by wolfgang klippel, klippel gmbh · 2017. 8. 23. · without shorting rings 0.0 0.5 1.0 1.5 2.0...

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


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.


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


Generation of Signal Distortion

InputSignal

MeasuredSignal

linear distortion

nonlinear distortion

“Rub&Buzz” and other irregular

distortion


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


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


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


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


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


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


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


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


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


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


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


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)


1

nonlinear damping Band-pass (velocity v)


1

Inductance Le(x) self-induced voltage Band-stop (current i)


differentiator

reluctance force Band-stop (current i)


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)


differentiator

Time delay τ(x) nonlinear sound radiation (Doppler effect)



differentiator

micro-speaker


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)


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


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%


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


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)


-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)


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


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


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


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


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


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)


Many Thanks !


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

by wolfgang klippel, klippel gmbh · 2017. 8. 23. · without shorting rings 0.0 0.5 1.0 1.5 2.0...

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