Klippel, Modeling of Micro-speakers, 1
Modeling the Large Signal Behavior of Micro-speakers
by Wolfgang Klippel,
KLIPPEL GmbHInstitute of Acoustics and Speech Communication
Dresden University of Technology
133rd AES Convention 2012
Klippel, Modeling of Micro-speakers, 2
AbstractThe mechanical and acoustical losses considered in the lumpedparameter modeling of electro-dynamical transducers may becomea dominant source of nonlinear distortion in micro-speakers,tweeters, headphones and some horn compression drivers wherethe total quality factor Qts is not dominated by the electricaldamping realized by a high force factor Bl and a low voiceresistance Re. This paper presents a nonlinear model describingthe generation of the distortion and a new dynamic measurementtechnique for identifying the nonlinear resistance R¬ms(v) as afunction of voice coil velocity v. The theory and the identificationtechnique are verified by comparing distortion and other nonlinearsymptoms measured on micro-speakers as used in cellular phoneswith the corresponding behavior predicted by the nonlinear model.
Klippel, Modeling of Micro-speakers, 3
Scope of the Paper
• Which are the dominant nonlinearities ?• How to verify the new modeling ?• How to measure those nonlinearities ?• What kinds of nonlinear symptoms (distortion, compression) are
generated ?• How good is the prediction of those symptoms using the
measured nonlinear parameters ?• What are the consequences for passive transducer design? • How important are the nonlinearities for digital systems
providing mechanical protection of microspeakers ?
microspeakers
Klippel, Modeling of Micro-speakers, 4
Generation of Signal Distortion
InputSignal
MeasuredSignal
linear distortion
nonlinear distortion
“Rub&Buzz” and other irregular
distortion
Klippel, Modeling of Micro-speakers, 5
Transducer Nonlinearities
displacement
30
3
10
1
0,3
X[mm]
Destruction
Nonlinear Behavior
Linear Modeling
Large signal performance
Small signal performance
•Bandwidth•Sensitivity•Flatness of Response•Impulse Accuracy
• Maximal Output• Distortion• Power Handling• Stability• Compression
Regular Nonlinearities
• generate deterministic distortion which are predictable
• are related with the design (geometry and material )
• are compromised by size, weight and cost
Klippel, Modeling of Micro-speakers, 6
Nonlinear Transducer Modeling
Electro-mechanicalTransducer
i(t)
u(t)
Dominant nonlinearities
Bl(x)Kms(x)Le(x)Le(i)Rms(v)
Air compression
Wave steepeningDoppler effect
Port nonlinearity
RoomInterference p(r2)
p(r1)
p(r3)
RoomAcoustics
RoomInterference
soundfield
Radiation
Radiation
Radiation
SoundPropagation
SoundPropagation
SoundPropagation
Mechano-acoustical
Transducerx(t)
Multiple Outputs
Single Input
Cone vibration
linearlinear nonlinear
Klippel, Modeling of Micro-speakers, 7
Force Factor Bl(x)Bl(x) determined by
• Magnetic field distribution
• Height and overhang of the coil
• Optimal voice coil position
0.00.51.01.52.02.53.03.5
5.0
-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5
N/A
<< Coil in X mm coil out >>
Bl(x)displacement
0 mm x
pole piece
pole platemagnet
coil
back plate
Φdc
B-field
F
Back EMF Voice coil velocityvxBlU )(
ixBlF )(Electro-dynamical driving force Voice coil current
Klippel, Modeling of Micro-speakers, 8
Stiffness Kms (x) of Suspension
Kms(x) determined by
• suspension geometry
• impregnation
• adjustment of spider and surround
xF
F
x1
2
3
4
5
6
-10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0
spider
total suspension
diplacement x mm
surround
N/mm
K
xxKF ms )(
displacementrestoringforce
Klippel, Modeling of Micro-speakers, 9
Voice Coil Inductance Le(x)
Le(x) determined by
• geometry of coil, gap, magnet
• optimal size and position of short cut ring
With shorting rings
Without shorting rings
0.0 0.5 1.0 1.5 2.0 2.5
4.0
-15 -10 -5 0 5 10 15
Le [mH]
<< Coil in X [mm] coil out
without shorting ring
voice coil displacement
Φcoil(+9 mm)
9 mm -9 mm xshorting ring
0 mm
Φcoil(-9 mm)
Φcounter
with shorting ring
DifferentiatedMagnetic flux
dt
ixLddt
ixdUind)(),(
dxxdLtiFrel)(
2)(2
Reluctanceforce
Klippel, Modeling of Micro-speakers, 10
Nonlinear Mechanical Resistance Rms(v)
Rms(v) depends on velocity v of the coil due to air flow and turbulences at vents and porous material (spider, diaphragm)
Rms(v)
v
microspeaker
Air flow v
Klippel, Modeling of Micro-speakers, 11
Nonlinear Lumped Parameter Modeling
Mechanical Resistance Rms(v)
Force factor Bl(x)
Parametric Excitation
Stiffness Kms(x)
Reluctance Force Fm
Inductance
Le(x,i)
Differentiated Flux
dx
xdLidt
ixiLdtu
RxBl
dtdvMv
RxBlvRxxK ee
ems
emsms
)(2
),()()()()()(
22
Nonlinear damping
Nonlinear Restoring force
Klippel, Modeling of Micro-speakers, 12
Ranking List ofTransducer Nonlinearities
1. Force Factor Bl(x) 2. Compliance Cms(x)3. Inductance Le(x)4. Flux Modulation of Le(i)5. Mechanical Resistance Rms(v)6. Nonlinear Sound Propagation c(p)7. Doppler Distortion (x)8. Flux Modulation of Bl(i)9. Nonlinear Cone Vibration 10. Port Nonlinearity RA(v)11. many others ...
horns
tweeter
woofers
microspeaker
microspeaker
Klippel, Modeling of Micro-speakers, 13
Nonlinear Mechanical Resistance Rms(v)
Nonlinear Damping
dx
xdLidt
ixiLdtuR
xBldtdvMvvR
RxBlxxK ee
emsms
ems
)(2
),()()()()()(22
Source of distortion: Multiplication of velocity with a function of velocity
)()( 2
vRRxBl
mse
This nonlinearity is not relevant for• woofers• subwoofers• midrange drivers (tweeters)• transducers with dominant electrical
damping
This nonlinearity is important for• microspeakers • air compression drivers• microphones• headphones• transducers with dominant mechanical
damping
)()( 2
vRRxBl
mse
Klippel, Modeling of Micro-speakers, 14
Block-oriented Model of loudspeaker with Rms(v) under current drive
fs
band-pass
multiplier
distortion
s
first-orderdifferentiator
p
soundpressure
current i
Rms(v)-Rms(0)
vVelocity
forceFBl
vRvRBlisMsRK
sLv msmsmsmsms
)0()(*)0( 2
1
nonlinear operation
band-pass filtering
Klippel, Modeling of Micro-speakers, 15
Generalized Signal Flow Modeldescribing a separated loudspeaker nonlinearity
pre-filterH1,1(f)
1st state variable
multiplier
distortion
fsVoltagesound
pressurehighpass
Static Nonlinearity
pre-filterH1,2(f)
post-filterH2(f)
2nd state variable
feed-back loop
distortion added to the inputpost-shaping
post-shaping
pre-shaping
Klippel, Modeling of Micro-speakers, 16
The Particularities of Each Nonlinearity NONLINEARITY
INTERPRETATION
PRE-FILTER H1,1(f) (output)
PRE-FILTER H1,2(f) (output)
POST-FILTER H2(f)
Stiffness Kms(x) of the suspension
restoring force Low-pass (displacement x)
Low-pass (displacement x)
1
Force factor Bl(x) electro-dynamical force Band-stop (current i)
Low-pass (displacement x)
1
nonlinear damping Band-pass (velocity v)
Low-pass (displacement x)
1
Inductance Le(x) self-induced voltage Band-stop (current i)
Low-pass (displacement x)
differentiator
reluctance force Band-stop (current i)
Low-pass (displacement x)
1
Inductance Le(i) varying permeability Band-stop (current i)
Band-stop (current i)
differentiator
Mechanical resistance Rms(v)
nonlinear damping Band-pass (velocity v)
Band-pass (velocity v)
1
Young’s modulus E() of the material
cone vibration Band-pass (strain
Band-pass (strain
1
Speed of sound c(p) nonlinear sound propagation (wave steepening)
High-pass (sound pressure p)
High-pass (sound pressure p)
differentiator
Time delay τ(x) nonlinear sound radiation (Doppler effect)
High-pass (sound pressure p)
Low-pass (displacement x)
differentiator
micro-speaker
Klippel, Modeling of Micro-speakers, 17
Interaction Between Nonlinearitiescoupling via fundamental component
Feedback to the nonlinearities
Bl(x)
Le(x)
Cms(x)
Le(i)
Rms(v)
voice coil displacement
electrical input current
voice coilvelocity
Force(fundamentalcomponent)
Klippel, Modeling of Micro-speakers, 18
Using the Loudspeaker as Sensorto identify 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, Modeling of Micro-speakers, 19
Nonlinear Parameter IdentificationMicrospeaker
-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3X mm
in vacuum
in air1,25
1,00
0,75
0,50
0,25
0,00
KmsN/mm
0,0
0,1
0,2
0,3
0,4
0,5
0,6
Bl(x)N/A
-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3X mm
in vacuum
in air
-2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0V m/s
in air
in vacuum
Rms(v)kg/s
0,12
0,16
0,10
0,08
0,06
0,04
0,02
0,00
-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3X mm
in vacuum
in air
0,006
0,008
0,012
LemH
0,000
0,002
0,004
DISTORTIONcaused by AIR VACUUM
Kms(x) 28% 36 %
Bl(x) 20 % 17 %
Le(x) 2% 2%
Rms(v) 45% 6%
Klippel, Modeling of Micro-speakers, 20
measured
0.2 0.3 0.5 0.7 1.0 2.0Frequency f kHz]
0,4
X
mm
0,2
0,1
0,0
-0,1
-0,2
-0,3
-0,4
AgreementMeasured and predicted peak and bottom displacement
linear model
nonlinear model
GENERATION OF A DC COMPONENT
COMPRESSION OF THE FUNDAMENTAL COMPONENT
Klippel, Modeling of Micro-speakers, 21
0.2 0.3 0.5 0.7 1.0 2.0Frequency f kHz]
0,4
X
mm
0,2
0,1
0,0
-0,1
-0,2
-0,3
-0,4
Analysis of Peak and Bottom Displacement
L(x)
nonlinear model
Bl(x) and Kms(x) gemerate dc-component
Rms(v) causescompression of thefundamental at resonancecomponent caus
Bl(x)
Kms(x)
Rms(v)
Klippel, Modeling of Micro-speakers, 22
-0,040
-0,035
-0,030
-0,025
-0,020
-0,015
-0,010
0,000
0,005
0,010
0,015
Xmm
0.2 0.3 0.5 0.7 1.0 2.0Frequency f kHz
DC Displacementof the Voice Coil measured by a single tone
softer side of thesuspension
Bl maximum
rest positionLe(x)
predicted
measured
Bl(x)
Rms(v)
Kms(x)
Klippel, Modeling of Micro-speakers, 23
Analysis of THD Total Harmonic Distortion
0
5
10
15
20
25
35
40
45
0.1 1 10
Percent
Frequency f kHz
measured
Le(x)
Bl(x)
Rms(v)
Kms(x)
predicted
Bl(x) and Kms(x) isdominant source of THD below resonance
Rms(v) and Kms(x) isdominant source of THD atresonance
Klippel, Modeling of Micro-speakers, 24
Analysis of Intermodulation 2nd-order component
4
Percent
Frequency f2 [kHz]5 6 7
10
1098
0.1
1
Bl(x) is the dominant source of 2nd-order IMD
all nonlinearities
Doppler
Le(x)
Kms(x)
Bl(x)
Rms(v)
constant frequency f1=700 Hz
varying frequency f2
Klippel, Modeling of Micro-speakers, 25
Analysis of Intermodulation 3rd-order component
Bl(x) distortions areindependent of frequency
Doppler distortions arenegligible
Frequency f1 [kHz]4 5 6 7 109
Percent
10
0.1
1
Doppler
Kms(x)Le (x)
Rms(v)all nonlinearities
Bl(x)
Kms(x) distortions arefalling withdisplacement
Rms(v) distortions arefalling falling with 6dB per octave
inductancedistortions arenegligible
constant frequency f2=700 Hz
varying frequency f1
Klippel, Modeling of Micro-speakers, 26
Nonlinear Symptoms of Rms(v)
• Harmonics in SPL (maximal at resonance fs)• 3rd-order component is larger than 2nd-order
distortion• decreas by 18dB per octave to lower and higher
frequencies• Intermodulation decreasing by 6dB/octave • Compression of the fundamental at resonance• no Xdc component
Klippel, Modeling of Micro-speakers, 27
Loudspeaker Nonlinearities –Causes, Parameters, Symptoms
• Detailed discussion on practical examples in theJournal of Audio Eng. Soc., Oct. 2006.
• Get a free poster foryour workshop at ourbooth
Klippel, Modeling of Micro-speakers, 28
Summary
• variation of the (mechanical) resistance Rms(v) versus velocity is a dominant nonlinearity in micro-speakers
• caused by turbulences in air leaks (disappears in vacuum)
• contributes significantly to harmonic distortion atresonance (high impact on sound quality)
• dominant compression of the amplitude atresonance (important for mechanical protectionsystems)
Klippel, Modeling of Micro-speakers, 29
Many Thanks !
Klippel, Modeling of Micro-speakers, 30
Monday 10:15 -12:15
Product Design Session PD11
“Rub & Buzz and Other Irregular Loudspeaker Distortion”
Loose particleCoil Rubbing Air LeakBuzzingBottoming
• Root Cause Analysis • Defect Classification and Process Control• Measurement in R&D and Manufacturing• Perceptive Assessment using Auralization Techniques• Audibility and Impact on Sound Quality