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MICROSPEAKERS – HYBRIDS BETWEEN HEADPHONES AND

by Wolfgang Klippel

KLIPPEL GmbH Dresden University of Technology

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

Content

1. Motivation – similarities and particularities 2. Basic 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

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 3 Similarities between headphones, microspeakers and loudspeakers

Electro-dynamical Distributed parameter transduction principle modeling at high mostly used required

headphone Lumped parameter modeling at low Voice coil + frequencies applicable

microspeaker system system

low efficiency using a mechanical suspension system

low acoustical load

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 4

Particularities between headphones, microspeakers and loudspeakers

flat radiators  low bending stiffness Single transducer Large coil  early break-up no spider high magnetic AC Flux

microspeaker loudspeaker prone to headphone rocking mode system system large motor 2 strength Bl /Re

dominant electrical low electrical damping small size damping (acoustical and mechanical low efficiency damping required) generates thermal problems

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 5 Basic Electroacoustical Modeling

RE LE

F=Bli FA q i SD

-1 u Blv Bl MMS CMS RMS p Zload pout(r) v

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)

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

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 6

Extended Electroacoustical Modeling

RE(t) LE(ω,x,i) F=Bl(x,t)i q

FA RL(ω,x,i) i SD(ω,x) Frel(x,i) Zload(ω)

-1 u Bl(x,t)v Bl(x,t) MMS CMS(ω,x,t) RMS(ω,v) p pout(r) v

dL(q)

higher order Radiation mechanical into lumped parameter modeling (piston mode) modes 3D space

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

Nonlinearities Time variant properties

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 7 Lossy Inductance ZL(j) measured curves fitted by an ideal inductance

Re ZL(f)

Bli i L e • 1 Parameter

-1 U Blv Bl Mms Cms(f) Rms V=dx/dt only • Large deviation • limited use

6dB/octave

10 100

90 90 degree Phase (fitted)

80 [deg] 1 70 []

Magnitude 60 (measured) Phase (measured) 0.1 50 Magnitude (fitted) 40 1 2 5 10 20 50 100 200 500 1k [Hz] Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 8

Mechanical Compliance Cmd(f)

  f / f  C ( f )  C 1 log  min  MD min  10 2   1 f / f     min  creep factor  or 

Mechanical compliance (driver in vacuum)

Compliance Cmd(f) fmin

Minimum c omplianc e Cmd0 EFFECT: compliance 0,00100 C (f ) increases to lower md d C (f )≈C (Ritter) frequencies md d md0 0,00075 CAUSE: creep factor  or  viscoelasticity of [mm/N] 0,00050 describes relative the material increase of compliance 0,00025 per decade CONSEQUENCES: more displacement fmin 0,00000 than predicted by 101 102 103 104 traditional modeling Frequency [Hz]

fd

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 9 Mechanical Resistance Rmd(f)

   f  R ( f )  R C log e   tan1  MD 0 min 10     2  fmin 

Magnitude of mechanical impedance

1 KLIPPEL 10 Compliance Cmd(f) Mass Mmd Losses R (f) EFFECT: 10 0 md losses increases to lower frequencies 10 -1 Rmd(fd) Total Impedance CAUSE: 10 -2 [kg/s] viscoelasticity transfers 10 -3 compliance into Residual Zres losses 10 -4

CONSEQUENCE: 101 102 103 104 electrical Frequency [Hz] impedance increased below resonance frequency fd resonance (not critical)

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 10

Voice Coil Displacement Laser measurement on Microspeakers and Headphones

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

Centre 0 degree rim 90 degree rim Measured 1 2

180 degree rim 270 degree rim 3 4 5 0,125 KLIPPEL KLIPPEL

0,125 0,100

0,100

0,075

0,075 [mm/V] [mm/V] 0,050 0,050

0,025 0,025 Measurements at 5 points Repeatability at one point

0,000 0,000 50 100 200 500 1k 2k 5k 10k 50 100 200 500 1k 2k 5k 10k Frequency [Hz] Frequency [Hz]

Conclusion: x 2 • No piston mode x(,r ,)d • Spatial averaging is required  avg xx x x ()  0 coil 2 x

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 11 Experimental Modal Analysis not restricted to round radiators

Vibration Data

r c  X(f, rc) X  ΨΣ H f

Scanner Singular Value Decomposition Natural frequency,  Loss factor, Ψ H Modal compliance, Σ fitting error MODE SHAPE Frequency Responses Fitting S1 1st Mode 1st Mode 1st Mode : f , η ,C ,e S2 1 1 1 1

2nd Mode 2nd Mode 2nd Mode: f2, η2,C2,e2

Sn

nth Mode nth Mode nth Mode : fn,ηn,Cn,e3 Singular values f rc

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 12

Modalanalysis of a Microspeaker

1 2 3

10 RRL = -30 dB

17

Rocking mode

Rocking mode

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 13 Modalanalysis of a Headphone

5 2 3 1 8 4 6

RRL = -10 dB

Rocking mode

Rocking mode

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 14

Loudspeaker Defect: Voice Coil Rubbing

Cause: rocking mode at 328 Hz • contains reproducible and stochastic components

Voice coil

gap voice coil rubbing

distortion signal

time one period

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 15 What Causes Rocking Modes ?

µk

Stiffness Imbalances µ m Mass Imbalances

µBl

force factor imbalance Which root cause excites the rocking ?  mass, stiffness, force factor Where is the root cause located ?  angle showing the direction How to assess the magnitude of the excitation ?  moments

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 16

Mass Imbalance

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

DM(y,z0)

xcoil0

rigid body y1 y1

FM y

z Mms x x2 x2 0 yCG y

nodal lines pivot point diaphragm pole plate

coil magnet z backplate

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

Imbalances Moments Tilting angles (mass, stiffness, Bl)  2 1 1 2

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 17 A New Measurement Technique

System Identification

SCANNER

one piston modes, Root-causes Mode Boosting Total Vibration two Rocking Modes (imbalances) Coupling Mechanism Acumulated Acceleration Level (AAL)

DIAGNOSTICS

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 18

Application in Transducer Diagnostics (1) Example Headphone transducer

AAL KLIPPEL 0 70 KLIPPEL 70 AAL0 60 60 AAL2,Bl AAL1,T

50 50

40 40 AAL2,T

30 –Undeformed Region 30 ] AAL1,M V 1 / 20 AAL1,K 20 AAL AAL 10 2,K AAL [dB AAL 10 1,Bl

AAL [dB/1V] AAL[dB/1V] – Undeformed Region AAL2,M Measured 0 0 40 60 80 100 200 400 600 800 40 60 80 100 200 400 600 800 Frequency [Hz] Frequency [Hz]

Conclusions: Relative Rocking Level Dominant Second RRL(dB) • Good agreement between (n=1) (n=2) measurement and modelling

Total contribution (T) RRL1,T = 5.4 RRL2,T = -12.9 • First rocking mode has

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

Stiffness Imbalance (K) RRL1,K = 1.4 RRL2,K = -17.7 energy than piston mode)

Force factor Imbalance (Bl) RRL1,Bl = -9.6 RRL2,Bl = -12.6 • Stiffness imbalance provides the largest contribution (dominant cause)

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 19 Application in Transducer Diagnostics (3) Example Headphone transducer

Root Cause of the Rocking Mode (Imbalance) Excitation of the Rocking Resonator Center of Coordinates Value Imbalance Characteristics Value

Gravity (M) d 0.08 mm M Mass (M) CFRM 0.83 %

γM 168° βM 345.9°

Stiffness (K) dK 0.73 mm Stiffness (K) CFRK 2.22 %

γK 17.54° βK 14.6° Force factor (Bl) d 0.9 mm Bl Force factor (Bl) CFRBl 0.71 %

γBl 320° βBl 320.8°

Total (M,K,Bl) CFRT 3.49%

βT 1.5°

CFR CFR CFR CFR M K Bl T Conclusions: 0° • A small stiffness imbalance (0.73 mm offset from pivot point) is the root cause stiffer Second • High Quality factor (> 30) of the modal mode at α2 %

E rocking resonator generates high 90° 270° amplitudes at resonance (150 Hz) CFR

Modal resonator First mode (n=1) Second mode (n=2) Dominant (n=1,2) Resonance frequency f1 = 151 Hz f2 = 129 Hz mode at α1 180° Relative gain at fn RG1= 36 dB RG2= 31.6 dB Loss factor η1 = 0.016 η2= 0.014 Quality factor Q = 30.2 Q = 34.7 CFRE % 1 2

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 20

Effective Radiation Area SD Definition

Radiator‘s surface replaced by Rigid piston

v(,r )dS S D ()  c c Sc S D ()  vcoil () vcoil ()

v(,rc ) using mean voice coil velocity

2 rcoil v(,rcoil ,)d q()  q() v ()  0 coil 2

Reading the absolute value at fundamental S D  S D (0 ) resonance

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.

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 21 Laser Scanner Technique

Method: 1. Measurement of vibration and radiatior‘s geometry 2. Integration over surface and voice coil position

3. Calculation of effective radiation area SD() 4. Reading SD(s) at fundamental frequency s

 x(,rc,i )  Sc,i Problems: S D ()  xcoil () • Surface is covered by grill (surface is not visible for laser)

cm2

Reading the absolute value at Voice coil 3,0 fundamental resonance gives 2,5 SD  S D (0 ) 2,0

1,5 S D (0 ) 1,0

0,5

f 1 10 0 Frequency [kHz]

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 22

Predicting the Acoustical Output at higher frequencies using lumped parameters

Effective radiation Surface (Sd)

Sd 1000 KLIPPEL

900

800

700 600 using effective radiation area 500

Sd [cm^2] Sd 400 S (f) as a function of 300 D 200 frequency f 100

0 102 103 104 f [Hz]

Re ZL(f,x)

F=Bl(x)i pSd(f,x) q=Sd(f,x)v i Sd(f,x)

-1 U Bl(x)v Bl(x) MMD CMD(x) RMS(v) p Zload(f,x) pout(r) radiated SPL, v=dx/dt power,

Total Level Total Sound Pressure Level

80

70

60

useful for having SPL [dB] 50

40

30 • high complexity of the mechanical vibration 102 103 104 Frequency [Hz] • low complexity in radiation directivity (ka < 1) e.g. (in-ear) headphones, microspeaker application

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 23 Example Microspeaker in Laptop Far field information

Vertical (phi = 0 degree)

right left

Horizontal (phi=90 degree) 3 kHz

The left and right speaker generate a complex directivity pattern !

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 25

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

Apparent Sound Power vs. Distance at f=501 Hz N=0 N=1 N=2 N=3 N=4 N=5 N=6 N=7 N=8 N=9 N=10 N=11 N=12 N=13 N=14

KLIPPEL

250

200

user 150 Far-field Lw / dB

100 monopole dipoles Power is independent of distance 50 quadrapoles

0 Near-field Multipoles of 0.01 0.1 1 10 DISTANCE r / m nth-order

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

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 26 Comprehensive 3D Information supports the evaluation of spacial sound effects

Near Field SPL Response

100 KLIPPEL

95 Left Ear

90

85 V / Listening 80 Right Ear Observation plane dB SPL Points 75

70

65

60 1 frequency / kHz 10

SPL distribution Wave front propagation 3kHz Comprehensive 3kHz Information

(Amplitude) (Phase)

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 27

Transducer Nonlinearities

higher order Radiation mechanical into lumped parameter modeling (piston mode) modes 3D space

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

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

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 28 Dynamic Measurement of motor and suspension nonlinearities

Stimulus Noise, A Audio (music, noise) V

Power Multi-tone & current Speaker complex NonlinearDigital State Variables processingSystem • peak displacement during measurement Identification • voice coil temperature unit • eletrical input power,

Linear Parameters Nonlinear Parameters Thermal Parameters • T/S parameters at x=0 • nonlinearities Bl(x), Kms(x), Cms(x), • Thermal resistances Rtv, Rtm • Box parameters fb,Qb Rms(v), L(x), L(i) • Thermal capacity Ctv, Ctm • Impedance at x=0 • Voice coil offset • Air convection cooling • Suspension asymmetry • Maximal peak displacement (Xmax)

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 29

Example: Microspeaker Nonlinear Parameters measured in air and in vacuum

Force factor Bl (X) Stiffness of suspension Kms (X) Nonlinear Damping Rms(v) 05:41:30

-Xprot < X < Xprot in vacuum -Xprot < X < Xprot in vacuum Rms(v) in vacuum 0,150 0,8 KLIPPEL KLIPPEL KLIPPEL 0,7 1,50 0,125 In air In air In air

0,6 In vacuum 1,25 0,100 0,5 1,00 0,075 0,4 0,75 Bl [N/A] 0,3 [N/mm] Kms 0,050 Rms(v) [kg/s] In vacuum 0,50 0,2 0,025 In vacuum 0,1 0,25

0,000 0,0 0,00 -1,0 -0,5 0,0 0,5 1,0 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 v [m/s] << Coil in X [mm] coil out >> << Coil in X [mm] coil out >>

Distortion Analysis Distortion Analysis Db Dc Dl Dl(i)D (v) 25 KLIPPELrms Db Dc Dl DDl(i)(v) KLIPPELrms In air 35 In vacuum 20 D (v) 30 rms

25 15

20 [%] [%] 10 15

10 5 5 Drms(v) 0 0 250 500 750 1000 1250 1500 1750 2000 18750 19000 19250 19500 19750 20000 20250 20500 20750 t [sec] t [sec] Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 30 Nonlinear Mechanical Resistance Rms(v)

v

dome Air flow spider Rms(v)

gap magnet

v Pole piece woofer

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

microspeaker

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 31

Nonlinear Interactions between Vibration Modes

pp((rraa)) uu vv pp((rrs)s)

FF Q X uucc Q X TT KK SS RR p‘p‘((rrs)s) DD

uul l NNl l NN

NN22

ΨΨ (Q) (Q)

20log(|Q(f)/q0|) Activation Mode Q0(f) High amplitudes Q of the activation mode (e.g. fundamental mode Q0) changes • Natural frequencies of the transfer modes Q1(f) (higher-order break up modes) Transfer Modes Qm(f) • Mode shape Ψ (Q) of the transfer mode

QM(f) • Excitation T of the transfer modes • Sound radiation by the transfer modes

f0 fp f1 fm fM 20 log(f/f0)

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 32 Nonlinear Variation of the Mode Shape Interaction with the fundamental mode

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.

Negative voice coil displacement

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

Mode shape at rest position

q FA q()  S (, x )v() SD(ω,x) D DC N p i v   si ()v()xDC i0 Positive voice coil displacement

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 33

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

20-50 % IMD

Sd Volume velocity for a DC displacement xdc 1,7 q()  S D (, xDC )v() 2 N cm i   si ()v()xDC 1,5 i0 q

1,4 FA SD(ω,x) 1,3 10 % IMD p 1,2 xdc= -0.3 mm v

1,1 x = =0.0 mm 1,0 dc N q(t)  F -1s () * v(t) x(t) i 0,9  i xdc= +0.3 mm i0

0,8 N -1 i FA (t)  F si () * q(t) x(t) 0,7 i0 1 10 f [kHz]

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

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 34 Modeling of the Acoustic System

diaphragm port Example: Microspeaker front volume mounted in an enclosure with sidefire exit

q qp SD(ω,x) front volume RAP(qp) diaphragm port diaphragm

pole plate CAB(x,pbox) magnet RAB

backplate p rear volume pbox MAP CAR(prear)

p The voice coil displacement of rear microspeaker operated in a side fire system is not small compared rear volume R to the geometrical dimensions of AR the front volume and rear volume

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 35

Dynamic Nonlinear Elements

volume q()  S D (, x)v() velocity N i   si ()v()x i0

sound pressure at receiving point r in the far field v q qp -1 SD(ω,x) qc pout (r,t)  F H(r,) * q(t)  da (r,t) RAP(qp) linear nonlinear CAB(x,pbox) transfer function distortion F RAB p

pbox MAP CAR(prear) Transfer function describing sound radiation and propagation to the point r p rear in the far field using Rayleigh equation

RAR j e  jk rrc H(r,)  0 v(,r ) dS  c c 4S D ()v() r  rc -1 Sc sound p(t)  F Z load () *q(t)  d L (t) pressure acoustical load nonlinear impedance distortion Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 36 Air Compliance in Small Vented Enclosures

displacement x

qp SdV

RAP(qp) diaphragm area S CAB(x,pbox) D air volume VB(x) Sd RAB radiation

pole plate pbox MAP port CAR(prear) magnet prear backplate RAR

Compliance C (x,p) of enclosed air AB SPL x 2 V  S x   1 p   1 1  p   C ( p, x)  0 D 1    2     AB p 2  p  6   p  0   0    0   with

static air pressure p0 static air volume V0 at coi‘s rest position adiabatic coefficient κ f f s fp(x)

 voice coil displacement x varies air volume VB (x)  V0  SD x  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

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 37

Measurement of Symptoms

Measurement Generation Transfer of Analysis of Stimulus Behavior State Variables

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

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 38 Nonlinear Symptom: New Spectral Components generated by Two-tone Stimulus

Response 1 Frequency Domain Response 1 Frequency Domain

20 10 output 20 0 input 10 -10 0 -20 -10

dBu (Uo 1V) = -30 -20 -40 -30 -50 dBu (Uo = 1V) 101 102 103 -40 f [Hz] -50 101 102 103 f [Hz] Nonlinear System

Amplitude sound pressure spectrum

Intermodulation nd 2nd 2 2nd Distortion 3rd 3rd 3rd

nth nth nth harmonics difference tones summed tones

frequency nf f2  (n 1) f1 f2  f1 f2  f1 f  (n  1) f 2 f1 1 2 1 f1 f2 “bass tone” “voice tone”

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 39

Exercise: Woofer Analysis of Multi-tone Distortion

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

Spectrum sound pressure output 120 KLIPPEL fundamental components

100 total distortion Bl(x) Kms(x) out of band distortion

80 Le(x) ] B d

[ 60 Le(i)

40

20

0 102 10 3 fs=60 Hz Klippel, Microspeaker – HybridsFrequency between [Hz] loudspeakers and headphones …, 40 Exercise: Microspeaker Analysis of Multi-tone Distortion

causes: Le(x) Kms(x) Bl(x) Rms(x,v) Le(i) Doppler Effect Cone Vibration Distortion Components

130 KLIPPEL 120 fundamental components Kms(x) 110 total distortion out of band distortion 100

90 Bl(x)

] 80 B d [ 70

60 Rms(x,v) Le(x) 50

40

30 Le(i) 20 10 2 10 3 10 4 fs=600 Hz Frequency [Hz] Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 41

Compression of SPL Fundamental for a sinusoidal tone versus frequency

Sound Pressure Response

Long Term Response linear response 130 KLIPPEL 125

120 Long term response was measured by 115 using a stepped sine 110 wave and cycling 1 105 min on/1 min off Limited by coil temperature 100 dB - [V] (rms) 95

Limited90 by peak displacement

85

80 20 50 200 500 2k Frequency [Hz]

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 42 Nonlinear Symptom: Amplitude Compression

Fundamental component | X ( f1, U1 ) |

23.4 Hz 2,5 KLIPPEL

Linear 2,0System

1,5

1,0 X [mm] (rms) X [mm]

0,5

0,0 0,0 2,5 5,0 7,5 10,0 12,5 15,0 Voltage U1 [V]

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 43

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

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

0.10 V 1.08 V 2.05 V 3.03 V 4.00 V 0.10 V 1.08 V 2.05 V 3.03 V 4.00 V KLIPPEL -35,0 KLIPPEL -37,5 -37,5

-40,0 -40,0

-42,5 -42,5

-45,0 -45,0

-47,5 -47,5

[dB] - [mm] (rms) -50,0 [dB] - [mm] (rms)

-50,0 operated in air -52,5 operated in vacuum -52,5 -55,0

-57,5 -55,0 2*102 4*102 6*102 8*102 103 2*103 2 3 10 10 Frequency f1 [Hz] Frequency f1 [Hz]

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

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 44 DC-Air Flow generated by a smart phone with side-fire port

Compliance of enclosed air

diaphragm pole plate magnet Air mass in the port backplate

 Rectification of the AC flow generates jet stream

Courtesy by Qneo see App „Blower“

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 45

Flow Resistance RA(v) of a Port at Medium Amplitudes

• air in the port does not behave like RA(v) an air plug • energy dissipated in the far field • Harmonics at low frequencies • R (v) ~ |v|*m A v Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 46 Nonlinear Symptom: Instability

Small Signal Domain Large Signal Domain

x x

t t

Bifurcation into two states Stimulus: Single tone (f = 1.5fs ) at high amplitude

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 47

Time Variant Properties

RE(t) LE(ω,x,i) F=Bl(x,t)i q

FA RL(ω,x,i) i SD(ω,x) Frel(x,i) Zload(ω)

-1 u Bl(x,t)v Bl(x,t) MMS CMS(ω,x,t) RMS(ω,v) p pout(r) v

dL(q)

higher order Radiation mechanical into lumped parameter modeling (piston mode) modes 3D space

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

Nonlinearities • nonlinear AC flux, reluctance force, inductance Time variant properties • electro-dynamical motor • heating, climate impact, load, • stiffness and damping of suspension fatigue, aging, gravity • acoustical system

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 48 Influence of Ambient Conditions Environmental Testing

Delta Tv Tambient P real P Re Pnom 150 12 KLIPPEL 11 125 10

9 100 8

7 P [W] No additional sensor 75 6

50 5

Delta Tv [K] Sommer 4

25 3 Ambient temperature 2 0 Winter 1

0 0 500 1000 1500 2000 2500 3000 3500 Xpeak Xdc Xdcmax Xbottom t [sec] 3,0 KLIPPEL Peak displacement 2,5

2,0 resonance frequency fs (t) at rest position X=0 1,5 0.5 mm dc displacement fs (X=0) 170 1,0 generated dynamicall 160 KLIPPEL 150 0,5

140 0,0

130 [mm] More than -0,5 Hz 120 -1,0 110 one octave 100 -1,5

Kms [N/mm] shift 90 -2,0 80 -2,5 70

60 -3,0

50 0 500 1000 1500 2000 2500 3000 3500 0 500 1000 1500 2000 2500 3000 3500 t [sec] t [sec] Significant reduction of displacement Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 49

Influence of the Climate on Stiffness Kms(x)

Stiffness of suspension Kms (X)

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

17,5 KLIPPEL

15,0

12,5

10,0 20oC

7,5 Kms [N/mm] -18oC At low ambient temperature 5,0 (-18 degree C) the rubber surround becomes 4 times o 2,5 60 C stiffer and limits negative peak displacement at -1.5 0,0 mm -4 -3 -2 -1 0 1 2 3 4 X [mm]

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 50 Resonance Frequency versus Ambient Temperature two transducers with different surround material

stiffness increased by factor 16 (compared to 60oC

impregnated textile surround

foam surround

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

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 51

Consequences of Climate Impact SPL response of a vented loudspeaker system

sommer performance

driver resonance frequency

winter performance

port resonance (Helmholtz)

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

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 52 Overview of transducer characteristics Characteristic Interpretation Importance for Importance for Importance for Micro-speaker Headphone Loudspeaker

Time variance of the voice coil DC resistance due to thermal R (t) high medium high e dynamics Voice coil inductance and AC resistance depending on L (ω), R (ω) negligible negligible high e L frequency Voice coil inductance and AC resistance depending on L (x), R (x) low negligible high e L displacement Voice coil inductance and AC resistance depending on L (i), R (i) negligible negligible medium e L current Reluctance force depending on voice coil current and Frel(x,i) displacement x negligible negligible small Bl(x) Nonlinear force factor depending on displacement x high high high Time variance of the force factor due an offset in the voice Bl(t) high high medium coil rest position Nonlinear compliance depending on displacement x CMS(x) high high high Time variance of the compliance due aging, climate CMS(t) high high high C (ω) Visco-elastic behavior (creep) of the suspension MS high medium low RMS(ω) Nonlinear mechanical resistance depending on velocity v RMS(v) high low negligible Deviation between distributed voice coil velocity and mean v(r )-v high high negligible c value v RRL Relative rocking level high high small

SD(ω) Frequency dependency of radiation area low high medium Nonlinear effective radiation area depending on S (x) high high medium D displacement x

ZA(p) Nonlinearity of the acoustic Load high small small Complexity of the frequency dependency of the acoustic Z (ω) low high low A load Complexity of the directional radiation characteristic HA(r, ω) low low high dL(q) Nonlinear load distortion generated by the acoustical system high negligible medium Nonlinear output distortion generated by the acoustical d (r,t) medium low low A system Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 53

Conclusions

• Microspeakers  major source of innovation • Innovative transducer design requires more accurate modeling • Identification of free model parameters  new measurement techniques • Diagnostics based on parameters becomes more important • Testing with audio like stimuli required for assessing thermal, nonlinear and time varying properties • Suspension and radiator is the weakest component !

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 54 Thank you !

Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 55