Small, Loud-Speakers: Taking Physics To The Limit

Transcription

1 Small, Loud-Speakers: Taking Physics To The Limit 134th AES Convention Heyser Lecture by Wolfgang Klippel, KLIPPEL GmbH Dresden University of Technology Small, Loud-Speakers: Taking Physics To The Limit, 1

2 OUR TOPIC TONIGHT Small loudspeakers producing sufficient output at acceptable quality...that s what most customers want! How far away is this target? Why is it so difficult to develop such products? How to cope with the physical limitations? Small, Loud-Speakers: Taking Physics To The Limit, 2

3 The Weakest Part of the Audio Reproduction Chain source microphone Recording Environment Sound Engineering transmission storage media amplifier Listening Environment Loudspeaker Listener because it limits the acoustical output causes significant linear and nonlinear distortion varies with time due to fatigue and ageing depends on climate condition contributes to weight, size and cost has low efficiency and produces heat Small, Loud-Speakers: Taking Physics To The Limit, 3

4 Electro-Acoustic Conversion Range of Operation Amplitude Overload Large signal performance Small signal performance Our fundamental problem with small loudspeakers: Power efficiency Small, Loud-Speakers: Taking Physics To The Limit, 4

5 Pass-Band Efficiency of direct-radiator loudspeaker in an infinite baffle 0 P P a e ( Bl) R M e 2 2 0Sd 2 c 2 ms for f >f s and ka<1, radiation on one side considered Example: Micro-speaker η % Re 7.80 Ohm Bl N/A M MS g S d 1.03 cm² electric input power P e 100 mw i DC resistance R e transduction parameter (force factor) pole plate diaphragm U Blv coil Bl F=Bli magnet F L =ps d S d microspeaker 2a < λ/π ka < 1 v moving mass M MS backplate effective radiation surface S d q=s d v p=f L /S d 2R AR (f) acoustic output power P a 7 μw Small, Loud-Speakers: Taking Physics To The Limit, 5

6 What makes the efficiency so low? Pass-Band Efficiency: 0 ( Bl) R M e voice coil resistance force factor 2 2 MS moving mass 0S 2 c 2 D effective radiation area R e M MS q=s d v i v F i F U Blv Bl F=Bli F L =ps d S d p=f L /S d F L R 2R AR (f) MR S 2 d Z AR ( f ) acoustical radiation impedance R e i > Blv acoustical load depends on radiation area S d inertia F i of the moving mass M MS is larger than force F L at the acoustical load electric power is dissipated in the resistance R e Small, Loud-Speakers: Taking Physics To The Limit, 6

7 Alternative Transducer Principles? voltage current electromechanic transducer force velocity mechanoacoustic transducer volume velocity sound pressure sound field lower mass lower peak displacement electro-static electro-dynamic (moving coil, ribbon, planar magnetics) magneto-strictive higher mass higher resistance electro-magnetic (balance armature, moving iron, moving magnet) piezo-electric higher force higher price others Small, Loud-Speakers: Taking Physics To The Limit, 7

8 Leverage a mechanical transformator R e R e M MS M MS v 2 =v/r q=s d v i i v v U Blv Blv Bl BlF=Bli F=Bli F 2 2 p 2R F L =ps AR (f) L d Rr=l MR 1 /lr 2 Sd Z AR ( Ff 2 =rf S dl U ) electro-mechanical transducer high force low velocity U r l l F L Transducer 1 2 F2 F L v v 2 l 1 v l 2 F 2 Problem: increase of moving mass v 2 lower force higher velocity F v 2 2 source impedance matching R MR acoustical load Small, Loud-Speakers: Taking Physics To The Limit, 8

9 Horn an Acoustic Transformer to increase the passband sensitivity R e M MS q=s d v q M i U Blv Bl F=Bli F L =ps d RS d v F L Benefit: strong acoustical load (F F L ) 2 high efficiency S (η> 50 %) S M p=f L /S d R AR (f) p R 0c D AR c M SM S ST MR 0 T Drawback: large for bass reproduction S S M T qm q p p M S T >100 Hz U Transducer F L p q S M p M S( x) fx S T e x q M l > λ/2 Small, Loud-Speakers: Taking Physics To The Limit, 9

10 Efficiency at Low Frequencies below the fundamental resonance frequency f s wavelength λ compression driver of air in baffle 20 log 10 ( ) 12dB/oct. efficiency versus frequency efficiency versus frequency ΔV= 1 liter F transducer 20 Hz 3 m distance 95 db SPL bass f s f T ka 1 1 pass-band f F Benefits: minimal enclosure volume constant displacement for f< f T equalization possible for 1-2 octaves 20log10( ) efficiency versus frequency Drawbacks: low efficiency f s f T ka 1 f Small, Loud-Speakers: Taking Physics To The Limit, 10

11 Compressing Air by an Additional Resonator extending the bandwidth to lower frequencies box volume V F (air compliance + C AB ) using a Helmholtz Resonator vented box System 20 log10 10 ( ) 24 db/oct. bass efficiency versus frequency air mass M AP f 1 f s s ka 1 f V 2 < V F smaller box lower compliance C AB higher mass M AP longer port F passive radiator Benefits: increases efficiency at f s Drawbacks: system alignment air noise (port) cost (passive radiator) Small, Loud-Speakers: Taking Physics To The Limit, 11

12 Efficiency at High Frequencies Exploiting Modal Vibration 20 log 10 ( ) efficiency versus frequency break-up modes increases efficiency rigid radiator 6 db/oct. Full Band Loudspeaker f 1 f s ka 1 high frequencies f Slim (TV Speaker) surround geometry deformed rigid piston break-up modes Flat (Automotive) speaker Distributed Mode Loudspeaker (flat panel) other surfaces used as radiator (enclosure, window, post card) Small, Loud-Speakers: Taking Physics To The Limit, 12

13 Assessing the Mechanical Vibration stimulus (input) output mechanical vibration Simulation (FEM) Measurement (Laser) electro-mechanical efficiency Mechanical power (AAL) mechano-acoustical efficiency electrical power Electro-acoustical efficiency sound power Small, Loud-Speakers: Taking Physics To The Limit, 13

14 db for 1.00V, 0.4 m Assessing the Mechanical Power by using the Accumulated Acceleration Level (AAL) 850 Hz rigid body mode AAL 3.8 khz 11 khz 6.4 khz peaks in AAL show the natural frequencies of the modal resonances Sound Power Hz Hz break-up modes f [khz] Small, Loud-Speakers: Taking Physics To The Limit, 14

15 Mechano-Acoustical Efficiency 90 db 80 AAL 1078,1 Hz q Sound Power 0.1 f [khz] 1 10 node divides radiator in two areas producing a positive and negative volume velocity generating a dip in the power response q 1 q 1 +q 2 =0 acoustical cancellation Problem: sufficient mechanical vibration generates low sound power output Small, Loud-Speakers: Taking Physics To The Limit, 15

16 Sound Distribution in the 3D Space Range of Operation Amplitude Overload Large signal performance Small signal performance Generating the desired Sound pressure field Small, Loud-Speakers: Taking Physics To The Limit, 16

17 Directivity of the Loudspeaker assessing the radiated direct sound in the far field db distance r = 0.4 m, Input voltage u= 1Vrms Omni-directional behavior (like a point source) KLIPPEL Power SPL on-axis SPL 30 degree SPL 60 degree SPL 90 degree Directivity Index Example: woofer f [Hz] Small, Loud-Speakers: Taking Physics To The Limit, 17

18 azimutal angle Sound Pressure Distribution on a sphere in the far field 4.1 khz at distance r=4m 6.1 khz at distance r=4m SPL on-axis frequency Balloon Plot -90 Distance r >> dimensions d of the loudspeaker Distance r >> wavelength Beam Pattern Small, Loud-Speakers: Taking Physics To The Limit, 18

19 Complete 3D Information Required Sound Pressure at 7.6 khz In the following application the listerner is closely located to the source: personal audio equipment (smart phone) multimedia (tablet, notebook) studio-monitor car audio loudspeaker Near Field far field data are less important Small, Loud-Speakers: Taking Physics To The Limit, 19

20 Example: Evaluation of a Notebook Using nearfield Acoustical Holography 1. Measurement of the sound pressure distribution 3. Extrapolation of the sound pressure at any point 2. Expansion outside the into scanning spherical surface waves far field near field r r 0 r s scanning surface close to the source Small, Loud-Speakers: Taking Physics To The Limit, 20

21 The Loudspeaker at Higher Amplitudes Range of Operation Amplitude Overload Large signal performance Small signal performance Thermal and Nonlinear Model Linear Model Maximal Output Distortion Compression Stability Small, Loud-Speakers: Taking Physics To The Limit, 21

22 Compression of SPL Output SPL output at maximal permissable input db Sound Pressure Response Long Term Response (1 min) linear response +20dB amplitude compression caused by nonlinearities and voice coil heating k Frequency [Hz] Linear response predicted from a small signal measurement (-20dB) Long term response measured after applying the sinusoidal stimulus for 1 min Small, Loud-Speakers: Taking Physics To The Limit, 22

23 Compression of SPL Output SPL output at maximal permissable input db Sound Pressure Response Short Term Response (1 s) Long Term Response (1 min) amplitude compression caused by nonlinearities only linear response +20dB k Frequency [Hz] Linear response predicted from a small signal measurement (-20 db) Short term response measured within 1 s (without voice coil heating) Small, Loud-Speakers: Taking Physics To The Limit, 23

24 Example: Visible Nonlinear Symptoms Generated by a Loudspeaker stroboscope Generator tone at f pointer scale Resonance frequency f s 1. Experiment f < f s 2. Experiment f f s 3. Experiment f > f s Small, Loud-Speakers: Taking Physics To The Limit, 24

25 Vibration Behavior Small, Loud-Speakers: Taking Physics To The Limit, 25

26 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 Small, Loud-Speakers: Taking Physics To The Limit, 26

27 dbu (Uo = 1V) dbu (Uo = 1V) Nonlinear Symptom: New Spectral Components spectrum of two-tone Stimulus Response 1 Frequency Domain input output Response 1 spectrum of reproduced Frequency Domain stimulus f [Hz] Nonlinear System f [Hz] Amplitude 2 nd 3 rd sound pressure spectrum 2nd 2 nd 3 rd 3 rd Intermodulation Distortion harmonics n th n th difference tones summed tones n th 2 f f 1 1 bass component nf 1 f 2 n 1) ( f 1 f2 f 1 f2 f1 f 2 voice component f 2 n 1) ( f 1 frequency Small, Loud-Speakers: Taking Physics To The Limit, 28

28 Stiffness K ms (x) of Suspension K 6 N/mm 5 total suspension F F x spider x 1 surround diplacement x mm restoring force F Kms ( x) x displacement Kms(x) determined by suspension geometry impregnation adjustment of spider and surround x Small, Loud-Speakers: Taking Physics To The Limit, 29

29 Distortion generated by K ms (x) Re Re L ee -1 M ms ms R ms K ms(x) -1 R ms linear transfer systems uu i i Blv Blv Bl(x) v F=Bli Stimulus u H(f,r 1 ) 1 ) p(r p(r 1 ) 1 ) sound field field H(f,r 2 ) 2 ) p(r p(r 2 ) 2 ) u D Nonlinear System H(f,r 3 ) 3 ) p(r p(r 3 ) 3 ) K 6 N/mm nonlinear suspension Nonlinear Distortion 2 1 Linear suspension displacement x mm Variation of stiffness K ms (x) versus displacement x generates distortion at low frequencies makes the reproduced bass signal harder and more aggressive Small, Loud-Speakers: Taking Physics To The Limit, 30

30 Nonlinear Force Factor Bl(x) Bl Bl [N/A] 3,0 2,5 2,0 force factor of a linear loudspeaker back plate pole plate 1,5 1,5 1,0 1,0 Φ dc magnet F pole piece B-field coil displacement 0 mm x 0,5 0,5 0,0 0, Bl(x) is a nonlinear function of displacement x depending on Magnetic B field Displacement X [mm] Gap geometry (depth) Height of the coil Voice coil rest position Small, Loud-Speakers: Taking Physics To The Limit, 31

31 Distortion generated by Bl(x) Re L e -1 M ms K ms R ms linear transfer systems u i Bl(x)v Blv Bl(x) v F=Bl(x)i Bli Stimulus u H(f,r 1 ) 1 ) p(r p(r 1 ) 1 ) sound field field H(f,r 2 ) 2 ) p(r p(r 2 ) 2 ) Bl Bl [N/A] [N/A] 3,0 u D Nonlinear System H(f,r 3 ) 3 ) p(r p(r 3 ) 3 ) 2,5 2,0 1,5 force factor of a linear loudspeaker Nonlinear Distortion 1,0 0,5 0, Electro-dynamical driving force Displacement X [mm] F Bl( x) i Voice coil current Nonlinear Bl(x) causes a multiplication of displacement x and current i generates amplitude intermodulation distortion in the audio band perceived as roughness in the sound Back EMF U EMF Bl( x) v Voice coil velocity Small, Loud-Speakers: Taking Physics To The Limit, 32

32 L(I) / Le(0) Le [mh] Bl [N/A] Kms [N/mm] Root Cause Analysis of Displacement measured by DIS using Laser and predicted by SIM using all nonlinearities identified by LSI 80 Kms(X) KLIPPEL Kms(x) Peak and Bottom Displacement Displacement X [mm] Force factor Bl vs. displacement X Bl(X) 3,0 KLIPPEL 2,5 2,0 1,5 Bl(x) 5 X mm 2 Kms(x) Bl(x) measured L(x,i) predicted measured linear) 1,0 0,5 0, Displacement X [mm] Le(X) 1 0 0,30 0,25 0,20 0,15 0,10 0,05 0, Displacement X [mm] L(I) (relative) 1,0 KLIPPEL 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 L(x) L(i) KLIPPEL I [A] Kms(x) measured Bl(x) L(x,i) measured predicted Frequency [Hz] 100 fundamental resonance frequency Small, Loud-Speakers: Taking Physics To The Limit, 35

33 L(I) / Le(0) Le [mh] Bl [N/A] Kms [N/mm] Root Cause Analysis of Harmonics in Sound Pressure measured by DIS and a microphone predicted by SIM using a nonlinear model Kms(X) 80 KLIPPEL ,0 2,5 2,0 1,5 1,0 0,5 0,0 0,30 0,25 0,20 0,15 0,10 0,05 0,00 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 Kms(x) Displacement X [mm] Force factor Bl vs. displacement X Bl(X) KLIPPEL Bl(x) Displacement X [mm] Le(X) L(x) KLIPPEL Displacement X [mm] L(I) (relative) KLIPPEL L(i) I [A] Percent Relative third-order harmonic distortion ( dh3 ) L(i) fundamental resonance frequency measured Kms(x) L(x) Bl(x) predicted 0, Frequency [khz] Kms(x) Small, Loud-Speakers: Taking Physics To The Limit, 36

34 The Impact on Sound Quality Range of Operation Amplitude Overload Large signal performance Thermal and Nonlinear Model Auralization Perceptual Evaluation Small signal performance Linear Model Small, Loud-Speakers: Taking Physics To The Limit, 37

35 Bl [N/A] Kms [N/mm] Auralization of Signal Distortion Parameters Music Test signals U(f) Force factor Bl (X) Stiffness of suspension Kms (X) -Xprot < X < Xprot Xp- < X KLIPPEL < Xp ,25 -Xprot < X < Xprot Xp- < X KLIPPEL < Xp ,00 2 1,75 1 1,50 0-7,5-5,0-2,5 0,0 2,5 5,0 7,5 1,25 X [mm] 1,00 0,75 0,50 0,25 0,00-7,5-5,0-2,5 X 0,0 [mm] 2,5 5,0 7,5 Nonlinear System S Dis Linear Postfilter H(f,r 2 ) H(f,r 1 ) H(f,r 2 ) p(r 1 ) p(r 2 ) Listener in in sound field gain S DIS scales the distortion in the output signal does not affect the state variables (displacement ) does not affect the generation of the nonlinear distortion in the feedback loop Linear Signal H(f,r 1 ) Listener with headphone Distortion auralization output Small, Loud-Speakers: Taking Physics To The Limit, 38

36 Finding Audibility Thresholds histogram of the audibility thresholds of participants of a listening test at weighted up and down method enhanced S DIS attenuated audibility threshold S DIS =-15 db low distortion Small, Loud-Speakers: Taking Physics To The Limit, 39

37 Subjective and Objective Evaluation in Transducer Development Objective Subjective Engineering Evaluation Listening Test + Auralization Evaluation Marketing Management Perceptual Modeling S DIS Physical Data Distortion, Maximal Output Displacement, Temperature Audibility of distortion Preference, Evaluation of Design Choices Clues for Improvements Defining target performance Tuning to the market Performance/cost ratio Small, Loud-Speakers: Taking Physics To The Limit, 40

38 Improving Loudspeakers by Electrical Means Range of Operation Amplitude Overload protection Large signal performance Small signal performance linearization equalization Exploiting of the useable working range Small, Loud-Speakers: Taking Physics To The Limit, 41

39 Loudspeaker Control audio input Controller Objectives: More acoustical output increased sound power Optimal sound distribution in 3D space directivity Acceptable quality reduction of signal distortion Lower power consumption increased efficiency of the overall system Small, slim, flat, light considering geometrical constraints Lower cost optimal use of resources, simplified transducer manufacturing Overload protection detection of thermal and mechanical limits Long-term stability coping with climate, aging, fatigue Small, Loud-Speakers: Taking Physics To The Limit, 42

40 Nonlinear Control Structure Active Control Transducer z parameters mirror symmetry - u H(f,r 1 ) H(f,r 2 ) p(r 1 ) p(r 2 ) sound field Nonlinear System u D u D Nonlinear System H(f,r 3 ) p(r 3 ) synthesized distortion Control structure derived from loudspeaker modeling using loudspeaker parameters (Bl(x), Mms, Kms(x), Re,...) interpretable state variables (displacement, velocity,..) Small, Loud-Speakers: Taking Physics To The Limit, 43

41 Bl [N/A] Problem: Variation of Loudspeaker Parameters pole plate voice coil pole plate voice coil magnet Influence of Gravity magnet [N/m] 4500 Suspension Stiffness 2,5 Force Factor Motor Load induced aging, fatigue over time 2,0 1,5 1,0 Voice coil offset , displacement x [mm] 0, << Coil in X [mm] coil out >> Small, Loud-Speakers: Taking Physics To The Limit, 44

42 Resonance Frequency depends on ambient temperature Resonance frequency of two woofers used in cars Influence of the Loudspeaker System Alignment 80 C woofer B 30 db 2 octaves -30 C woofer A winter summer Properties of the mechanical suspension depend on humidity, temperature voice coil displacement cannot be predicted by time-invariant parameters learning process required Small, Loud-Speakers: Taking Physics To The Limit, 45

43 Identification of Speaker Parameters Music Equalization Protection audio Linearization signal - Diagnostics messages transducer transducer parameters parameters amplifier Adaptive Parameter Identification voltage current transducer Solution: 1) Adaptive Modeling self-lerning system permanent updating 2) Speaker used as Sensor high accuracy ambient noise immunity robust sensor, minimal hardware low cost Objectives: optimal speaker control (linearization, equalization, protection) compensation of parameter variation and time dependency (aging, climate) detection of critical working condition (wrong polarity, blocked port, leak in enclosure) early detection of loudspeaker defects (rub & buzz) generation of diagnostic information Small, Loud-Speakers: Taking Physics To The Limit, 46

44 [Percent] [Percent] Bl [N/A] Kms [N/mm] Reduction of Harmonic Distortion 3,0 Force factor Bl (X) 00:11:33 -Xprot < X < Xprot Xbottom < X < Xpeak Bl (-X) KLIPPEL 0,9 Stiffness of suspension Kms (X) 00:11:33 -Xprot < X < Xprot Xbottom < X < Xpeak Kms (-X) KLIPPEL 0,8 2,5 0,7 2,0 0,6 1,5 1,0 0,5 0,5 0,4 0,3 0,2 0,1 0, X [mm] 0, X [mm] LINEAR CONTROL without Control 3rd-order Control Signal at IN1 NONLINEAR CONTROL KLIPPEL NONLINEAR CONTROL 2nd-order Harmonics Signal at IN1 LINEAR CONTROL without Control KLIPPEL with Nonlinear Control 5 with Nonlinear Control Frequency [Hz] Frequency [Hz] Small, Loud-Speakers: Taking Physics To The Limit, 47

45 IN1 [V] IN1 [V] [Percent] [Percent] Reduction of Intermodulation Distortion Relative second-order intermodulation distortion ( d2 ) Signal at IN1 NONLINEAR Control LINEAR Control KLIPPEL without Control Relative third-order intermodulation distortion ( d3 ) Signal at IN1 NONLINEAR CONTROL LINEAR Control without Control KLIPPEL 10 5 with Nonlinear Control with Nonlinear Control 0 2*10 2 4*10 2 6*10 2 8* Frequency f1 [Hz] 0 2*10 2 4*10 2 6*10 2 8* Frequency f1 [Hz] 0,15 0,10 0,05 0,00-0,05-0,10-0,15 IN1 (t) Waveform IN1 f1 = Hz U1 = 0.40 V without Control KLIPPEL Time [ms] The bass tone at 50 Hz intermodulates the 1kHz tone 0,15 0,10 0,05 0,00-0,05-0,10-0,15 Waveform IN1 f1 = Hz U1 = 0.40 V -0, Time [ms] Small, Loud-Speakers: Taking Physics To The Limit, 48 IN1 (t) with Nonlinear Control

46 Can We Fix Loudspeaker Defects by nonlinear control? Coil hitting backplate Buzzing loose joint Rubbing voice coil Flow noise at air leak Loose particle hitting membrane vibration Loose particle deterministic IRREGUAL DISTORTION ( Rub & buzz ) random caused by overload, damage, manufacturing and design failures generates high frequency components (harmonics, noise) unpleasant, high impact on perceived sound quality unacceptable when detected by a human ear! no accurate modeling and compensation possible Small, Loud-Speakers: Taking Physics To The Limit, 49

47 Protection System Prevents Generation of Irregular Distortion audio signal attenuator Protection Variable System High-pass Equalization Linearization amplifier transducer Example: Thermal Protection transducer parameters Mechanical Protection displacement Adaptive Parameter Identification voltage current Voice coil offset in the rest position of the coil voice coil temperature State Predictor backplate REMEDY: Voice coil Control system identifies the coil s rest position determines the maximal peak displacement without bottoming activates a high-pass filter to attenuate low frequency components shifts the coil to the optimal rest position (dc coupled amplifier required backplate bottoming at the backplate Small, Loud-Speakers: Taking Physics To The Limit, 50

48 Towards Green Speakers Range of Operation Amplitude Overload Large signal performance Small signal performance Optimal Use of Resources - minimal hardware lower cost, weight, size - low power consumption longer battery life time Small, Loud-Speakers: Taking Physics To The Limit, 51

49 Software or Hardware Solution? New Degrees of Freedom in Loudspeaker Design Active Speaker System Signal Processing Passive Transducer Overload Protection Linear and Nonlinear Distortion Optimal Design Size, weight, shape (slim, flat) Sound output (power, directivity) Robustness (rub & buzz) Efficiency Cost Small, Loud-Speakers: Taking Physics To The Limit, 52

50 Example: Loudspeaker Magnet Materials Ferrits Neodymium Neodym-Magnets are the most powerful magnets which are currently available better Performance! higher Cost! A magnet made of neodym can lift up a mass 2000-times more than it s own weight A human (75 kg) has to lift up a Boeing 747 ( kg) Magnets made of ferrits dominated the loudspeaker magnets for a long time 500% price over the last three years Small, Loud-Speakers: Taking Physics To The Limit, 53

51 Optimal Motor Topology for Control? gap depth voice coil gap depth coil height pole piece pole plate magnet coil height equal-length configuration over-hung coil under-hung coil dual voice coil dual gap variable coil density Small, Loud-Speakers: Taking Physics To The Limit, 54

52 A nonlinear motor is more efficient! Bl(x) N/A Amplitude constant coil height 10 mm 10 mm gap (same length coil & gap) 5 mm gap (overhang coil) 15 mm gap (underhang coil) mm gap (very underhang coil) voice coil displacement X mm FEM derived graph of force factor BL(x) for 10mm height x 50mm diameter voice coil with 88 turns in various depth gaps. NdFeB magnet volume unchanged. Small, Loud-Speakers: Taking Physics To The Limit, 55

53 PDF [1/mm] Bl [N/A] Power Required for Linearization? z Nonlinear System - ud synthesized Distortion amplifier u u D Nonlinear System H(f,r 1 ) H(f,r 2 ) H(f,r 3 ) p(r 1 ) sound field p(r 2 ) p(r 3 ) Nonlinear Force Factor Target: force factor becomes constant virtually 300 % compensation The input power depends on the probability density function of the displacement! Music: The coil is most of the time in the gap exploiting the high Bl-value Linearization requires a small amount of additional input power The total system provides higher efficiency at low distortion! << Coil in X [mm] coil out >> Probability Density Function << Coil in X [mm] coil out >> MUSIC protection system just active maximal displacement Small, Loud-Speakers: Taking Physics To The Limit, 57

54 Digital Signal Processing dedicated to Loudspeakers Linear processing Multi Channel processing Nonlinear processing transmission crossover time alignment equalisation directivity room correction protection linearisation voice coil rest position adjustment perceptual loudness correction artificical bass enhancement Small, Loud-Speakers: Taking Physics To The Limit, 58

55 Sources for Loudspeaker Innovations Manufacturing cost, quality, automation Research new principles of operation Marketing Target performance, Tuning to the market Signal processing transducer related How should we work together? Loudspeaker an interdisciplinary product Transducer Design FEA, BEM, other simulations Electronics amplification, power supply, wireless Assessment measurement techniques New Materials motor, radiator, suspension, enclosure Small, Loud-Speakers: Taking Physics To The Limit, 59

56 Thank you! Small, Loud-Speakers: Taking Physics To The Limit, 60