Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 1
MICROSPEAKERS – HYBRIDS BETWEEN HEADPHONES AND LOUDSPEAKERS
by Wolfgang Klippel
KLIPPEL GmbHDresden University of Technology
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 3
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 4
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 5
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 6
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 7
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 8
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)
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 9
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 10
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 11
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
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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
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Modalanalysis of a Microspeaker
Rocking mode
Rocking mode
RRL = -30 dB
1 2 3
10
17
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Modalanalysis of a Headphone
12 3
56
Rocking mode
Rocking mode
RRL = -10 dB
8 4
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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
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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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 17
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 18
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 19
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 20
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 21
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 22
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 23
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)
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 25
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, Microspeaker – Hybrids between loudspeakers and headphones …, 26
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 27
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 28
Transducer Nonlinearities
Nonlinearities • nonlinear AC flux, reluctance force, inductance • electro-dynamical motor• stiffness and damping of suspension• acoustical system
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 29
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 30
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)
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 31
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 32
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)
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 33
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)
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 34
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)
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 35
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 36
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 37
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 38
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 39
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 40
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)
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 41
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 42
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 43
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 44
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 !!!
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 45
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“
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 46
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)
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 47
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 48
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)
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 • heating, climate impact, load,
fatigue, aging, gravity
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 49
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 50
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 51
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 52
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)
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 53
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
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 54
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 !
Klippel, Microspeaker – Hybrids between loudspeakers and headphones …, 55
Thank you !