David Ho Electrical and Computer Engineering (ECE)

David Ho
Electrical and Computer Engineering (ECE)
This thesis is approved, and it is acceptable in quality
and form for publication on microfilm:
Approved by the Thesis Committee:
, Chairperson
Dean, Graduate School
BPSK System Analysis Using MEMS Filters
David Ho
BS., Electronics Engineering Technology, DeVry University, 2002
Submitted in Partial Fulfillment of the
Requirements for the Degree of
Master of Science
Electrical Engineering
The University of New Mexico
Albuquerque, New Mexico
May, 2008
©2008, David Ho
In memory of Mary, Jeremiah, and our unborn children. To my family, especially my
wife, Sarah, for all of her love and support. To Summer, Faith and Abigail, God has big
plans for your life; work hard to glorify His name!
I would like to thank God, for the blessings of knowledge, perseverance, and
patience. He deserves credit for all I do, because what I see as an impossible task, is
made possible through Him. I would also like to say thanks to my wife, Sarah, for her
constant love and support. Also, to my daughters, Summer, Faith, and Abigail for giving
me their continuous patience over the years. A special thanks goes to my Life Group.
Your prayers have not been wasted and I thank you for your continuous support.
I would also like to thank my co-workers and management at Sandia National
Laboratories for supporting this effort. The management was supportive in my decision
to further my education and to all my co-workers, especially Nick Bikhazi, Troy Olsson,
and David Heine. You patiently and clearly explained answers to all my questions.
Finally, I would like to thank my parents for loving me and supporting me
throughout this process. You’ve given me the foundation I needed to complete this task.
BPSK System Analysis Using MEMS Filters
David Ho
Submitted in Partial Fulfillment of the
Requirements for the Degree of
Master of Science
Electrical Engineering
The University of New Mexico
Albuquerque, New Mexico
May, 2008
BPSK System Analysis Using MEMS Filters
David Ho
BS., Electronics Engineering Technology, DeVry University, 2002
MS., Electrical Engineering, University of New Mexico, 2008
For some military applications, there exists a need for small custom radios. These
radios need to be able to survive extreme environments and transmit the necessary data.
This can be achieved by using banks of micromechanical filters. These small filters are
post-CMOS compatible, allowing hundreds of high-Q filters to be incorporated over a
typical RF transceiver die. Selection of these filters allows the band, channel, and
Microelectromechanical Systems (MEMS) filters eliminates the need for off-chip
components such as crystal references and Surface Acoustic Wave (SAW) filters. This
allows for smaller, low power, high performance, shock hardened radios to be developed.
This thesis will examine the simulation and system analysis of MEMS filters. In
past literature, there have been advances in transceiver architecture that have reduced the
number of parts, but many of these approaches have sacrificed RF performance. The
zero-IF and LOW-IF direct conversion sacrifices RF performance, but is good enough for
normal applications.
For specific military applications, this RF sacrifice is not
acceptable. This thesis will simulate a BPSK architecture to develop an understanding
that the post-CMOS filters can reliably be trusted upon in communication systems. The
initial system to be simulated will be a 5-channel MEMS filter. This thesis will also
present actual results of the 5-channel MEMS filter.
List of Figures
List of Tables
RF MEMS Areas...................................................................................... 2
1.1.1 RF MEMS Switches, Varactors, and Inductors ............................... 3
1.1.2 Transmission Lines and Antennas ................................................... 4
1.1.3 FBAR (Thin Film Bulk Acoustic Resonators) and Filters............... 6
1.1.4 RF Microelectromechanical Resonators and Filters ........................ 7
Organization of Thesis............................................................................. 9
IC Fabrication ........................................................................................ 11
2.2 Front End Processing ............................................................................. 12
Back End Processing.............................................................................. 13
MEMS Fabrication................................................................................. 14
2.4.1 Sacrificial Surface Micromachining .............................................. 15
2.4.2 Bulk Micromachining .................................................................... 16
2.4.3 LIGA (Lithographie, Galvanoformung, Abformung).................... 17
Sandia National Laboratories MEMS Fabrication................................. 18
Dual Mode Aluminum Nitride Filter ..................................................... 20
Summary ................................................................................................ 22
MEMS Devices
The MEMS Filter................................................................................... 24
Performance Analysis ............................................................................ 30
Equivalent Circuit .................................................................................. 33
Simulation Results ................................................................................. 37
Summary ................................................................................................ 45
BPSK Analysis
Simulations ............................................................................................ 48
Transmitter............................................................................................. 53
Receiver ................................................................................................. 57
Actual Results ........................................................................................ 64
Summary ................................................................................................ 75
Conclusions and Future Work
5.1 Future Work ........................................................................................... 77
List of Figures
Figure 1.1 RF MEMS Switch [5]........................................................................................4
Figure 1.2 Synthesized low dielectric-constant antenna at 94 GHz [7]..............................5
Figure 1.3 Agilent FBAR’s on a Grain of Rice (Courtesy of Agilent)...............................7
Figure 1.4 Dual Mode Aluminum Nitride Band Pass Filter. ..............................................8
Figure 2.1 Aluminum Nitride Microresonator Process Flow. ..........................................20
Figure 2.2 Dual Mode Aluminum Nitride Band Pass Filter. ............................................21
Figure 2.3 Simulation showing the two mode shapes of the AlN dual mode filter..........22
Figure 3.1 Picture of AlN dual mode MEMS filter. R is 140 μm and W is 41 μm
(Courtesy of Sandia National Laboratories). .............................................................27
Figure 3.2 Simulation showing the two mode shapes of the AlN dual mode filter..........28
Figure 3.3 Photo of dual mode AlN nitride filter..............................................................31
Figure 3.4 Measured and simulated response of dual mode filter. ...................................32
Figure 3.5 Equivalent Circuit Model of Dual Mode Filter. ..............................................33
Figure 3.6 Equivalent Circuit Model of Dual Mode Filter. ..............................................37
Figure 3.7 Simple Circuit to Demonstrate MNA [18]. .....................................................39
Figure 3.8 Matrix results of MNA Analysis on Circuit Shown in Figure 3.7 [18]...........40
Figure 3.9 Netlist Result of 107.75 MHz MEMS Filter. ..................................................43
Figure 3.10 Simulated Results of 5-Channel MEMS Filter Bank. ...................................44
Figure 3.11 Measured Results of 5-Channel MEMS Filter Bank.....................................45
Figure 4.1 Test Board Simulated MEMS 5-Channel Filter. .............................................49
Figure 4.2 FVTOOL Manipulation of 5-Channel Filter. ..................................................52
Figure 4.3 Digital Spectrum of MEMS Filter...................................................................53
Figure 4.4 BPSK Signal Constellation..............................................................................54
Figure 4.5 The Simulated Transmitted Signal. .................................................................57
Figure 4.6 Constellation Diagram of BPSK System.........................................................59
Figure 4.7 Eye Diagram of the Receiver. .........................................................................61
Figure 4.8 BPSK Simulation With PLL Applied..............................................................62
Figure 4.9 Ideal BPSK Simulation With PLL and Raised Cosine Filtering.....................63
Figure 4.10 5-Channel MEMS Filter Layout....................................................................64
Figure 4.11 5-Channel MEMS Filter on an IC. ................................................................65
Figure 4.12 Filter Bank IC With Respect toSurface Mount Resistors..............................66
Figure 4.13 Test Board Schematic: High Level (left) Details of RX Chain (right)..........67
Figure 4.14 Test Board with MEMS Filters Integrated on Board. ...................................67
Figure 4.15 BPSK Constellation Diagram of Test Board.................................................70
Figure 4.16 Several “Frames” With Respect to Time.......................................................73
Figure 4.17 Test Board BPSK Constellation with PLL Implemented..............................74
List of Tables
Table 2.1 Summary of Process Equipment Specific to MEMS [13]. ...............................18
Table 3.1 Dual mode measured filter specifications.........................................................32
Table 3.2 Circuit Component Values................................................................................34
Table 3.3 New Inductor and Capacitor Values.................................................................36
Chapter 1
In today’s society, we want things as small and as fast as possible when it comes to
electronics. The cell phone, GPS units, and many other commercially available devices
are continuously trying to take advantage of the advances in engineering to incorporate a
product that has been miniaturized and utilizes low power. Let’s take the cell phone as a
prime example. A cell phone is more than just a few chips and a battery pack. Buried
inside the cell phone is a communications system made up of many passive components.
These filters, resonators, and duplexers help sort out all the radio frequencies to insure
that you receive your calls and not someone else’s. What would it be like to have no
dropped calls and a smaller phone? The marketplace for cell phones, GPS units, and
other consumer friendly devices has shifted the focus of research in the microwave and
millimeter wave area towards consumer applications. The long-established defenserelated applications still have a high need for these products too. Consequently, industry
has been investigating and taking advantage of the Microelectromechanical Systems
(MEMS) that have been developed.
Chapter 1. Introduction
Microelectromechanical Systems (MEMS) devices have been around in the
electronic industry since the 1970s.
These devices were used for pressure and
temperature sensors, accelerometers, and other sensor devices [1]. Although, the actual
acronym MEMS wasn’t coined until the 1980s [2], MEMS encompasses all miniaturized
devices. It wasn’t until the 1980s and into the mid 1990s that MEMS devices could be
used for Radio Frequency (RF) Microwave Applications. The mid 1990s to present day
has seen the MEMS technology move from technology research to fabrication process
development to commercialization of MEMS products.
This area has gained such
publicity and success in recent years that by 2003 there are over 130 companies pursuing
different MEMS applications [3]. The MEMS based industry is a billion dollar industry
in the United States and is expected to grow even more in the future.
1.1 RF MEMS Areas
The term RF MEMS “refers to the design and fabrication of MEMS for RF integrated
circuits [4].” Traditional MEMS is divided into two classes, actuators and sensors [4],
but the research of RF MEMS technology is broken down into four distinct areas. Those
four areas of RF MEMS research are:
RF MEMS switches, varactors, and inductors
Micromachined transmission lines, high-Q resonators, filters and antennas
FBAR (thin film bulk acoustic resonators) and filters
Chapter 1. Introduction
RF micromechanical resonators and filters
1.1.1 RF MEMS Switches, Varactors, and Inductors
This area is considered a “mature technology” because it has been thoroughly
demonstrated from Direct Current (DC) -120 GHz [1]. Common MEMS switch types are
a thin metal cantilever, air bridge, diaphragm, or some other structure electrically
configured in series or parallel with an RF transmission line and designed to open the line
or shunt it to ground upon actuation of the MEMS. Such switches have displayed
excellent RF characteristics, including low insertion loss values, high linearity, better
isolation, and the potential for integration. Figure 1.1 shows an example of a RF MEMS
switch that NASA has been investigating for their systems. In all spacecrafts with
communications systems, there is a possibility to implement some type of RF switching
network. These communication systems usually suffer from high insertion loss and low
isolation in solid-state switches [5]. MEMS switch development can help cure these
problems compared to the regular pin-diodes and metal semiconductor field-effect
transistors. NASA’s extensive research has shown that the RF MEMS technology offers
the necessary performance advantages over the existing solid-state switches that they
currently use. Other devices such as varactors and inductors can also benefit from
MEMS manufacturing to produce smaller products with the same results as conventional
semiconductor devices.
Chapter 1. Introduction
Figure 1.1 RF MEMS Switch [5].
1.1.2 Transmission Lines and Antennas
This area is usually good for frequencies of 12-200 GHz [1]. These types of MEMS
devices are static and do not move [6]. The majority of MEMS devices that fall under
this category are fabricated using silicon technologies such as Complimentary Metal
Oxide Semiconductor (CMOS). They are able to use a process called wet etching to form
transmission lines, inductors, capacitors, and couplers [4]. The way the MEMS are
fabricated will be the discussion of Chapter 2. The MEMS antenna is important to
Chapter 1. Introduction
making the size of electronics smaller because many electronic devices are governed by
antenna size. Figure 1.2 shows how a micromachined antenna is put together. The
increased reliance of modern electronics on higher frequencies forces antenna size to
become smaller and smaller, so fabrication of antennas is slowly transitioning to the use
of micromachining procedures.
Figure 1.2 Synthesized low dielectric-constant antenna at 94 GHz [7].
Chapter 1. Introduction
1.1.3 FBAR (Thin Film Bulk Acoustic Resonators) and Filters
The FBAR technology is the most successful RF MEMS technology so far.
It is
fabricated using MEMS technology and they are able to produce many FBAR filters in a
very small size. FBAR filters exploit acoustic vibrations in thin films and this has
produced some very good results. They exhibit good performance up to 3 GHz and have
a very high Q (>2000). This has resulted in the development of miniature low-loss filters
for wireless applications [8]. The problem with FBAR filters is their center frequency is
dependent upon the thickness of the thin film. Thus, multiple frequencies can not be
fabricated on the same die and it is very costly to get two filters exactly alike from
different dies. Figure 1.3 shows a California Short Grain of rice with four FBAR filters.
FBAR filters are designed for cell phone applications, primarily by Avago (formerly
Agilent). Integrating FBARS of different operating frequencies is very difficult because
the frequency of operation is dependent upon Aluminum Nitride (AlN) or Zinc Oxide
(ZnO) thickness. Using lithography it would be simplest (highest probability for success)
to attempt to obtain one layer thickness upon a wafer. To produce any substantial number
of FBAR filters would cost a lot of money. It is desirable, using RF MEMS filters, to put
multiple oscillators/filters upon a single chip to mitigate size and power.
Chapter 1. Introduction
Figure 1.3 Agilent FBAR’s on a Grain of Rice (Courtesy of Agilent).
1.1.4 RF Microelectromechanical Resonators and Filters
These use the mechanical vibrations of the device to achieve high-Q resonance. The Q is
a measure of quality, how well a resonator or filter retains its energy. SiTime’s products,
technical papers from Discera Corp., and other literature have proven that MEMS
resonators are capable of Q factors greater than 500,000 [9]. In the cell phone example,
the designers want the filter’s frequency selectivity to be as high as possible. The higher
a filter's Q, the greater its selectivity in isolating frequencies. Integrated circuit filters
have a Q of about 20, compared with SAW devices, in which the Q rises to 2,000. And
MEMS-based filters are at least five times better than SAW filters. The MEMS filters are
in a research phase of development and have yet to be introduced into system
implementation [10].
Chapter 1. Introduction
Figure 1.4 shows a photo of dual mode Aluminum Nitride (AlN) band pass filter
at 108.4 MHz which was developed at Sandia National Laboratories. This filter was
made out of AlN and fabricated using a post-CMOS compatible process.
Figure 1.4 Dual Mode Aluminum Nitride Band Pass Filter.
This technology is what is being developed by Sandia National Laboratories and
the fabricated MEMS filter will be the baseline of this thesis. The MEMS filter will be
explained in more detail on its fabrication process and its operating requirements. It will
be implemented into a BPSK architecture and the results will be presented.
Chapter 1. Introduction
1.2 Organization of Thesis
Many communications applications, each with their own performance requirements,
could benefit from their own custom type radio. The primary application of interest in
this thesis is the development of Radio Frequency Microelectromechanical (RF MEMS)
Filters. The development of the RF MEMS filter is in process at Sandia National
Laboratories. This is the first type of device of its kind in industry and this thesis will
examine the performance of these devices through simulations and actual measured
The remainder of the thesis is organized as follows:
Chapter 2 contains a
background of MEMS devices that are being created in industry and at Sandia National
Laboratories. It will discuss some of the processes in which RF MEMS devices are being
In Chapter 3, the RF MEMS devices that were created is introduced and
simulated in a MATLAB model. Chapter 3 includes a performance analysis based on
MATLAB simulation results of a 5-channel MEMS filter.
Chapter 4 extends the
performance analysis of the MEMS filter into a BPSK system. Chapter 4 extends that
performance analysis by presenting an analysis based on results gathered from simulating
the system in MATLAB and performing an actual test using a real device.
concludes this thesis and provides suggestions for future work.
Chapter 5
Chapter 2
MEMS technology is a result of a long history of technological development that started
way back when semiconductors were discovered. MEMS products were initially limited
to sensors. Throughout the years, it has developed into a technology that impacts our
daily life. An example of how it is used in our daily life is the automobile [11]. Many of
the tiny sensors that are on the automobile use some type of MEMS technology. MEMS
integrates the accelerometers and electronics onto a single silicon chip that is used to
control the air bag deployment systems. Another example is the advancement of High
Definition Television (HDTV). The digital light processors (DLPs) in projectors and
television sets are also in the broad range of categories which MEMS is affecting. These
two simple examples are just a small portion of how MEMS impacts our society. MEMS
devices are also in the medical market, robotics, and space applications. MEMS have
grown into an industry which affects our economy.
This chapter will explore the process used to develop an Integrated Circuit (IC).
This same process is then altered slightly to develop a MEMS device. Sandia National
Laboratories has also altered their process to develop a post-CMOS compatible MEMS
Chapter 2. Background
device. This process will be introduced in this Chapter and this device will be the device
that will be used for simulations and for actual measurements when integrated into a
BPSK receiver.
2.1 IC Fabrication
Integrated circuits are “the physical realization of a number of electrical elements
inseparably associated on or within a continuous body of semiconductor material to
perform the functions of a circuit” (Electronic Industries Alliance (EIA) definition [12]).
Most everyday electrical devices are made up of several IC’s. These IC’s are developed
with semiconductor materials.
Semiconductors are a group of materials that have
electrical conductivities intermediate between those of metals and insulators. Silicon is
used for the majority of semiconductor devices. These devices are constructed out of the
semiconductor fabrication processes that have made technological companies such as
Intel, ON Semiconductor, and Samsung prosper over the past decades. These companies
have expanded the economy and with the high demand to continue researching this area,
it is expected to grow even more. So a lot of time and money has been invested into this
process. This process takes a wafer and develops semiconductor integrated circuits in
many processing steps. These steps can usually be grouped into a front end and back end
processing technique. The front end processing is generally where the IC is created and
Chapter 2. Background
processed on the wafer, while the back end processing is the test, assembly, and
packaging of the IC.
Front End Processing
The following process describes most of the key processes in developing IC’s, but it is
much more extensive than will be mentioned here. Front end processing is the wafer
development and processing. A wafer of silicon is fabricated, sliced and polished from
an ingot of silicon. The thickness at which the silicon is sliced and polished is dependent
upon the application. The performance characteristics of all semiconductor devices are
sensitive to the cleanliness in processing. In order to create the best IC possible, there are
many substrate cleaning procedures that are done at initiation of the process and
throughout various steps in the process. Any type of contaminant defects will destroy the
operation of an IC, so it is crucial that the silicon is ultra-pure. In order to create the best
possible quality of silicon, a pure layer of silicon is grown on the raw wafer through an
epitaxial growth process. This layer is known as the epi-layer. All IC processes involve a
number of thin films. These films are formed through various techniques, but they are
integral to the structure of the particular IC. The next step is to design a mask. This
mask is like a photographic negative, which is called lithography. It defines the pattern
that forms the physical elements of the integrated circuit. The wafer is coated with a
resist material, and then baked to make it harder. The pattern is then exposed over the
Chapter 2. Background
wafer. The resist is then developed to create the pattern on the wafer. Now that the
wafer is fully coated in an oxide, we need to pattern that oxide with a process called
etching. There are two categories of etching, wet and dry. This process removes the
oxide where there is no pattern. This also removes the mask that was used to develop the
As mentioned previously, the silicon process needs to be very clean, so the
etching step needs to be done with great care in order to completely remove the resist
material. The electronic and optical properties of semiconductor materials are strongly
affected by impurities, which may be added in precisely controlled amounts.
process of controlled addition of impurities is called doping. By selectively patterning
the stack of thin film materials with the appropriate set of masks, we can create the IC
that we would like. The final step in front end processing is to add some passivation
oxide layers to protect the surface of the wafers during back end processing.
2.3 Back End Processing
Back end processing is the testing, assembly, and packaging of the individual IC’s. Once
the front end processing is complete, the wafers go through extensive testing to verify the
functionality of the IC’s. There are many special tools to verify functionality of the IC’s.
These testing processes and tools will not be discussed in this thesis. Once the wafer has
been thoroughly tested, feedback is given to the fabrication process. This gives them a
Chapter 2. Background
yield of good chips/bad chips. This will help them to improve the process for future
wafers. The wafer is then carefully dissected into individual chips and each IC is tested
for final functionality. The final IC is packaged and then it is sold to the customers for
integration into whatever design they need it for. As stated previously, the process is
much more detailed than what was mentioned here, but a general idea has been presented.
2.4 MEMS Fabrication
MEMS devices are fabricated using microfabrication technology similar to that used for
integrated circuits. In most cases MEMS exist on a common silicon substrate; however,
MEMS can be combined as discrete microcomponents in a single package.
MEMS electronics are fabricated using IC process materials and process sequences,
many times the micromechanical components, sensors, and actuators are fabricated using
compatible “micromachining” processes that deposit new layers or selectively etch away
parts of the silicon wafer to form the mechanical and electromechanical devices [12].
Even though MEMS fabrication uses many of the materials and processes of IC
fabrication, there are important distinctions between the two technologies. The number,
sequence, type of deposition, removal, and patterning steps used to fabricate devices are
different. There are also differences in the method of wafers, freeing of parts designed to
move, packaging, and testing. It’s not so much the process that is being used, but how
the process is being used. There are three dominant MEMS fabrication technologies [3]:
Chapter 2. Background
Sacrificial surface micromachining
Bulk micromachining
LIGA (Lithographic, Galvanoformung, Abformung)
2.4.1 Sacrificial Surface Micromachining
Sacrificial surface micromachining uses the same concept as IC fabrication.
technique uses deposition, patterning, and etching of materials upon a typical silicon
substrate. Essentially, it is a deposition of layers on the silicon wafer’s surface. The
materials consist of alternating layers of a structural material and a sacrificial material.
As each layer is deposited, it is patterned, leaving material only where it is desired.
When the sacrificial material is removed, the complete mechanical device is left. The
sacrificial material is removed at the end of the fabrication process using a selective etch
process that will not damage the structural material. In this method, all the MEMS
structures are built on top of the silicon wafer. MEMS devices that have complicated
components, such as a cantilever beam, are built using this technique. A cantilever beam
is built by depositing and structuring a sacrificial layer, which is then selectively removed
at the locations where the future beams must be attached to the substrate. The structural
layer is then deposited on top of the polymer and structured to define the beams. The last
step is to remove the sacrificial layer by using a selective etch process.
micromachining promotes large arrays of devices because no assembly is required.
Chapter 2. Background
2.4.2 Bulk Micromachining
Bulk micromachining is primarily a silicon based technology that utilizes wet or dry etch
processes. It uses techniques such as etch stops and material selectivity to make useful
devices. This type of machining is different from surface machining because it defines
structures by selectively etching inside a substrate (typically silicon).
Bulk micromachining begins with a silicon wafer and it selectively etches into the
substrate. It uses photolithography to create the pattern into the substrate. Once the
pattern is created, wet or dry etching occurs. Most commonly this type of process uses
wet etching, because wet etching takes advantage of how the silicon crystal structure is
bonded together. The wafer is photo patterned, and then the wafer is dipped into a liquid
etchant to eat away at the unwanted silicon. This makes the process simple and very
inexpensive when making mass quantities. This type of processing is usually what
creates most of the pressure sensors that we have today. Ultimately, sacrificial surface
micromachining creates structures on top of a substrate, while bulk micromachining
produces structures inside a substrate.
Chapter 2. Background
2.4.3 LIGA (Lithographie, Galvanoformung, Abformung)
LIGA is a German acronym for lithography, electroplating, and molding. It is a process
that is capable of making small complex structures of electroplateable metals with very
high aspect ratios (structures that are much taller than wide) with thicknesses up to
millimeters [3].
It uses x-ray lithography, thick resist layers, and electroplated metals to form
complex structures.
The process starts with a sheet of Polymethyl Methacrylate
(PMMA). This sheet is covered with a photomask and then exposed through radiation.
The exposed PMMA is then etched away and it leaves vertical walls in the structure that
are very accurate. Metal is then plated into the structure to replace the PMMA that was
etched away. The metal is the final part of the LIGA process. From this, they can
fabricate an injection mold made of metal which then can be used to form parts typically
made with plastic. LIGA was first developed in the 1980’s and further developed in the
1990’s and early 2000’s by Sandia National Laboratories.
The LIGA process is
appropriate when you need higher aspect ratios than those obtainable from surface
micromachining. Table 2.1 summarizes the three fabrication technologies for MEMS
devices and the specialized equipment needed to process the devices.
Chapter 2. Background
Process Equipment
Sacrificial Surface
Release and drying systems to realize free-standing
Dry etching systems to produce deep, 2D free-form geometries
with vertical sidewalls in substrates Anisotropic wet etching
systems with protection for wafer front sides during etching
Bonding and aligning systems to join wafers and perform
photolithography on the stacked substrates
Batch-plating systems to create metal molds in LIGA process
Plastic injection molding systems to create components from
metal molds
Table 2.1 Summary of Process Equipment Specific to MEMS [13].
Sandia National Laboratories MEMS Fabrication
Sandia National Laboratories has been investing in the development of small CMOS
compatible MEMS resonators and filters. The common MEMS processes, as described
previously, can not achieve low impedance filters and are not post-CMOS compatible.
Therefore, a post-CMOS compatible aluminum nitride (AlN) MEMS resonator process
Chapter 2. Background
was developed [14]. This process is defined as a simple four-mask, low-temperature, and
CMOS compatible (Tmax < 350 °C) process. This process flow has been used to
fabricate MEMS devices and uses conventional surface micromachining techniques to
manufacture high quality AlN resonators with high yield [15]. The process flow is
shown in Figure 2.1.
The process replaces the platinum bottom electrode with standard CMOS metals,
aluminum (Al) and tungsten (W). (a) The process begins with an anisotropic silicon (Si)
etch and the deposition of a thin oxide to isolate the bottom electrode from the substrate.
Tungsten is then deposited and polished until it remains only where Si was etched above.
An oxide touch polish is then performed to further smooth the top of the wafer prior to
AlN deposition.
A 50 nm Al bottom electrode is deposited and patterned prior to
sputtering 750 nm of AlN at 350 ◦C. AlN is piezoelectric and is used to drive and sense
the resonators. Using this process, highly oriented c-axis AlN films with a rocking curve
full width half maximum of < 1.5◦ measured using x-ray diffraction can be reliably
formed. (b) Contacts to the W areas are etched in the AlN and a 100 nm thick Al top
electrode is deposited and patterned. (c) Finally, the resonator frequency is defined by
etching trenches in the AlN down to bulk Si and the devices are released in dry SF6. The
maximum temperature in this process is 350 ◦C and all of the materials, SiO2, Al, W, and
AlN are CMOS compatible and can be deposited and etched using standard CMOS tools.
Chapter 2. Background
It is important to note that the processing of the devices is dependent on the width/length
and not height dependent.
Figure 2.1 Aluminum Nitride Microresonator Process Flow.
2.6 Dual Mode Aluminum Nitride Filter
The process that is shown in Figure 2.1 is the process that was used to develop the dual
mode Aluminum Nitride (AlN) Filter that was shown previously in Figure 1.4. It is
shown in Figure 2.2 for convenience. This dual mode filter is a new technology in the
RF MEMS filter area.
Chapter 2. Background
Figure 2.2 Dual Mode Aluminum Nitride Band Pass Filter.
The device utilizes two closely spaced modes to achieve a band pass response in a single
device. These devices are built to specifications based on width/length as compared to
height. These devices have features just big enough for good performance, yet small
enough to achieve higher frequencies. These features will be discussed later in this
thesis. Figure 2.3 shows the two mode shapes of the dual mode filter. The MEMS filter
that is shown here is integrated into a 5-channel filter on one chip that is the baseline for
this thesis.
Chapter 2. Background
fmode1= 108.18 MHz
fmode2= 108.66 MHz
Figure 2.3 Simulation showing the two mode shapes of the AlN dual mode filter.
2.7 Summary
This chapter presented the various technologies used to develop IC’s and MEMS. As
previously discussed, MEMS fabrication uses many of the materials and processes of
semiconductor fabrication, but there are important distinctions between the two
technologies. The basic challenge of using semiconductor processes for MEMS
fabrication is not so much in the type of processes and materials used, but more in the
way those processes and materials are used. Once the basic MEMS processes were
established, Sandia National Laboratories was able to expand on that technology to
produce MEMS resonators and filters. The filters are still in a research stage, but are the
basis for this thesis. In the following chapters, we will further explore the characteristics
that these filters have and implement them into a full communication system.
Chapter 3
MEMS Devices
The primary focus of this chapter is to understand the MEMS devices, mainly the MEMS
filter, that have been created at Sandia National Laboratories.
These devices are
constantly being experimented with to meet design parameters so our discussion will be
limited to the first set of filters that were designed. This chapter will also discuss how the
filters are to be simulated in MATLAB. The results of the simulations will be compared
to actual results of the filters that were designed. This simulation is of interest because it
provides the baseline for this thesis. Without a working simulation of the filters, it is not
possible to develop a full BPSK communications system.
Additionally, the work
developed in Chapter 3 will be further analyzed in Chapter 4 of this thesis, which
contains BPSK simulation results of the filters in a full communications system. Chapter
4 will also show a comparison of the actual devices implemented on a test board.
This chapter is organized as follows. First the MEMS filters will be described
with regards to development and performance. Then the MEMS filters will be shown as
the equivalent circuit in a circuit theory discussion.
The nodal equations will be
developed and this will help aid in the process to simulate the MEMS filters in
MATLAB. The results will be shown in comparison to actual results from a 5-channel
Chapter 3. MEMS Devices
MEMS filter bank. The final result is necessary to implement the device into a BPSK
communication system.
The MEMS Filter
A MEMS development area that is receiving a lot of attention in industry is the RF
MEMS area. The goal is to be able to create a single-chip that includes resonators,
filters, switches and other IC electronics. If RF MEMS can be produced on a single chip,
the advantages for daily items such as the cell phone would be better performance at a
lower cost. It has been and still is a technical challenge to develop these items. Sandia
National Laboratories has taken a step by developing a post-CMOS compatible filter.
These filters entail a form of wave propagation at some stage between their input and
output terminals. These waves are usually vibrations amongst the different modes. Most
RF communication systems have a need for band pass filters with an extremely narrow
pass band and rapid roll off on either side of the pass band [4]. This is accomplished by
these filters.
The important characteristic of a filter is the insertion loss. This is the ratio of the
signal at the output with respect to the filter at the input. Insertion loss in filters is usually
defined in decibels (dB). This can be found by the following equation:
Insertion loss (dB) = 20 log (V1/V2)
Chapter 3. MEMS Devices
where V1 is the signal level in a test configuration without the filter installed, and V2 is
the signal level with the filter installed.
The pass band characteristics of a filter are generally expressed as a quality factor (Qfactor). The Q-factor is a measure of the energy stored in the system to the energy
dissipated. It is defined as:
where fo is the center frequency and Δf = f2 – f1. The equation shown gives the user an
idea of the filter’s effectiveness in the frequency response.
Other important characteristics that define filters are stop band rejection, roll off
rate, bandwidth, and in our case, the filter size. The stop band rejection is the signal
transmitted through the system at frequencies beyond the pass band.
This also is
expressed in dB. The roll off rate is the rate at which the transfer response of the filter
changes from pass band to stop band. Bandwidth is the frequency range at which our
filter operates.
The filter size is one of the key aspects in pursuing microresonator based filters.
If MEMS based filters are able to be produced as post-CMOS compatible, the industry
would be able to replace current technologies such as surface acoustic wave (SAW) and
Chapter 3. MEMS Devices
quartz filters with MEMS filters. The size of MEMS filters leads to smaller parts and this
in turn leads to radio miniaturization, but also enables large banks of filters to be
integrated on the same substrate. This would allow multi-channel radios or real time
spectral analysis on a single chip [16]. Another advantage of fabricating these chips
through the aforementioned technology is the ability to produce hundreds of these tiny
filters on one single chip. This would replace off-chip filters, resonators, and mixers
reducing the physical size needed by RF hardware.
As discussed in Chapter 2, Sandia National Laboratories has invested in the
development of a dual mode MEMS filter.
These filters are piezoelectric devices.
Piezoelectricity refers to the ability of certain types of materials to change shape with the
application of electrical voltage or, conversely, to produce an electric charge as a result of
these mechanical changes. Sandia National Laboratories has taken advantage of this
piezoelectric effect to develop these filters. These filters implement a 4th order bandpass
filter using a single resonator for reduced size [16]. Figure 3.1 shows the dual mode
MEMS filter with filter dimensions. The mechanical properties of these filters depend on
the shape and modes of vibration. By simply tweaking the radius (R) or width (W), we
can change the frequency and other properties of the filters. A common parameter to
adjust the frequency is the width. The first set of filters that were created were based on
selecting an arbitrary width. As shown in the picture, 41 microns is the width. This was
a nice round number that created a frequency in the 110 MHz range. We will discuss this
Chapter 3. MEMS Devices
in more detail later. Also, if you place the electrodes in different locations, you can sense
different phases of the electric wave generated. Simple techniques such as these change
the mechanical properties of the MEMS filters. This will be discussed in more detail
later in this Chapter. Figure 2.3 showed the two modes of vibration that can be achieved
with the AlN MEMS filter. This is shown in Figure 3.2 for convenience.
Figure 3.1 Picture of AlN dual mode MEMS filter. R is 140 μm and W is 41 μm
(Courtesy of Sandia National Laboratories).
Chapter 3. MEMS Devices
fmode1= 108.18 MHz
fmode2= 108.66 MHz
Figure 3.2 Simulation showing the two mode shapes of the AlN dual mode filter.
The dual mode filter operates by closely spacing the frequencies of two resonant
modes in a single device. While dual mode filters have been previously reported at lower
frequencies [17], this filter utilizes the mode shapes shown in Fig. 3.2, which is
appropriate for realizing low impedance filters at frequencies in excess of 100 MHz [16].
The loaded Q’s of the two modes for the MEMS filters have been recorded at 800
and 1000. The two modes that are shown in Fig. 3.2 represent the mode shapes where the
sense half of the ring vibrates out of phase with the drive while the other mode is the
mode shape where the drive and sense halves of the ring vibrate in phase. The bottom
electrode is grounded in this configuration which significantly reduces the feedthrough
capacitance between the drive and sense electrodes, vastly increasing the filter stop band
Chapter 3. MEMS Devices
The dual mode filter is a reciprocal device allowing the drive and sense electrodes
to be interchanged. The filter passband is located at approximately:
f ≈
where W is the width of the ring shown in Figure. 3.1 and Ε and ρ are the effective
Young’s modulus (225 GPa) and density (2956 kg/m3) of the resonator film stack.
Increasing the radius of the filter decreases the resonant frequency for both modes
but at a different rate, allowing the filter bandwidth and center frequency to be
independently set by adjusting W and R [16]. The smaller the width, the higher the
frequency, but the trade off is more insertion loss. The devices explored in this work
have filter frequencies between 105 – 115 MHz. This will be discussed later. The design
is completed by anchoring the dual mode filter using notched supports in the middle of
the ring which is a nodal point of zero displacement using beams sized to be an odd
multiple of a quarter wavelength for both compression and flexural modes. Using this
anchoring scheme minimizes acoustic losses to the substrate [16]. As you can see, a lot
of work has gone into developing this device with very good results so far. The next step
is to apply these devices and see how they react with real world systems.
Chapter 3. MEMS Devices
Performance Analysis
In this section, the results of a single dual mode MEMS filter are presented. The section
will display how a single MEMS filter can be integrated into circuitry and be measured.
The simulated response and measured response will be shown of a single MEMS filter.
Finally, some measured filter specifications will be displayed.
Figure 3.3 shows the dual mode filter in a circuit with termination. You can see
that this termination is not the normal 50 Ω termination. Matching integrated circuits to
50 Ω off-chip components requires power hungry circuitry. Because MEMS filters are so
small and they can be placed so close to the integrated circuits, the power saved is an
advantage. This is desirable because you want to operate on an impedance standard
higher than 50 Ω, because 50 Ω drivers consume large amounts of power and matched
lines are not necessary in integrated transceivers where the line length between
components is less than 1 mm [14]. As mentioned previously, MEMS devices can
replace the need of off-chip components. This single MEMS filter is conveniently set up
so that you are able to measure the input and output of the MEMS filter, easily change
out the termination resistors, and do any type of testing necessary to validate the
characteristics of the single MEMS filter. This was done for simple evaluation purposes.
Chapter 3. MEMS Devices
RS = 250 Ω
RL = 750 Ω
Figure 3.3 Photo of dual mode AlN nitride filter.
The measured response of the dual mode filter is shown in Figure 3.4. This
compares the measured filter with the modeled filter. The measured response is with a 50
Ω termination resistor. The simulated response is based on a 4th order differential
equation from two equivalent RLC networks. This will be discussed in further detail in
the next section. Table 3.1 is a summary of important characteristics that were measured
from the dual mode filter. This table was measured with the circuitry of Figure 3.3. As
mentioned previously, this termination scheme is optimal because it is operating on an
impedance higher than 50 Ω. The table includes some of the important characteristics of
filters as previously discussed. As you can see from the results, the filter is able to
achieve the desired results as expected.
Chapter 3. MEMS Devices
Figure 3.4 Measured and simulated response of dual mode filter.
Table 3.1 Dual mode measured filter specifications.
Chapter 3. MEMS Devices
3.3 Equivalent Circuit
Mechanical properties of resonators depend on their shape, type of material used and the
relevant modes of vibration. Modeling of these systems is generally done by using their
equivalent circuits, which can be translated to the electrical domain by simple
transformations for design and optimization. Figure 3.5 shows the equivalent circuit
model of the dual mode AlN MEMS filter. The circuit elements within the square
represent the components inherent to the filter. The transformer captures the 180° phase
between modes. Table 3.2 shows the values of all components for filter center frequency
of 108.4 MHz.
Figure 3.5 Equivalent Circuit Model of Dual Mode Filter.
Chapter 3. MEMS Devices
Circuit Element
151.41 μH
14.302 fF
98 Ω
143.65 μH
14.949 fF
103 Ω
8.8 fF
1.85 pF
1.78 pF
50 Ω
50 Ω
Table 3.2 Circuit Component Values.
This filter represents a radius of 140 μm and a width of 41 μm. This frequency
can be changed by changing various components to equivalently change the size and
shape of the resonator. As mentioned previously, this is done by adjusting the radius or
width of the actual filter. So to tweak the frequency, we play with the MODES of the
device. Since these are piezoelectric devices, they are comparable to waveguides. As
with waveguides, the piezoelectric mode frequencies (fundamental and other harmonics)
are determined mostly by the size and shape of the piezoelectric material (and the
material properties). Also, similar to wave guides the electrodes can be placed in different
locations to sense different phases of the electric wave generated. Although, when you
Chapter 3. MEMS Devices
try to get different phases, you’ll also receive different amounts of power. This is unlike a
waveguide, because as you move a feed down a waveguide (so long as the feed is at the
mode profile maximum) you can always receive the same amount of power. As these
parts physically vibrate, the piezoelectric effect creates an output current. These devices
are purely designed with mechanical resonances. The theory seems simple, but there are
many factors to worry about to get these devices to operate consistently and efficiently.
In order to change the frequency in the equivalent circuitry, you need to solve for the
new values of L and C. This will adjust the size of the resonator. The components that
correspond to adjusting the size of the resonator in the equivalent circuit are LM0, LM1,
CM0, and CM1. There are two assumptions that are made here before proceeding. These
two assumptions are:
The Q factor remains constant
The Insertion Loss remains constant
Therefore to change the resonant frequency, we use the following equations:
Lnew = Lold
C new =
Lnew (2 π Fnew )
Chapter 3. MEMS Devices
The frequencies of interest for this simulation are based on the actual MEMS
filter that has already been created. As mentioned previously, these frequencies were
chosen based on a convenient W value to start (i.e. 40, 41, or 42 microns would be used
because they are nice round numbers) that would produce a frequency in the 110 MHz
range. As the experimentation became more advanced, the width was adjusted to meet
the desired frequencies. The frequencies of interest for the simulation are 107.75, 109,
110.25, 111.50, and 112.75 MHz. The desired bandwidth is ~650 kHz. The new values
calculated are shown in Table 3.3.
Desired Center
152.46 μH
150.71 μH
148.99 μH
147.32 μH
145.68 μH
14.397 fF
14.231 fF
14.070 fF
13.911 fF
13.757 fF
144.33 μH
142.68 μH
141.07 μH
139.49 μH
137.95 μH
15.025 fF
14.853 fF
14.685 fF
14.521 fF
14.361 fF
Table 3.3 New Inductor and Capacitor Values.
Chapter 3. MEMS Devices
Simulation Results
The calculated components were inserted into a software program called PSPICE to
simulate the expected output of the circuit. This is to verify that the frequency of the
filter is as expected. The convenience of using a SPICE program is it develops a netlist
which can be readily converted into the MATLAB program as will be seen later.
Figure 3.6 Equivalent Circuit Model of Dual Mode Filter.
Chapter 3. MEMS Devices
The next step is to simulate the circuit in MATLAB so it can be implemented in a
system. There are several ways to try to accomplish this. The first way is to take the
equivalent 2 RLC networks that represent the dual mode filter, which is governed by a 4th
order equation, and derive this in MATLAB. The second way is to do nodal analysis on
the equivalent circuitry. Since there are 5 filters that need to be modeled, the latter way
was chosen to make the process more automated. Eight nodes have been chosen to
evaluate. The method to evaluate the circuitry will be done by a process of Modified
Nodal Analysis (MNA) [18]. The general steps that are involved in MNA are provided
1. Select a reference node (usually ground) and name the remaining n-1 nodes.
2. Assign a name to the current through each voltage source.
3. Apply Kirchoff's current law to each node.
4. Write an equation for the voltage for each voltage source.
5. Solve the system of n-1 unknowns.
By following this process by hand, you will see that you can develop several matrix
equations. From these equations, there are several patterns that become apparent. These
patterns are crucial in developing an algorithm for MNA. The first apparent pattern is:
All of the circuits resulted in an equation of the form [18].
Chapter 3. MEMS Devices
Ax = z
From this equation, we know that we can use a powerful tool such as MATLAB
to manipulate matrices that equate to Equation 3.6. Figure 3.7 is a simple example of a
Modified Nodal Analysis (MNA) circuit and Figure 3.8 shows the corresponding matrix.
The simple circuitry and simplistic nodes will give you an idea of how to apply this
analysis and develop the netlist for the program. By examining Figure 3.8, you can start
to see the pattern developing. This will be explained in further detail below.
Figure 3.7 Simple Circuit to Demonstrate MNA [18].
Chapter 3. MEMS Devices
Figure 3.8 Matrix results of MNA Analysis on Circuit Shown in Figure 3.7 [18].
The A matrix is defined by [18]:
1) (n+m) * (n+m) in size, and consists only of identified quantities
2) the nxn part of the matrix that is in the upper left:
a) has only passive elements
b) has elements connected to ground appear only on the diagonal
c) has elements that are not connected to ground as both diagonal and offdiagonal terms
3) the rest of the A matrix (not included in the nxn upper left part) contains only 1, 1, and 0
Chapter 3. MEMS Devices
The x matrix is defined by [18]:
1) an (n+m) * (1) vector that holds the unknown quantities (node voltages and the
currents through the independent voltage sources).
2) the top n elements are the n node voltages.
3) the bottom m elements represent the currents through the m independent voltage
sources in the circuit.
The z matrix is defined by [18]:
1) an (n+m) * (1) vector that holds only known quantities
2) the top n elements are either zero or the sum and difference of independent
current sources in the circuit.
3) the bottom m elements represent the m independent voltage sources in the circuit.
Finally, the circuit is solved by a simple matrix manipulation:
x = A −1 z
The solved result shows the voltages and currents of the respective nodes. There is
currently a MNA tool that is readily available to process these types of circuits. This
program is called Symbolic Circuit Analysis in MATLAB (SCAM). This program takes
a circuit analysis netlist that the user defines and symbolically solves for the voltages and
currents of the respective nodes. Once these values are known in MATLAB, we can use
Chapter 3. MEMS Devices
the values and manipulate them for other things. In our case, we want to find the transfer
function of the filter. From this transfer function, we are able to plot the result and see if
the filter is equivalent to the circuitry that we designed. The original SCAM MATLAB
code is a generic set of code that is compatible with certain components, such as
Resistors, Inductors, Capacitors, and Op-Amps. This code did not include a transformer
function that we have in our circuitry. In order to make this code work, we needed to
modify the code. The code that was added to help with the transformation of the
transformer is shown below:
case 'T'
g = ['1/s/' Element(i).Name];
%If neither side of the element is connected to ground
%then subtract it from the appropriate location in the matrix.
if (Element(i).Name(1)=='T')
G{n1,n2} = [G{n1,n2} '+' g];
G{n2,n1} = [G{n2,n1} '+' g];
elseif (n1~=0) & (n2~=0),
G{n1,n2}=[ G{n1,n2} '-' g];
G{n2,n1}=[ G{n2,n1} '-' g];
%If node 1 is connected to ground, add an element to the diagonal
%of the matrix.
if ((n1~=0) || (Element(i).Name(1)=='T'))
G{n1,n1}=[ G{n1,n1} '+' g];
%Same for node 2.
if ((n2 ~= 0) || (Element(i).Name(1)=='T'))
G{n2,n2}=[ G{n2,n2} '+' g];
Chapter 3. MEMS Devices
Now that we have the code needed to simulate the 5-channel MEMS filter, we
need to develop the netlist for each filter. This is accomplished by running 5 separate
PSPICE models with the correct values obtained from Table 3.3. An example of the
netlist created is shown in Figure 3.9.
Figure 3.9 Netlist Result of 107.75 MHz MEMS Filter.
This has laid the groundwork for the simulation of the 5-channel MEMS filter.
The netlist file is created in .txt format and is defined by the user with the appropriate
component values. SCAM accepts the .txt file and uses the appropriate data to run it
through the code. The SCAM program returns the transfer functions and evaluates them
Once the results are shown symbolically, I take those results and
Chapter 3. MEMS Devices
manipulate them into a form that is MATLAB friendly. These results are plotted for
visual comparison. This process is re-run 5 times to generate the 5-channel MEMS filter
bank. The MEMS filter bank that will be simulated has frequencies of 105.5, 106.75,
108, 109.25, and 110.5 MHz. The results are shown in Figure 3.10.
Frequency (MHz)
Figure 3.10 Simulated Results of 5-Channel MEMS Filter Bank.
Now that we have simulated the 5-channel filter bank, we need to verify that our
results are representative of a real filter bank. The next figure, Figure 3.11, shows the
measured results of 5-channel MEMS filter bank. As you can see from the Figures, the
simulated results are validated by the actual measurements. The actual filter banks seem
Chapter 3. MEMS Devices
to have a narrower bandwidth for each channel when compared to the simulated results.
This is caused by a parasitic resonance amongst the dual modes. You’ll also notice there
is ~5 dB difference in filter insertion loss between the two figures. This characteristic is
not as important as the shape of the experimental curves. But, the overall filter shape is
consistent for each simulated and measured channel.
Figure 3.11 Measured Results of 5-Channel MEMS Filter Bank.
3.5 Summary
This chapter illustrated the particular design of a MEMS filter that was fabricated at
Sandia National Laboratories. It showed the equivalent circuitry that was used to develop
and simulate a dual mode MEMS filter with frequency ranges in the 100 MHz.
Chapter 3. MEMS Devices
Furthermore, it provided an analysis of the simulated 5-channel filter bank with
comparisons to an actual 5-channel filter bank that was measured.
This chapter has provided further insight into the performance of the MEMS
filters. The designer can now feel confident that what is being simulated accurately
represents the actual device. However, this performance analysis might not be enough
since it does not insert actual RF channel effects such as noise, interference, or phase
The following chapter extends the performance analysis to a BPSK system. This
system will introduce random noise and be tested as a whole system. Once this is
simulated through MATLAB, a comparison will be made to an actual bench setup. This
will validate what is being simulated to the real world scenario. The RF channel effects
of phase noise, interference, etc. will be of interest.
Furthermore, this simulation
provides a good baseline for what can be accomplished in future systems. In particular,
the models will give the user a good idea of how certain RF channel effects will affect the
Chapter 4
BPSK Analysis
This chapter extends the performance analysis of Chapter 3 by presenting a performance
analysis based on MATLAB simulation results. The MATLAB simulations will consist
of modeling a BPSK receiver and transmitter, with the MEMS filter included in that
simulation. First, the simulations that were created in Chapter 3 must be manipulated to
be usable in the time domain. These filters will also be mixed down to baseband like
they would in a real system. Once this is accomplished, a MATLAB simulation of the
transmitter must be created. It will be shown that the simulation of the transmitter will
include random noise and we’ll have signals that represent real scenarios. Next, a
receiver with the MEMS filters implemented will be developed and simulated. The
results of the transmitter and receiver will be presented as a whole BPSK system.
These results of the simulated wireless system should be able to be replicated with
an actual system. Therefore, a real system will be implemented using an actual MEMS
device and test board.
The receiver from the simulation will be implemented in
MATLAB. The results will be presented and you can make a comparison from the
Chapter 4. BPSK Analysis
4.1 Simulations
The overall simulation is going to be set up in a main simulation function and then it calls
on the transmitter and receiver functions. In the main simulation function, the MEMS
filter array is set up from the previous simulation in Chapter 3. The function has some
initial setup where frequencies are normalized and initialization parameters are defined.
The simulation function also has the job of sending the information back and forth
between the functions. The final thing the simulation function does is plot the final
constellation diagram.
The first step to setting up the simulation is manipulating the MEMS 5-channel
filter bank and passing the correct data from the MEMS filters. As was seen in Figure
3.10, the MEMS device is operating in the 103 – 113 MHz range. For this portion of the
simulation, the frequencies have been adjusted to match the set of filters that were
available to test on the actual test board. These frequencies are in the 105 – 115 MHz
range. This filter bank is shown in Figure 4.1. This filter bank needs to be manipulated
before it can be loaded into the simulation function. Some of the manipulations that need
to occur are getting it in the right domain and normalizing the frequency.
manipulations will follow in the next few sections, along with the development of the
transmitter and receiver function.
Chapter 4. BPSK Analysis
Frequency (MHz)
Figure 4.1 Test Board Simulated MEMS 5-Channel Filter.
As mentioned previously, the filter banks need to be manipulated to be
compatible with the receiver and transmitter. The first issue is the domain that the filter
bank is in. It is currently observed that these signals are in the s-domain. In order to
digitally use these signals in a system, we need to transfer them to the z-domain. This
can be accomplished by using the Bilinear z-transformation or the Inverse Discrete
Fourier Transform (IDFT). The first method described is the Bilinear Transform. The
equation below transforms analog filters that were designed by classical filter techniques
into their discrete equivalents. It maps the s-plane into the z-plane by:
Chapter 4. BPSK Analysis
H d ( z) = H c (s)
s = 1− z −1
1+ z
where T is the sample time. It also creates a relation between the analog frequency
variable, Ω, and the digital frequency, ώ, by mapping the јΩ axis (from Ω = -∞ to +∞)
repeatedly around the unit circle (eјώ, from ώ = - π to π) by [19]:
ω = 2 tan
The Bilinear transform method was attempted on the simulated filter bank transfer
functions. The numerical values of each channel in the filter bank transfer function are
very big numbers. Some of the coefficient weights in the numerator range from 10148 to
powers of 10151. The same holds true for the coefficient weights of the denominator.
These values range in powers of 10161. Due to this large number, when the bilinear
transformation is applied, we lose the significance of the numbers and we get large
numerical inaccuracies.
The Fourier transform method takes a signal in the time domain and maps it into
the frequency domain. The frequency domain representation is the exact same signal, but
in a different form. The inverse Fourier transform maps the signal back from the
frequency domain into the time domain. The Fourier transform maps the time domain
sequence into a frequency domain sequence, where each value is a complex number that
is associated with a given frequency. The inverse Fourier transform takes the frequency
Chapter 4. BPSK Analysis
sequence of complex values and maps them back into the original time sequence. The
result of the IDFT will be complex numbers where the imaginary part is zero. By doing
this method, we can find all the parts of the filter where it is “Not A Number (NAN)” in
MATLAB and use this information accordingly. Either of these two methods is valid,
but since the bilinear transformation created large numerical inaccuracies, the IDFT
method was used for this thesis. The tradeoff is in the IDFT method we have to sample it
a lot, but this is much better than the numerical inaccuracies.
Once the filter bank is transformed into the correct domain, we have to normalize
the frequency. In the analog realm, a signal frequency is measured in hertz (Hz). In the
digital realm, a system uses a digital frequency. This is the ratio between the analog
frequency and the sampling frequency. It can be shown by the following equation:
fd =
where fd is the digital frequency, fa is the analog frequency, and fs is the sampling
frequency. The digital frequency is known as the normalized frequency and is measured
in cycles per sample.
The normalized frequency ranges from 0.0 to 1.0, which
corresponds to a real frequency range of 0 to the sampling frequency fs. The normalized
frequency also wraps around 1.0 so a normalized frequency of 1.1 is equivalent to 0.1.
We need to manipulate the MEMS filter bank to mix down the frequency from the
100 MHz range into baseband. By doing this, we are also able to get a reasonable
amount of samples when we are simulating it. After the frequencies have been mixed
Chapter 4. BPSK Analysis
down and normalized, we can plot the data to view the simulated filters in MATLAB.
The predefined function that is set up in MATLAB is the “fvtool” function. The “fvtool”
is used by MATLAB to help the user analyze digital filters. Figure 4.2 shows the first
filter in the 5-channel filter bank that has been normalized. Each of the filters was
analyzed individually by “fvtool” to find the normalized operating frequency.
Magnitude Response (dB)
Normalized Frequency: 0.2156982
Magnitude (dB): -15.14853
Magnitude (dB)
Normalized Frequency ( ×π rad/sample)
Figure 4.2 FVTOOL Manipulation of 5-Channel Filter.
All of the manipulations take place in the filter bank function which is stored in a
This final variable representation is shown in Figure 4.3.
It is a digital
spectrum representation of the MEMS filter bank in the time domain. This information is
set up in the simulation function and will also be used when we set up the transmitter in
Chapter 4. BPSK Analysis
the next section. These simple manipulations to the filter bank have made it compatible
for the transmitter and receiver that we are going to simulate.
This is a big step in
progressing forward as we need the results in a digital format. Now that we have what
we need, we can create the transmitter and receiver to see what our results will look like
in a communications system.
x 10
Normalized Frequency
Figure 4.3 Digital Spectrum of MEMS Filter.
Since this simulation is to test the functionality of the MEMS filter in a communication
system, a digital modulation scheme needs to be chosen. Phase Shift Keying (PSK) is a
Chapter 4. BPSK Analysis
digital modulation scheme that conveys data by modulating the phase of the carrier wave
where the input signal is a binary digital signal and a limited number of output phases are
possible [20]. The simplest form of PSK to test this simulation would be Binary Phase
Shift Keying (BPSK). It uses two phases which are separated by 180° and it does not
particularly matter exactly where the constellation points are positioned. A BPSK signal
can be defined by the waveform:
s ( t ) = A cos( 2 π f c t + m ( t )) + θ
0 ≤ t ≤T
, T is bit duration, A is constant, m(t) is 0° or 180° (which
represents +1 or -1), fc is the carrier frequency, and θ is random noise. Figure 4.3 shows
the constellation diagram for BPSK systems [21]. This modulation technique is the most
reliable of all the PSK’s since it takes a lot of distortion to make the demodulator reach
an incorrect decision. The downfall for this technique is it is only able to modulate at 1
bit/symbol and this makes it unsuitable for high data-rate applications when bandwidth is
limited. If a phase-shift is introduced by the communications channel or other circuitry,
the demodulator is unable to tell which constellation point is which. As a result, the data
is often differentially encoded prior to modulation [22]. This will be discussed later in
the results.
Figure 4.4 BPSK Signal Constellation.
Chapter 4. BPSK Analysis
The transmitter function is straight forward once a few things are defined. In
order to set up the BPSK transmitter for this system, we need to determine certain
parameters such as normalized frequencies, number of bits, sampling rate, etc.
determine the normalized frequencies, we have to use our manipulated filter bank that we
previously discussed in the chapter. By looking at Figure 4.2, we can see that the center
normalized frequency of this filter is 0.215. When we do that for the remaining filter
banks, we get the 5 normalized frequencies that we need for the transmitter function. For
completeness, the five normalized frequencies in MATLAB form are shown below:
[0.215 0.350 0.482 0.615 0.750]
The number of bits that are chosen is a user defined parameter. This number that
was chosen was 1000. This appeared to be enough points to correctly simulate a signal
without losing any information. In order to receive BPSK, the receiver needs to be tuned
to the exact frequency of the signal. This frequency is found by setting up a ratio of the
normalized frequencies to the actual frequencies. This ratio is normally:
where fs is the fixed sample frequency for the receiver. In our case, the normalized
frequencies have a frequency shift difference of 1.25 MHz (each filter’s center frequency
is spaced 1.25 MHz apart). The normalized frequencies that we found earlier in the
Chapter 4. BPSK Analysis
chapter have a frequency shift difference of 0.133 (averages of all the ratios). When you
put this in ratio form, you get:
0 . 133
1 . 25
where x = (fs/2). Solving for this equation, x = 9.3785. Then solving for fs = 18.797
MHz. The fixed frequency of the receiver should be 18.797 MHz. With this value
solved for, we’re able to determine the number of samples that are needed. This is done
by solving:
# of samples
Our fs is 18.797 MHz and the bitrate is 125 kHz. The bitrate can be chosen by the
user as long as you do not exceed the bandwidth of the filter. The bandwidth of the
filters is 650 kHz. So 125 kHz was chosen and that is what is used in the actual results
that will be shown later. When you run the numbers through Equation 4.8, the number of
samples that are needed is 150. This is all the information we need to set up the
The transmitter function is passed three variables: a random signal of 1 and -1, the
normalized frequencies, and the number of samples. It takes these three signals and
generates a BPSK signal with random noise attached. The transmitted signal is shown in
Figure 4.4. The transmitter function returns the generated signal back to the main
Chapter 4. BPSK Analysis
simulation function. As you can see, the transmitter function generated signals at the
desired normalized frequencies.
Magnitude Response (dB)
Normalized Frequency: 0.2145996
Magnitude (dB): 72.70961
Magnitude (dB)
Normalized Frequency ( ×π rad/sample)
Figure 4.5 The Simulated Transmitted Signal.
The main simulation function takes the transmitted signal that we just developed and it
runs it through the 5-channel MEMS filter. The simulation also adds a gain stage to
make it more realistic. This would be similar to the front end of a receiver system. Next,
the simulation function is ready to send information to the receiver function. There are
Chapter 4. BPSK Analysis
three variables passed to the receiver function. These variables include the filtered
transmitted data, the normalized frequencies, and the number of samples. The receiver
then defines the in-phase and quadrature baseband signals. A low pass filter is also
defined to reject all the unwanted images. Next, the data stream is mixed with the
inphase and quadrature signals, and the low pass filter is applied. Essentially, the noise
has been stripped out and the signal has been integrated. The decision device is coded
next with the output being stored in a matrix to plot on a constellation diagram. This is
the most visually attractive diagram for this case.
The simulated data from the receiver is shown in Figure 4.6. This constellation
diagram shows that the BPSK signal was successfully transmitted and received. You’ll
notice how there are 5 different set of constellations. There are two constellations on
each side of the zero plane. This is caused by intersymbol interference.
Chapter 4. BPSK Analysis
Figure 4.6 Constellation Diagram of BPSK System.
Intersymbol interference (ISI) is a form of distortion of a signal in which one
symbol interferes with subsequent symbols. Usually, this is an unwanted occurrence, but
in this case, it turns out to be constructive interference. Usually, ways to fight against
intersymbol interference would include some type of equalization and error correcting
codes. In our case, since it is constructive in the BPSK system, no action is needed, but
we will show a simple method to correct the ISI later in this chapter.
Another observation that can be made from the results is the phase error. You
will notice how the phase of each channel is off, except for one channel. This was
expected because there is no guarantee that there would be coherence between the
channels, but the challenge now is to see if we are able to correct this with some type of
Chapter 4. BPSK Analysis
circuitry or a software implementation. The circuitry that it needs to have is a Phase
Locked Loop (PLL). This can also be added to the receiver to try to correct the phase
error. Since this is a simulation, we will add a PLL portion to the receiver. This should
correct the phase error and possibly the ISI that is created in the system.
Another analysis tool to see the results of the simulation is in the eye diagram in
Figure 4.7. The eye diagram shows where the signal is repetitively sampled and applied
to the vertical input, while the data rate is shown on the horizontal sweep. This is what
the receiver is seeing in the baseband domain. From the results of the eye diagram, you
can see that the receiver sees a reasonably square wave and there are two times at which
the power is greatest. By sampling the system appropriately, we are able to maximize
power. You can see the most power is not where all the transitions occur.
Chapter 4. BPSK Analysis
Eye Diagram for In-Phase Signal
Eye Diagram for Quadrature Signal
Figure 4.7 Eye Diagram of the Receiver.
After seeing these results, it was noted that a PLL must be implemented into the
system. Figure 4.8 shows the results of the system with a PLL implemented. As you can
see from the results, the phase error is corrected.
Chapter 4. BPSK Analysis
Figure 4.8 BPSK Simulation With PLL Applied.
In an effort to get rid of the multiple symbols (also known as ISI), a raised cosine
filter was incorporated. The raised cosine filter is a specific electronic filter that is often
used for pulse shaping in digital modulation schemes because it has the ability to
minimize ISI. The raised cosine filter is an implementation of a low pass Nyquist filter
and when applied properly to a digital stream, it has the property of eliminating ISI
because its impulse response is zero at all nT (where n is an integer), except n = 0.
Therefore, if you sample at the receiver correctly, you can completely recover the
symbols that were transmitted. Ideally, a matched filter must be used in the receiver due
Chapter 4. BPSK Analysis
to white noise. The white noise creates a constraint and the way to deal with the
constraint is to implement a root raised cosine filter to maintain zero ISI. In our system,
MATLAB has a function called rcosfir.m. This implements a simple raised cosine filter
and will suffice for our simulation purposes. The implementation of this will alleviate
the ISI that is introduced by the MEMS filter and should just leave us with a BPSK
constellation that is equivalent to an ideal system. Figure 4.9 shows the results of this
simulation. As you can see, it has accomplished the task that we expected it to do.
Figure 4.9 Ideal BPSK Simulation With PLL and Raised Cosine Filtering.
Chapter 4. BPSK Analysis
Actual Results
This section presents actual results for the actual 5-channel MEMS filters that
were developed at Sandia National Laboratories. For this setup, a test board was built
that integrated these filters with a VCO, gain stage, mixers, and other necessary circuitry.
The boards have two of the filters installed on them. One filter bank is set in the corner
for evaluation purposes. The other filter bank is right in the middle of the test board and
that is the focus of these results. Figure 4.10 shows the layout of the 5-channel MEMS
filter integrated on one chip. The size of the surface mount chip is 2.1 mm X 2.1mm.
2.1 mm
Figure 4.10 5-Channel MEMS Filter Layout.
Chapter 4. BPSK Analysis
Figure 4.11 shows a picture of the actual 5-channel MEMS filter. This filter bank
that is installed on the test board has measured center frequencies of 107.77, 110.53,
111.76, and 113.32 MHz. The fifth channel (~109 MHz) is not currently working on this
test board. Only two of these channels are going to be verified in the actual simulation
due to the modifications that need to be implemented. This will be discussed later in the
Figure 4.11 5-Channel MEMS Filter on an IC.
Figure 4.12 shows the chip with respect to some resistor circuitry around it. As
you can see, the 5-channel filter bank is not much bigger than the standard surface mount
Chapter 4. BPSK Analysis
resistors. Figure 4.13 shows the test board schematic. The picture on the left is a high
level schematic, while the picture on the right shows the details of the individual RX
chain. Figure 4.14 shows the entire test board with all the parts. Some of the parts
included are VCO’s, amplifiers, mixers, potentiometers, and the basic resistors and
As you can see, the MEMS filter banks are not the limiting factor in
development of the size of the board. The remaining parts are typically the same size if
not bigger, making it a reality that filter banks and miniaturization is achievable. The
biggest component is the VCO. All the traces on the board are 50 Ω impedances.
Figure 4.12 Filter Bank IC With Respect toSurface Mount Resistors.
Chapter 4. BPSK Analysis
Figure 4.13 Test Board Schematic: High Level (left) Details of RX Chain (right).
Figure 4.14 Test Board with MEMS Filters Integrated on Board.
Chapter 4. BPSK Analysis
In order to actually use the test board, a transmitter was originally going to be
coded using a program called WinIQSIM and supporting hardware, such as waveform
WinIQSIM is specifically developed for the generation of digitally
modulated signals. Complex signals can also be easily generated. It is based on a
graphical user interface and is a convenient way of creating any signal that you would
like to use. The signals that are generated are then sent out to a waveform generator.
Due to time constraints, a transmitter was coded in VHSIC (Very High Speed Integrated
Circuits) Hardware Description Language (VHDL). The VHDL transmitter was created
by taking some ordinary text and converting it into a digital form like Equation 4.4. The
text is just some random words that were used to create a BPSK stream. The output of
the transmitter was sent to the test board and processed.
The test board takes the transmitted signal on a single input SMA. The test board
is powered by 12 Volts. The input signal was originally supposed to be sent through the
MEMS filter chip first. After initial testing, it was realized that the signal level needed to
be amplified first. So a few haywires were installed to modify the way things were
routed on the test board. This allowed the flexibility to use the same test board to amplify
the signal. After the signal is amplified, it is sent through the MEMS filter. This
separates and filters the signal into the five bands that we’re interested in.
processed by the MEMS filter, it is mixed down to base band. Each channel has its own
VCO to aid in this process and the potentiometers are installed to manually control the
Chapter 4. BPSK Analysis
VCO voltage. The signals are then output on the OUTPUT SMA for each individual
channel. The output of the board was then sent to a National Instruments (NI) Data
Acquisition (DAQ) system. The NIDAQ system was chosen for its compatibility with
MATLAB. The NIDAQ is able to take the incoming data from the test board and sample
it appropriately (up to 2.5MS/s). The data is stored in MATLAB .mat files. These files
are stored and implemented in a bpsk_dac.m file. This file is similar to the simulation
file that was created for the simulation earlier in the chapter. The bpsk_dac.m file loads
the .mat files and it calls the receiver function. The final thing the file does is plot the
data and makes a digital movie.
The receiver function executes the same commands as previously done in the
The results of the receiver function are shown in Figure 4.15 as a
constellation diagram. This only shows 2 channels as the test board was not designed
robustly enough to handle all 5 channels with the haywire modifications. A future test
board will be fabricated to implement better engineering ideas.
The constellation diagram shown in Figure 4.15 is not a good representation of
the results because it is static. For thoroughness, each point is plotted and held, but in
reality, the BPSK constellation is moving.
Chapter 4. BPSK Analysis
x 10
x 10
Figure 4.15 BPSK Constellation Diagram of Test Board.
The movie that was created by MATLAB shows this very well. The constellation
is very interesting when you watch it in real time. The constellations start by behaving
very nicely on the vertical plane and horizontal plane. We know the vertical plane is
caused by phase noise as we previously determined by the simulations. The VCO is the
cause of the phase noise. As the VCO frequency starts to slowly change, the phase shift
of each constellation starts to “dance”.
It continues to do this in a clockwise and
counterclockwise nature. The reason it changes direction is due to the DC resonance of
the components. Essentially, the frequency of the local VCO is varying and therefore the
Chapter 4. BPSK Analysis
constellation rotates up and down as the frequency changes. The faster it rotates the faster
the frequency is changing. It is a very interesting phenomenon. Figure 4.16 shows
several “frames” of the movie to illustrate what is happening over time.
Chapter 4. BPSK Analysis
Chapter 4. BPSK Analysis
Figure 4.16 Several “Frames” With Respect to Time.
Obviously, we’d like to see if this phase shift can be corrected. So, just like the
previous simulation, we will implement a PLL on the system. This PLL is implemented
in the software in the receiver. The PLL circuit is used to demonstrate that even though
the phase (frequency) is changing fast, a PLL can lock onto it. The PLL is able to lock
on the data and keep the constellations very stable as expected. The PLL removes the
phase rotation as expected, but a single PLL cannot fully correct for a frequency
Chapter 4. BPSK Analysis
Figure 4.17 shows the results of the PLL implemented on the system. Once
again, the static picture does not do the results justice. The observations during real time
show that the BPSK constellation does not vary much at all from the range that is shown
in the figure below.
Figure 4.17 Test Board BPSK Constellation with PLL Implemented.
It is good news that the actual results resemble the simulated results. The system
is functioning properly and now many more complex systems will be able to be built out
of this.
Chapter 4. BPSK Analysis
4.5 Summary
This chapter extended the performance analysis presented in Chapter 3 by simulating a
full BPSK system and also implementing an actual BPSK system using the MEMS 5channel filter bank. First, baseline results were presented for the simulated system when
simulating a BPSK system. Next, it was shown that the simulated systems could be
validated by implementing the chips in a real circuit board. The results were as expected;
however, an interesting phenomenon of intersymbol interference took place. In our case,
it was constructive. The eye diagram showed how there are two places of peak power, so
we are essentially stealing power in this setup.
It was also noted that there was
substantial phase noise. This was created in the actual setup by the VCO and in the
simulations it was also present. A PLL was implemented into the receiver and this phase
noise was corrected. The overall results of the simulations and test results prove that
these post-CMOS compatible MEMS filters can be implemented into a full
communication system.
Chapter 5
Conclusions and Future Work
This thesis first described the many RF MEMS devices that are available in industry,
from switches to resonators to antennas. MEMS are redefining the micro-technology
industry by making things smaller and more compatible. In Chapter 2, the various
processes that are used to develop integrated circuits were introduced. These same
processes have been adapted to develop the various MEMS technologies. The dual mode
filter that was developed by Sandia National Laboratories was introduced for the very
first time.
Chapter 3 presented a performance analysis of the MEMS filters. The
performance analysis showed that the MEMS filter could be simulated in MATLAB and
could be verified by measuring an actual MEMS filter. This was then built into a 5channel filter in MATLAB and that was also verified through simulation and an actual
chip. This was a very important step in order to be able to use the MATLAB simulation
in a BPSK system. Chapter 4 then extended the performance analysis presented in
Chapter 3 by simulating a full BPSK system in MATLAB. The simulation results
showed that a full BPSK system could be realized with good results.
With that
information, a board was designed to handle the 5-channel MEMS device. The board
was tested and the results were presented. The results showed that the simulations were
Chapter 5. Conclusions and Future Work
correct. This information is very important because it proves that a post-CMOS 5channel MEMS filter is achievable and will work in a system.
5.1 Future Work
Future work options that are currently taking place for continuing this analysis would be
to develop a new test board to accommodate a better engineering design. The new test
board would be able to test all 5 channels of the MEMS filter. Other concurrent work
that is taking place for this project is experimentation with the filters. This includes
further research and development of the filters to get better results.
Some of the
experiments that are currently taking place to further develop the filters are notching and
other mechanical experiments with the design. It has been proven that physical design
changes results in changes in the shape of the filters. In these experiments, the goal is to
increase the frequency that the MEMS filter bank can operate at and also try to get rid of
the ripple in the filter. By changing the physical characteristics of the filters, we hope we
can achieve this goal. Once these steps have been accomplished and fine tuned, it is
desired to implement the test board with a MEMS resonator test board into a full radio
When a full radio system is accomplished, there are many commercial systems
that could benefit from this working system. Simulations should be done with many
types of wireless communication systems. Investing in trying to increase the operating
Chapter 5. Conclusions and Future Work
frequency range would also help in creating better communication systems. Future
simulations could include QPSK and Frequency Hopping Spread Spectrum (FHSS).
There are various radio architectures that you could experiment with to implement these
Not only can commercial systems benefit, but the military need would also
benefit. The MEMS devices, such as resonators, have the added benefit of being smaller
and so they are less prone to vibration than crystals. MEMS filters are smaller so you can
pack more of them on a single die. Also, because these MEMS processes are CMOS
compatible they can be built and put alongside (or on top of) typical circuit logic. Many
systems in the military field could utilize unattended ground sensor applications or
communication radios that talk to each other.
Rebeiz G., ‘RF MEMS: Theory, Design and Technology’, John Wiley and
Sons,February 2003
[2] http://en.wikipedia.org/wiki/Microtechnology
[3] Allen J.J, “Micro Electro Mechanical System Design”, Taylor and Francis
Group, 2005
Varadan V. K., Vinoy J. J., Jose K. A., “RF MEMS and Their Applications”,
John Wiley and Sons, 2002
[5] http://nepp.nasa.gov/index_nasa.cfm/811/
A. R. Brown and G. M. Rebeiz, A high-performance integrated K-band
diplexer, IEEE Trans. Microwave Theory Tech., Vol 47, No. 8, pp. 1477-1481,
August 1999.
[7] http://www.eecs.umich.edu/rebeiz/Current_VII_Press.html
R. C. Ruby, A. Barfknecht, C. Han, Y. Desai, F. Geefay, G. Gan, M. Gat, and
T. Verhoeven, “High-Q FBAR filters in a wafer-level chip-scale package”, in
IEEE International Solid-State Circuits Conference Digest, 2002, pp. 184-458.
J. McDonald, “Electronic Products”, MEMS oscillators 101, November 2007.
[10] J.R. Clark, M. Pai, B. Wissman, G. He, and W.-T. Hsu, “Parallel-Coupled
Square-Resonator Micromechanical Filter Arrays”, International Frequency
Control Symposium and Exposition, IEEE, June 2006, pp. 485-490
[11] D. Forman, Automotive applications, smalltimes, 3(3), 42-43, May/June 2003.
[12] W.M. Middleton, M.E. Van Valkenburg, “Reference Data for Engineers:
Radio, Electronics, Computer, and Communications” Newnes, 2002.
[13] H. Helvajian, M. Mehregany, S. Roy “Microengineering Aerospace Systems”,
AIAA, Aerospace Press Series, 1999.
[14] K. J. Smart, R. H. Olsson III, D. Ho, D. R. Heine, and J. G. Fleming,
“Frequency agile radios using MEMS resonators,” Proc. of the Govt.
Microcircuit App. and Critical Tech. Conf., pp. 409-412, March 2007.
[15] G. Piazza, P.J. Stephanou, J.P. Black, R.M. White and A. P. Pisano, "SingleChip Multiple-Frequency RF Microresonators based on Contour-Mode and
FBAR Technologies," 2005 IEEE Ultrasonic Symposium, Rotterdam, pp. 1187 1190, 2005.
[16] Roy H. Olsson III, James G. Fleming, Kenneth E. Wojciechowski, Michael S.
Baker, and Melanie R. Tuck, “Post-CMOS Compatible Aluminum Nitride
MEMS Filters and Resonant Sensors” Frequency Control Symposium, 2007
Joint with the 21st European Frequency and Time Forum. IEEE International,
pp. 412-419, May 29 2007-June 1 2007.
[17] P. J. Stephanou, G. Piazza, C. D. White, M. B. J. Wijesundara, and A.
P. Pisano, “Piezoelectric thin film AlN annular dual contour mode
bandpass filter,” Proc. ASME IMECE2005, 2005.
[18] E. Cheever, http://www.swarthmore.edu/NatSci/echeeve1/Ref/mna/MNA2.html
[19] A.V. Oppenheim, A.S. Willsky, S.H. Nawab, “Signals and Systems,” Prentice
Hall, Upper Saddle River, New Jersey 07458, 1997, 2nd Edition.
[20] W. Tomasi, “Electronic Communication Systems Fundamentals Through
Advanced” , Prentice Hall Upper Saddle River, New Jersey 07458, 2001, 4th
[21] M. Schwartz, Information Transmission, Modulation, and Noise, 4/e, McGraw
Hill, 1990.
[22] J.G. Proakis, “Digital Communications”, McGraw-Hill 1221 Avenue of the
Americas New York, NY 10020, August 2000, 4th Edition.