Small, Loud-Speakers: Taking Physics To The Limit
135th AES Convention NY
by Wolfgang Klippel,
KLIPPEL GmbH Dresden University of Technology
Small, Loud-Speakers: Taking Physics To The Limit, 1 OUR TOPIC TODAY
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 The Weakest Part of the Audio Reproduction Chain
microphone Listening Environment transmission Recording Sound Environment Engineering source storage amplifier Listener media Loudspeaker
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 Electro-Acoustic Conversion
Range of Operation
Amplitude Overload
Large signal performance
Our fundamental problem with small Small signal loudspeakers: performance Power efficiency
Small, Loud-Speakers: Taking Physics To The Limit, 4 Pass-Band Efficiency of direct-radiator loudspeaker in an infinite baffle
Example: Micro-speaker 2 2 Pa (Bl) S 0 d η0 0.007 % 0 2 Re 7.80 Ohm Pe R M 2c e ms Bl 0.774 N/A for f >fs and ka<1, MMS 0.082 g radiation on one side considered Sd 1.03 cm²
effective DC transduction moving radiation resistance parameter 2a < 휆/πmass (force factor) surface Sd Re ka < 1 MMS q=Sdv v diaphragm acoustic output electric inputi power Pa power Pe pole plate
p=FL/Sd 2RAR(f) U Blv cBolil F=Bmliagnet FL=pSd Sd 7 μW 100 mW backplate
microspeaker
Small, Loud-Speakers: Taking Physics To The Limit, 5 What makes the efficiency so low ?
force factor effective (Bl)2 S 2 radiation area Pass-Band Efficiency: 0 D 0 2 ReM MS 2c voice coil moving resistance mass
Re MMS q=Sdv
v ii Fi ≈F
2 p=FL/Sd 2RAR(f) U Blv Bl F=Bli FL=pSd Sd FL RMR Sd ZAR( f ) acoustical radiation impedance
Re i > Blv
• acoustical load depends on radiation area Sd • inertia Fi of the moving mass MMS is larger than force FL at the acoustical load • electric power is dissipated in the resistance Re Small, Loud-Speakers: Taking Physics To The Limit, 6 Alternative Transducer Principles ?
volume voltage force velocity electro- mechano- sound mechanic acoustic field transducer transducer current velocity sound pressure
higher electro-static magneto-strictive mass lower mass electro-dynamic higher lower peak (moving coil, ribbon, resistance displacement planar magnetics) electro-magnetic (balance armature, piezo-electric moving iron, moving higher magnet) force higher price others
Small, Loud-Speakers: Taking Physics To The Limit, 7 Leverage – a mechanical transformator
R e Re MMS MMS v2=v/r q=Sdv
v v i i
2 2 p 2RAR(f) U U Blv Blv Bl BlF=Bli F=Bli FFL L=pSd RrMR=l1/lr2 Sd Z AR (Ff )2=rSFdL
l1 FL Problem: electro-mechanical U Transducer v transducer increase of high moving mass l2 force F2 RMR lower v2 low v2 velocity force acoustical F2 source load higher velocity l F v r 1 2 impedance l2 FL v2 matching
Small, Loud-Speakers: Taking Physics To The Limit, 8 Horn – an Acoustic Transformer to increase the passband sensitivity
Re MMS q=Sdv qM
v i Benefit: • strong acoustical load (F ≈ FL) • high efficiency (η> 50 %) 2 S 0c FL SD R (f)M RAR U Blv Bl F=Bli FL=pSd RSd pc=FL/Sd AR pM S MR 0 S M ST T Drawback: • large for bass reproduction
S q p M M ST q pM
ST FL SM >100 Hz U Transducer q pM p fx S(x) ST e qM x l > λ/2
Small, Loud-Speakers: Taking Physics To The Limit, 9 Efficiency at Low Frequencies
below the fundamental resonance frequency fs
efficiency versus frequency wavelength λ 20log () 10 efficiency versus frequency compressionbaffle driverof airin baffle 12dB/oct.
ΔV= 1 liter F 95 dB SPL transducer 3 m distance f 20 Hz f s f T ka 1 bass pass-band
20log () Benefits: 10 efficiency versus frequency • minimal enclosure volume • constant displacement for f< f F T • equalization possible for 1-2 octaves
Drawbacks: • low efficiency f f s f T ka 1
Small, Loud-Speakers: Taking Physics To The Limit, 10 Compressing Air by an Additional Resonator extending the bandwidth to lower frequencies
efficiency versus frequency 20log10() efficiency versus frequency using a box volume V Helmholtz F 24 dB/oct. (air compliance Resonator CAB) vented box + System bass air mass M AP ff f s ka 1
smaller box Benefits: V < V 2 lower compliance • increases efficiency at fs C F F AB F Drawbacks: higher mass MAP • system alignment longer port passive radiator • air noise (port) • cost (passive radiator)
Small, Loud-Speakers: Taking Physics To The Limit, 11 Efficiency at High Frequencies Exploiting Modal Vibration
break-up modes increases efficiency 2020loglog1010(()) efficiency versus frequency
Full Band rigid radiator 6 dB/oct. Loudspeaker
Slim (TV Speaker) high frequencies ff ff ss kaka11
Flat (Automotive) speaker surround geometry break-uprigidmodes piston deformed Distributed Mode Loudspeaker (flat panel)
other surfaces used as radiator (enclosure, window, post card) Small, Loud-Speakers: Taking Physics To The Limit, 12 Assessing the Mechanical Vibration
stimulus (input) output
mechanical vibration
Simulation (FEM) Measurement (Laser)
electro-mechanical mechano-acoustical efficiency efficiency Mechanical power (AAL) electrical power Electro-acoustical sound power efficiency
Small, Loud-Speakers: Taking Physics To The Limit, 13 Assessing the Mechanical Power by using the Accumulated Acceleration Level (AAL)
850 Hz 90 3.8 kHz AAL 11 kHz 85 6.4 kHz rigid body mode 80 peaks in AAL show the natural 75 frequencies of the modal resonances 70
65
60 Sound Power
55 dB for 1.00V, 0.4 m 0.4 1.00V, for dB 50
45
40
35 20 Hz - 600 Hz break-up modes
30 0.1 1 10 f [kHz]
Small, Loud-Speakers: Taking Physics To The Limit, 14 Mechano-Acoustical Efficiency
90 AAL 1078,1 Hz q2 dB 80
70
60
50 q Sound 1 40 Power
30 0.1 f [kHz] 1 10 q1+q2=0 acoustical cancellation Problem: • sufficient mechanical vibration generates low sound power output • node divides radiator in two areas producing a positive and negative volume velocity generating a dip in the power response
Small, Loud-Speakers: Taking Physics To The Limit, 15 Sound Distribution in the 3D Space
Range of Operation
Amplitude Overload
Large signal performance
Generating the desired Small signal performance Sound pressure field
Small, Loud-Speakers: Taking Physics To The Limit, 16 Directivity of the Loudspeaker assessing the radiated direct sound in the far field
distance r = 0.4 m, Input voltage u= 1Vrms dB
90 KLIPPEL
85 Omni-directional behavior (like a point source) 80
75 SPL on-axis 70 Power
65
60 SPL 30 degree
55 270° SPL 60 degree Directivity 50 Index 180° SPL 90 degree 0° 45
90° 40
35
30 0.1 1 10 f [Hz] Example: woofer
Small, Loud-Speakers: Taking Physics To The Limit, 17 Sound Pressure Distribution on a sphere in the far field
SPL 4.1 kHz at distance r=4m 6.1 kHz at distance r=4m
90° on-axis
270° azimutal angle angle azimutal
180° 0°
frequency 90°
-90° Balloon Plot
Beam Pattern Distance r >> dimensions d of the loudspeaker Distance r >> wavelength
Small, Loud-Speakers: Taking Physics To The Limit, 18 Complete 3D Information Required
Sound Pressure at 7.6 kHz
In the following application the listerner is far field data closely located to the source: are less important • personal audio equipment (smart phone) • multimedia (tablet, notebook) • studio-monitor Near Field
• car audio loudspeaker
Small, Loud-Speakers: Taking Physics To The Limit, 19 Example: Evaluation of a Notebook Using nearfield Acoustical Holography
far3. fieldExtrapolation of the sound pressure at any 1. Measurement of the sound point2. Expansionoutside the intoscanningsphericalsurfacewaves pressure distribution
near field r
r0
r s
scanning surface close to the source
Small, Loud-Speakers: Taking Physics To The Limit, 20 The Loudspeaker at Higher Amplitudes
Range of Operation
Amplitude Overload
Thermal Maximal Output Large signal and performance Nonlinear Distortion Model Compression Stability
Small signal Linear performance Model
Small, Loud-Speakers: Taking Physics To The Limit, 21 Compression of SPL Output SPL output at maximal permissable input
Sound Pressure Response 130 Linear response 125 linear response +20dB dB predicted from a 120 small signal measurement 115 (-20dB) 110
105 Long Term Response (1 min) Long term response 100 measured after 95 amplitude compression caused applying the by nonlinearities and voice coil 90 sinusoidal chirp for 1 heating min 85
80 20 50 200 500 2k Frequency [Hz]
Small, Loud-Speakers: Taking Physics To The Limit, 22 Compression of SPL Output SPL output at maximal permissable input
Sound Pressure Response 130 Linear response 125 linear response +20dB dB predicted from a 120 small signal Short Term Response (1 s) measurement 115 (-20 dB) 110
105 Long Term Response (1 min) Short term response 100 measured within 1 s 95 (without voice coil heating) 90 amplitude compression caused 85 by nonlinearities only 80 20 50 200 500 2k Frequency [Hz]
Small, Loud-Speakers: Taking Physics To The Limit, 23 Nonlinear Symptom: New Spectral Components
spectrum of twoResponse-tone 1 Stimulus Frequency Domain Response 1 spectrum of reproducedFrequency Domain stimulus
20 10 output 20 0 input 10 -10 0 -20 -10
-30dBu (Uo = 1V) -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 component” “voice component”
Small, Loud-Speakers: Taking Physics To The Limit, 24 Example: Visible Nonlinear Symptoms Generated by a Loudspeaker
stroboscope
Generator tone at f scale
pointer Resonance
frequency fs
1. Experiment 2. Experiment 3. Experiment
f < fs f fs f > fs
Small, Loud-Speakers: Taking Physics To The Limit, 25 Vibration Behavior
Small, Loud-Speakers: Taking Physics To The Limit, 26 Nonlinear Symptom: Amplitude Compression
Fundamental component | X ( f1, U1 ) |
23.4 Hz 2,5 Linear System KLIPPEL
2,0
1,5
1,0
X [mm] (rms)
0,5
0,0 0,0 2,5 5,0 7,5 10,0 12,5 15,0 Voltage U1 [V]
Small, Loud-Speakers: Taking Physics To The Limit, 27 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, 28 Stiffness Kms (x) of Suspension
K 6 N/mm total 5 suspension
4 F x 3 F
2 spider 1 surround x
-10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 diplacement x mm
Kms(x) determined by • suspension geometry F Kms (x)x restoring • impregnation force displacement • adjustment of spider and surround
x Small, Loud-Speakers: Taking Physics To The Limit, 29 Distortion generated by Kms(x)
linear transfer systems -1 -1 MMmmss RRmmss KKmmss(x) LLee RRe e
vv i i
HH(f(,fr,1r)1) u Blv Bl Bli p(pr(1r)1) u Blv Bl(x) F=Bli Stimulus sosuonudn d fiefiledld
HH(f(,fr,2r)) 2 p(pr(2r) ) u 2
Nonlinear HH(f(,fr,3r)3) System p(pr(3r)3) uD
K 6 N/mm nonlinear suspension 5 Nonlinear
4 Distortion
3
2 Linear suspension suspension Variation of stiffness Kms(x) versus 1 displacement x generates distortion at low frequencies -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 displacement x mm makes the reproduced bass signal „harder“ and more „aggressive“
Small, Loud-Speakers: Taking Physics To The Limit, 30 Nonlinear Force Factor Bl(x)
BlBl [N/A] [N/A] 3,03,0
2,52,5 force factor 2,02,0 of a linear loudspeaker
1,51,5 back plate pole plate 1,01,0
0,50,5 Φdc 0,00,0 --66 --44 --22 00 22 44 66 DisplacementDisplacement XX [mm][mm] magnet Bl(x) is a nonlinear function of B-field displacement x depending on F coil • Magnetic B field pole piece • Gap geometry (depth) displacement • Height of the coil 0 mm x • Voice coil rest position
Small, Loud-Speakers: Taking Physics To The Limit, 31 Distortion generated by Bl(x)
linear transfer systems --11 Mmss Rmmss Kmmss Le Re
v i
HH(f(,fr,1r)1) u BBl(xlv)v BBl(xl ) F=Bll(ix)i p(pr(1r)1) Stimulus sosuonudn d fiefiledld
HH(f(,fr,2r)) 2 p(pr(2r) ) u 2
Nonlinear HH(f(,fr,3r)3) System p(pr(3r)3) uD BlBl [N/A] [N/A] 3,03,0
2,52,5 force factor Nonlinear 2,02,0 of a linear loudspeaker Distortion 1,51,5
1,01,0
0,50,5
0,00,0 Nonlinear Bl(x) causes a multiplication of --66 --44 --22 00 22 44 66 DisplacementDisplacement XX [mm][mm] displacement x and current i generates amplitude intermodulation Electro-dynamical F Bl(x)i Voice coil current distortion in the audio band driving force 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 Voice Coil Inductance Le(x)
4.0 Without shorting rings Le [mH] Φcoil(+9 mm) 2.5 Φcoil(-9 mm) With shortingrings 2.0 1.5 1.0 0.5 0.0 -15 -10 -5 0 5 10 15 voice coil displacement << Coil in X [mm] coil out >>
-9 mm 0 mm 9 mm x
Le(x) depends on • geometry of coil, gap, magnet • optimal size and position of short cut ring
Small, Loud-Speakers: Taking Physics To The Limit, 33 Distortion generated by Le(x)
linear transfer systems -1-1 Frel(x,i) MMmmss RRmmss KKmmss LLee(x) RRe e
vv i i
HH(f(,fr,1r)1) u Blv Bl Bli p(pr(1r)1) u Blv Bl F=Bli Stimulus sosuonudn d fiefiledld
HH(f(,fr,2r)) 2 p(pr(2r) ) u 2
Nonlinear HH(f(,fr,3r)3) System p(pr(3r)3) uD 4.0 Without shorting rings Le [mH]
2.5 With shortingrings Nonlinear 2.0 Distortion 1.5 1.0 0.5 0.0 Nonlinear Le(x) causes multiplications of -15 -10 -5 0 5 10 15 << Coil in X [mm] coil out >> displacement with current
generates amplitude intermodulation d(x,i) dL(x)i U ind Differentiated distortion at high frequencies dt dt Magnetic flux
i 2 (t) dL(x) Reluctance perceived as roughness in the sound F rel 2 dx force Small, Loud-Speakers: Taking Physics To The Limit, 34 Root Cause Analysis of Displacement
measured by DIS using Laser and predicted by SIM using all nonlinearities identified by LSI
Kms(X) 80 KLIPPEL
70 60 Kms(x) 50 Peak and Bottom Displacement
40
Kms [N/mm] Kms 30
20 5
10 L(x,i)
0 linear) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Displacement X [mm] X Force factor Bl vs. displacement X Bl(x) Bl(X) 3,0 KLIPPEL mm Kms(x) 2,5 Bl(x) 2,0 measuredpredicted 1,5 Bl [N/A]Bl 2 measured 1,0 0,5 1 0,0 -6 -4 -2 0 2 4 6 Displacement X [mm]
0 Le(X)
KLIPPEL 0,30 0,25 L(x) -1 0,20
0,15 Le [mH] Le measured measuredpredicted 0,10 -2 0,05 Kms(x)
0,00 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Displacement X [mm] -3
L(I) (relative) Bl(x) fundamental 1,0 KLIPPEL 0,9 -4 resonance 0,8 0,7 L(x,i) frequency 0,6 L(i) 0,5
L(I) /L(I) Le(0) -5 0,4
0,3 0,2 10 100 0,1
0,0 Frequency [Hz] -6 -4 -2 0 2 4 6 I [A]
Small, Loud-Speakers: Taking Physics To The Limit, 35 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
70 60 Kms(x) 50 Relative third-order harmonic distortion ( dh3 ) 40
Kms [N/mm] Kms 30
20 100
10
0 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 10 Displacement X [mm] measured Force factor Bl vs. displacement X Bl(X) 1 predicted 3,0 KLIPPEL 2,5 Bl(x) 0.1 2,0
1,5 Bl [N/A]Bl 0.01- 1,0
0,5 Percent L(i)
0,0 -6 -4 -2 0 2 4 6 L(x) Displacement X [mm] 10-4
Le(X)
KLIPPEL 0,30 10-5 0,25 L(x) Bl(x) 0,20 10-6 0,15
Le [mH] Le 0,10 10-7 0,05 Kms(x) -8 0,00 fundamental -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 10 Displacement X [mm] resonance L(I) (relative) 1,0 -9 KLIPPEL 10 0,9 frequency
0,8 0,7 10-10 0,6 L(i) 0,5
L(I) /L(I) Le(0) 0,4 10-11 0,3
0,2
0,1 0,1 1 10 0,0 Kms(x) -6 -4 -2 0 2 4 6 Frequency [kHz] I [A]
Small, Loud-Speakers: Taking Physics To The Limit, 36 The Impact on Sound Quality
Range of Operation
Amplitude Overload
Thermal Auralization Large signal and performance Nonlinear Perceptual Model Evaluation
Small signal Linear performance Model
Small, Loud-Speakers: Taking Physics To The Limit, 37 Auralization of Signal Distortion
Parameters
Force factor Bl (X)Stiffness of suspension Kms (X) -Xprot < X < XprotXp- < X < Xp+ 6 KLIPPEL 5 -Xprot < X < XprotXp- < X < Xp+ 4 2,25 KLIPPEL gain S 3 2,00 2 Bl [N/A] 1,75 DIS 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 Kms [N/mm] 0,25 0,00 • scales the distortion in the -7,5 -5,0 -2,5X 0,0[mm]2,5 5,0 7,5 Linear Postfilter
pp((rr11)) output signal HH((ff,,rr22)) UU((ff)) Music LLiisstteenneerr • does not affect the state Test signals iinn ssoouunndd field variables (displacement ) NNoonnlliinneeaarr field SSyysstteemm H(f,r ) H(f,r11) • does not affect the
pp((rr22)) SDis generation of the nonlinear distortion in the H(f,r2) feedback loop Listener with headphone Linear Signal
H(f,r1) auralization Distortion output
Small, Loud-Speakers: Taking Physics To The Limit, 38 Finding Audibility Thresholds
histogram of the audibility thresholds of 55000 participants of a listening test at www.klippel.de
weighted up and down method
low distortion S audibility threshold enhanced DIS attenuated SDIS=-15 dB
Small, Loud-Speakers: Taking Physics To The Limit, 39 Subjective and Objective Evaluation in Transducer Development
Objective Subjective
Engineering Evaluation Evaluation Marketing Management Listening Test + Auralization
Perceptual Modeling SDIS Physical Data • Distortion, Maximal Output Audibility of distortion • Displacement, Temperature Preference,
• Evaluation of Design Choices • Defining target performance • Clues for Improvements • Tuning to the market
Performance/cost ratio
Small, Loud-Speakers: Taking Physics To The Limit, 40 Improving Loudspeakers by Electrical Means
Range of Operation
Amplitude Overload protection
Large signal linearization performance Exploiting of the useable working range Small signal performance equalization
Small, Loud-Speakers: Taking Physics To The Limit, 41 Loudspeaker Control
Controller audio input 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 Nonlinear Control Structure
Active Control Transducer
parameters H(f,r1) p(r1) mirror symmetry sound field
H(f,r2) p(r2) z - u
Nonlinear Nonlinear H(f,r3) System System p(r3) uD uD
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 Problem: Variation of Loudspeaker Parameters
voice coil voice coil pole plate pole plate Influence of magnet Gravity magnet
Suspension Stiffness Force Factor [N/m] 4500 2,5 Motor
4000 2,0 3500 Voice coil offset 3000 1,5 Load induced aging,
2500 [N/A] Bl fatigue over time 1,0 2000
1500 0,5 1000 0,0 500 -4 -3 -2 -1 -0 1 2 3 4 << Coil in X [mm] coil out >> -15 -10 -5 0 5 10 displacement x [mm]
Small, Loud-Speakers: Taking Physics To The Limit, 44 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 Identification of Speaker Parameters
amplifier transducer Equalization Protection Solution: audio Linearization signal - 1) Adaptive Modeling
voltage • self-lerning system Adaptive Music Parameter • permanent updating transducer Identification tranpsardaumceeterrs parameters current 2) Speaker used as Sensor Diagnostics • high accuracy • ambient noise immunity
messages • 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 Reduction of Harmonic Distortion
Force factor Bl (X) Stiffness of suspension Kms (X) 00:11:33 00:11:33 -Xprot < X < Xprot Xbottom < X < Xpeak Bl (-X) -Xprot < X < Xprot Xbottom < X < Xpeak Kms (-X) 0,9 3,0 KLIPPEL KLIPPEL 0,8 2,5 0,7
2,0 0,6 0,5 1,5
Bl [N/A]Bl 0,4
Kms [N/mm] 1,0 0,3
0,2 0,5 0,1
0,0 0,0 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 X [mm] X [mm]
3rd-order Control 2nd-order Harmonics Signal at IN1 Signal at IN1 LINEAR CONTROL NONLINEAR CONTROL NONLINEAR CONTROL LINEAR CONTROL 30 KLIPPEL KLIPPEL 70 without Control 25 without Control 60
20 50
40 15
[Percent]
[Percent] 30 10 20
5 10 with Nonlinear Control with Nonlinear Control
0 0 50 100 200 500 50 100 200 500 Frequency [Hz] Frequency [Hz]
Small, Loud-Speakers: Taking Physics To The Limit, 47 Reduction of Intermodulation Distortion
Relative second-order intermodulation distortion ( d2 ) Relative third-order intermodulation distortion ( d3 ) Signal at IN1 Signal at IN1 NONLINEAR Control LINEAR Control NONLINEAR CONTROL LINEAR Control KLIPPEL 35 KLIPPEL 25 without Control 30 20 25 without Control 15 20
[Percent]
[Percent] 15 10 10 with Nonlinear Control with Nonlinear Control 5 5
0 0 2 2 2 2 3 2*102 4*102 6*102 8*102 103 2*10 4*10 6*10 8*10 10 Frequency f1 [Hz] Frequency f1 [Hz]
Waveform IN1 Waveform IN1 f1 = 1007.8 Hz U1 = 0.40 V f1 = 1007.8 Hz U1 = 0.40 V IN1 (t) IN1 (t) KLIPPEL 0,15 0,15 The bass tone at 50 Hz 0,10 0,10 intermodulates the 1kHz 0,05 0,05 tone 0,00 0,00 without Control with Nonlinear Control
IN1 [V] [V] IN1
IN1 [V] -0,05 -0,05
-0,10 -0,10
-0,15 -0,15
-0,20 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Time [ms] Time [ms] Small, Loud-Speakers: Taking Physics To The Limit, 48 Can We Fix Loudspeaker Defects by nonlinear control ?
Loose particle Coil hitting Buzzing loose Rubbing Flow noise at air hitting backplate joint voice coil leak 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 Protection System Prevents Generation of Irregular Distortion
attenuator amplifier transducer audio ProtectioVnariable Equalization Example: signal SystemHigh-pass Linearization
transducer parameters voltage offset in the Adaptive Thermal Mechanical Voice coil Parameter rest position of Protection Protection Identification the coil displacement current
State voice coil temperature Predictor
backplate
Voice coil REMEDY:
Control system • identifies the coil‘s rest position • determines the maximal peak displacement without bottoming backplate • activates a high-pass filter to attenuate low frequency components bottoming at • shifts the coil to the optimal rest position (dc coupled amplifier the backplate required
Small, Loud-Speakers: Taking Physics To The Limit, 50 Towards Green Speakers
Range of Operation
Amplitude Overload
Large signal performance Optimal Use of Resources - minimal hardware lower cost, weight, size - low power consumption longer battery life time Small signal performance
Small, Loud-Speakers: Taking Physics To The Limit, 51 Software or Hardware Solution ? New Degrees of Freedom in Loudspeaker Design
Active Speaker System
Signal Passive Processing Transducer
Size, weight, shape (slim, flat) Overload Protection Sound output (power, directivity) Linear and Nonlinear Distortion Optimal Design Robustness (rub & buzz) Efficiency Cost
Small, Loud-Speakers: Taking Physics To The Limit, 52 Example: Loudspeaker Magnet Materials
Ferrits Neodymium
Neodym-Magnets are the most powerful magnets which are currently available
better A magnet made of neodym can lift up a mass Performance ! 2000-times more than it‘s own weight
A human (75 kg) has to lift up a Boeing 747 (150.000 kg) higher Cost !
Magnets made of ferrits dominated the loudspeaker 500% magnets for a long time
price over the last three years
Small, Loud-Speakers: Taking Physics To The Limit, 53 Optimal Motor Topology for Control ?
gap depth voice coil gap depth
coil pole plate coil height height pole magnet piece 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 A nonlinear motor is more efficient !
constant coil height 10 mm Amplitude 18 Bl(x) 16 10 mm gap (same length coil & gap) N/A 14 5 mm gap 12 (overhang coil) 15 mm gap 10 (underhang coil)
8 20 mm gap 6 (very underhang coil)
4
2
0 -10 -8 -6 -4 -2 0 2 4 6 8 10
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 Towards Green Speaker
Equal-length Configuration (Coil height hcoil gap height hgap )
f orce f actor b(x) force factor Bl(x) h -x_max < x < x_max coil KLIPPEL 3,5 h gap 3,0 magnet 50% 2,5 h pole plate coil 2,0
voice coil b [N/A] 1,5
1,0
0,5
0,0 pole piece -7,5 -5,0 -2,5 0,0 2,5 5,0 7,5 << coil in x [mm] coil out >> x Advantages: Disadvantages: • highest Bl(x≈0) for small displacement, • early decay of the force factor • low voice coil mass • significant 3rd-order distortion
• low DC resistance Re • sensitive to offset in rest position • low voice coil inductance • sensitive to instabilities f>fs • low ac flux modulation by Le(i), Bl(i) nonlinear control required
Small, Loud-Speakers: Taking Physics To The Limit, 56 Power Required for Linearization ?
Target: force factor becomes H(f,r ) amplifier 1 p(r ) 1 sound Nonlinear Force Factor constant virtually field
H(f,r2) p(r ) 3.5 z - u 2 3.0 Nonlinear Nonlinear uD H(f,r ) System System 3 p(r ) u 3 D 2.5
synthesized 2.0 300 % Distortion compensation
Bl [N/A] Bl 1.5
1.0
0.5
0.0 -5 -4 -3 -2 -1 -0 1 2 3 4 5 The input power depends on the << Coil in X [mm] coil out >> probability density function of the Probability Density Function displacement ! 1.5 Music: • The coil is most of the time in the gap 1.00 exploiting the high Bl-value
PDF PDF [1/mm] 0.50 • Linearization requires a small amount of additional input power 0.00 protection • The total system provides higher -5 -4 -3 -2 -1 -0 1 2 3 4 5 << Coil in X [mm] coil out >> system efficiency at low distortion ! just active MUSIC
maximal displacement Small, Loud-Speakers: Taking Physics To The Limit, 57 Digital Signal Processing dedicated to Loudspeakers
• transmission Linear • crossover processing • time alignment • equalisation Multi • directivity Channel processing • room correction • protection • linearisation Nonlinear processing • voice coil rest position adjustment • perceptual loudness correction • artificical bass enhancement
Small, Loud-Speakers: Taking Physics To The Limit, 58 Sources for Loudspeaker Innovations
Research Manufacturing new principles Marketing cost, quality, of operation Target performance, automation Tuning to the market
Signal HowLoudspeakershould–we Transducer processing an interdisciplinary Design work together ? FEA, BEM, other transducer related product simulations
New Materials Electronics Assessment motor, radiator, amplification, power measurement suspension, supply, wireless techniques enclosure
Small, Loud-Speakers: Taking Physics To The Limit, 59 Thank you !
Small, Loud-Speakers: Taking Physics To The Limit, 60