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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.