Table Of ContentTESTING AND CHARACTERIZATION OF SECOND-ORDER
DIFFERENTIAL MICROPHONES
BY
JOSHUA HOWARD MERLIS
BS, State University of New York at Binghamton, 2009
THESIS
Submitted in partial fulfillment of the requirements for
the degree of Master of Science in Mechanical Engineering
in the Graduate School of
Binghamton University
State University of New York
2011
UMI Number: 1499813
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© Copyright by Joshua Howard Merlis 2011
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Accepted in partial fulfillment of the requirements for
the degree of Master of Science in Mechanical Engineering
in the Graduate School of
Binghamton University
State University of New York
2011
August 11, 2011
Dr. Ronald N. Miles, Distinguished Professor and Associate Dean for Research
Department of Mechanical Engineering, Binghamton University
Dr. Bruce T. Murray, Professor
Department of Mechanical Engineering, Binghamton University
Dr. Mark L. Fowler, Professor and Director of Graduate Studies
Department of Electrical and Computer Engineering, Binghamton University
iii
ABSTRACT
Directional microphones are designed specifically to respond to a differential pressure
along one spatial axis. Dr. Ronald Miles and his research group have developed
directional microphones using MEMS processing technology that are based on the
biomimicry of the ear of Ormia ochracea, a small parasitoid fly. The specific focus of
this research is the testing and characterizing of these miniature directional microphones.
A linear model has been developed to describe the response of the Ormia-inspired
microphones. This response is comprised of a linear combination of the sound pressure
and the sound pressure gradients. A least squares approach has been employed in order
to determine the transfer functions between the response of the microphone and the
zeroth, first, and in some cases second-order pressure gradients of the sound field.
Knowledge of these complex transfer functions is crucial in understanding the nature and
quality of the response of these microphones.
These least squares transfer functions were then used to simulate the plane wave response
of the prototype microphones. This unique process eliminates the need for an anechoic
chamber to generate this standard acoustic response. This process was also implemented
on an industry standard differential microphone, and was compared with the true plane
wave response of the same device. This experiment verified the reliability of the
simulated plane wave processing.
iv
In loving memory of
Sidney Watnick
v
ACKNOWLEDGEMENTS
I would like to extend my deepest gratitude to Dr. Ronald Miles for his generous support
and guidance throughout my graduate education. He has been a positive role model and
mentor to me for the past four years. It has been an honor to work under a man of such
great intelligence and character, and a priceless opportunity to take part in working on a
humanitarian project such as this. My respect and admiration for Dr. Miles seem to know
no bound.
I am also endlessly indebted to Dr. Quang Su for all of his help throughout my master’s
research. Much of this thesis is an extension of the work that he laid the foundation for.
He was always willing to take time to help me when I needed it. Dr. Su spent much of
his time training me and sharing with me his great knowledge of the subject matter. I
thank him for all of his patience and his natural inclination to go above and beyond when
explaining material.
I also would like to thank Dr. Mark Fowler for serving on my committee and providing
me with background knowledge for the estimation theory portion of the project. The
classes that I was fortunate enough to take under him were thought-provoking,
challenging, and fun.
My thanks go out to Dr. Bruce Murray for serving on my committee and providing me
with his spline interpolation code, which was used to approximate the gradients of the
sound field. Thank you Dr. Murray for volunteering to help with last-minute
administrative business.
vi
Thanks also go out to Dr. James Pitarresi for his guidance throughout all of my years at
Binghamton University. His lectures were educational, inspiring, and entertaining.
I am grateful to William Butler and Dr. Anju Sharma for training me on the usage of the
Veeco Wyko Optical Profiler and Zeiss Supra 55 VP Field Emission Scanning Electron
Microscope, respectively.
Thank you to Dr. Weili Cui for fabricating the microphones, making the job of testing
and characterizing them possible.
Thank you to Dan Antonelli, Dr. Shehab Albahri, Vlad Bogachuk, Assad Tabatabaie,
Brenno Varanda, Abe Hyunchoong Lee, and everyone else in working in the
Microacoustic Sensors Laboratory at Binghamton University for all of their help, insight,
ideas, assistance, and friendship. It has been great working with all of you in D2.
I thank Lisa Gallagher for all of her help with payroll issues, coordinating meetings, and
any and all miscellaneous questions I have had over the years.
I am extremely thankful for my wonderful family. Special thanks go out to my parents,
who have been so supportive, generous, kind, understanding and loving to me for my
whole life, beyond any reasonable expectations.
Funding provided by the National Institute on Deafness and Other Communication
Disorders (NIH, NIDCD), Development of a Miniature Second-order Directional
Microphone Diaphragm for Hearing Aids, (grant 1R01DC009859) and Low-noise
Directional Hearing Aid Microphone using Optical Sensing with Electronic Feedback,
(grant 1R01DC009429).
Lastly, I would like to thank gravity, without which none of this would have been
possible.
vii
TABLE OF CONTENTS
LIST OF TABLES..............................................................................................................x
LIST OF FIGURES...........................................................................................................xi
NOMENCLATURE........................................................................................................xiii
CHAPTER 1.......................................................................................................................1
1.1 Directional Microphones......................................................................................1
1.2 First and Second-Order Directional Microphones................................................1
1.3 Ormia Design........................................................................................................7
1.4 Uses and Applications.........................................................................................10
1.5 Overview and Organization................................................................................10
CHAPTER 2.....................................................................................................................12
2.1 Overview.............................................................................................................12
2.2 Lumped Parameter Model...................................................................................13
2.3 Directivity Index.................................................................................................15
2.4 Characterization..................................................................................................17
CHAPTER 3.....................................................................................................................19
3.1 Why Sound Fields Need to be Measured............................................................19
3.2 Current Techniques.............................................................................................19
3.3 Alternate Approaches for Measuring Sound Fields............................................20
CHAPTER 4.....................................................................................................................28
4.1 Accuracy of Pressure Measurements..................................................................28
4.2 Accuracy of Positioning System.........................................................................29
4.3 Spacing Issues.....................................................................................................31
4.4 Finite Diameter of Probe Tip..............................................................................33
4.5 Issues at Low Frequencies: Small Gradients......................................................33
CHAPTER 5.....................................................................................................................35
viii
5.1 Measuring Ormia Differential Microphones......................................................35
5.2 Estimating the Least Squares Transfer Functions for Differential Microphones37
5.2.1 Introducing the Estimation Problem...................................................................37
5.2.2 The Linear Model...............................................................................................38
5.2.3 Theoretical Data Collection................................................................................40
5.2.4 Cramer-Rao Lower Bound..................................................................................43
5.2.5 Least Squares Estimation....................................................................................45
5.2.6 Simulation of Experiment...................................................................................48
5.2.7 Measurement Versus Estimation........................................................................52
5.3 Simulated Plane Wave Response........................................................................55
CHAPTER 6.....................................................................................................................67
APPENDIX A...................................................................................................................69
APPENDIX B...................................................................................................................93
REFERENCES.................................................................................................................94
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