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The Carbon Nanotube Thermophone: A Near-Weightless Audio Driver With No Moving Parts
Michigan Technological University
Dr. Andrew R. Barnard, INCE Bd. Cert.
Mahsa Asgarisabet
Troy Bouman
The Carbon Nanotube Thermophone: A Near-Weightless Audio Driver With No Moving Parts
Presenters:
Dr. Andrew R. Barnard, INCE Bd. Cert.
Mahsa Asgarisabet
Troy Bouman
Michigan Technological University
Introduction to our Team
Ph.D. Students: Mahsa Asgarisabet (left) and Troy Bouman (right)
Dr. Andrew BarnardAssistant Professor
Mechanical EngineeringMichigan Tech
Undergraduate Researcher:
Stephania Vaglica
*CNT forests provided by Univ. of Cincinnati, NanoWorld Labs
OverviewPart 1: Introduction to Carbon Nano Tube (CNT) Thermophones
• Thermophones and Thermoacoustic Effect• Carbon Nanotube Sheet• Advantages And Disadvantages• Applications• Ongoing Research & The Path Forward
Part 2: Surface Velocity
• Methodology ; Near-Field Acoustic Holography• Surface Velocity Distribution• SPL, Intensity, Directivity
Part 3: Power Efficiency of CNT Speakers
• Test Methodology• Power Efficiency• Total Harmonic Distortion
Part 1
Introduction to Carbon Nanotube (CNT)
Thermophones
Andrew R. Barnard, Ph.D., INCE Bd. Cert.
Live Demo of the CNT Thermophone
The thermophone concept, originating with Braun in 1898 [1], was shown in theory and practice by Arnold and Crandall in 1917 [2,3].
2o in
K s
f WP
T rCα ρπ
= Materials with ultra-low HCPUA didn’t exist in 1917, making the
thermophone impractical.
Tmax
Tmin
700 nm Pt Foil
A thermophone produces sound without vibration
HCPUA – Heat Capacity per Unit Area
Thermophone History
The Thermoacoustic Effect
Thermoacoustics is the interaction between temperature, density and pressure variations causing acoustic waves
How does CNT thin film loud speaker work via thermoacoustic Effect?
Alternating current passes through a thin conductor
Periodic heating takes place in the conductor
Oscillating nearfield temperature produces pressure waves which arepropagated into the surrounding medium
Temperature
Time
In 2008, researchers resurrected the thermophone concept but with ultra-low HCPUA carbon nanotube thin-films thus
making it practical [4]!
22 2
1 2 1
2 ( )1
o in
K a s
ff W fP
T T rC f f ff f f
α ρπ
=+
+ + +
Correction term for low HCPUA materials
Thermophone History: Ultra-Low HCPUA Materials
20
1 2f αβπκ
= 02
s
fCβπ
=02
ina
WTaβ
=o PCκα
ρ=
Advantages and Disadvantages
Advantages• Ultralight Weight• Transparent (Optical and Acoustical)• Flexible, Stretchable (Building in
Different Size and Shape easily)• Magnet-free(No need to rare-earth
materials)• Lower cost of building
Disadvantages• Fragile • Low efficiency• Heat• Non-Linear (Doubling of
frequency)
To produce an appreciable amplitude of pressure waves:
The conductor be very thinThe Heat capacity of conductor must be small
The conductor must be able to conduct at once to its surface the heatproduced in its interior, in order to follow the temperature changesproduced by a rapidly varying current
Heat Capacity Per Unit Area
The pressure produced by CNT loud speaker in the
open medium
CNT films have all of these features
Sound Pressure Level (SPL)
The Buckingham-Pi theorem can be used to evaluate the complex sound pressure equation in terms of 5 non-
dimensional variables.
( ) ( )1
2 2 21
5 3 1 2 4 1 22 3
12 1
π π−
Π Π = Π + Π Π + Π + Π Π Π + Π
( )3
1 2o K
in
T faW
κρΠ =
2 2P KC Tf a
Π =
03
K
in
T aWβ
Π =
4s K
in
C fT aW
Π =
5m
in in
P fa PrfaW W
Π = =
Thermal Conductivity and Density of Gas
Specific Heat of Gas
Rate of heat dissipation per unit area per unit temperature rise above ambient (β0)
Heat capacity per unit area of film
Sound pressure
Non-Dimensional Analysis
* Work done by Dr. Barnard and others while at the Applied Research Lab at Penn State
Varying each of the parameters individually enables us to evaluate the effects of gas and film characteristics.
10-3
10-2
10-1
100
101
102
103
-60
-40
-20
0
20
40
SP
L G
ain
(dB
)
Scale Factor
Π1
Π2
Π4
ArHeXeSF6
1-layer CNT in Air @ STPf = 2 kHzWin = 7 Wa = 0.0025 m2
Therm. Cond. * Dens.HCPUA
HCPUA of Pt Foil
Non-Dimensional Analysis
* Work done by Dr. Barnard and others while at the Applied Research Lab at Penn State
Design criteria for a CNT speaker were established based on analysis of the fundamental equations.
Primary Criteria
Secondary Criteria
Input Waveform Film Gas
inW
f
a
HCPUA ≤ CNT(O) 10-3 J/m2K
PC
KT
o airκρ ≥
Design Criteria for Thermophones
* Work done by Dr. Barnard and others while at the Applied Research Lab at Penn State
Carbon Nanotube Thin Film
CNT thin-film is a sheet of super-aligned carbon nanotubes, made by drawing from a vertically aligned CNT forest
HCPUA – Heat Capacity per Unit Area
HCPUA of CNT is 0.001 that of Pt foil!
Photo courtesy of U. Texas - Dallas
Photo courtesy of U. Texas - Dallas
Early Experiments: Gaseous Immersion
Experimental data correlated very well to the analytical model when immersing the CNT thin-films in different gases.
2” x 2” Film Sample
Errors likely do to inability to purge all air from system.
Enclosure and diaphragm resonances should be optimized.
Measured PredictedXenon 17.5 0.16 10.5 15.5 5SF6 3.9 0.66 5 3.9 1.1
Helium 37.2 5.2 -7.9 -13 5.1Argon 22.4 0.52 4 6.1 2.1
SPL Gain (dB)Gas Error (dB)κρo
(Gas/Air)CP
(Gas/Air)
* Work done by Dr. Barnard and others while at the Applied Research Lab at Penn State
Early Experiments: Maximum Sound Pressure Level
Mark II Prototype, we achieved a tonal sound pressure level of 93 dB @ 1 m
Experimental Data Point2.5 kHz @ 1m in air @ STP
(10 cm x 10 cm, ~70% filled)
* Work done by Dr. Barnard and others while at the Applied Research Lab at Penn State
Early Experiments: Maximum Sound Pressure Level
Mark III Prototypes
* Work done by Dr. Barnard and others while at the Applied Research Lab at Penn State
Early Experiments: Maximum Sound Pressure Level
Mark III Prototypes
Stacked CNT sheets are “acoustically transparent” and placed on a rigid baffle
Measured SPL @ 1m and temperature maps
* Work done by Dr. Barnard and others while at the Applied Research Lab at Penn State
Early Experiments: Acoustic Transparency
* Work done by Dr. Barnard and others while at the Applied Research Lab at Penn State
Early Experiments: Maximum Sound Pressure Level
Mark III Prototypes
WPK WRMS WPK WRMS WPK WRMS
1&2 97 1069 556 0.0288 37.1 19.3 66.7 69.53&4 100 1583 592 0.0616 25.7 9.6 68 72.35&6 111 5968 2239 0.1848 32.3 12.1 73.2 77.5
Input Power Power Density (kW/m2) Sensitivity (dB re 20 μPa/W @ 1m)Assembly #
CNT Area (m2)
SPL (dBA @ 1m)
111 dB @ 1m (2.9 kHz) using 6 kWpk (2.2 kWRMS) of power
Penn State ARL have since achieved 117 dB @ 1m with a Mark IV prototype and new amplification and enclosures
Efficiency is a key research area
* Work done by Dr. Barnard and others while at the Applied Research Lab at Penn State
Michigan Tech Research
Research at Michigan Tech is focusing on basic science, multi-physics modeling, and experimental validation
Simple CNT thermophones to evaluate directivity, volume velocity, true power efficiency, failure modes,
etc…
Building CNT Thermophones
Failure of CNT Thermophones
Applications
Commercial loudspeakers
Active noise control- In MRI machines- Building windows- Automotive/aero-space
Helicopter blade de-icing
Underwater transducers
High Potential Industries - Automotive -Military- Aerospace -Consumer electronics
Source Noise
Cancelling Noise from CNT
Result+ =
Applications must require lightweight at the expense of
power
Where We are Heading
Multi-Physics Modeling (Electrical-Thermal-Acoustic)
Measurement of True Efficiency
Signal Processing to Eliminate Frequency Doubling
Enclosing The CNT for Protection
Application of CNT on Substrate for Durability
Use in Active Noise Control We are looking for corporate partners interested in further investigating this
technology. Please talk to us afterward if you may be interested.
Although there are challenges, this technology is promising enough to warrant continued investigation
Part 2
Source Velocity
Mahsa Asgarisabet, PhD Student
Pressure Distribution
Rayleigh Integral:
𝑝𝑝 𝑥𝑥,𝑦𝑦, 𝑧𝑧; 𝑡𝑡 =−𝑗𝑗𝑗𝑗𝜌𝜌0𝑐𝑐0
2𝜋𝜋�𝑆𝑆
𝑒𝑒−𝑗𝑗𝑗𝑗 𝑟𝑟−𝑟𝑟′
𝑟𝑟 − 𝑟𝑟′�̇�𝑤 𝑥𝑥,𝑦𝑦, 𝑧𝑧𝑠𝑠, 𝑡𝑡 𝑑𝑑𝑑𝑑 𝑧𝑧𝑠𝑠 < 𝑧𝑧
Velocity on the source surface𝑧𝑧, 𝑧𝑧′
𝑥𝑥, 𝑥𝑥′
𝑦𝑦,𝑦𝑦′
𝑝𝑝(𝑥𝑥,𝑦𝑦, 𝑧𝑧)
�̇�𝑊(𝑥𝑥′,𝑦𝑦′, 𝑧𝑧′)
𝑑𝑑𝑥𝑥′𝑑𝑑𝑦𝑦′
Importance of Surface Velocity
CNT sheet is very fragile Can not measure velocity and pressure on the CNT surface directly
Uniform surface velocity distribution has been assumed in the literature
To model the speakers it is important to know the velocity distribution on thesource surface
Thermal profile of the thin film is non-uniform in reality due to the heat sinkeffect of the copper electrodes and free convection of a vertical CNTspeaker [4]
Measuring Exact Surface Velocity is Important
Importance of Surface Velocity
Work done by Dr. Barnard and others while at the Applied Research Lab at Penn State
Thermal images of the source surface clearly indicate that the temperature profile is non-uniform, so the velocity profile
should not be assumed uniform either. [4]
Methodology
Methods to measure the Velocity
• Dual-microphone intensity measurements• Laser vibrometry• Near-field acoustic holography (NAH)
NAH images the acoustic quantities of thesource system using the set of acousticpressure measurements on a holographicplane parallel to the source surface (InverseProblem).
Advantages of NAH:
• Can be done with 2 Microphones• Low cost• Non-contact
Replicated Apertures
Measured Apertures
Measurement Plane
Source Plane
Methodology: NAH with only 2 microphones
Reference Microphones y
Moving Microphones xMeasurements were done in differenttimes for different locations
Phase difference should be considered
Reference Microphone should be useto obtain phase
Phase difference is the phase of crosspower 𝐺𝐺𝑥𝑥𝑦𝑦
The exact measured data for eachlocation will be: 𝐺𝐺𝑥𝑥 = 𝐺𝐺𝑥𝑥𝑒𝑒𝑖𝑖∗𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎(𝐺𝐺𝑥𝑥𝐺𝐺)
Test Setup to Measure Source Velocity
PCB 377B26 Probe Microphones with
thermocouples attached
Rollers to change the location of moving microphone
Distance Measurements
Distance (m)10 -3 10 -2 10 -1 10 0
Nor
mal
ized
SP
L (d
B r
e 20
P
a)
-40
-35
-30
-25
-20
-15
-10
-5
0
5
Frequency = 250 Hz
Frequency = 500 Hz
Frequency = 630 Hz
Frequency = 1250 Hz
Frequency = 2000 Hz
Frequency = 2500 Hz
Frequency = 3150 Hz
-6 dB / Doubling Distance
Near field and Far field are shown
Distance Measurements
Distance (m)10 -3 10 -2 10 -1 10 0
Te
mp
era
ture
(C
)
20
30
40
50
60
70
80
90
Temperature decays rapidly with increasing distance from the source
x (cm)
y (c
m)
Average Temperature (oC)
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
25
30
35
40
45
50
55
60
65
CNT Sheet
x (m)y
(m)
Measured SPL (dB) Distribution Frequency=2000 Hz
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
50
52
54
56
58
60
62
64
66
CNT Sheet
Measured SPL and temperature 5mm Away
Maximum SPL and Temperature are approximately in front of the centerline of the CNT sheet
x (m)
y (m
)
Velocity Distribution(m/s) f = 2000 Hz
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
x 10-5
CNT Sheet
Velocity Distribution on CNT Sheet
Frequency (Hz)
200 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000
So
urc
e V
elo
city (
m/s
)
10 -5
0
1
2
3
4
5
6
7
8
Maximum Source Velocity
Mean Source Velocity
Minimum Source Velocity
Source Velocity is varying on the source surface and is maximum on the center of CNT Sheet
Source Velocity increases as frequency increases
SPL 1m Away From Source
Frequency (Hz)
200 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000
SP
L 1m
Aw
ay F
rom
Sou
rce
(dB
re
20
Pa)
0
10
20
30
40
50
60
70
80
90
100
SPL From NAH
Minimum SPL From Experiment
Mean SPL From Experiment
Maximum SPL From Experiment
Background SPL
NAH and Experimental results are in good agreement
x (m)
y (m
)
Intensity Distribution Frequency=3000 Hz
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
1
2
3
4
5
6
7
8
x 10-7
CNT Sheet
Intensity Distribution
𝛱𝛱(𝜔𝜔) = �𝑆𝑆𝐼𝐼𝑧𝑧 𝑥𝑥,𝑦𝑦, 𝑧𝑧𝑠𝑠,𝜔𝜔 𝑑𝑑𝑑𝑑Sound Power
Directivity
-45
-40
-35
-30
-25
-20
-15
-10
-5
0 dB
180 o
150 o
120 o
90 o
60 o
30 o
0 o
-45-40-35-30-25-20-15-10-50 dB
180 o
150 o
120 o90 o
60 o
30 o
0 o
Frequency=3500 Hz
Frequency=3000 Hz
Frequency=2500 Hz
Frequency=2000 Hz
Frequency=1500 Hz
Similar to a baffled piston, directivity index increases with increasing frequency
What’s Next?
Source velocity for different size and shape of CNT speaker
Multi-Physics Modeling (Electrical-Thermal-Acoustic)
• Using Velocity results to model in Amesim
Use in Active Noise Control
Part 3
CNT Efficiency & THD Quantification
Troy Bouman, PhD Student
Pressure Produced by CNT Thermophone
𝐼𝐼 = 𝐴𝐴 sin 𝜔𝜔𝑡𝑡 + 𝐵𝐵
𝑉𝑉 = 𝑅𝑅𝐼𝐼
𝑃𝑃 = 𝑅𝑅𝐼𝐼2= ⁄𝑉𝑉2 𝑅𝑅 𝑃𝑃 = 𝑅𝑅[( ⁄𝐴𝐴2 2 + 𝐵𝐵2) + 2𝐴𝐴𝐵𝐵 sin 𝜔𝜔𝑡𝑡 − 𝐴𝐴2/2𝑐𝑐𝑜𝑜𝑜𝑜(2𝜔𝜔𝑡𝑡)]
𝑉𝑉 = 𝑅𝑅(𝐴𝐴 sin 𝜔𝜔𝑡𝑡 + 𝐵𝐵)
Current:
Voltage:
Power:
Current Loudspeakers
CNT thin film loudspeakers
Pressure is related to Voltage ( 𝑃𝑃𝑟𝑟𝑒𝑒𝑜𝑜𝑜𝑜𝑟𝑟𝑟𝑟𝑒𝑒 ∝ 𝑉𝑉 )
Pressure is related to Power ( 𝑃𝑃𝑟𝑟𝑒𝑒𝑜𝑜𝑜𝑜𝑟𝑟𝑟𝑟𝑒𝑒 ∝ 𝑉𝑉2 )
Doubled Frequency
CNT speakers are Non-Linear
Speaker Used
Test Methodology (ANSI S12.54)
Test Methodology (ANSI S12.54)
Test Methodology
Single tone OTO octave
Methods• No Processing (AC)• DC Offset (DCAC)• Amp Modulation (AMAC)
72 Wrms input power
PCB 378C01 and 130A23 Microphones
Impedance of CNT Sheet
Pure Resistors Until ~ 10 kHz
AC - Efficiency
Matches Xiao theoretical model for frequencies < 1,600 HzEfficiency increases with frequency
ACDC - Efficiency
Optimal B/A = 0.62
DC – Efficiency (B vs A)
Only increasing A for a constant B increases efficiency
AMAC SPL Response
Two new side lobes around the carrier that create a tone at 2 times modulation
AMAC Efficiency
Carrier frequency does not effect efficiency
AMAC Efficiency (Mod Index)
Optimal modulation index for efficiency is 1.5
Total Harmonic Distortion (THD) - DCAC
Increasing B/A decreases THD
THD AMAC
Carrier frequency does not effect THD
THD AMAC (Mod Index)
Increasing modulation index increases THD (note log scale)
Efficiency (μ %) THD (%)
AC 18.0 - 319 ≈ ∞
DCAC 1.69 - 308 11 - 105
AMAC 1.24 - 228 5 - 61
STD Loudspeaker 70,000 – 200,000 0.0003-0.0157
Summary – Efficiency & THD
What’s Next?
Enclosure DesignAcoustic ConcernsThermal ConcernsOptimization
RuggednessBacking
References
[1] F. Braun, Ann. Der Physik, 65, 358-360, (1898).
[2] P. de Langle, Proc. R. Soc. London, 91A, 239-241, (1915).
[3] H. D. Arnold, I. B. Crandall, “The Thermophone as a Precision Source of Sound,” Phys.Rev., 10, 22-38, (1917).
[4] Lin Xiao, Zhuo Chen, Chen Feng, Liang Liu, Zai-Qiao Bai, Yang Wang, Li Qian, YuyingZhang, Qunqing Li, Kaili Jiang, Shoushan Fin, “Flexible, Stretchable, Transparent CarbonNanotube Thin Film Loudspeakers,” Nano Letters, 8(12), (2008).
[5] Barnard, A.R., et al., Advancements toward a high-power, carbon nanotube, thin-filmloudspeaker. Noise Control Engineering Journal, 2014. 62(5): p. 360-367.