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Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 1

MICROSPEAKERS – HYBRIDS BETWEEN HEADPHONES AND LOUDSPEAKERS

by Wolfgang Klippel

KLIPPEL GmbHDresden University of Technology


Content

1. Motivation – similarities and particularities

2. Basic Transducer Modeling– linear, time-invariant, lumped parameter

3. Progress in Transducer Modeling – higher-order system function,– modal vibration– radiation into 3D space– nonlinear, time variant

4. Consequences for Transducer Design


Similaritiesbetween headphones, microspeakers and loudspeakers

headphone

microspeakersystem

loudspeakersystem

Voice coil + Magnet

low acoustical load

Electro-dynamicaltransduction principlemostly used

low efficiency

Lumped parametermodeling at lowfrequencies applicable

using a mechanicalsuspension system

Distributed parametermodeling at high frequencies required


Particularitiesbetween headphones, microspeakers and loudspeakers

headphoneloudspeaker

system

Single transducer

large motorstrength Bl2/Re

Large coil

prone torocking mode

small sizelow electrical damping(acoustical and mechanicaldamping required)

low efficiencygeneratesthermal problems

no spider

dominant electricaldamping

high magneticAC Flux

flat radiators low bending stiffness early break-up

microspeakersystem


Basic Electroacoustical Modeling

Assumptions:• no heating of the voice coil ( RE= const.)• eddy currents neglected (loss-less inductance LE)• nonlinearities neglected (e.g. Bl= const.)• visco-elasticity neglected ( CMS= const.)• simplified damping model (viscously damped system CMS)• higher-order modes neglected (piston mode described by SD)

MMS CMS RMS-1Bl

RE

v

i

Blvu p

LE

F=Bli

p

qFA

SD

Zload pout(r)

linear, time invariant, single input based on lumped parameter modeling


Extended Electroacoustical Modeling

Nonlinearities

MMS CMS(ω,x,t) RMS(ω,v)-1Bl(x,t)

RE(t)

v

i

Bl(x,t)vu p

LE(ω,x,i) F=Bl(x,t)i

p

q

FA

SD(ω,x)Zload(ω)

pout(r)

Frel(x,i)

RL(ω,x,i)

dL(q)

lumped parameter modeling (piston mode)

higher ordermechanicalmodes

Radiation into3D space

Higher-order linear transfer function • Lossy inductance • visco elastic creep modeling• Modal vibration, radiation

Time variant properties


Lossy Inductance ZL(j)measured curves fitted by an ideal inductance

0.1

1

10

40

50

60

70

80

90

100

1 2 5 10 20 50 100 200 500 1k

[Ohm

]

[deg]

Frequency [Hz]

Magnitude (measured)

Magnitude (fitted)

Phase (measured)

Phase (fitted)

6dB/octave

90 degree

• 1 Parameter only• Large deviation• limited use

Le

Mms Cms(f) Rms-1Bl

Re

V=dx/dt

i

Blv

Bli

U

ZL(f)


0,00000

0,00025

0,00050

0,00075

0,00100

101 102 103 104

Mechanical compliance (driver in vacuum)

[mm

/N]

Frequency [Hz]

Compliance Cmd(f) fmin

Minimum compliance Cmd0

Mechanical Compliance Cmd(f)

fmin

EFFECT:compliance increases to lower frequencies

CAUSE: viscoelasticity of the material

CONSEQUENCES:more displacement than predicted by traditional modeling

creep factor or describes relative increase of compliance per decade

fd

creep factor or

Cmd(fd)≈Cmd0 (Ritter)

Cmd(fd)

2min

min10min

/1

/log1)(

ff

ffCfCMD


Mechanical Resistance Rmd(f)

KLIPPEL

-410

-310

-210

-110

010

110

101 102 103 104

Magnitude of mechanical impedance

[kg/

s]

Frequency [Hz]

Total Impedance

Compliance Cmd(f)Mass Mmd

Residual Zres

Rmd(fd)

resonance frequency fd

EFFECT:losses increases to lower frequencies

CAUSE: viscoelasticity transfers compliance into losses

CONSEQUENCE:electrical impedance increased below resonance (not critical)

Losses Rmd(f)

min

110min0 tan

2log)(

f

feCRfRMD


Voice Coil Displacement Laser measurement on Microspeakers and Headphones

Conclusion:• No piston mode• Spatial averaging is required

KLIPPEL

0,000

0,025

0,050

0,075

0,100

0,125

50 100 200 500 1k 2k 5k 10k

Magnitude of transfer function Hx(f)= X(f)/U(f)

[mm

/V]

Frequency [Hz]

Measured 1 2

3 4 5

KLIPPEL

0,000

0,025

0,050

0,075

0,100

0,125

50 100 200 500 1k 2k 5k 10k

Magnitude of transfer function Hx(f)= X(f)/U(f)

[mm

/V]

Frequency [Hz]

Centre 0 degree rim 90 degree rim

180 degree rim 270 degree rim

Repeatability at one pointMeasurements at 5 points

x

x

xx x

2

),,(

)(

2

0

drx

xavg

coil


Experimental Modal Analysis not restricted to round radiators

Scanner

Vibration Data

Singular ValueDecomposition

Fitting

X(f, rc)rc

f

1st Mode

2nd Mode

nth Mode

rc

Natural frequency,Loss factor,Modal compliance,fitting error

MODE SHAPE

f

1st Mode

2nd Mode

nth Mode

Frequency Responses

1st Mode : f1, η1,C1,e1

2nd Mode: f2, η2,C2,e2

nth Mode : fn,ηn,Cn,e3

Singularvalues

S1

S2

Sn

HΨΣX

ΨΣ

H


Modalanalysis of a Microspeaker

Rocking mode

Rocking mode

RRL = -30 dB

1 2 3

10

17


Modalanalysis of a Headphone

12 3

56

Rocking mode

Rocking mode

RRL = -10 dB

8 4


Cause: rocking mode at 328 Hz

Loudspeaker Defect: Voice Coil Rubbing

timeone period

distortion signal

Voice coil

gapvoice coil rubbing

• signal contains reproducible and stochastic components


What Causes Rocking Modes ?

Mass Imbalances

force factor imbalance

µm

µk

µBl

Stiffness Imbalances

Which root cause excites the rocking ? mass, stiffness, force factorWhere is the root cause located ? angle showing the direction

How to assess the magnitude of the excitation ? moments


Mass Imbalance

diaphragm

magnet

pole plate

coil

DM(y,z0)

y

yyCG

FM

0

backplate

Mms

Imbalances(mass, stiffness, Bl)

Moments Tilting angles21 21

x

y y

x

coilx

z

11

22

z

x0

x

diaphragm

rigid body

nodal lines pivot point

If the center of gravity is not at the pivot point (yCG≠0, zCG≠0) the translational displacement x0 and the tilting angles τ1 and τ2 will generate the moments exciting the rocking modes

mass distribution function Dm(y,z) of the moving mass in x direction


A New Measurement Technique

Root-causes (imbalances)

Boosting Mechanism

one piston modes,two Rocking Modes

SCANNER

Total VibrationAcumulated

Acceleration Level (AAL)

System Identification

DIAGNOSTICS

Mode Coupling


Application in Transducer Diagnostics (1)Example Headphone transducer

Conclusions:• Good agreement between

measurement and modelling• First rocking mode has

significant amplitude (moreenergy than piston mode)

• Stiffness imbalance providesthe largest contribution(dominant cause)

KLIPPEL

0

10

20

30

40

50

60

70

Frequency [Hz]40 60 80 100 200 400 600 800

AAL1,Bl

AAL1,K

AAL1,M

AAL1,T

AAL0

AA

L [

dB/1

V]

– U

ndef

orm

ed R

egio

n

KLIPPEL

0

10

20

30

40

50

60

70

Frequency [Hz]40 60 80 100 200 400 600 800

AA

L [d

B/1

V]

– U

ndef

orm

ed R

egio

n

AAL2,Bl

AAL2,K

AAL2,M

AAL2,T

AAL0

Measured

Relative Rocking Level RRL(dB)

Dominant

(n=1)

Second

(n=2)

Total contribution (T) RRL1,T = 5.4 RRL2,T = -12.9

Mass Imbalance (M) RRL1,M = -8.6 RRL2,M = -18.4

Stiffness Imbalance (K) RRL1,K = 1.4 RRL2,K = -17.7

Force factor Imbalance (Bl) RRL1,Bl = -9.6 RRL2,Bl = -12.6


Application in Transducer Diagnostics (3)Example Headphone transducer

Conclusions:• A small stiffness imbalance (0.73 mm

offset from pivot point) is the root cause• High Quality factor (> 30) of the modal

rocking resonator generates high amplitudes at resonance (150 Hz)

stiffer

Dominant mode at α1

Second mode at α2

CFRM CFRK CFRBl CFRT

CF

RE

%

CFRE %

0°

90°

180°

270°

Imbalance Characteristics Value

Mass (M) CFRM 0.83 %

βM 345.9°

Stiffness (K) CFRK 2.22 %

βK 14.6°

Force factor (Bl) CFRBl 0.71 %

βBl 320.8°

Total (M,K,Bl) CFRT 3.49%

βT 1.5°

Center of Coordinates Value

Gravity (M) dM 0.08 mm

γM 168°

Stiffness (K) dK 0.73 mm

γK 17.54°

Force factor (Bl) dBl 0.9 mm

γBl 320°

Modal resonator (n=1,2)

First mode (n=1) Second mode (n=2)

Resonance frequency f1 = 151 Hz f2 = 129 HzRelative gain at fn RG1= 36 dB RG2= 31.6 dBLoss factor η1 = 0.016 η2= 0.014Quality factor Q1 = 30.2 Q2 = 34.7

Root Cause of the Rocking Mode (Imbalance) Excitation of the Rocking Resonator


replaced by

)(

),(

)(

coil

cc

SD v

dSv

S c

r

using mean voice coil velocity

2

),,(

)(

2

0

drv

vcoil

coil

)(q

),( cv r

Radiator‘s surface

coilr)(q

)(DS

)(coilv

Rigid piston

The effective radiation area SD is an important lumped parameter describing the surface of a rigid piston moving with the mean value of the voice coil velocity vcoil and generating the same volume velocity q as the radiator‘s surface. The integration of the scanned velocity can cope with rocking modes and other asymmetrical vibration profiles.

Effective Radiation Area SDDefinition

)( 0DD SS Reading the absolute value at fundamental resonance


0,5

1,0

1,5

2,0

2,5

3,0

cm2

1 10Frequency [kHz]

)( 0DS

f0

)( 0DD SS

Reading the absolute value at fundamental resonance gives

)(

),()( ,,

coil

icicD x

SrxS

Method:1. Measurement of vibration and radiatior‘s geometry2. Integration over surface and voice coil position3. Calculation of effective radiation area SD()4. Reading SD(s) at fundamental frequency s

Problems:• Surface is covered by grill (surface is not visible for laser)

Laser Scanner Technique

Voice coil


Predicting the Acoustical Output at higher frequencies using lumped parameters

useful for transducers having• high complexity of the mechanical vibration• low complexity in radiation directivity (ka < 1)e.g. (in-ear) headphones, microspeaker application

radiated SPL,sound power,

using effective radiation areaSD(f) as a function of frequency f

KLIPPEL

0

100

200

300

400

500

600

700

800

900

1000

102 103 104

Effective radiation Surface (Sd)

Sd [

cm^2

]

f [Hz]

Sd

30

40

50

60

70

80

102 103 104

Total Sound Pressure Level

SP

L [d

B]

Frequency [Hz]

Total Sound Pressure Level

MMD CMD(x) RMS(v)-1Bl(x)

Re

v=dx/dt

i

Bl(x)v

F=Bl(x)i

U p

pSd(f,x)

ZL(f,x)

Sd(f,x)

MMD CMD(x) RMS(v)-1Bl(x)

Re

v=dx/dt

i

Bl(x)v

F=Bl(x)i

U p

q=Sd(f,x)vpSd(f,x)

ZL(f,x)

Sd(f,x)

Zload(f,x) pout(r)


Example Microspeaker in LaptopFar field information

3 kHz

Vertical (phi = 0 degree)

Horizontal (phi=90 degree)

The left and right speaker generate a complex directivity pattern !

left

right


KLIPPEL

0

50

100

150

200

250

0.01 0.1 1 10

Apparent Sound Power vs. Distance at f=501 Hz

Lw/d

B

DISTANCE r / m

N=0 N=1 N=2 N=3 N=4 N=5N=6 N=7 N=8 N=9 N=10 N=11N=12 N=13 N=14

Is the User Located in the Near-Field or Far-Field?

Determining the location of the near and far-fields is important for personal and handheld audio devices !!

Far-field

Near-field

user

monopoledipolesquadrapoles

Multipoles of nth-order

Power is independent of distance


Comprehensive 3D Informationsupports the evaluation of spacial sound effects

KLIPPEL

60

65

70

75

80

85

90

95

100

1 10

Near Field SPL Response

dB

SP

L/

V

frequency / kHz

Left Ear

Wave front propagation

3kHz

SPL distribution

3kHz

Observation plane

ComprehensiveInformation

(Amplitude) (Phase)

Right EarListening Points


Transducer Nonlinearities

Nonlinearities • nonlinear AC flux, reluctance force, inductance • electro-dynamical motor• stiffness and damping of suspension• acoustical system





Time variant properties


Dynamic Measurement of motor and suspension nonlinearities

Linear Parameters• T/S parameters at x=0• Box parameters fb,Qb• Impedance at x=0

Thermal Parameters• Thermal resistances Rtv, Rtm• Thermal capacity Ctv, Ctm• Air convection cooling

State Variables• peak displacement during measurement• voice coil temperature • eletrical input power,

Nonlinear Parameters• nonlinearities Bl(x), Kms(x), Cms(x), Rms(v), L(x), L(i)• Voice coil offset• Suspension asymmetry

• Maximal peak displacement (Xmax)

AV

Digitalprocessing

unit

Poweramplifier Speaker

NonlinearSystem

Identification

Voltage & current

Noise,Audio signals(music, noise)

Multi-tonecomplex

Stimulus


Example: MicrospeakerNonlinear Parameters measured in air and in vacuum

KLIPPEL

0,000

0,025

0,050

0,075

0,100

0,125

0,150

-1,0 -0,5 0,0 0,5 1,0

Nonlinear Damping Rms(v)

Rm

s(v)

[kg

/s]

v [m/s]

Rms(v) in vacuum

In vacuum

In air

KLIPPEL

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3

Force factor Bl (X)

Bl [

N/A

]

<< Coil in X [mm] coil out >>

-Xprot < X < Xprot in vacuum

In vacuumIn air

KLIPPEL

0,00

0,25

0,50

0,75

1,00

1,25

1,50

-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3

Stiffness of suspension Kms (X)05:41:30

Km

s [N

/mm

]

<< Coil in X [mm] coil out >>

-Xprot < X < Xprot in vacuum

In vacuum

In air

KLIPPEL

5

10

15

20

25

18750 19000 19250 19500 19750 20000 20250 20500 20750

Distortion Analysis

[%]

t [sec]

Db Dc Dl Dl(i)

In airKLIPPEL

0

5

10

15

20

25

30

35

0 250 500 750 1000 1250 1500 1750 2000

Distortion Analysis

[%]

t [sec]

Db Dc Dl Dl(i)

In vacuum

Drms(v)Drms(v)

Drms(v)

Drms(v)


Nonlinear Mechanical Resistance Rms(v)

woofer

gap

domespider

magnet

Pole piece

Air flow

Rms(v) depends on velocity v of the coil due to air flow and turbulences at vents and porous material (spider, diaphragm)

v

Rms(v)

v

microspeaker

Air flowv


Nonlinear Interactions between Vibration Modes

v

TF

p(rs)

p‘(rs)

Nlul

QK S R

Xuc

u

p(ra)

High amplitudes Q of the activation mode (e.g. fundamental mode Q0) changes• Natural frequencies of the transfer modes

(higher-order break up modes)• Mode shape Ψ (Q) of the transfer mode• Excitation T of the transfer modes• Sound radiation by the transfer modes

20log(|Q(f)/q0|)

20 log(f/f0)f0 f1 fMfm

Qm(f)

Q0(f)

Q1(f)

QM(f)

fp

Transfer Modes

Activation Mode

v

T

D

F

N

p(rs)

p‘(rs)

Nlul

QK S R

Xuc

u

p(ra)

v

T

D

F

N

p(rs)

p‘(rs)

Nlul

QK S R

Xuc

u

N2

Ψ (Q)

p(ra)

v

T

D

F

N

p(rs)

p‘(rs)

Nlul

QK S R

Xuc

u

N2

Ψ (Q)

p(ra)

v

T

D

F

N

p(rs)

p‘(rs)

Nlul

QK S R

Xuc

u

N2

Ψ (Q)

p(ra)


Nonlinear Variation of the Mode ShapeInteraction with the fundamental mode

The displacement generated by the bass tone generates the geometry of the surround Other mode shape at higher frequencies

Mode shape at rest position

Negative voice coil displacement

Positive voice coil displacement

N

i

iDCi

DCD

xvs

vxSq

0

)()(

)(),()(

Performing an incremental measurement of the effective radiation area at the original rest position and with a positive and negative offset of 0.3 mm.

v

pp

q

FA

SD(ω,x)


Effective Radiation Surface Sd(f,x)versus frequency f and voice coil displacement x

0,7

0,8

0,9

1,0

1,1

1,2

1,3

1,4

1,5

1,7

1 10

Sd

cm2

f [kHz]

xdc= +0.3 mm

xdc= -0.3 mm

xdc= =0.0 mm

10 % IMD

20-50 % IMD

The displacement varying Sd(x) generates high values of intermodulation distortion

N

i

ii txtvstq

0

1- )()(*)()( F

N

i

iiA txtqstF

0

1- )()(*)()( F

N

i

iDCi

DCD

xvs

vxSq

0

)()(

)(),()(

Volume velocity for a DC displacement xdc

v

pp

q

FA

SD(ω,x)


Modeling of the Acoustic System

CAR(prear)

CAB(x,pbox)

pbox

RAB

RAP(qp)

MAP

q qp

prear

RAR

SD(ω,x)

p

diaphragm

backplate

magnet

pole plate

rear volume

rear volume

front volume

front volume

port

port

The voice coil displacement of microspeaker operated in a sidefire system is not small comparedto the geometrical dimensions of the front volume and rear volume

Example: Microspeakermounted in an enclosure with sidefire exit

diaphragm

diaphragm


Dynamic Nonlinear Elements

CAR(prear)

CAB(x,pbox)

pbox

RAB

RAP(qp)

MAP

q qp

prear

RAR

SD(ω,x)

p

F

v

)()(*)()( -1 tdtqZtp Lload F

),()(*),(),( -1 tdtqHtp aout rrr F

c

S c

jk

cD

dSe

vvS

jH

c

c

rrrr

rr

),()()(4

),( 0

N

i

ii

D

xvs

vxSq

0

)()(

)(),()(

sound pressure at receiving point r in the far field

Transfer function describing sound radiation and propagation to the point rin the far field using Rayleigh equation

lineartransfer function

nonlineardistortion

volumevelocity

acoustical loadimpedance

sound pressure nonlinear

distortion

qc


Air Compliance in Small Vented Enclosures

voice coil displacement x varies air volume air is not compressed but exchanged with ambience Helmholtz resonance fp(x) varies with displacement x displacement generates intermodulation distortion at port resonance critical in small personal audio devices with complex outlet geometry

backplate

magnet

pole plate port

air volume VB(x)

displacement x

xSVxV DB 0)(

Compliance CAB(x,p) of enclosed air

2

000

0 12

6

1

2

11),(

p

p

p

p

p

xSVxpC D

AB

withstatic air pressure p0

static air volume V0 at coi‘s rest positionadiabatic coefficient κ

Sd

CAR(prear)

CAB(x,pbox)

pbox

RAB

RAP(qp)

MAP

SdVqp

prear

radiation

RAR

diaphragm area SD

fp(x) fs f

SPL x


Measurement of Symptoms

Generationof Stimulus

AnalysisTransferBehavior

Measurementof

State Variables

• requires stimulus • requires special sensor (micro, laser, anemometer)• applied to selected state variables (pressure, current)• requires prototype


Nonlinear Symptom: New Spectral Componentsgenerated by Two-tone Stimulus

difference tones summed tonesharmonics

frequency

Amplitude sound pressure spectrum

Nonlinear System

input output

-50

-40

-30

-20

-10

0

10

20

101 102 103

Response 1Frequency Domain

dB

u (

Uo =

1V

)

f [Hz]

-50

-40

-30

-20

-10

0

10

20

101 102 103

Response 1Frequency Domain

dB

u (

Uo =

1V

)

f [Hz]

IntermodulationDistortion

3rd 3rd

nth

12 )1( fnf

nth

12 )1( fnf

2nd2nd

12 ff 12 ff

3rd

2nd

12 f

nth

1nf

“bass tone”1f

“voice tone”2f


Exercise: WooferAnalysis of Multi-tone Distortion

KLIPPEL

0

20

40

60

80

100

120

102 103

Spectrum sound pressure output

[dB

]

Frequency [Hz]

fundamental components

Bl(x)Kms(x)

Le(x)

Rms(x,v) Le(i)Bl(x)Kms(x)Le(x) Doppler Effect Cone Vibrationcauses:

total distortion

fs=60 Hz

out of band distortion

Le(i)


Exercise: MicrospeakerAnalysis of Multi-tone Distortion

KLIPPEL

30

40

50

60

70

80

90

100

110

120

130

Distortion Components

[dB

]

Le(i)

fundamental components

20102 103 104

Frequency [Hz]

Bl(x)

Kms(x)

Le(x)

Rms(x,v) Le(i)Bl(x)Kms(x)Le(x) Doppler Effect Cone Vibrationcauses:

out of band distortiontotal distortion

Rms(x,v)

fs=600 Hz


Compression of SPL Fundamentalfor a sinusoidal tone versus frequency

KLIPPEL

80

85

90

95

100

105

110

115

120

125

130

20 50 200 500 2k

Sound Pressure Response

dB

- [

V]

(rm

s)

Frequency [Hz]

Long Term Response linear response

Limited by peak displacement

Limited by coil temperature

Long term response was measured by using a stepped sine wave and cycling 1 min on/1 min off


Nonlinear Symptom: Amplitude Compression

KLIPPEL

0,0

0,5

1,0

1,5

2,0

2,5

0,0 2,5 5,0 7,5 10,0 12,5 15,0

Fundamental component| X ( f1, U1 ) |

X

[mm

] (

rms)

Voltage U1 [V]

23.4 Hz

Linear System


Unique Symptom of Rms(v) Compression of the Fundamental Component in a microspeaker

KLIPPEL

-55,0

-52,5

-50,0

-47,5

-45,0

-42,5

-40,0

-37,5

102 103

Compression| X ( f1, U1 ) | * Ustart / U1

[dB

] -

[mm

] (r

ms)

Frequency f1 [Hz]

0.10 V 1.08 V 2.05 V 3.03 V 4.00 V

KLIPPEL

-57,5

-55,0

-52,5

-50,0

-47,5

-45,0

-42,5

-40,0

-37,5

-35,0

2*102 4*102 6*102 8*102 103 2*103

Compression| X ( f1, U1 ) | * Ustart / U1

[dB

] -

[mm

]

(rm

s)

Frequency f1 [Hz]

0.10 V 1.08 V 2.05 V 3.03 V 4.00 V

operated in vacuumoperated in air

Note: The nonlinear damping caused by Bl(x) generates the same expansion (moredisplacement at resonance) in vacuum and in air !!!


DC-Air Flow generated by a smart phone with side-fire port

diaphragm

backplate

magnet

pole plate

Air mass in the port

Compliance of enclosed air

Rectification of the AC flow generates jet stream

Courtesy by Qneo see App „Blower“


Flow Resistance RA(v) of a Portat Medium Amplitudes

• air in the port does not behave like an air plug

• energy dissipated in the far field

• Harmonics at low frequencies

• RA(v) ~ |v|*mv

RA(v)


Nonlinear Symptom: Instability

t

x

t

x

Bifurcation

into two states

Small Signal Domain Large Signal Domain

Stimulus: Single tone (f = 1.5fs ) at high amplitude


Time Variant Properties

Nonlinearities • nonlinear AC flux, reluctance force, inductance • electro-dynamical motor• stiffness and damping of suspension• acoustical system

MMS CMS(ω,x,t) RMS(ω,v)-1Bl(x,t)

RE(t)

v

i

Bl(x,t)vu p

LE(ω,x,i) F=Bl(x,t)i

p

q

FA

SD(ω,x)Zload(ω)

pout(r)

Frel(x,i)

RL(ω,x,i)

dL(q)





Time variant properties • heating, climate impact, load,

fatigue, aging, gravity


KLIPPEL

50

60

70

80

90

100

110

120

130

140

150

160

170

0 500 1000 1500 2000 2500 3000 3500

resonance frequency fs (t) at rest position X=0

Km

s [N

/mm

]

t [sec]

fs (X=0)

Hz

Influence of Ambient ConditionsEnvironmental Testing

KLIPPEL

-3,0

-2,5

-2,0

-1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

2,0

2,5

3,0

0 500 1000 1500 2000 2500 3000 3500

[mm

]

t [sec]

Xpeak Xdc Xdcmax Xbottom

No additional sensor

More than one octave

shift

Significant reduction of displacement

KLIPPEL

0

25

50

75

100

125

150

0

1

2

3

4

5

6

7

8

9

10

11

12

0 500 1000 1500 2000 2500 3000 3500

De

lta T

v [K

] P [W

]

t [sec]

Delta Tv Tambient P real P Re Pnom

Winter

Sommer

Ambient temperature

0.5 mm dc displacement generated dynamicall

Peak displacement


Influence of the Climate on Stiffness Kms(x)

KLIPPEL

0,0

2,5

5,0

7,5

10,0

12,5

15,0

17,5

-4 -3 -2 -1 0 1 2 3 4

Stiffness of suspension Kms (X)

Km

s [N

/mm

]

X [mm]

Tamb = 60 deg C Tam = -18 deg C Tamb = 20 deg C

At low ambient temperature(-18 degree C) the rubbersurround becomes 4 timesstiffer and limits negative peak displacement at -1.5 mm

-18oC

20oC

60oC


Resonance Frequency versus Ambient Temperaturetwo transducers with different surround material

stiffness increased by factor 16 (compared to 60oC

impregnated textilesurround

foamsurround

Experiments performed at controlled conditions (30 % relative humidty)Details: Diploma Thesis Ch. Kochendörfer TU Dresden, 2011


Consequences of Climate ImpactSPL response of a vented loudspeaker system

winter performance

sommer performance

Passive system alignment (box tuning) assumes constant properties of the transducer !!

driver resonance frequency

port resonance(Helmholtz)


Overview of transducer characteristicsCharacteristic Interpretation Importance for

Micro-speakerImportance forHeadphone

Importance for Loudspeaker

Re(t) Time variance of the voice coil DC resistance due to thermal dynamics high medium high

Le(ω), RL(ω) Voice coil inductance and AC resistance depending on frequency negligible negligible high

Le(x), RL(x) Voice coil inductance and AC resistance depending on displacement low negligible high

Le(i), RL(i) Voice coil inductance and AC resistance depending on current negligible negligible medium

Frel(x,i)Reluctance force depending on voice coil current and displacement x negligible negligible small

Bl(x) Nonlinear force factor depending on displacement x high high high

Bl(t) Time variance of the force factor due an offset in the voice coil rest position high high medium

CMS(x) Nonlinear compliance depending on displacement x high high high

CMS(t) Time variance of the compliance due aging, climate high high high

CMS(ω)RMS(ω)

Visco-elastic behavior (creep) of the suspension high medium low

RMS(v) Nonlinear mechanical resistance depending on velocity v high low negligible

v(rc)-v Deviation between distributed voice coil velocity and mean value v high high negligible

RRL Relative rocking level high high smallSD(ω) Frequency dependency of radiation area low high medium

SD(x) Nonlinear effective radiation area depending on displacement x high high medium

ZA(p) Nonlinearity of the acoustic Load high small small

ZA(ω) Complexity of the frequency dependency of the acoustic load low high low

HA(r, ω) Complexity of the directional radiation characteristic low low high

dL(q) Nonlinear load distortion generated by the acoustical system high negligible medium

dA(r,t) Nonlinear output distortion generated by the acoustical system medium low low


Conclusions

• Microspeakers major source of innovation

• Innovative transducer design requires more accuratemodeling

• Identification of free model parameters newmeasurement techniques

• Diagnostics based on parameters becomes moreimportant

• Testing with audio like stimuli required for assessingthermal, nonlinear and time varying properties

• Suspension and radiator is the weakest component !


Thank you !

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