. Adding a second layer to the coil would bring the connection point back to the perimeter of the die and would double the number of turns. A novel fabrication process to create the second layer is presented in [96] Figure 71. B ack side of the third generation concept sensor s A) Single layer coil. B) Dual layer coil. A B

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156 The fabrication of this sensor can follow the same process flow developed for the second gen eration sensor with the addition of a few steps. At the beginning of the process, coils and vias can be first created in the Pyrex wafer. At the end of the process, copper plugs can be deposited to connect the device layer to the vias. The fabrication steps in between have all been proven with the successful creation of the second generation sensor. The additional steps needed have also been developed separately. Through Pyrex, vias have been drilled using picosecond laser ablation, and the 500 m deep vias have been cut down to 50 m in diameter. The results for a 200 m via are shown in the SEMs in Figure 72A This can then be filled by copper electroplating to connect the topside capacitive structures to the backside coils. These coils have also been developed by electroplating copper in photore sist molds. A copper seed layer is sputtered onto the surface of the Pyrex, and photolithography is used to define the coil geometry. After plating, the photoresist and seed layer are removed, and a coil, shown in F igure 72 B is left behind to complete the integrated wireless shear stress sensors. Figure 72. Fabrication technologies require d to realize third generation integrated wireless shear stress sensors. A) Laser drilled Pyrex through holes. B) Electroplated planar copper coils. A B

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157 Once fabricated, this design will require virtually no packaging to test the sensors. A mounting strategy, s imilar to the one used before, can be used in which the chips are mounted in a recess on a PCB that has the interrogating antenna patterned on the opposite side. This board will then be compression fit into the Lucite plug used for experimental tests. With no metal traces or wire bonds protruding into the flow, the packaged sensors should be hydraulically smooth. The devices can be mounted in single and array formats and tested in the same way as the previous sensors. The sensor array layout can be designed into the mask, depending on the application. Cutting the standard wafer layout into blocks of devices would produce an array on a single large die, as illustrated in Figure 7 3. The chip itself would be the package and needing only to be mounted on a supporting structure in proximity to the antenna. This would also enable micron level position accuracy of the sensors in the array. Circular packages are more common than squares in testing environments and could be realized by using the laser, used for the vias to cut out the array. Figure 73. Wireless arrays realized by dicing devices in blocks. 7.3.2 Additional Testing The wireless sensors presented were used to detect static shifts in shear stress. The frequency sweep time of the network analyzer limited the frequency response to less than 1 Hz. Wafer Array

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158 The sensors themselves have a bandwidth of several kHz, set by the mass spring damper resonance of the mechanics. To achieve dynamic sensing, a new electronics system is needed. There are many possible RF circuit topologies that can be used to convert the frequency shift of the sensor into an electronic signal [97102] One of the best candidates is shown in Figure 74. This circuit works b y placing the antenna into the feedback loop of an oscillator. When the antenna is placed in proximity to the sensor, the resonance of the sensor will affect the frequency characteristics of the feedback, and the oscillator frequency will shift with change s in shear stress. The output is a frequency modulated signal, in which the shear stress input on the sensor modulates the carrier frequency of the oscillator. An FM demodulator can then be used to convert this signal to baseband, and the voltage on the output can be read by a data acquisition card. Figure 74. Basic concept for RF circuitry that would enable dynamic shear stress testing. With appropriate RF electronics, dynamic characterization would be pos sible. For dynamic calibration, the setup and theory are much more complex than the static flow cell calibration. As shown in Figure 75, a speaker cr eates acoustic waves that propagate down a square duct. These waves are terminated at the end with an anechoic wedge to reduce reflections and prevent standing waves from forming. The compression waves set up oscillating pressure gradients that form a Stok es boundary layer along the walls. The one dimensional solution for Stokes layer excitation in a square duct [103] is FM Demodulator Antenna Oscillator Output

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159 2 2() tanh 2jthj tPe c ( 71) P' is the magnitude of the acoustic excitation from the speaker and is measured by the reference microphone. The constants are the acoustic excitation frequency the kinematic viscosity of air the speed of sound in air c and the height of the chamber h. T he dynamic sensitivity is found by varying the amplitude of the excitation while keeping the frequency constant. This ramps up the input shear stress in a similar manner to the flow cell experiment. The response of the sensor is measured at each amplitude and plotted versus the input shear stress. Like the mean measurement, this should be a linear relationship, the slope of which is the sensitivity. Figure 75. Diagram of the plane wave tube used for dynamic shear stress characterization 7.3.3 System Optimization Using the full model developed and confirmed in this dissertation, it will now be possible to employ formal design optimization techniques to realize the best possible performance. The material properties are assumed constant while the geometries are left as variables. The mechanical and capacitive structures can be included in the optimization as well as the coils and RF electronics. The minimum detectable signal should be chosen for the objective function used in the optimization loop. To achieve the best MDS (Equation 369), the Q of the system and B&K Pulse Analyzer RF Circuitry Mic-PreAmp Tone () Generator Sensor Reference Microphone h AmplifierSpeaker P Anechoic Termination Planewave Tube Plane Waves

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160 sensitivity must be maximized while limited to size and fabrication constraints. A basic flow for the optimization program should look like Figure 76. Figure 76. General system optimization loop. These optimized designs can be integrated into all future generations of the sensor. In the future if this device is commercialized there will be a need to vary the specifications based on customer applications. The work presented in this dissertation will make that process possible. Calculate Model Parameters Evaluate MDS Check For Optimality Vary Input Geometry Check Constraints Initial Design Final Design

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161 A PPENDIX A A LINEARITY DERIVATION S The sensitivity equations given in the modeling Chapter 3 are all small perturbation linear approximations. The maximum input shear stress is determined by the point at which these linearization's deviate from the true sensitivity by 3%. There are three sensitivities defined as Stw for the mechanical deflection, Swc for the capacitive transduction and Scf for the resonant frequency shifts. These sensitivities are cascaded to find the total input shear stress to resonant frequency shift. The 3% nonlinearity point is defined for the total sensitivity. The linear and nonlinear sensitivities are derived in this appendix and compared using a generic geometry from the second generation sensors with a maximum input shear stress of 5 Pa A.1 Mechanical Nonlinearity The linear and nonlinear beam equations for the sensor struct ure are given in V. Chandrasekharan's dissertation [21] The linear equation is 32 () 1 4ett teALA w EhWA ( A 1) and is used in the sensitivity derivation in Chapter 3. The nonlinear "Duffing Spring" equation adds an axial force Fa to the analysis [21] The displacement w is 2cosh1 sinh 2 1cosh 2sinht t t t tt atL L P QL Q w L LL FLP P ( A 2) Th e axial force is given by 2 02tL t a tEhWw F dx Lx ( A 3)

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162 where sinh 22 1coshcosh 1 2sinht t atx wP QL Qx Lx xFLP P ( A 4) The input shear is incorporated into P an Q by e PA ( A 5) and tQW ( A 6) The Eigen function is given by 312a tF EhW ( A 7) This shows that the displacement w is a function of the force Fa and the force Fa is a function the displacement w. This loop means that it cannot be solved for analytically, i nstead the displacement is determined by an iterative approach A guess of the axial force is used to solve for the displacement. This displacement is then used to find the force and the loop continues until the axial force derived changes by less than 108 from iteration to iteration. The mechanical nonlinearity sol ution is plotted in Figure A 1. By comparing with the linear plot given by Equation A 1 the 3% nonlinearity point can be determined. This would be the maximum input shear stress for the sensor based purely on mechanical deflection. There are two more stages to get the output frequency change used for the se nsor so they must be analyzed and cascaded to determine the final 3% point. The maximum input shear stress shown is less than the 5 Pa that it was designed for This will be explained at the end of this appendix. A.2 Capacitive Nonlinearity The next stage in the sensitivity derivation that has to be linearized is the deflection to change in capacitance. The capacitance at any given deflection w is by

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163 122 23 2fot foet o s ooNxL NxLL h C gwgw ( A 8) This equation is nonlinear with respect to w but a linear approximation can be made by finding the slope given by 22 122 232fot foet so ooNxL NxLL dCh dw gwgw ( A 9) At zero shear there will be no deflection so at the origin w = 0 and 22 122 23 () 2fot foet o s ooNxL NxLL hw Cw gg ( A 10) Both the linear and nonlinear equations are plotted in Figure A 2. For small deflections the linear approximation holds to within 3%. This gives the range of displacements for the full scale input shear stress. A.3 Resonant Nonlinearity The same linearization technique is used for the change in the resonant frequency which is the final output of the sensor. The resonant frequency is given by 1 2cspcf LCCC ( A 11) The sensor has a static capacitance at zero shear of Cos and the slope is found at this point by 1 4soss CC ospccospcdf dC CCCLCCC ( A 12) The linear change in frequency is given by 2os ospcfC f CCC ( A 13)

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164 where 1 2o cospcf LCCC ( A 14) Both the linear and nonlinear equations are plotted in Figure A 3. For small changes in capacitance the linear approximation holds to within 3%. This gives the range of capacitance change for the full scale input shear stress. Figure A 1. Capacitive shear stress sensor mechanical nonlinearity plot. Figure A 2. Capacitive shear stress sensor capacitive nonlinearity plot. 0 1 2 3 4 5 6 7 8 9 10 0 50 100 150 200 250 Displacment (nm) Input Shear Stress (Pa) Nonlinear Linear 0 50 100 150 200 250 0 10 20 30 40 50 60 70 80 Change in Capacitance (fF) Displacment (nm) Nonlinear Linear 3% 3%

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165 A.4 Cascaded Results The maximum input shear stress for the wireless shear stress sensor is found by cascading all three of these sensiti vities together. The product of the linear approximations and t he total nonlinear results are plotted in Figure A 4. This shows that the maximum input shear stress for the total wireless case (~5 Pa for this example) is actually higher than just the capacitive shear stress sensor (~4 Pa for this example). This is because the linear approximations of stage 1 and 3 over predict while stage 2 under predicts This balances out and extends the total range. Figure A 3. Capacitive shear stress sensor resonant nonlinearity plot. Figure A 4. Capacitive shear stress sensor cascaded nonlinearity plot. 0 10 20 30 40 50 60 70 80 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 Change in Frequency (MHz) Change in Capacitance (fF) Nonlinear Linear 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 Change in Frequency (MHz) Input Shear Stress (Pa) Nonlinear Linear 3% 3%

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166 A PPENDIX B B IMPEDANCE DERIVATIONS The derivations for the full impedance models from Section 3.3 are presented. First the single senor equation is developed base on the T model for the coupled coils and including all of the parasitic values. The simplified a rray model is presented for an arbitrary number of wireless sensors. This model assumes zero inter sensor coupling and only resistive parasitics. Based on this analysis a complete model is derived for the array that considers all coupling terms and parasit ics. B.1 Single Sensor The single sensor model presented in Chapter 3 is shown in Figure B 1. The derivation of the input impedance ZL is done in sections starting from the right. The impedance of all of the capacitance terms in parallel with the conductance G is given by 1 1 cpsZGjCCC ( B 1 ) Th is is combined in series with the inductance and resistance such that 1 2 cc cpsZRjLGjCCCjM ( B 2 ) The parallel connection of the mutual coupling term gives 1 3 1 cc cps cc cpsRjLGjCCCjMjM Z RjLGjCCCjM jM ( B 3 ) Adding the antenna terms in series simplifies the expression to 4 aaZRjLjM 1 cc cpsRjLGjCCC 1 cc cpsjMjM RjLGjCCC ( B 4 )

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167 The parasitic antenna capacitance is left with a simplified parallel notation to give the final solution 22 11L aa a cc cpsM Z RjL jC RjLGjCCC ( B 5 ) Figure B 1. Full single wireless sensor model for impedance derivations. B.2 Array of Sensors With No Inter Sensor Coupling For the array derivations it is assumed that the coupling between the wireless sensors is zero In this case the impedance can be derived using the results found for the single sensor. The circuit model for this case is shown in Figure B 2. The impedance for each of the sensors is given by the generic equation 1iii iZRjL C ( B 6 ) where i is the index of the sensor in the array. The sensor parasitic capacitance and condu ctances have been lumped into Ri and Ci for this derivation. The capacitive term is given by 2 22 2 i cipisi i cipisiGCCC C CCC ( B 7 ) The resistive term is given by 2 22 i ici i cipisiG RR GCCC ( B 8 ) For an array of Ns sensors the impedance is given by M (La-M) (Lc-M) Cp Cs CaRaRc G Cc ZL

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168 22 1sN ai Laa i iM ZRjL Z ( B 9 ) Figure B 2. Wireless sensor array model for impedance derivations with no inter sensor coupling. B.3 Array of Sensor With Inter Sensor Coupling In reality there will be some finite coupling between the sensors. All of these coupling terms are given by the FastHenry simulations in Chapter 3 a nd so a model was developed to use these values for a complete model that considers all parasitics and coupling terms. The circuit in Figure B 3 shows the added coupling terms. For this solution an Ns by Ns matrix inversion must be calculated 1 12 111 12 1 1 2 212 2 2 2 121 1 1a a a ai ai ai ia i i i i ijLjM jM jM jMRjL jM jM C jMjMRjL jM B C jMjM jMRjL C ( B 10 ) where B is an arbitrary matrix designator. Again R and C contain both the capacitive and conductive parasitics given by Equations B 7 and B 8.This matrix gives the admittance for all of La Ma1Ma2ZL Mai Ra R1L1C1 R2L2C2 RiLiCi

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169 the terminals involved in the inductive coupling on the diagonal axis. It is based on the current and voltage matrices from an arbitrary number of ports as shown in Figure B 4 11 22 33 44 iiIV IV IV B IV IV ( B 11 ) The impedance at the input to the antenna is simply given by the inverse of the first component of B which gives 111LaZR B ( B 12 ) Figure B 3. Wireless sensor array for impedance derivations with full coupling model. Figure B 4. Multiport impedance model. La Ma1Ma2ZL MaiM12M2iM1i RiLiCi R2L2C2 R1L1C1RaLa I2I3I4IiI1 V1V2V3V4ViB

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170 A PPENDIX C C COUPLED RESONAT OR FREQUENC Y DEPENDANCE The resonant frequencies of ideal coupled resonators is analyzed in Section 3.3.2 to show the effect they have on each other's resonant frequencies. This appendix gives the derivations of Equations 363 and 366. First the case of two resonators with the same components and thus the same resonant frequency is derived. Next resonators with different resonant frequencies are presented. Simple Laplace filter analysis is used to derive the resonant frequencies in these two cases. C.1 Same Resonant Frequencies The resonant frequencies will be determined by the denominator of the characteristic equation for the circuit shown in Figure C 1. The characteristic equation is 1 1 1 11 111 ZsLMsMsLM sC sC ( C 1) Simplifying from the inside out gives 1 1 1 1 1 21 1 sC Z sMsLM sC sLCMC ( C 2) 1 1 1 1 2 3211 sLC Z sLM sC sLMCMCsM ( C 3) 1 1 32 1 21 1 sLMCMCsM Z sLM sC sLC ( C 4) 1 1 322 1 21 1 sLCMCsL Z sC sLC ( C 5)

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171 1 2 3221 sLC Z sC sLCMCsL ( C 6) 1 422222 32221 sLCMCsLC Z sLCMCsL ( C 7) 322 42222221 sLCMCsL Z sLCMCsLC ( C 8) Using the definition for the coupling factor 2MM k LLL ( C 9) gives 322 422221 121 sCLksL ZsCLksLC ( C 10) Converting this to the standard format gives 3 22 42 222211 1 21 11 ss C CLk Z ss CLkCLk ( C 11) Factoring the denominator gives 3 22 2211 1 11 11 ss C CLk Z ss kLCkLC ( C 12) which gives two resonant frequencies 11 21of LCk ( C 13) and 21 21of LCk ( C 14)

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172 Figure C 1. Simple coupled resonator circuit. C.2 Different Resonant Frequencies The resonant frequencies will be determined by the denominator of the characteristic equation for the circuit shown in Fi gure C 2. Following the same procedure as the simple case. The characteristic equation is 1 1 1 11 1 21 2111 ZsLM sMsLM sC sC ( C 15) Simplifying from the inside out gives 1 1 1 1 1 2 1 2 1 2221 1 sC Z sMsLM sC sLCMC ( C 16) 1 1 1 1 2 22 1 32 1 22211 sLC Z sLM sC sLMCMCsM ( C 17) 1 1 1 32 222 1 2 1 221 1 sLMCMCsM Z sLM sC sLC ( C 18) 1 1 1 32 12221 2 1 221 1 sLLCMCsL Z sC sLC ( C 19) 1 2 22 1 32 122211 sLC Z sC sLLCMCsL ( C 20) 1 422 121212112232 122211 sLLCCMCCsLCLC ZsLLCMCsL ( C 21) M (L-M ) C (L-M) C

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173 32 12221 422 12121211221 sLLCMCsL Z sLLCCMCCsLCLC ( C 22) Using the definition for the coupling factor 2 12M k LL ( C 23) gives 32 122 1 4 22 1212 11221 11 sLLCksL Z sLLCCksLCLC ( C 24) Converting this to the standard format gives 3 2 1 212 42 1122 22 1212 121211 1 1 11 ss C LCCk Z LCLC ss LLCCkLLCCk ( C 25) Factoring the denominator gives 3 2 1 212 2222 1211 1ooss C LCCk Z ss ( C 26) where 2222 2 112211221212 2 1 2 121224 21oLCLCLCLCLLCCk LLCCk ( C 27) and 2222 2 112211221212 2 2 2 121224 21oLCLCLCLCLLCCk LLCCk ( C 28) This gives two resonant frequencies 1 1 2 1212 2222 2 1122112212121 2 21 2 24o of LLCCk LCLCLCLCLLCCk ( C 29)

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174 and 2 2 2 1212 2222 2 1122112212121 2 21 2 24o of LLCCk LCLCLCLCLLCCk ( C 30) Figure C 2. Coupled resonator circuit. M C1(L2-M) (L1-M) C2

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175 A PPENDIX D D QUALITY FACTOR DERIVATIONS The quality factor Q for the wirel ess shear stress sensor is given in Section 3.3. The definition and derivations of Q are presented in this appendix. First the quality factor is de fined in general using simple RL and GC circuits. Next the quality factor at resonance is defined and derived for simple RLC and GLC circuits. This work all leads to the eventual derivation of the quality factor for the sensor. D.1 Inductors and Capacitors The quality factor, Q is defined as the peak energy stored in a circuit divided by the energy dissipated in one cycle. This is commonly expressed in terms of radians as 2peak dissipatedW Q W ( D 1) The quality factor will be derived from energy equations for two circuit examples shown in Figure D 1. Figure D 1. Simple RL and GC circuits. First the quality factor for the RL circuit is derived. The energy stored in an inductor is 21 2peakpeakWLI ( D 2) The energy lost in one period T in a resistor is dissipateddissipatedWPT ( D 3) where 2 dissipatedrmsPIR ( D 4) For a sine wave the rms current is related to the peak current by R G C L

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176 2peak rmsI I ( D 5) Combining Equations D 2 through D 5 into the definition of Q gives 2 21 2 2 2peak peakLI Q I RT ( D 6) Replacing the period by a radian frequency 2 T ( D 7) the quality factor simplifies down to L Q R ( D 8) For the GC circuit the same procedure is followed with 21 2peakpeakWCV ( D 9) 2 dissipatedrmsPVG ( D 10) and 2peak rmsV V ( D 11) Combining these equations gives 2 21 2 2 2peak peakCV Q V GT ( D 12) Once again replacing the period and simplifying gives C Q G ( D 13)

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177 Both of the equations are a function of frequency. The quality factor for all real inductors and capacitors is either defined as the max value or the value at the frequency of interest. D.2 Simple RLC Resonant Circuits For resonant circuits the same definition of quality factor applies. There are two simple resonator circuits that will be discussed The RL C and G L C resonant circuits are shown in Figure D 2. Since the energy in a resonant circuit alternates back and forth between a current through the inductor and a voltage on the capacitance the peak energy can be defined by either component. U sing the inductor for the RL C circuit and the capacitor for the G L C circuit the quality factors are given by Equations D 8 and D 13 respectively Figure D 2. Simple RL C and G L C resonant circuits. For a resonant circuit it is common to define a quality factor at resonance. The resonant frequency in radians for both of these equations is given by 1nLC ( D 14) The quality factor at resonance for the RL C circuit is given by 1n nLL Q RRC ( D 15) and for the G L C circuit by 1n nCC Q GGL ( D 16) L G C R L C

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178 D.3 Wireless Shear Stress Sensor Quality Factor The circuit model for the wireless shear stress sensor, including all of its parasitics is shown in Figure D 3. The value of the quality factor at resonance is needed for the model in Chapter 3. The circuit is analyzed as an RLC circuit where the stored energy is calculated on the inductor Lc and R and C are functions of the rest of the parameters shown in the figure. Figure D 3. Wireless shear stress sensor circuit including parasitics. For this analysis the resistive term is given by the transf ormation 2 22 c cpsG RR GCCC ( D 17) The capacitive term is given by the transformation 2 22 2 2 cps cpsGCCC C CCC ( D 18) The inductive term is cLL ( D 19) These transformations result in the RLC circuit shown in Figure D 2 and using Equation D 15 gives 2 22 2 22 2 21c n ncps c ncps ncpsL Q G GCCC R GCCC CCC ( D 20) The resonant frequency for this circuit is G Cc+Cp+CsLc Rc

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179 1n ccpsLCCC ( D 21) Simplifying Equation D 20 gives 2 211n cps c cps c cQ G CCC R G CCC L G L ( D 22)

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180 A PPENDIX E E COMB FINGER ELECTROS TATIC PULL IN DERIVATIONS The electrostatic force equati ons used to derive the pull in voltage for Section 4.1.2. are derived in this appendix. The derivation is based on the simple pull in equations for a pair of parallel plates with one plate fixed and t he other plate connected to a spring. A voltage is applied to the plates that causes an electrostatic attraction of the two plates. In equilibrium this force is balanced by the force of the spring in the opposite direction. When the voltage is raised to a certain point this equilibrium condition breaks down and the plates will collapse together or "pull in". First the simple case is derived and then the changes are introduced to apply this analysis to the comb fingers of the capacitive shear stress sensors. E.1 Parallel Plates The derivation starts with a pair of parallel plates as illustrated in Figure E 1. A force balance is used to find the limit to the e quilibrium condition. The upward mechanical spring force is given by the simple equation mFkx ( E 1) where k is the spring constant and x is the displacement of the plate from the rest position go. The electrostatic force is derived from a differential change in the electrostatic potential energy in the gap with a change in x by pe eW F x ( E 2) The potential energy for a capacitor is 21 2peWCV ( E 3) where oA C gx ( E 4)

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181 is the capacitance between parallel plates The area of the plates is A and is the permittivity of free space. Combining E quation E 2 through E 4 and taking the derivative gives 2 22e oAV F gx ( E 5) Figure E 1. Basic parallel plate diagram for electrostatic pullin derivation. The pull in voltage is to found by setting the total force on the movable plate to zero where 2 20 2net oAV Fkx gx ( E 6) This gives the voltage on the plates in terms of the geometry 2 232okxgx V A ( E 7) The pull in voltage Vpi is given by Equation E 7 when x = xpi the pull in displacement The displacement where the equilibrium condition breaks down is determined by the point where the slope of the net force becomes zero 2 30net odFAV k dx gx ( E 8) Solving Equation E 8 for k and substituting into E 6 gives k V gox

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182 22 322ooxAVAV gxgx ( E 9) and the pull in displacement is 3o pig x ( E 10) Substituting this result into Equation E 7 gives the final re sult for the pull in voltage for a pair of parallel plates. 38 27o pikg V A ( E 11) E.2 Comb Fingers The pull in voltage for the capacitive shear stress sensor follows the same steps as outlined in the previous section. The difference in the geometry is shown in Figure E 2. I n addition to the downward electrostatic force there is also an upward electrostatic force due to an adjacent finger. The two electrostatic forces are never equal because there are different gap widths in the design of the sensor. The force balance and equilibrium condition therefore become 2 2 22 121 0 22net ooNAV NAV Fkx gxgx ( E 12) and 2 2 33 121 0net ooNAV dFNAV k dx gxgx ( E 13) The spring constant is determined by the tethers attached to the floating element of the sensor. The gaps are given by go1 and go2 and the total number of fingers on the floating element is given by N Solving Equation E 12 for V gives

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183 33 121ff ook V NN A gxgx ( E 14) Solving Equation E 13 for k and substituting into Equation E 12 gives 12 33 12(3)() 1opi opi opi opigxgx N N gxgx ( E 15) This is a nonlinear equation for xpi and must be solved numerically. Once xpi is found it can be inserted in Equation E 14 to find the pull in voltage 33 121pi ff opiopik V NN A gxgx ( E 16) Figure E 2. Comb finger diagram for electrostatic pullin derivation. V x k go2go1

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192 BIOGRAPHICAL SKETCH Jeremy Sells was born in Key West, Florida, and raised on the island of St. John in the US Virgin Islands. He returned to the mainland to finish high school in New Hampshire and went on to receive his B.S. degree in electrical engineering from the Universi ty of Maine at Orono in 2005. His interests in sensors and RF devices brought him to the University of Florida, where he joined the Interdisciplinary Microsystems Group working on capacitive shear stress sensors and wireless sensor array integration. He received his M.S. degree in 2009 and is currently working toward a Ph.D. degree in electrical engineering. He is also a NASA fellow and research assistant at the University of Florida