U.S. patent application number 16/360504 was filed with the patent office on 2019-09-19 for frequency tuning and/or frequency tracking of a mechanical system with low sensitivity to electrical feedthrough.
This patent application is currently assigned to THE REGENTS OF THE UNIVERSITY OF CALIFORNIA. The applicant listed for this patent is THE REGENTS OF THE UNIVERSITY OF CALIFORNIA. Invention is credited to Bernhard Boser, Richard Przybyla, Hao-Yen Tang.
Application Number | 20190288696 16/360504 |
Document ID | / |
Family ID | 53778434 |
Filed Date | 2019-09-19 |
United States Patent
Application |
20190288696 |
Kind Code |
A1 |
Boser; Bernhard ; et
al. |
September 19, 2019 |
FREQUENCY TUNING AND/OR FREQUENCY TRACKING OF A MECHANICAL SYSTEM
WITH LOW SENSITIVITY TO ELECTRICAL FEEDTHROUGH
Abstract
An apparatus and method for frequency tuning/tracking between an
electrical subsystem and a mechanical transducer subsystem is
presented. An electromechanical transducer generates acoustic
pulses as it is driven by a transmit signal from an electrical
subsystem. As the transmit signal goes inactive, the settling
behavior of the transducer is registered from which the difference
in frequency between the resonance of the electromechanical
transducer and the transmit signal frequency is determined and
utilized for locking the electrical subsystem to the mechanical
transducer subsystem by either tuning operating frequency of the
electrical subsystem, or the mechanical transducer, to keep them
matched (locked).
Inventors: |
Boser; Bernhard; (Berkeley,
CA) ; Przybyla; Richard; (Berkeley, CA) ;
Tang; Hao-Yen; (Berkeley, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
THE REGENTS OF THE UNIVERSITY OF CALIFORNIA |
Oakland |
CA |
US |
|
|
Assignee: |
THE REGENTS OF THE UNIVERSITY OF
CALIFORNIA
Oakland
CA
|
Family ID: |
53778434 |
Appl. No.: |
16/360504 |
Filed: |
March 21, 2019 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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15226470 |
Aug 2, 2016 |
10284208 |
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16360504 |
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PCT/US2015/014588 |
Feb 5, 2015 |
|
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15226470 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H03L 7/00 20130101; H03K
5/2481 20130101; G01S 15/8961 20130101; H03K 3/0231 20130101; H03L
7/093 20130101; H03H 11/30 20130101; G01S 7/52004 20130101 |
International
Class: |
H03L 7/093 20060101
H03L007/093; H03H 11/30 20060101 H03H011/30; G01S 7/52 20060101
G01S007/52; H03K 3/0231 20060101 H03K003/0231; H03K 5/24 20060101
H03K005/24; H03L 7/00 20060101 H03L007/00 |
Claims
1. An apparatus for locking an electrical system to a resonant
mechanical system, the apparatus comprising: an electromechanical
transducer, of a resonant mechanical subsystem, configured for
operation in a transmission mode for generating acoustic pulses;
and an electrical subsystem having a transmitter circuit coupled to
said electromechanical transducer, in which acoustic pulses are
generated from said electromechanical transducer in response to
receipt of an electrical signal at an electronic transmission
frequency from said electrical subsystem; wherein said electrical
subsystem is configured to determine operating frequency of the
resonant mechanical subsystem from a resonance settling response of
the electromechanical transducer when not being driven in its
transmission mode; and wherein the electrical subsystem is
configured to lock transmitting frequency of said electrical
subsystem to that of said resonant mechanical subsystem by either
(a) tuning operating frequency of said electrical subsystem to
match that of said resonant mechanical subsystem or (b) tuning
operating frequency of said resonant mechanical subsystem to match
that of said electrical subsystem.
2. The apparatus as recited in claim 1, wherein frequency
difference between the electromechanical resonance settling
response and electronic transmission frequency is used to determine
required adjustment to said transmission frequency to make these
two frequencies match.
3. The apparatus as recited in claim 1, wherein said
electromechanical transducer comprises at least one ultrasonic
transducer.
4. The apparatus as recited in claim 1, wherein said
electromechanical transducer comprises at least one piezoelectric
transducer.
5. The apparatus as recited in claim 1, wherein said
electromechanical transducer comprises at least one capacitive
transducer.
6. The apparatus as recited in claim 1, wherein a switching circuit
selects between transmission mode or receiving mode for said
electromechanical transducer.
7. A method for locking an electrical system to a mechanical
transducer system, comprising: generating acoustic pulses from an
electromechanical transducer within a mechanical transducer
subsystem in response to receiving a transmit signal from a
transmitter in an electrical subsystem; registering settling
behavior of said mechanical transducer subsystem, when said
transmit signal goes inactive and is thus no longer driving an
output from said electromechanical transducer; determining
operating frequency of said mechanical transducer subsystem from
the settling behavior of said electromechanical transducer; and
locking the electrical subsystem to the mechanical transducer
subsystem by either (a) tuning operating frequency of said
electrical subsystem to match that of said mechanical transducer
subsystem or (b) tuning operating frequency of said mechanical
transducer system to match that of said electrical subsystem.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. patent
application Ser. No. 15/226,470 filed on Aug. 2, 2016, incorporated
herein by reference in its entirety, which is a 35 U.S.C. .sctn.
111(a) continuation of PCT international application number
PCT/US2015/014588 filed on Feb. 5, 2015, incorporated herein by
reference in its entirety, which claims priority to, and the
benefit of, U.S. provisional patent application Ser. No. 61/937,430
filed on Feb. 7, 2014, incorporated herein by reference in its
entirety. Priority is claimed to each of the foregoing
applications.
[0002] The above-referenced PCT international application was
published as PCT International Publication No. WO 2015/120132 on
Aug. 13, 2015, which publication is incorporated herein by
reference in its entirety.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
[0003] Not Applicable
INCORPORATION-BY-REFERENCE OF COMPUTER PROGRAM APPENDIX
[0004] Not Applicable
NOTICE OF MATERIAL SUBJECT TO COPYRIGHT PROTECTION
[0005] A portion of the material in this patent document is subject
to copyright protection under the copyright laws of the United
States and of other countries. The owner of the copyright rights
has no objection to the facsimile reproduction by anyone of the
patent document or the patent disclosure, as it appears in the
United States Patent and Trademark Office publicly available file
or records, but otherwise reserves all copyright rights whatsoever.
The copyright owner does not hereby waive any of its rights to have
this patent document maintained in secrecy, including without
limitation its rights pursuant to 37 C.F.R. .sctn. 1.14.
BACKGROUND
1. Technological Field
[0006] This technical disclosure pertains generally to
electromechanical transducers and sensors, and more particularly to
electromechanical transducers and sensors with enhanced frequency
stability and tracking.
2. Background Discussion
[0007] Mechanical systems (and subsystems) typically have one or
more resonant frequencies arising from various vibrational modes of
the system. One important category of these mechanical systems are
electromechanical transducers which convert mechanical motion into
electrical signals in a sensing operation, and/or convert
electrical signals into mechanical motion in an actuation
operation. A transducer can therefore be used to sense the motion
of a mechanical structure during actuation. It is often desirable
to use the same transducer to actuate and sense the motion of the
mechanical structure. However, there is often electrical
feedthrough from the actuation signal to the sensor signal, which
corrupts the sensor signal.
[0008] Electromechanical actuators may be configured to operate at
or near resonance in order to increase the motion of the device,
and mechanical sensors may also be operated at resonance to
increase the sensitivity of the device. However, these
electromechanical actuators and sensors suffer from variation in
mechanical resonance that can arise due to fabrication tolerances
and frequency drifting in response to changes in temperature,
stress, humidity, or other ambient conditions.
[0009] In practice, electrical systems (and subsystems) are
generally coupled to an electromechanical or electrical oscillator,
and themselves may also vary in frequency due to fabrication
tolerances, and be subject to frequency drift in response to
changes in temperature, stress, humidity, or other ambient
conditions. Therefore, in a system having an electrical subsystem
and a mechanical subsystem, the resonance of the mechanical
subsystem may drift independently of the operational frequency of
the electrical subsystem.
[0010] Accordingly, a need exists for apparatus and methods which
enables the resonance in an electromechanical system to be tracked
by an electrical subsystem. The disclosure presented fulfills that
need and provides additional benefits for resonant
electromechanical systems.
BRIEF SUMMARY
[0011] An apparatus and method are presented for stabilizing the
resonant frequency of an electromechanical subsystem as controlled
by an electrical subsystem. The electromechanical subsystem is
locked in frequency to the electrical subsystem by either: (a)
tuning the operating frequency of the electrical system to match
that of the mechanical system, or (b) tuning the operating
frequency of the mechanical system to match that of the electrical
system. Resonance frequency for the electromechanical subsystem is
determined from its settling response after cessation of
transmission during a ring down period. During the ring down
period, a ring down circuit is activated which attenuates resonance
of the electromechanical subsystem in a controlled manner allowing
settling response to be readily determined.
[0012] By way of example and not limitation, the system is
described utilized with an array of electromechanical
transducers/sensors (e.g., ultrasonic transducers/sensors)
configured for using pulse-echo time-of-flight ranging for
discerning objects, and object motion. Although objects can be
detected in a number of applications, the example presented is for
using these techniques in a gesture recognition process. This
pulse-echo time-of-flight utilizing MEMS ultrasonic rangers can
operate over distances of up to approximately one meter and achieve
sub-mm ranging accuracy. It will be noted, however, that the
frequency tuning process of the present disclosure can apply to a
wide variety of mechanical-coupled electro-mechanical systems,
without limitation as to range. Using a one-dimensional transducer
array, objects can be localized in two dimensions, while utilizing
a two-dimensional transducer array allows localizing objects in
three dimensions. The present disclosure may be utilized in an
application of ultrasonic 3D gesture recognition, such as those
based on a custom transducer chip and an ASIC to sense the location
of targets such as hands, or in other applications benefiting from
frequency tuning/tracking between a resonant mechanical system and
an electrical system.
[0013] In systems, such as those described above, in which an
electrical subsystem excites the resonance of the mechanical
subsystem with a narrowband signal, or the electrical subsystem
monitors the output of the mechanical subsystem in a narrow band of
frequencies, there is a need to lock the operational frequency of
the electrical subsystem to the desired resonant mode of the
mechanical subsystem.
[0014] In order to measure the resonant frequency of a mechanical
mode with high quality factor, it is desirable to excite the
transducer with a harmonic signal near the resonant frequency, in
order to elicit a large response, and to monitor this response to
determine the resonant frequency. In order to avoid corrupting the
response signal with the excitation signal, the excitation signal
is halted after sufficient time to excite the resonance.
[0015] Further aspects of the presented technology will be brought
out in the following portions of the specification, wherein the
detailed description is for the purpose of fully disclosing
preferred embodiments of the technology without placing limitations
thereon.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)
[0016] The disclosed technology will be more fully understood by
reference to the following drawings which are for illustrative
purposes only:
[0017] FIG. 1A is a block diagram for frequency tuning and/or
tracking of a mechanical system with low sensitivity to electrical
feedthrough according to an embodiment of the present
disclosure.
[0018] FIG. 1B is a rendition of a portion of a MEMS ultrasound
chip utilized according to an embodiment of the present
disclosure.
[0019] FIG. 1C is a plot of measured amplitude values of I and Q
according to an embodiment of the present disclosure.
[0020] FIG. 1D is a plot of position and depth of nearby objects
using a electromechanical transducer system according to an
embodiment of the present disclosure.
[0021] FIG. 2 is a plot of operating phases showing transmission,
ring down, and measurement of returned echoes according to an
embodiment of the present disclosure.
[0022] FIG. 3A is a block diagram of a switched-capacitor (SC)
resonator and continuous-time (CT) anti-aliasing (AA) filter
according to an embodiment of the present disclosure.
[0023] FIG. 3B is a schematic of a transconductance amplifier
according to an embodiment of the present disclosure.
[0024] FIG. 3C is a timing diagram of signals associated with FIG.
3A according to an embodiment of the present disclosure.
[0025] FIG. 4 is a plot of measured frequency error showing
significant reduction when tuning according to an embodiment of the
present disclosure is enabled.
DETAILED DESCRIPTION
[0026] A method and apparatus for locking an electrical system to a
resonant electromechanical system is disclosed. In at least one
embodiment, one or more ultrasonic (ultrasound) transducers, each
having a narrowband resonance, are used to transmit and receive
acoustic pulses. The transducer has maximum transmit and receive
sensitivity at the resonant frequency of the transducer. However,
the center frequency of transducer resonance can vary due to
fabrication tolerances, mechanical stress, change in atmospheric
pressure, or change in temperature. Atmospheric contaminants, such
as dust or humidity, can also affect the resonance of the
transducer.
[0027] An electrical subsystem actuates each transducer to launch
acoustic waves, and then switches to receive mode and listens for
acoustic echoes that return to the transducers. It will be
appreciated that a plurality of these transducers may be utilized,
such as configured into one dimensional arrays or multi-dimensional
arrays. The primary goal of the system is to transmit an acoustic
pulse at the proper resonant frequency of the mechanical subsystem.
Optionally, information about the returning echoes is measured
according to at least one embodiment, such as measuring the
time-of-flight. The electrical subsystem has an independent timing
reference, hereafter referred to as a clock, that may be generated
electrically or using an additional mechanical resonator. The
transmitted signal is preferentially a harmonic signal with a
center frequency equal to that of the transducer resonant
frequency. In at least one embodiment, the transmitted signal is
configured for containing a form of amplitude or phase modulation,
or a combination thereof. The received signal is preferentially
filtered with an electrical filter that has a center frequency
equal to that of the transducer.
[0028] FIG. 1A illustrates an example of a resonant frequency
tuning and/or tracking embodiment 10, shown for using pulse-echo
time-of-flight methods. An electromechanical subsystem 12 is shown
coupled to an electrical subsystem 14 having multiple transceiver
channels that interface with a micro-electromechanical system
(MEMS) transducer, each including a transmitter and a readout
circuit. By way of example the embodiment shown utilizes ten
transceiver channels 20. Echoes from off-axis targets arrive with
different phase shifts for each element in the array. The off-chip
digital beam former realigns the signal phase to maximize the SNR
and determine target location.
[0029] Electromechanical subsystem 12 is shown coupled to
electrical subsystem 14 through a series of switches 16, 18.
Multiple channel circuits 20 are shown with channel circuit 22
visible in the figure. The switches are configured to connect each
of the multiple electromechanical actuators (transducers) 24 in the
electromechanical subsystem to a transmitter circuit 32 or to a
receiver circuit 38 within each of the multiple channel circuits
20, such as channel circuit 22.
[0030] During a measurement, switch 18 is initially in transmit
(Tx) position 34, allowing the electrical subsystem to actuate one
or more transducers 24 to transmit an acoustic pulse, after which
switch 18 is switched to receive (Rx) position 36 to then monitor
the response of transducer 24 via receive amplifier 38. Optionally,
it can receive any echoes that return, and calculate the
time-of-flight of those echoes.
[0031] On the transmit side is shown a transmit pulse generator 26
coupled to each channel 22 of multiple channels 20. A phase input
28a and a frequency input 28b are used to configure the frequency
and phase of pulse generator 26, which outputs transmit pulses 30
to a driver 32 to a transmit connection of switch 34 coupled to
transducer 24. It should be appreciated that in at least one
embodiment, pulse generator 26 or clock circuitry 62, is configured
to include a modulator which receives at least one signal that is
encoded into the transmission using a form of amplitude modulation,
or phase modulation, or a combination of amplitude and phase
modulation.
[0032] Switch 16 controls a direct current (DC) voltage source
connection to electromechanical transducers 24, seen in this
example for selecting between 16 volts during the transmit period
and 0.9 volts during the receive period. In this example, the
transmitter driver 32 operates at 32V P-P centered on the 16V
supply (bias) voltage. In receiving mode, however, signal
amplitudes are significantly lower, and switch 16 sets the DC
voltage on transducers 24 to half the supply voltage of receive
amplifier 38 (e.g., 0.9V).
[0033] On the receive side, when switch 18 is in the receive
position 36, then signals from sensor 24 (transducer 24 operated in
its sensor mode) are coupled to an analog interface circuit 38,
such as comprising an analog amplifier (e.g., a transconductance
amplifier). After amplifying the analog signal from the sensor, it
is preferably filtered 40, using, for example, a fourth order
bandpass switched-capacitor filter, shown receiving a switching
clock f.sub.s 41, for example where f.sub.s=16 f.sub.o, and where
f.sub.o is the resonant frequency of the transducer. After
filtering the analog signal it is converted, for instance, by a
comparator 42, to digital signal 45. It will be noted that this
digital signal is fed back 44 (in a feedback arrangement) to filter
40. A complex demodulator 46 receives digital signal 45, along with
clock signals 48 at f.sub.o (phase-shifted by 0.degree. and
90.degree.), and outputs separate digital signals 52a, 52b, for
in-phase (I) and quadrature (Q), that are preferably filtered 50a,
50b, utilizing known digital filtering techniques, and output to a
digital beam-former 54. Output 56 from the digital beam-former 54
provides depth image from which target tracking 58 is performed to
output a target location 60.
[0034] A frequency adjustment circuit 62 is shown for performing
frequency tuning to maintain a frequency match between the
electromechanical and electrical subsystems. In the example shown,
the matching is arrived at by altering the transmitter pulse
generation frequency to match that of the resonant mechanical
subsystem. Digital I and Q outputs 52a, 52b, are received by a ring
down auto tuning circuit 64, whose output is subject to slope
detection (up/down) 66, which controls a clock divider 68, which
receives a reference clock 70 f.sub.ref, and outputs clock rate
f.sub.o. It should be appreciated, however, that frequency
generation according to the present disclosure is not limited to
utilizing a clock-divider configuration, as it will be recognized
that other methods can be similarly utilized (e.g., phase-locked
loop), which are controllable in response to receiving auto tuning
signals described herein. Additional details about the functioning
of these elements is described through the following sections.
[0035] Settling behavior during ring down was utilized for
determining the extent of frequency mismatch between the electrical
and mechanical systems. In the above example, this mismatch was
corrected by adjusting the clock frequency utilized in transmitter
pulse generation. It should also be appreciated that this mismatch
can be corrected via adjustments to the mechanical subsystem. In
this embodiment, the resonant frequency of the electromechanical
transducer is thus changed in response to receipt of a control
signal (e.g., voltage). First, it will be recognized that different
bias voltages applied across a piezoelectric material result in
changing the stress across the material and thus its resonant
frequency (by some small amount). In another embodiment, a
resistive heating element on the electromechanical transducer would
allow the temperature of the transducer to be varied, thereby
varying the frequency of the transducer. In addition, it will be
recognized that so called "smart materials" may be utilized in the
transducer (making the transducer of smart material, or
mechanically coupling a smart material to the transducer) to allow
making slight adjustments to resonant frequency. Smart materials
are designed materials that have one or more properties, stiffness
being one of these properties, that can be changed in a controlled
manner by an external stimulus, such as stress, temperature,
moisture, pH, electrical voltage, electrical current or magnetic
fields. One of ordinary skill in the art will also appreciate that
many different forms of MEMS actuators (e.g., comb-drives, parallel
plate capacitive drives) can be coupled to the transducer for
changing the mechanical stiffness and therefore resonance frequency
of the electromechanical resonator. For example using a voltage to
pull in a stiffening arm (or layer) against the transducer, or
changing the extent to which interlocked comb fingers extend across
a surface of the transducer. Thus, it will be seen that there are
two mechanisms for achieving this locking between the frequencies
of the mechanical and electrical subsystems.
[0036] FIG. 1B illustrates a portion of an ultrasonic chip
according to the presented disclosure. A readout integrated circuit
(IC) was fabricated in a 0.18 .mu.m CMOS process with 32V
transistors. To provide a 1 m maximum range, the system embodiment
presented herein required 13.6 .mu.J per measurement. At 30 fps,
the receive power consumption was 335 .mu.W and the transmit power
consumption at 66 .mu.W. The amount of energy consumption scaled
roughly linearly with maximum range. For a maximum range of 0.3 m,
the energy per frame was reduced to less than 0.5 .mu.J per channel
per frame. Single-element range measurements could be performed
with the apparatus at 10 fps using only 5 .mu.W.
[0037] FIG. 1C depicts measured amplitude values for in-phase (I)
and quadrature (Q) signals with respect to time as output by the
digital beam former.
[0038] FIG. 1D illustrates a single pulse measurement using a 2D
electromechanical transducer array according to at least one
embodiment of the apparatus. In this test, a target individual held
up their hands below head height at different positions and depths.
The graph shows how these were discerned as to position and depth
for head (H), right hand (R.H.) and left hand (L.H.).
[0039] FIG. 2 illustrates example waveforms 90 generally depicting
three phases of the described apparatus showing a transmit cycle
92, auto-tuning cycle 94, and receive cycle 96. During a first
phase 92, a transmitter signal 98 shown with bottom electrode
voltage 100, drives a transducer with a harmonic signal having a
frequency of f.sub.TX. It will be appreciated that by way of
example and not limitation, the time durations of these cycles were
set for 140, 140, and 5.5 .mu.s. During the transmit phase, the
velocity in the transducer builds up 102 and an acoustic pulse is
emitted. At the end of transmit phase 92 energy remains stored in
the transducer as it resonates. This energy rings down, seen as
ring down signal 102', at the natural frequency of the transducer
f.sub.o. This ring down arises in a phase utilized for performing
an auto-tuning cycle 94, the transmit switch is opened and the
receive switch is closed, and the receive electronics are enabled
and used to convert the transducer ring down signal to a digital
representation, utilized for adjusting transmit frequency. The
receive electronics may contain a narrowband analog filter which is
tunable, and which is tuned to f.sub.TX prior to the start of a
measurement cycle. This narrowband filter could be constructed
using switched capacitor (SC) or continuous time (CT) techniques.
The analog filter may have a tunable bandwidth.
[0040] Following the analog-to-digital conversion, the digital
signal is complex demodulated in a phase sensitive fashion, and the
in-phase (I) and quadrature (Q) signals are digitally filtered
separately. The digital filters may have tunable bandwidths. The I
and Q signals are converted into magnitude and phase signals. A
non-zero slope (f.sub.o-f.sub.TX) 104 of the phase signal indicates
a frequency mismatch between f.sub.TX and f.sub.o. The slope of the
line can be measured by averaging the difference of the phase
signal between several samples. The resulting phase slope is the
frequency offset between the transmit frequency f.sub.TX and the
resonant frequency f.sub.o. It is used to update f.sub.TX prior to
the next measurement cycle.
[0041] In at least one embodiment, a deadband controller is
utilized for this updating. In the deadband controller the sign of
the frequency error is measured, and the frequency is updated by a
fixed step .DELTA.f in the direction that minimizes the error,
unless the frequency error is less than a certain tolerance, in
which case f.sub.TX is not updated.
[0042] Additionally, the magnitude signal may be used to estimate
the time constant and therefore the bandwidth of the transducer.
The exponential decay of the magnitude of the ring down response
has a characteristic time constant .tau., and the response is given
by:
s(t)=s.sub.ie.sup.-t/.tau.,
where s(t) is the magnitude signal with respect to time, s.sub.i is
the initial magnitude of the ring down response, and where the
harmonic response due to mismatch between f.sub.TX and f.sub.o is
neglected. The value .tau. can be measured by storing the magnitude
s1 shortly after the auto-tuning cycle begins, and then measuring
the time until the magnitude reaches a certain fraction of its
initial value s2. The time constant is then given by
.tau. = t meas ln ( s 1 s 2 ) . ##EQU00001##
Alternatively, the magnitude signal may be measured after a fixed
time delay, and the ratio of the second magnitude measurement to
the first can be used to determine the time constant.
[0043] The measured time constant of the transducer can be used to
adjust the bandwidth of the passband of the analog filter and/or
the digital filter described herein.
[0044] Following the auto-tuning phase, the optional receive cycle
96 proceeds. During this cycle the receive electronics convert
received echoes to digital signals. The figure shows different time
of flight (TOF) values for channels 1-3, as waveforms 106, 108,
110. By way of example and not limitation, the same receive
electronics utilized for processing the ring down signal can be
utilized to process received echo signals.
[0045] In at least one embodiment, the receive electronics contain
a narrowband tunable analog filter 40 (FIG. 1A), which is tuned to
f.sub.TX prior to the start of a measurement cycle. By way of
example, this narrowband filter can be implemented using
switched-capacitor (SC) techniques or continuous-time (CT)
techniques, as will be known to those of ordinary skill in the art.
In at least one embodiment of the apparatus, the analog filter is
configured with a tunable bandwidth.
[0046] Following the analog-to-digital conversion, the digital
signal is complex demodulated 46 (FIG. 1) in a phase sensitive
fashion, and the in-phase (I) and quadrature (Q) signals are
digitally filtered 50a, 50b, separately. In at least one
embodiment, the digital filters are configured with tunable
bandwidths.
[0047] In at least one embodiment, the received echo signals are
monitored for frequency shifts between the received signal
frequency f.sub.RX and f.sub.TX, manifested as non-zero slope of
phase signals during a received echo, using the techniques
described herein. In at least one embodiment, the frequency shift
f.sub.RX-f.sub.TX is utilized for determining the relative axial
velocity between the transducers and the target position. This
frequency shift arises from the Doppler effect.
[0048] It will be appreciated that there are three general modes of
operation: transmit, auto-tuning (during ring down), and then
receive. After transmitting a series of pulses from the transducer,
the auto-tuning phase is entered. During auto-tuning, the receive
switch is turned on, along with a ring down switch and the
electrical system receives and processes the ring down signal. This
ring down signal from the transducer arises from the fact that
after transmitting, there is energy stored in the transducer, and
that energy rings down at a frequency equal to f.sub.o. After
auto-tuning, the ring down switch is deactivated, thus decoupling
the ring down circuit, and the system enters a measurement phase
(optional), in which acoustic echoes are registered on the
transducer (or transducers) and processed. It should be appreciated
that these received pulses are ancillary to the auto-tuning
operation, for in certain applications the auto-tuning of the
present disclosure tunes the electronics to the transmitter even if
the electrical subsystem does not receive acoustic echoes to be
processed.
[0049] In the example embodiment described, the electromechanical
transducers/sensors comprises an ultrasonic transducer/sensor, such
as a piezoelectric micromachined ultrasound transducers (pMUTs)
having a 450 .mu.m diameter with 2.2 .mu.m thick AlN/Mo/AlN/Al
stack deposited on a Si wafer and released with a back-side
through-wafer etch. The bottom electrode is continuous, while each
pMUT has a top electrode lithographically defined to actuate the
trampoline mode. Each pMUT can transmit and receive sound waves,
and is operated at its resonance of 217 kHz.+-.2 kHz with a
bandwidth of 12 kHz. The impedance of the transducers is dominated
by the 10 pF transducer capacitance, and the motional resistance at
resonance is .about.2.4 M.OMEGA.. The resonant frequencies of the
pMUTs vary due to fabrication, temperature, and packaging stress,
so online frequency tracking is used to maintain maximum SNR during
operation.
[0050] In one configuration two pMUTs are utilized for transmission
and seven pMUTs for reception. The receive array is 3.5 wavelengths
wide in the x-angle axis, allowing targets separated by more than
15.degree. to be distinguished. In the y-angle axis the array is
only 0.16 wavelengths wide, sufficient to determine the y-angle to
the target by measuring the average phase difference along the y
axis of the array. The center element of the receive array and the
element 900 .mu.m above it are used to launch a 138
.mu.sec.apprxeq.24 mm long pulse of sound into the environment. The
transmit configuration illuminates a wide field of view, permitting
the capture of an entire scene in a single measurement.
Applications requiring improved target resolution or increased
maximum range can also use transmit beamforming at the expense of
reduced measurement rate.
[0051] FIG. 3A illustrates an example embodiment 130 of a single
channel of switched-capacitor (SC) resonator with a continuous-time
(CT) anti-aliasing (AA) filter. An electromechanical subsystem 138
is shown with a transducer 140. A S.sub.TX signal 132 is
voltage-shifted using high voltage level shifters 134 (e.g., 32V)
through transmit switch 136a, in combination with a bias voltage
(16V) through switch 136b, to drive transducer 140 in a transmit
mode. It will be noted that setting the bottom electrode of the
transducer to 16V permits bi-polar actuation of the transducer,
when excited by a 32 V.sub.pp square wave. In the example, such as
seen by waveform 98 in FIG. 2, transmission is performed for 30
cycles at the transmit frequency f.sub.TX which is locked to 1/16th
of the sampling frequency f.sub.s.
[0052] At the end of the transmit phase, the mechanical energy
stored in the inertia of the pMUT dissipates through a ring down
path 144, 146 (e.g., switch and load), as the pMUT rings down at
its natural frequency. Thus, after cessation of the transmission
phase, then S.sub.TX switches 136a, 136b are deactivated (opened),
and S.sub.RX receiver isolation switches 142a, 142b are activated
(closed), along with an S.sub.ring switch 144 which is activated to
ring down the transducer in response to current flow through a load
(e.g., resistor) 146. It should be noted that in the embodiment of
FIG. 3A, S.sub.RX receiver isolation switches 142a, 142b can be
activated even when S.sub.TX switches 136a, 136b are still active.
During ring down and later during measurement of received echoes,
current from sensor 140 is amplified through a front end inverting
OTA amplifier 148, providing output signal 150 to an anti-aliasing
circuit 151, coupled to a second resonator 156, then a digitizing
circuit 158 by the receiver normally, to output d.sub.out 160.
During ring down, the ring down signal is I/Q demodulated with
f.sub.TX. The slope of the phase signal during the ring down
indicates the frequency offset and is used to update f.sub.s and
f.sub.TX used in the next measurement.
[0053] The following describes amplifier 148 subsequent circuits in
greater detail. The front-end current from operational
transconductance amplifier (OTA) 148 is integrated onto the
integrating capacitor 152b of a second stage having amplifier 154,
which also makes up an integrator in the first of two
switched-capacitor resonators. Although the second stage is a
switched capacitor integrator, the front-end current is processed
in a continuous time (CT) manner before it is sampled at the output
of the second integrator. As a result, the second integrator acts
as an anti-aliasing filter for the wideband noise generated by the
front-end and prevents this dominant noise source from being
aliased into the band of interest. The signal then passes through a
second switched capacitor resonator 156 and is quantized, as
exemplified by a comparator 158, and output as digital output
signal d.sub.out 160.
[0054] The CT AA circuit is shown in the figure receiving feedback
as the inverse of d.sub.out 160 through series switch 162,
capacitor 166, and switch 170. On either side of capacitor 166 are
switches 164, 168 coupled to a DC supply. It will be seen that
switches 162, 170 are controlled by a phase 1 (.PHI.1) control
signal, with switches 164, 168, controlled by a phase 2 (.PHI.2)
control signal. The signal through these switches is received at
input 172 at a first stage amplifier circuit 176, having an
integrating capacitor 174. Output from this first stage is coupled
through a similar switching arrangement as prior to the first
amplifier, having series switches 180, 188, on either side of
capacitor 184, and switches 182, 186 coupled to a DC supply
voltage. Output through this second switching arrangement is
received at the second stage amplifier 154, having integrating
capacitor 152b. The inverse of d.sub.out 160 received through
switch 178 through capacitor 152a is also applied to the positive
input of amplifier 154. A series capacitor 190 is seen coupled
between inverting output of amplifier 154 to positive input of
amplifier 176 through switch 194, controlled by phase 2 (.PHI.2)
signal, while a phase 1 (.PHI.1) switch 192 is coupled to a DC
supply. Although this implementation of CT AA filter is briefly
described above, it should be appreciated that the A/D conversion
mechanism can be achieved by various other circuits known to one of
ordinary skill in the art.
[0055] The high in-band gain provided by the 4th order bandpass
filter shapes the wideband quantization noise to be separated away
from the signal at f.sub.TX. In particular, the SC resonators are
configured to resonate at 1/16 of the sampling frequency f.sub.s
which is locked to the resonance of the transducer by the ring down
auto tuning circuit. This centers the .DELTA..SIGMA. bandpass noise
notch on the signal at f.sub.TX.
[0056] The output of each .DELTA..SIGMA.ADC is I/Q demodulated,
filtered, and down-sampled off-chip, such as depicted in FIG. 1A
with a digital beam former processing the received signals to
maximize the receive SNR and determine the x-angle location of the
target. This process can be repeated in the orthogonal angle axis
to implement 3D beamforming.
[0057] It should be noted that thermal noise in the front-end
amplifier and the thermal motion of air, constrain the minimum
detectable echo. The input referred noise of the amplifier is 11
nV/rt-Hz, and the noise voltage of the transducer is 6 nV/rt-Hz at
resonance.
[0058] FIG. 3B illustrates an example circuit for the front end
amplifier 148, shown by way of example and not limitation. The
front-end amplifier consists of an open-loop current-reuse
operational transconductance amplifier (OTA) with both NMOS and
PMOS differential pairs biased near subthreshold for current
efficiency. From a first supply voltage 210 is seen coupled
differentially-driven insulated gate FET transistors (e.g., PMOS)
212a, 212b, whose gates are driven respectively from differential
output voltages V.sub.O-, V.sub.O+, whose combined current passes
through a biasing stage with PMOS transistor 214 driven by a gate
voltage V.sub.bp. Another differential stage follows, followed by a
combined bias current leg. In the differential stage, complementary
transistors 216a, 216b (NMOS in series with PMOS) are in a first
current leg which are driven at their gates by input voltage
V.sub.I+, and a second current leg with transistors 216c, 216d,
driven at their gates by input voltage V.sub.I-. Sources on
transistors 216a, 216b are coupled together as output V.sub.O-,
with sources on transistors 216c, 216d coupled together as output
V.sub.O+. The final combined bias current leg is shown with a NMOS
transistor 218 whose gate is driven by bias voltage V.sub.bn with
its drain coupled to a second supply 212. It should be appreciated
that amplifier 148 may be implemented in many different ways, as
will be recognized by one of ordinary skill in the art, without
departing from the teachings of the present disclosure.
[0059] FIG. 3C depicts signal timing associated with FIG. 3A,
showing transmit activation signal .theta..sub.TX, ring switch
signal .theta..sub.ring, receive activation signal .theta..sub.RX,
and measured acoustic wave voltage signal v.sub.m. The transmitter
is enabled by activating .theta..sub.TX, and then switched off,
followed by a ring down activation .theta..sub.ring. After 86
.mu.sec, the ring down signal has decayed sufficiently for the
S.sub.ring switch to be opened by deactivating .theta..sub.ring.
Processing of ring down signals as well as the received echoes is
performed with switches .theta..sub.RX activated. In the receive
phase, the front-end measures a voltage which is proportional to
the displacement of the transducer's membrane that occurs due to
acoustic pressure incident on the membrane.
[0060] FIG. 4 depicts offset measured by the frequency auto tuning
loop as it is enabled (Tuning Enabled). An initial 57 kHz offset
frequency is nulled to 1 kHz within 30 measurement cycles after
auto tuning has been activated, illustrating a significant benefit
from the frequency tuning and tracking according to the present
disclosure.
[0061] The enhancements described in the presented technology can
be readily implemented utilizing the described analog
transmit/receive circuitry in combination with digital processing
of I and Q signals during digital beam forming. One of ordinary
skill in the art will recognize that the timing waveforms (e.g.,
exemplified in FIG. 2 and FIG. 3C) can be implemented with known
digital techniques, including clock circuits, logic circuits,
sequential circuits, programmable arrays, computer processing
circuits, and combinations thereof without limitation. It should
also be appreciated that computer processing circuits are
preferably implemented to include one or more computer processor
devices (e.g., CPU, microprocessor, microcontroller, computer
enabled ASIC, etc.) and associated memory (e.g., RAM, DRAM, NVRAM,
FLASH, computer readable media, etc.) whereby programming stored in
the memory and executable on the processor perform steps of the
digital beam forming process, and/or the control of circuit switch
states and other operations as described herein. The computer and
memory devices were not depicted in the diagrams for the sake of
simplicity of illustration. The presented technology is
non-limiting with regard to memory and computer-readable media,
insofar as these are non-transitory, and thus not constituting a
transitory electronic signal. It will also be appreciated that the
computer readable media (memory) in the system is "non-transitory",
which comprises any and all forms of computer-readable media, with
the sole exception being a transitory, propagating signal.
Accordingly, the disclosed technology may comprise any form of
computer-readable media, including those which are random access
(e.g., RAM), require periodic refreshing (e.g., DRAM), those that
degrade over time (e.g., EEPROMS, disk media), or that store data
for only short periods of time and/or only in the presence of
power, with the only limitation being that the term "computer
readable media" is not applicable to an electronic signal which is
transitory.
[0062] Embodiments of the present technology may be described with
reference to flowchart or timing diagram illustrations of methods
and systems according to embodiments of the technology, and/or
algorithms, formulae, or other computational depictions, which may
also be implemented as computer program products. In this regard,
each block or step of a flowchart, and combinations of blocks
(and/or steps) in a flowchart, algorithm, formula, or computational
depiction can be implemented by various means, such as hardware,
firmware, and/or software including one or more computer program
instructions embodied in computer-readable program code logic. As
will be appreciated, any such computer program instructions may be
loaded onto a computer, including without limitation a general
purpose computer or special purpose computer, or other programmable
processing apparatus to produce a machine, such that the computer
program instructions which execute on the computer or other
programmable processing apparatus create means for implementing the
functions specified in the block(s) of the flowchart(s).
[0063] Accordingly, blocks of the flowcharts, algorithms, formulae,
or computational depictions support combinations of means for
performing the specified functions, combinations of steps for
performing the specified functions, and computer program
instructions, such as embodied in computer-readable program code
logic means, for performing the specified functions. It will also
be understood that each block of the flowchart illustrations,
algorithms, formulae, or computational depictions and combinations
thereof described herein, can be implemented by special purpose
hardware-based computer systems which perform the specified
functions or steps, or combinations of special purpose hardware and
computer-readable program code logic means.
[0064] Furthermore, these computer program instructions, such as
embodied in computer-readable program code logic, may also be
stored in a computer-readable memory that can direct a computer or
other programmable processing apparatus to function in a particular
manner, such that the instructions stored in the computer-readable
memory produce an article of manufacture including instruction
means which implement the function specified in the block(s) of the
flowchart(s). The computer program instructions may also be loaded
onto a computer or other programmable processing apparatus to cause
a series of operational steps to be performed on the computer or
other programmable processing apparatus to produce a
computer-implemented process such that the instructions which
execute on the computer or other programmable processing apparatus
provide steps for implementing the functions specified in the
block(s) of the flowchart(s), algorithm(s), formula(e), or
computational depiction(s).
[0065] It will further be appreciated that "programming" as used
herein refers to one or more instructions that can be executed by a
processor to perform a function as described herein. The
programming can be embodied in software, in firmware, or in a
combination of software and firmware. The programming can be stored
local to the device in non-transitory media, or can be stored
remotely such as on a server, or all or a portion of the
programming can be stored locally and remotely. Programming stored
remotely can be downloaded (pushed) to the device by user
initiation, or automatically based on one or more factors. It will
further be appreciated that as used herein, that the terms
processor, central processing unit (CPU), and computer are used
synonymously to denote a device capable of executing the
programming and communication with input/output interfaces and/or
peripheral devices.
[0066] From the description herein, it will be appreciated that
that the present disclosure encompasses multiple embodiments which
include, but are not limited to, the following:
[0067] 1. An apparatus for locking an electrical system to a
resonant mechanical system, the apparatus comprising: an
electromechanical transducer, of a resonant mechanical subsystem,
configured for operation in a transmission mode for generating
acoustic pulses; and an electrical subsystem having a transmitter
circuit coupled to said electromechanical transducer, in which
acoustic pulses are generated from said electromechanical
transducer in response to receipt of an electrical signal at an
electronic transmission frequency from said electrical subsystem;
wherein said electrical subsystem is configured to determine
operating frequency of the resonant mechanical subsystem from a
resonance settling response of the electromechanical transducer
when not being driven in its transmission mode; and wherein the
electrical subsystem is configured to lock transmitting frequency
of said electrical subsystem to that of said resonant mechanical
subsystem by either (a) tuning operating frequency of said
electrical subsystem to match that of said resonant mechanical
subsystem or (b) tuning operating frequency of said resonant
mechanical subsystem to match that of said electrical
subsystem.
[0068] 2. The apparatus of any preceding embodiment, wherein
frequency difference between the electromechanical resonance
settling response and electronic transmission frequency is used to
determine required adjustment to said transmission frequency to
make these two frequencies match.
[0069] 3. The apparatus of any preceding embodiment, wherein a
phase difference between the electromechanical resonance settling
response and electronic transmission frequency is used to determine
required adjustment to said transmission frequency to make these
two frequencies match.
[0070] 4. The apparatus of any preceding embodiment, wherein a
decay time constant of said electromechanical resonance settling
response is estimated by measuring amplitude of said
electromechanical resonance settling response at two or more points
in time.
[0071] 5. The apparatus of any preceding embodiment, wherein said
settling response for said resonant electromechanical subsystem is
determined in response to utilizing in-phase (I) and quadrature (Q)
signals within an auto tuning circuit configured to adjust
transmission frequency.
[0072] 6. The apparatus of any preceding embodiment, further
comprising a ring down circuit selectively coupled to said
electromechanical transducer so that said ring down circuit
attenuates resonance energy on said resonant mechanical subsystem
when determining the operating frequency of said resonant
mechanical subsystem from a resonance settling response.
[0073] 7. The apparatus of any preceding embodiment, wherein said
electromechanical transducer comprises at least one ultrasonic
transducer.
[0074] 8. The apparatus of any preceding embodiment, wherein said
electromechanical transducer comprises at least one piezoelectric
transducer.
[0075] 9. The apparatus of any preceding embodiment, wherein said
electromechanical transducer comprises at least one capacitive
transducer.
[0076] 10. The apparatus of any preceding embodiment, wherein said
electromechanical transducer has a narrowband resonance, with a
maximum transmit and receive sensitivity at resonant frequency of
said electromechanical transducer.
[0077] 11. The apparatus of any preceding embodiment, wherein the
transmitted acoustic pulses are a harmonic signal with a center
frequency equal to resonant frequency of said electromechanical
transducer.
[0078] 12. The apparatus of any preceding embodiment, wherein said
resonance settling response is determined by processing a signal
from said electromechanical transducer by an amplifier, followed by
digitization circuitry whose output is utilized in a ring down auto
tuning circuit for controlling frequency output for driving said
transmitter circuit.
[0079] 13. The apparatus of any preceding embodiment, further
comprising an electrical filter on an output of said amplifier,
said filter configured with a center frequency equal to that of
said electromechanical transducer.
[0080] 14. The apparatus of any preceding embodiment, wherein said
electrical filter comprises a multiple-order filter.
[0081] 15. The apparatus of any preceding embodiment, wherein said
electrical filter comprises a fourth-order switched-capacitor
filter.
[0082] 16. The apparatus of any preceding embodiment, further
comprising a complex demodulator configured for receiving output
from said electrical filter, which has been digitized, along with
receiving phase signals at transmission frequency, and outputting
in-phase (I) and quadrature (Q) signals.
[0083] 17. The apparatus of any preceding embodiment, wherein said
in-phase (I) and quadrature (Q) signals are digitally filtered
prior to receipt within an auto tuning circuit configured to adjust
transmission frequency.
[0084] 18. The apparatus of any preceding embodiment, wherein a
switching circuit selects between transmission mode or receiving
mode for said electromechanical transducer.
[0085] 19. The apparatus of any preceding embodiment, further
comprising a modulator configured for receiving at least one
electrical signal that is encoded for transmission using a form of
amplitude modulation, or phase modulation, or a combination of
amplitude and phase modulation through said transmitter
circuit.
[0086] 20. An apparatus for frequency locking between an electrical
system and a resonant mechanical system, the apparatus comprising:
an electromechanical transducer, of a resonant mechanical
subsystem, configured for operation in a transmission mode for
generating acoustic pulses; an electrical subsystem having a
transmitter circuit coupled to said electromechanical transducer,
wherein acoustic pulses are generated from said electromechanical
transducer in response to receipt of an electrical signal at an
electronic transmission frequency from said electrical subsystem;
and a ring down circuit selectively coupled to said
electromechanical transducer for attenuating its resonance energy
when said electromechanical transducer is not operating in its
transmission mode; wherein said electrical subsystem is configured
to determine operating frequency of the resonant mechanical
subsystem from a resonance settling response of the
electromechanical transducer when it's not being driven in its
transmission mode; and wherein the electrical subsystem is
configured to lock transmitting frequency of said electrical
subsystem to that of said resonant mechanical subsystem by either
(a) tuning operating frequency of said electrical subsystem to
match that of said resonant mechanical subsystem or (b) tuning
operating frequency of said resonant mechanical subsystem to match
that of said electrical subsystem.
[0087] 21. The apparatus of any preceding embodiment, wherein
frequency difference between the electromechanical resonance
settling response and electronic transmission frequency is used to
determine required adjustment to said transmission frequency to
make these two frequencies match.
[0088] 22. The apparatus of any preceding embodiment, wherein a
phase difference between the electromechanical resonance settling
response and electronic transmission frequency is used to determine
required adjustment to said transmission frequency to make these
two frequencies match.
[0089] 23. The apparatus of any preceding embodiment, wherein a
decay time constant of said electromechanical resonance settling
response is estimated by measuring amplitude of said
electromechanical resonance settling response at two or more points
in time.
[0090] 24. The apparatus of any preceding embodiment, wherein said
settling response for said resonant electromechanical subsystem is
determined in response to utilizing in-phase (I) and quadrature (Q)
signals within an auto tuning circuit configured to adjust
transmission frequency.
[0091] 25. The apparatus of any preceding embodiment, wherein said
electromechanical transducer comprises at least one ultrasonic
transducer.
[0092] 26. The apparatus of any preceding embodiment, wherein said
electromechanical transducer comprises at least one piezoelectric
transducer.
[0093] 27. The apparatus of any preceding embodiment, wherein said
electromechanical transducer comprises at least one capacitive
transducer.
[0094] 28. The apparatus of any preceding embodiment, wherein said
resonance settling response is determined by processing a signal
from said electromechanical transducer by an amplifier, followed by
digitization circuitry whose output is utilized in a ring down auto
tuning circuit for controlling frequency output for driving said
transmitter circuit.
[0095] 29. The apparatus of any preceding embodiment, further
comprising an electrical filter on an output of said amplifier,
said filter configured with a center frequency equal to that of
said electromechanical transducer.
[0096] 30. The apparatus of any preceding embodiment, wherein said
electrical filter comprises a multiple-order filter
switched-capacitor filter.
[0097] 31. The apparatus of any preceding embodiment, further
comprising a complex demodulator configured for receiving output
from said electrical filter, which has been digitized, along with
receiving phase signals at transmission frequency, and outputting
in-phase (I) and quadrature (Q) signals.
[0098] 32. The apparatus of any preceding embodiment, wherein said
in-phase (I) and quadrature (Q) signals are digitally filtered
prior to receipt within an auto tuning circuit configured to adjust
transmission frequency.
[0099] 33. The apparatus of any preceding embodiment, further
comprising a modulator configured for receiving at least one
electrical signal that is encoded for transmission using a form of
amplitude modulation, or phase modulation, or a combination of
amplitude and phase modulation through said transmitter
circuit.
[0100] 34. The apparatus of any preceding embodiment, further
comprising utilizing said electromechanical transducer in a
receiving mode, and processing echoes of acoustic pulses to
determined time of flight.
[0101] 35. A method for locking an electrical system to a
mechanical transducer system, comprising: generating acoustic
pulses from an electromechanical transducer within a mechanical
transducer subsystem in response to receiving a transmit signal
from a transmitter in an electrical subsystem; registering settling
behavior of said mechanical transducer subsystem, when said
transmit signal goes inactive and is thus no longer driving an
output from said electromechanical transducer; determining
operating frequency of said mechanical transducer subsystem from
the settling behavior of said electromechanical transducer; and
locking the electrical subsystem to the mechanical transducer
subsystem by either (a) tuning operating frequency of said
electrical subsystem to match that of said mechanical transducer
subsystem or (b) tuning operating frequency of said mechanical
transducer system to match that of said electrical subsystem.
[0102] Although the description herein contains many details, these
should not be construed as limiting the scope of the disclosure but
as merely providing illustrations of some of the presently
preferred embodiments. Therefore, it will be appreciated that the
scope of the disclosure fully encompasses other embodiments which
may become obvious to those skilled in the art.
[0103] In the claims, reference to an element in the singular is
not intended to mean "one and only one" unless explicitly so
stated, but rather "one or more." All structural and functional
equivalents to the elements of the disclosed embodiments that are
known to those of ordinary skill in the art are expressly
incorporated herein by reference and are intended to be encompassed
by the present claims. Furthermore, no element, component, or
method step in the present disclosure is intended to be dedicated
to the public regardless of whether the element, component, or
method step is explicitly recited in the claims. No claim element
herein is to be construed as a "means plus function" element unless
the element is expressly recited using the phrase "means for". No
claim element herein is to be construed as a "step plus function"
element unless the element is expressly recited using the phrase
"step for".
* * * * *