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www.klippel.deBBig Sound from Small Speakers, 1

Big Sound from Small SpeakersPart 1

Wolfgang KlippelInstitute of Acoustics and Speech Communication

University of Technology Dresden, KLIPPEL GmbH

Email address: [email protected]


Abstract:

This seminar focuses on modern methods for designing and manufacturing microspeakers and other small, light and cost-effective loudspeakers reproducing the sound at high efficiency and sufficient sound quality as required in telecommunication, automotive, multi-media and other professional applications. The seminar gives an overview on physical modeling of loudspeakers in the large signal domain which is necessary to explain the relationship between geometry and the properties of the materials on the one side and the transfer behavior and the performance onthe other side. Meaningful loudspeaker parameters (T/S, nonlinear and thermal) and other specifications (amplitude response, directivity, power) are discussed which allow a comprehensive description of the transducer. Prof. Klippel addresses the fundamentals of loudspeaker diagnostics which is important to interpret the measurement results and to localize the causes of the defects and to develop alternative design choices.


Questions addressed Questions addressed in in the the Seminar:Seminar:

How to get the desired frequency response and directivity pattern?How to find the optimal geometry of the cone?•How to measure the power handling?•How to perform meaningful measurements in the large signal domain?•How to find the optimal size of voice coil in the gap? •Which loudspeaker nonlinearities are desired?•How to get maximal power handling and acoustical output?•How to get maximal bass out of a small enclosure? •How to measure the power handling? •What is a good and what is a bad speaker?How to select an optimal driver for loudspeaker system design?


LoudspeakersLoudspeakers are everywhereare everywhere

• Cars • Cellular phones• Multimedia, Computers• Hearing aids• Home hifi reproduction• Professional audio• Active noise control• …


RequirementsRequirements on Modern on Modern LoudspeakersLoudspeakers

• Small dimensions • Low weight • Low cost• High output at low distortion• Maximal efficiency

“Loud“speakers are required


List of List of ContentContent

• Small Signal Modeling – Lecture

• Assessing Small Signal Performance - Practical Workshop

• Large Signal Modeling – Lecture

• Assessing Large Signal Performance - Practical Workshop

• Detection of Defective Speakers - Lecture

• Discussion

• Summary


--LoudspeakerLoudspeaker -- a a dynamicdynamic systemsystem

Cone break up

Length of sound wave

30 cm 15 mm3 m

Resonance

Frequency

1 kHz 20 kHz100 Hz1 Hz

Creep

Time constant

1 ms 0.05ms10 ms1 s1 h

heat transfer

lumped model useful CRLdistributed model required

Audio band


Motor and Suspension DesignMotor and Suspension Design

VibrationMotor Radiation

F X(r)

soundfieldu


F

V

X(r)

F(r)

soundfieldu

inner cone edge

Cone‘s surface

FEA BEA

CoupledMechanic-acoustical

analysis

Admittance Y(f) used in

lumped parameter

model

Materialparameters geometry


Equivalent Equivalent Circuit Circuit of a of a drive unitdrive unitImpedance Impedance Type Type AnalogyAnalogy ((FuFu) )

Electrical domain Mechanical domain

MmsCms(f) Rms

Bl

Re

vI

Blv BliU

ZL(j )

Electrical dcResistance

Impedance describing Lossy inductance

Force factor

Mechanical Losses

Moving mass

compliance

Voltage

current

Back EMF Driving force


Linear Linear Lumped ParamtersLumped ParamtersBasic parameters :• dc resistance Re • Voice coil Inductance Le (+ additional parameters describing impedance at higher frequencies)• Moving mass Mms (with air load) • Force factor Bl • Mechanical resistance Rms • Stiffness Kms of the suspension at fs

• Vicsco-elastic stiffness parameters („creep factor lambda“)• Effective Radiation Area SD

Derived Parameters (Thiele/Small) ( T/S ):• Resonance frequency fs • Electrical Q-factor Qes • Mechanical Q factor Qms • Total Q-factor Qts • Equivalent box volume Vasof mechanical stiffness

• Pass-band sensitity

ImportantImportant

Time Time varyingvarying


• Discrepancy to traditional modeling

• compliance increases for f


Perturbation methodPerturbation method: : SealedSealed Test BoxTest Box11

Pro :Simple technique Cms is measured primarily

Problems :• Depends highly on precise valueof effective radiation area Sd

• Residual air volume (inside the transducer) can not be considered

• requires sealed diaphragm

• can not be used to measure mechanical mass without air load

•Time consuming


Perturbation methodPerturbation method: : Added MassAdded Mass22

Pro :Simple technique Mms is measured primarily

Problems : :• can not be applied to tweeter and microspeakers

•Time consuming • Mechanical Resistance or stiffness are assumed as frequency independent parameters


Laser Laser TechniqueTechnique

Pro :• Fast (one step technique) • Simple to use • Bl is measured primarily

• Most precise results • Can be applied to most transducers

Problems :• Optical problems (angle, surface)

• Coil displacement is not axialsymmetrical


MeasurementMeasurement in in air orair or in in vacuumvacuum ??

In AirMms and Cms consider air load

Useful input for system design

In vacuumMms and Cms consider mechanical elements only

Useful for driver design and comparison with the weight of the loudspeaker parts


Effective Radiation Area SEffective Radiation Area SddDefinitionDefinition

x

dSrx

xV

S Sd

)(

C

C

dr

drrxx

)(

Mean voice coil displacement

displacement air volume

Real surface area S

very importan

t for

microspeaker

s


HowHow to to Measure Radiation Area SMeasure Radiation Area Sdd ??Pistophone Pistophone technique technique

xp

pVSd

0

0

adiabatic coefficient

closed volume V0

static air pressure p0.

Sound pressure p

Displacement x

Laser

Microphone

See KLIPPELApplication note AN32


HowHow to to Measure Radiation Area SMeasure Radiation Area Sdd ??Differential Differential methodmethod ((sophisticatedsophisticated, , preciseprecise) )

adiabatic coefficient

Difference volume V

static air pressure p0. 1

1

2

20 p

xpxp

VSd

Sound pressurep1

Sound pressurep2

Displacement x2Displacement x1

syringe (medical injection pump See KLIPPELApplication note AN32


HowHow to to Measure Radiation Area SMeasure Radiation Area Sdd ??Laser Scanner Laser Scanner TechniqueTechnique ((preciseprecise, robust), robust)

Integration of x on curve C

x

dSrx

xV

S Sd

)(

C

C

dr

drrxx

)(

C

Under klippel development


HowHow to to Measure Radiation Area SMeasure Radiation Area Sdd ??Precise TechniquePrecise Technique III (III (usingusing Laser Scanner )Laser Scanner )

woofer

headphone

microspeaker


Why isWhy is a a precise measurementprecise measurement of of SSdd importantimportant ????

Effective Radiation Area Sd Sd• determines the acoustical output

sensitivity, efficiency

• affects the precision of the parameter measurement if thetest box perturbation technique is used

Moving mass Mms, force factor Bl and stiffness values Kms, compliance Cms

Mms, BL, Kms, Cms


Effective Coil Effective Coil VibrationVibrationAveraged Averaged Transfer Transfer Function between Displacement Function between Displacement and and VoltageVoltage

oPoint 1

o

Point 2

o

Point 3

KLIPPEL

-65

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

103 104

Magnitude Transfer Function Hx(f)=X(r,f)/U(f)

1 2 3

Laser Measurement gives three different transfer functions

Fitting of Mechanical Parameters

KLIPPEL

-410

-310

-210

-110

103 104

averaged Hx(f)

mm

/V

f [Hz]

averaged Hx

Displacement averaged over

voice coil circumference

differences


--LoudspeakerLoudspeaker -- a a dynamicdynamic systemsystem

Cone break up

Length of sound wave

30 cm 15 mm3 m

Resonance

Frequency

1 kHz 20 kHz100 Hz1 Hz

Creep

Time constant

1 ms 0.05ms10 ms1 s1 h

heat transfer

lumped model useful CRLdistributed model required

Audio band


Measurements are the basis for loudspeaker diagnosticsMeasurements are the basis for loudspeaker diagnostics


F

V

X(r)

F(r)

soundfield

unearfield

farfield

inner cone edge

Cone‘s surface

Cone Vibration+ Geometry

Distributed Parameters

Electrical Measurement

Ze(f)=U(f)/I(f)

Lumped Parameterselectricalelectrical

Mechanical Measurement

Hx(f)=X(f)/U(f)

mechanicalmechanical

Far Field Response

AcousticalMeasurement


Cone Scanning TechniquesCone Scanning Techniques

Doppler Doppler InterferometryInterferometry

((PolytechPolytech, 1995), 1995)

Frankort Frankort 19781978

OlsonOlson, 1950, 1950Triangulation Triangulation Laser ScannerLaser Scanner

(Klippel, 2007)(Klippel, 2007)

Geometry

DisplacementVelocity destribution on the cone

Intensity

Amplitude+ phase +

Amplitude Amplitude+ phase+ geometry


New Tools New Tools forfor Loudspeaker DesignLoudspeaker Design

Analyzer Software•

Visualization of cone vibration

• Predictionof sound pressure output

• Directivity• Decomposition

Scanner Hardware•

Dedicated to loudspeakers• Price effective• Scanning

geometry• Many

other applications


z

phi

r

SCNScanning System

The scanning starts at the outside rim and proceeds inwards

Mechanical scanning system with one rotational ( ) and two linear actuators (r, z)

Automatic Scanning Process


Scanning ModesScanning Modes

Profile Scan Explore Scan Detailed Scan

8 min 8 hours

Scanning Time

1 hour

Good for•

Radiation of axial-symmetricalGeometries only

Good for•

Radiation all cones• Rocking modes

Good for • Irregularities


A A Profile Profile ScanScan is already usefulis already useful !!

Profile Scan Detailed Scan

8 8 min 8 8 hours


MeasurementMeasurement of of GeometryGeometry

• High Precision < 10 m for 0 < z< 300 mm< 2.5 m for –5 mm < z < 5 mm

• Dual Measurement with correlation

• Automatic detection of optical errors

• Export in common formats ( such as *.txt, *.dxf)


3D Animation Cross-sectional Cut

Amplitude Distribution

VisualizationVisualization of Vibration Dataof Vibration Data

Phase Distribution


Analysis SoftwareAnalysis Software

Tasks:

• Detect and suppress errors • Animate vibration • Make interpretation simpler • Enhance information which are important for

design • Predict sound pressure output


Vibration and Radiation DiagnosticsVibration and Radiation Diagnostics needs complex vibration data + cone geometryneeds complex vibration data + cone geometry

Drive Unit(woofer, tweeter, ...)

Geometry

Vibration

Acoustical Characteristics( , , )(SPL, directivity, power,...)

ANALYSIS

Indications for mechanical improvement

Mechanical Characteristics (AAL)

Indications for acoustical improvement

Visual Visual AnimationAnimation

3937,5 Hz

Modal & DecompositionAnalysis


Checking ConeChecking Cone VibrationVibration

•Do we have enough vibrational amplitude ?

•On which cone part first break-up modes occur ?

•Does the break-up modes gradually replace the pistonmode ?

•Do we have membran or bending modes ?


Accumulated Accumulated Acceleration LevelAcceleration Level

dBprja

rAALo

aqa

),(log20),(

Acceleration level

Total sound Pressure levelRigid body modes

KLIPPEL

30

40

50

60

70

80

90

100 1000 10000

SPL

[dB]

f [Hz]

Acceleration Level

cS ca

caa dSrr

rjXrja

c

),(

2),( 0

2 Weighted Sum of the accelaration

amplitude


KLIPPEL

50

55

60

65

70

75

80

85

90

100 1000 10000

AAL

[dB]

f [Hz]

Acceleration Level

positive value

8296,9 Hz

11109,4 Hz

13312,5 Hz

16289,1 Hz

HowHow to to perform perform modal modal analysis analysis ??

02

20

)(

//12)(

ic

S ca

ci

iii

a dSrr

r

jja

c

Search for maxima in accumulated acceleration

105.01 01.02


??HowHow to to Specify the Specify the Radiator ?Radiator ?

ConeCone, , DiaphragmDiaphragm and and SurroundSurround

Total sound Pressure levelRigid body modes

KLIPPEL

30

40

50

60

70

80

90

100 1000 10000

SPL

[dB]

f [Hz]

Acceleration Level

8296,9 Hz

11109,4 Hz

loss factor

13312,5 Hz

Modal Modal loss factor loss factor ii of of each each mode imode ithth--mode mode withwithi=1,2,...i=1,2,...

Natural frequencyNatural frequency ffii of of thethe iithth--mode mode withwithi=1,2,...i=1,2,...

Natural FuncitonNatural Funciton ii ((rrcc)of )of eacheach mode imode ithth--mode mode withwithi=1,2,...i=1,2,...

YoungYoung‘‘ssYoungYoung‘‘s E s E ModulusModulus of of the the materialmaterial

LossLoss factor factor of of the the materialmaterial

(( ))GeometryGeometry of of the the Radiator Radiator ((shapeshape, , thicknessthickness, ..), ..)


?? ? ? ??SmoothSmooth SPL Response ?SPL Response ?

Woofer A with paper cone

Woofer B with magnesium cone

Woofer C with flat radiator

KLIPPEL

40

45

50

55

60

65

70

75

80

102 103

SPL

[dB]

f [Hz]

-30 degree

on -axis

+30 degree

KLIPPEL

20

30

40

50

60

70

80

90

102 103 104

SPL

[dB]

f [Hz]

-30 degree

on -axis

+30 degree

KLIPPEL

20

30

40

50

60

70

80

102 103 104

-30 degree

on -axis

+30 degree


??Sufficient ConeSufficient Cone Vibration ?Vibration ?

KLIPPEL

50

55

60

65

70

75

80

102 103

SP

L [d

B]

f [Hz]

Total SPL

acceleration level

Woofer A with paper cone :low Q factor of cone resonances

KLIPPEL

50

55

60

65

70

75

80

85

90

102 103 104

SPL

[dB]

f [Hz]

Total SPL

acceleration level Woofer B with magnesium cone: natural modes cause high peaks in SPL

KLIPPEL

30

40

50

60

70

80

90

102 103 104

SP

L [d

B]

f [Hz]

Total SPL

acceleration level

Woofer C with flat radiator dips are not visible in AAL AAL cause peak at 0.8 kHz

800 Hz


Sufficient DampingSufficient Damping of of thethe Material ?Material ?

WooferWoofer C C with flat radiatorwith flat radiator

65

70

75

80

85

90

102 103 104

Total Acceleration Level

ACC

[dB]

Frequency [Hz]

1.084080

i

iii f

ff Increase loss factor of material

Read 3dB bandwidth in AAL


??WhereWhere to to applyapply additional additional dampingdamping ??

wwooferoofer C C with flat radiatorwith flat radiator

820,3 Hz 12398,4 Hz

65

70

75

80

85

90

102 103 104

Total Acceleration Level

AC

C [d

B]

Frequency [Hz]


??WhereWhere to to applyapply additional additional dampingdamping ??

WooferWoofer B Magnesium B Magnesium conecone

KLIPPEL

50

55

60

65

70

75

80

85

90

100 1000 10000

AAL

[dB]

f [Hz]

Acceleration Level

105.01 01.02

11109,4 Hz

Rubber surround has sufficient losses Cone requires damping


Finding Circumferential ModesFinding Circumferential Modes

KLIPPEL

20

25

30

35

40

45

50

55

60

10 3 10 4

AAL

[dB]

f [Hz]

Radial Component

Circular Component

Search for maxima in AAL of Circular or Quadrature Component


Decomposition intoDecomposition into radial and radial and circular componentscircular components

At 580 Hz

circradtotal xxx

Radial vibration mode Circular vibration mode

causes Rub & Buzz


Dominant Dominant Circumferential ModesCircumferential Modes ??

WooferWoofer C C with flat with flat radiatorradiator

KLIPPEL

50

55

60

65

70

75

80

85

90

10 2 10 3 10 4

SP

L [d

B]

f [Hz]

Acceleration Level

Circular Component (Acceleration)

4 kHz4 kHz


Decomposition intoDecomposition into radial and radial and circular componentscircular components

At 580 Hz

circradtotal xxx

Radial vibration mode Circular vibration mode

causes Rub & Buzz


HowHow to find to find rocking modesrocking modes ??WooferWoofer A A with paper conewith paper cone

KLIPPEL

30

35

40

45

50

55

60

65

70

75

80

102 103

AA

L [d

B]

f [Hz]

Total AAL

AAL of Quadrature Component

Search for maximum in quadrature component in AAL at low frequencies

380 Hz


??HowHow to find to find irregular Vibrationsirregular Vibrations ??

Aluminum diaphragmAluminum diaphragm of a horn of a horn compression drivercompression driver

KLIPPEL

40

45

50

55

60

65

70

75

80

85

103 104

SP

L [d

B]

f [Hz]

Total (AAL)

Quadrature (AAL)

Circular (AAL)

6 kHz

Search for maximum in quadrature or circular

component of AAL


Checking radiation problemsChecking radiation problems

•Do we have a strong cancellation effect?

•Does the cancellation affect out-off axis points ?

•Which cone part radiates sound ?

•Does the size of radiating area decreases gradually ?


PredictionPrediction of Sound of Sound PressurePressure

Rayleigh Rayleigh Integral Equation

•

• driver in infinite baffle

•

• good approximation for most angles

• short calculation time 55

60

65

70

75

80

103 104

Total Sound Pressure Level

SPL

[dB]

Frequency [Hz]


??SmoothSmooth SPL Response ?SPL Response ?


Woofer B with magnesium cone

Woofer C with flat radiator

KLIPPEL

40

45

50

55

60

65

70

75

80

102 103

SPL

[dB]

f [Hz]

-30 degree

on -axis

+30 degree

KLIPPEL

20

30

40

50

60

70

80

90

102 103 104

SPL

[dB]

f [Hz]

-30 degree

on -axis

+30 degree

KLIPPEL

20

30

40

50

60

70

80

102 103 104

-30 degree

on -axis

+30 degree


Most Most important Resultsimportant Results

KLIPPEL

30

40

50

60

70

80

90

101 102 103 104

Sound Pressure SPL @ 1m, 1V Accumulated Acceleration (AAL)

Power Level + 47 dB @ 1V

Power

Accumulated Acceleration AAL

SPL on axis

Example: headphone

Rocking mode

Directivity


KLIPPEL

-30

-20

-10

0

10

20

30

102 103 104

Magnesium Cone

Flat Piston

Paper Cone

KLIPPEL

40

45

50

55

60

65

70

75

80

102 103

Pow

er

[dB

]

f [Hz]

Sound Power Level SPL on-axis


power

SPL on-axis

KLIPPEL

40

45

50

55

60

65

70

75

80

85

90

102 103 104

Pow

er

[dB

]

f [Hz]


Woofer B with magnesium conepower

SPL on-axis

KLIPPEL

30

35

40

45

50

55

60

65

70

75

80

85

90

102 103 104

Pow

er [

dB

]

f [Hz]


Woofer C with flat radiator power

SPL on-axis

??Desired DirectivityDesired Directivity ??


??Desired DirectivityDesired Directivity ??

Directivity of SPL in the horizontal plane predicted for woofer CKLIPPEL

20

30

40

50

60

70

80

102 103 104

-30 degree

on -axis

+30 degree

0°330

300

270

240

210180°

150°

120°

90°

60°

30°

-10

1.1 kHz.0°

330

300

270

240

210180°

150°

120°

90°

60°

30°

-10

0.9 kHz.0°

330

300

270

240

210180°

150°

120°

90°

60°

30°

-10

1.4 kHz.


HeadphoneHeadphone –– Vibration 2760 HzVibration 2760 Hz2760Hz 2760Hz

AsymmetricalAsymmetrical Bending ModeBending Mode


HeadphoneHeadphone –– RadiationRadiation 2760 Hz2760 Hz2760Hz2760Hz

20

30

40

50

60

70

80

103 104

Total Sound Pressure Level

SP

L [d

B]

Frequency [Hz]

0°

330

300

270

240

210

180°

150°

120°

90°

60°

30°

-15 -10 -5

+ - + -


KLIPPEL

30

40

50

60

70

80

90

102 103 104

SP

L [d

B]

f [Hz]

Total SPL

acceleration level

??What causes the dipsWhat causes the dips in SPL ?in SPL ?

WooferWoofer C C with flat radiatorwith flat radiator

Compare Accumulated Acceleration (AAL) with sound pressure (SPL)

There is enough vibration on the cone !! Radiation Problem


Sound Sound Pressure related DecompositionPressure related Decomposition

generates sound Reduces sound no sound

ofoutantiintotal xxxx quadrature


How the decomposition worksHow the decomposition works

Referencephase I

R

I

R

Contribution tosound pressure output

at point rj

Summation on all points

H(f, ,Ri,rj)X( ,Ri)

H(f, ,Ri,rj)-1Xquadrature

Xin phase

generates soundno sound

X( ,Ri)

P(rj )


KLIPPEL

556065707580859095

103 104

dB

- [V

] (

rms)

Frequency [Hz]

In-Phase Component Anti-Phase Component

Where is the sound radiatedWhere is the sound radiated ??WooferWoofer C C with flat radiatorwith flat radiator

Cancellation frequencies

Localization of the in-phase component


??HowHow to Fix to Fix Acoustical Cancellation problemsAcoustical Cancellation problems ??

-

Area of in -phase component

o onode

Target:• Make in-Phase component dominant • Suppress anti-phase component

Steps: 1. find location of in-phase component2. use FEA to simulate behavior3. ( , , )

increase bending stiffness at this area (thickness, curvature, rips)

INCREASE


Where is the sound radiatedWhere is the sound radiated ??

WooferWoofer A: Paper A: Paper ConeCone

0.1 kHz 1 kHz0.7 kHz 10 kHz4 kHz1 kHz

• In-phase component isdominant• No acoustical cancellation• In-phase component stays in the centre • radiation area shrinks with frequency

KLIPPEL

0

10

20

30

40

50

60

70

80

10 2 103

SPL

[dB]

f [Hz]

In-Phase Component

Anti-Phase Component

In-Phase Components


1 kHz

rb

::TIP: TIP: ReductionReduction of of effective cone areaeffective cone area

2 kHz

rb

4 kHz

rb

6 kHz

rb• Breakup starts outside• Outer ring

area does not radiate significant sound • ( ) Inner part

should radiate sound (in-phase component)

500 Hz 3 kHz 7 kHz


Providing Input Data for FEAProviding Input Data for FEA

Drive Unit(woofer, tweeter, ...)

Geometry

Vibration

Measured Víbration(accumulated level + shape)•of total vibration•of separated components

3937,5 Hz

Radiator(cone, diaphragm, panel)

MaterialParameters

E,


FiniteElementAnalysis

Predicted Víbration(accumulated level + shape)•of total vibration•of separated components

3937,5 Hz


Fitting


ConclusionConclusion

Displacement sensors + scanner + signal processing

cost effective solution for loudspeakervibrometry

Geometry + Vibration data is basis for analysis

Interaction between vibration + radiation are important

New decomposition techniques simplifies interpretation

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