Deploying Amplifier and Signal Processing Advancements for Loudspeaker Control. Gregor Höhne

Transcription

1 Deploying Amplifier and Signal Processing Advancements for Loudspeaker Gregor Höhne

2 Agenda Introduction/Motivation o What is loudspeaker control? o Why do we need active control? Nonlinear Transducer Modeling o Modeling of static nonlinearities o Description of DC-components Nonlinear Adaptive o Overview on control structure o How to cope with time varying parameters Evaluation o Comparison between different control techniques

3 Introduction Micro-processor architectures deliver more and more signal processing power for low prices Voltage and current sensing are easily implemented by using cheap ADCs of MCUs or already offered by amplifier Modern amplifiers tend offer direct digital input making DCcoupling easily feasible Digital signal processing becomes a price competitive solution to solve design problems in many areas of the audio industry 3

4 Digital Signal Processing Dedicated to Loudspeakers Linear processing Multi Channel processing Nonlinear processing transmission crossover time alignment equalization directivity room correction protection linearization voice coil rest position adjustment perceptual loudness correction artificial bass enhancement 4

5 Using Electrical Means for ling Loudspeakers sensor audio input ler Goals: More output Higher efficiency Lower distortion Overload protection Defined overall behavior Requirements: Stable, robust Optimal performance while loudspeaker properties and ambient conditions are changing Simple to use, self-learning capabilities Inexpensive hardware 5

6 Linear Loudspeaker audio input Linear System Capabilities: Equalization Mechanical and Thermal Protection based on linear modeling Requirements: Linear Model Initial Parameters 6

7 Linear Adaptive Loudspeaker audio input Linear System state measurement Capabilities: Equalization Mechanical and Thermal Protection based on linear modeling Compensation of Aging Effects Requirements: Linear Model Initial Parameters Sensor 7

8 Nonlinear Adaptive Loudspeaker audio input Nonlinear System state measurement Capabilities: Equalization Mechanical and Thermal Protection based on nonlinear modeling Compensation of Ageing Effects Linearization Requirements: Nonlinear Model Initial Parameters Sensor 8

9 Which State Variables Should be Measured? L (x) R E (T V ) L E (x) C MS (x) M MS R MS F m (x,i) i v Acoustical Environment R (x) u b(x)v b(x) b(x)i Radiation p(t) Electrical domain Mechanical domain Acoustical domain Sensor Type Current & voltage sensor Optical Laser Sensor Microphone Advantages Robust, reliable, inexpensive sensor Absolute measurement of mechanical quantities Sensitive to acoustical problems Disadvantages Reflects mechanical and acoustical system indirectly Price, Resolution, Sensor Linearity, Handling Acoustical disturbances Time delay 10

10 / Using Speaker as Sensor? mh 1,00 inductance A 5,5 5,0 4,5 4,0 N force factor z(t) Audio Processing w(t) Enclosure u(t) Amplifer Woofer p(t) 0,75 3,5 0,50 0,5 0,00-7,5-5,0 -,5 0,0,5 5,0 7,5 x [mm] 3,0,5,0 1,5 1,0 0,5 0,0-7,5-5,0 -,5 0,0,5 5,0 7,5 x [mm] Parameter memory M P[n] Detector i(t) Leakage R e L(x) v M ms K ms (x) -1 R ms i Using the transducer model to estimate the voltage u Bl(x)v Bl(x) Bl(x)i Z load d L( x) i u' Re i Bl( x) dt dx dt Voltage current Back EMF Bl(x)v Mechanical signal (displacement) dl( x) i dx 1 R i Bl( x Bl( x) i K ( x) K (0) x L sz ( s) x u e ) dt dt ms ms m * Parameter identification by minimizing the error signal e( t) u' ( t) u( t) 11

11 Goals we Want To Reach with Digital source microphone Recording Environment Sound Engineering transmission storage media amplifier Listening Environment Loudspeaker Listener maximum acoustical output increased bass response low distortion high efficiency low weight, size and cost compensate for varying properties due to fatigue, ageing and climate 1

12 Goals we Want To Reach with Digital source microphone Recording Environment Sound Engineering transmission storage media amplifier Listening Environment Loudspeaker Listener maximum acoustical output increased bass response low distortion high efficiency low weight, size and cost compensate for varying properties due to fatigue, ageing and climate 13

13 Efficiency of a Loudspeaker Efficiency of a direct-radiator loudspeaker in a closed box η 0 f > f s ቚ = Bl ρ 0 S d ka<1 R e M ms πc η 0 f < f s ቚ = πf 4 p 0c 3 Bl C AT ka<1 π R e κ S d 0log10( ) Pass-Band R e M MS q=s d v f s f i v Example: Micro-speaker U Blv Bl F=Bli F L =ps d S d p=f L /S d R AR (f) Re 7.80 Ohm Bl N/A M MS 0.08 g S d 1.03 cm² Model for Closed Box Efficiency in Pass-Band η % 15

14 [db] Increasing Efficiency by Decreasing Moving Mass Fundamental component Pfar ( f1, U1 ) Mms = 10g Mms = 18g Mms = 14g Increased resonance frequency Increased efficiency In pass band KLIPPEL Example: Automotive Woofer 6 R e = 4Ω, Bl = 6, M ms = 14g, K ms = 1.15N/mm Closed Box 5l F s = 110Hz, Q ts = 0.9 Influence of Mms variation η 0 f > f s ቚ = Bl ρ 0 S d ka<1 R e M ms πc Frequency f1 [Hz] Simulated Sound Pressure in Far Field η 0 f < f s ቚ = πf 4 p 0c 3 Bl C AT ka<1 π R e κ S d Larger pass-band through decreased resonance No influence below pass-band (Stiffness is dominant) In many speakers moving mass is determined by voice coil -> high impact on Bl 16

15 [db] Increasing Efficiency by Increasing Compliance Kms = 1.15N/mm Kms= 5N/mm Fundamental component Pfar ( f1, U1 ) Increased efficiency below resonance Kms = 1.15N/mm Vbox=1l Kms = 0.N/mm Decreased resonance frequency Frequency f1 [Hz] Simulated Sound Pressure in Far Field KLIPPEL Example: Automotive Woofer 6 R e = 4Ω, Bl = 6, M ms = 14g, K ms = 1.15N/mm Closed Box 5l F s = 110Hz, Q ts = 0.9 Influence of C at variation η 0 f > f s ቚ = Bl ρ 0 S d ka<1 R e M ms πc η 0 f < f s ቚ = πf 4 p 0c 3 Bl C AT ka<1 π R e κ S d No influence on pass-band efficiency but increased frequency range Increased efficiency below resonance Either stiffness of suspension or of air volume is dominant Decreased compliance might lead to instable behavior 17

16 [db] Increasing Efficiency by Increasing Force Factor Fundamental component Pfar ( f1, U1 ) Bl = 4 Bl = 6 Bl = 8 Increased electrical damping at resonance Increased efficiency below resonance Frequency f1 [Hz] KLIPPEL Increased passband efficiency Simulated Sound Pressure in Far Field Example: Automotive Woofer 6 R e = 4Ω, Bl = 6, M ms = 14g, K ms = 1.15N/mm Closed Box 5l F s = 110Hz, Q ts = 0.9 Influence of Bl variation η 0 f > f s ቚ = Bl ρ 0 S d ka<1 R e M ms πc η 0 f < f s ቚ = πf 4 p 0c 3 Bl C AT ka<1 π R e κ S d Increased efficiency at and below pass-band Increased damping at resonance -> not critical Increasing the force factor leads to either a increased mass or a nonlinear motor 18

17 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. 0

18 PDF [1/mm] Bl [N/A] Pass-band Efficiency in the Large Signal Domain Nonlinear Force Factor Pa P 0 e Bl R M e ms 0Sd c Bl Bl( x 0) using the effective force factor Bl Bl( x) pdf ( x) dx with the probability function pdf(x) of the audio signal << Coil in X [mm] coil out >> Probability Density Function 1.5 An efficient speaker design provides highest force factor Bl(x=0) at rest position x=0 high effective force factor Bl Bl( x 0) maximum efficiency η << Coil in X [mm] coil out >> MUSIC maximal displacement 1

19 Increasing Efficiency Increasing efficiency often means trading off: o Stability o Linearity Increasing Efficiency only becomes feasible if upcoming problems are kept low or are solved differently

20 Goals we Want To Reach with Digital source microphone Recording Environment Sound Engineering transmission storage media amplifier Listening Environment Loudspeaker Listener maximum acoustical output increased bass response low distortion high efficiency low weight, size and cost compensate for varying properties due to fatigue, ageing and climate 3

21 Increasing the Bass Response Closed box Increasing output at low frequencies can be reached by: Increasing the passband Higher volume Softer suspension Boosting low frequencies High AC-displacement Prone to mechanical damage Requires mechanical protection Prone to aging, climate effects etc. Sensitivity of a closed box loudspeaker 0log10( ) f s Pass-Band f 4

22 Increasing the Working Range Amplitude Range of Operation Overload Large signal performance Small signal performance Most transducers are driven in the small signal domain: Low distortion Stable behavior Low risk of overload Increasing the small signal domain means: Higher hardware effort/costs Lower sensitivity Increasing the working range: Maximum output with a minimum of hardware Nonlinear behavior High risk of mechanical damage 5

23 Goals we Want To Reach with Digital source microphone Recording Environment Sound Engineering transmission storage media amplifier Listening Environment Loudspeaker Listener maximum acoustical output increased bass response low distortion high efficiency low weight, size and cost compensate for varying properties due to fatigue, ageing and climate 6

24 Transducer Nonlinearities displacement X [mm] Nonlinear Behavior Destruction Large signal performance Maximal Output Distortion Power Handling Stability Compression 1 0,3 Linear Modeling Small signal performance Bandwidth Sensitivity Flatness of Response Impulse Accuracy 7

25 X [mm] (rms) Nonlinear Symptom: Amplitude Compression,5,0 3.4 Hz Fundamental component X ( f1, U1 ) KLIPPEL 8 6 Peak and bottom value of waveform X peak + bottom.00 V 6.67 V V V.00 V (b) 6.67 V (b) V (b) V (b) Compression KLIPPEL 4 1,5 1,0 Linear System X [mm] 0-0, ,0 0,0,5 5,0 7,5 10,0 1,5 15,0 Voltage U1 [V] -8 *10 1 4*10 1 6*10 1 8* Frequency f1 [Hz] 9

26 dbu (Uo = 1V) dbu (Uo = 1V) Nonlinear Symptom: New Spectral Components Response 1 Frequency Domain input output Response 1 Frequency Domain f [Hz] Nonlinear System f [Hz] Amplitude sound pressure spectrum nd 3 rd nd nd 3 rd 3 rd Intermodulation Distortion harmonics n th n th difference tones summed tones n th f f ( n 1) f1 f f 1 f f1 1 nf f ( n 1) f f 1 1 f bass tone voice tone 1 frequency 30

27 X [mm] Nonlinear Symptom: DC-Displacement ZOOM Y(t) Input s ignal Y (t) v s tim e KLIPPEL K MS (x) 7,5 5,0,5 0,0 -,5 DC displacement rest position of the coil x -5,0 0,00 0,05 0,10 0,15 0,0 0,5 Time [s] DC-displacement is generated dynamically by rectification of AC components Caused by asymmetrical nonlinearities Working point is shifted away from rest position Significant amplitude X DC (comparable with fundamental) Usually in displacement (not in velocity, acceleration, input current) 3

28 Impact on Sound Quality Simulation of a woofer with a nonlinear transducer model linear nonlinear nonlinear +1db Spending costs and material for a shorting ring nonlinear with shorting ring nonlinear with shorting ring +1db 34

29 Increasing the Working Range Amplitude Range of Operation Overload Driving the transducer into the large signal domain causes: Significant nonlinear distortion Unstable behavior Large signal performance stabilization linearization Small signal performance Digital might solve the need for linearization and stabilization. 35

30 Goals we Want To Reach with Digital source microphone Recording Environment Sound Engineering transmission storage media amplifier Listening Environment Loudspeaker Listener maximum acoustical output increased bass response low distortion high efficiency low weight, size and cost compensate for varying properties due to fatigue, ageing and climate 36

31 [mm] Determining the Working Range Voice coil displacement 00:15: 30 Xpeak Xdc Xdcmax Xbottom 5 KLIPPEL 4 Dynamic DC displacement X DC displacement x rel rest position of the voice coil -1 - Coil s rest position X t [sec] Absolute voice coil position is determined by x abs x ( t) x ( t) X0( t, DUT) rel Voice coil displacement rel ( t) x ( t) x ( t) AC DC Voice coil rest position X 0 depends on time t and the device under test (DUT) DC displacement X DC depends on the audio signal and transducer nonlinearities Only AC component x AC generates sound pressure output 37

32 [mm] Upper and Lower Boundaries Voice coil displacement Grill 00:15: 30 Xpeak Xdc Xdcmax Xbottom hitting the grill L + KLIPPEL 1 0 bottoming at the backplate L xabs ( t) L t [sec] Upper and lower boundaries are defined by the geometry of the transducer limit the voice coil position damage of the transducer generate excessive signal distortion (rub&buzz, bottoming,...) L - Backplate 38

33 Protection Limits and Safety Margin x abs X clear X p ( t) M ( t) x x rel rel ( t) X ( t) X p ( t) clear ( t) M Positive and negative safety margins M are required to cope with Time variance (aging, climate) Production spread DC Displacement X DC offset in voice coil rest position ΔX 0 modeling and measurement error Activation of attenuation x rel L + (t) X 0( t ) upper clearance lower clearance upper boundary X clear+ (t) X clear- (t) M + X p+ (t) X p- (t) M - safety margin safety margin upper protection limit rest position lower protection limit L - lower boundary 39

34 Amplitude of AC Displacement x abs AC displacement x AC ( t) x ( t) x ( t) Maximum amplitude of the AC displacement X x ( t) AC rel AC DC while assuming that the audio signal w(t) has a symmetrical probability density function pdf(w(t)) X AC L + (t) x rel X 0( t ) X 0 upper clearance X ( t 0 ) lower clearance upper boundary X clear+ (t) X clear- (t) M + X p+ (t) X p- (t) M - safety margin X AC safety margin upper protection limit rest position lower protection limit L - lower boundary 40

35 Goals we Want To Reach with Digital source microphone Recording Environment Sound Engineering transmission storage media amplifier Listening Environment Loudspeaker Listener maximum acoustical output increased bass response low distortion high efficiency low weight, size and cost compensate for varying properties due to fatigue, ageing and climate 41

36 Variation of the Suspension System Kms(x)- versus time [N/m] 4500 K(t) 4000 K(t=1h) Kms Measurements in 15 min intervals Speaker time K(t=100h) Speaker Displacement x [mm] hour t Significant variation of Kms(x=0) at the rest position x=0 Small variation of Kms(xpeak) at the maximal displacement Xpeak 4

37 Kms [N/mm] [mm] Delta Tv [K] P [W] Influence of Ambient Conditions Temperature Environmental Testing Delta Tv Tambient P real P Re Pnom KLIPPEL Hz res onance f requency f s (t) at res t position X=0 fs (X=0) Winter t [sec] Resonance Frequency Sommer Ambient temperature KLIPPEL More than one octave shift t [sec] Xpeak Xdc Xdcmax Xbottom 3,0 KLIPPEL,5,0 1,5 1,0 0,5 0,0-0,5-1,0-1,5 -,0 -,5-3,0 Displacement Significant reduction of displacement t [sec] No additional sensor 43

38 How can we handle this problems? Amplitude Range of Operation Overload protection Adaptive Large signal performance stabilization linearization audio input ler Feedback of loudspeaker information Small signal performance equalization 45

39 Summary Producing small and efficient speakers with a high acoustical output requires an extended working range Extending the working range makes the speaker prone to nonlinear distortion, instabilities and overload Digital control may help to lower these symptoms Time varying properties of transducers demand such systems to be adaptive 46

40 Nonlinear Transducer Modeling Enclosure z(t) Audio Processing w(t) Amplifer u(t) Woofer p(t) Parameter memory M P[n] Parameter Identification i(t) Adaptive Nonlinear Requires a Nonlinear Transducer Model! Questions addressed in this section: How can the transducer nonlinearities be modeled? How can the DC-generation be described? What are the constraints of the model? 47

41 Stiffness K ms (x) of Suspension K 6 N/mm 5 total suspension F F x 4 3 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 48

42 Nonlinear Force Factor Bl(x) Bl Bl [N/A] 3,0,5,0,0 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, Displacement X [mm] Bl(x) is a nonlinear function of displacement x depending on Magnetic B field Gap geometry (depth) Height of the coil Voice coil rest position 50

43 Voice Coil Inductance L e (x) 4.0 Le [mh] Without shorting rings Φ coil (-9 mm) Φ coil (+9 mm) With shorting rings << Coil in X [mm] coil out >> voice coil displacement -9 mm 0 mm 9 mm x L e (x) depends on geometry of coil, gap, magnet optimal size and position of short cut ring 5

44 Nonlinear Transducer Model R e (T v ) L e (x,i) F m (x,i) M ms R K ms (x) -1 ms (v) i v u Bl(x)v Bl(x) Bl(x)i Stiffness K ms (x) Mechanical Resistance R ms (v) Force factor Bl(x) Inductance L e (x,i) K ms ( x) x R ms ( v) Bl( x) R e v M ms dv dt Bl( x) u( t) R e d L e ( i, x) i dt i dl e dx ( x) Nonlinear Restoring force Nonlinear damping Parametric Excitation Differentiated Flux Reluctance Force F m 54

45 Causes for DC Generation R E (t) L E (ω,x,i) F=Bl(x,t)i q i R L (ω,x,i) F rel (x,i) F A S D (ω,x) Z load (ω) u Bl(x,t)v Bl(x,t) v M MS C MS (ω,x,t) R MS (ω,v) -1 p p out (r) d L (q) electrical domain mechanical domain acoustical domain Nonlinearities reluctance force generated by inductance nonlinear force factor of the motor nonlinear compliance of the suspension acoustical system Time variant properties heating, climate impact, load, fatigue, aging, gravity 55

46 Generation of Signal Distortion by a Static Nonlinearity e.g. power Series expansion of nonlinear stiffness... ) ( x k x k k x k x K n n n ms... ) ( cos... ) ( cos ) ( cos ) ( cos ) cos(3 ) cos(3 4 ) cos( ) cos( ) )cos( 4 3 ( ) )cos( 4 3 ( ) ( ) ( t X X t X X k t X X t X X k t X t X k t X t X k t X k X k t X k X k X X k t F ) cos( ) cos( ) ( 1 1 t X t X t x for a two-tone signal input: K ms (x) x k 0 k 1 k... ) ( x k x k x k x x K F ms restoring force dc component nd -order intermodulation nd -order harmonics 3 rd -order intermodulation 3 rd -order harmonics fundamental 56

47 DC-Component Generated by K MS (x)-nonlinearity F rest K ms ( x) x k x k1 x k x k3 x... rectification process Frequency of Excitation Tone Cause Amplitude and Phase of x Direction of DCdisplacement Stability f < f s asymmetry in K MS (x) K MS (x) x stable f = f s asymmetry in K MS (x) K MS (x) x stable f > f s asymmetry in K MS (x) negligible stable f >> f s dc component moves coil to softer side of Kms(x) curve 57

48 DC-Component Generated by Bl(x)-Nonlinearity F motor Bl( x) i b 3 0 i b1 x i b x i b3 x i... rectification process Frequency of Excitation Tone Cause Phase Relationship Direction of DCdisplacement Stability f < f s asymmetrical Bl(x) x i Bl(x) x stable f = f s x i = 0 (no dc generated) f > f s asymmetrical Bl(x), i Bl(x) unstable f >> f s any excursion x i negligible x x 58

49 DC Displacement Generated by Motor and Suspension The frequency response of the dc displacement reveals the dominant asymmetry caused by Kms(x) caused by Bl(x) caused by L(x) X dc 1 mm - Unique symptom softer side of suspension X dc 5 mm - X dc 1 mm - L(x) Maximum 0 f s frequency 0 f s unstable f s Bl-maximum frequency 0 f s frequency Comparing the DC displacement generated at the resonance frequency with the values below and above reveals the root cause. 59

50 Adiabatic Compression of Enclosed Air in perfectly sealed enclosure (t) p t air pressure V (t) air volume ΔV V(t) V 0 p 0 p with static air pressure p 0 static air volume V 0 adiabatic coefficient κ p t (t) p t ( t) V ( t) const. p p t) V V ( t). C AB C AB 0 ( 0 const ( p) ( p) V ( t) p( t) Compliance of enclosed air depends on sound pressure V 1 1 p( t) 1/ 0 p( t) p 0 C AB (p) with ( 1 ) 1 gives the power series expansion p C AB ( p) V p p p 1 p p 0 60

51 Total Compliance of Transducers Operated in R e (T v ) Perfectly Sealed Enclosures L (x) L e (x) F m (x,i) M MS R MS (v) C MS (x) C MB (x) i v u R (x) Bl(x,i)v Bl(x,i) Bl(x,i)i C M, Total total mechanical stiffness K M,TOTAL (x) K M, Total K MS ( x) K supension air 1 1 C ( x) C ( x) MS MB MB ( x) C 1 M, Total K MB (x) K MS (x) 0 x Conclusion: Air nonlinearity can be compensated by suspension nonlinearity!! 61

52 Generating a DC Displacement by the Air Nonlinearity in a Perfectly Sealed Enclosures L (x) R e (T v ) L e (x) F m (x,i) M MS R MS (v) C MS (x) v i R (x) C MB (0) u Bl(x,i)v Bl(x,i) Bl(x,i)i The addition force describes the distortion injected by the air nonlinearity S p0 1 Sx F K ( x) K (0) x... 0 V dist MB MB V0 F B F dist (x) F=pS d separating the force F B generated at the linear air compliance C MB from the nonlinear distortion force F dis The DC displacement x DC generated by the mean distortion force (DC component) is x DC K ms ( x Fdis( t) 0) K MB (0) 6

53 Air Nonlinearity in Leaky Enclosures q l (t) p t air pressure S Cone surface x V F=pS d S d S d V C ab (p) p R AL displacement V (t) air volume barometric vent The DC component (mean value) in the sound pressure p in the box is p R AL F S d 1 S jc AB d F ( x) F 0 dis 1 ( p 0) B for for steady state condition because leak F v F B F dist (x) C MB (0) R ML 64

54 Asymmetrical Flow Resistance R A (v) p 0 p box p box x DC x DC R A (v 0 ) > R A (-v 0 ) R A (v) DC component in pressure p box dynamical voice coil offset x v 67

55 Dynamic DC-Generation stimulus AC displacement Parameter Asymmetry Bl(x), Le(x), Kms(x) X ac F(f 0) DC Force voice coil offset stiffness asymmetry Leakage Cab(f) K ms (f 0) Stiffness at DC creep factor Viscoelastic behavior X DC (t) DC Displacement Note: the DC displacement depends on the stimulus and is time variant 68

56 Suspension at Low Frequencies Magnitude of transfer function Hx(f)= X(f)/U(f) Magnitude of transfer function Hx(f)= X(f)/U(f) mm/v 0,45 Measured Fitted without creep KLIPPEL mm/v 0,55 Measured Fitted without creep KLIPPEL 0,40 0,50 0,45 0,35 0,30 0,5 Increased Compliance Through Leakage 0,40 0,35 0,30 Increased Compliance Through Creep 0,0 0,5 0,15 0,0 0,15 0,10 0,10 0,05 0,05 0, k k 5k 10k 0k Frequency [Hz] 0, k k 5k Frequency [Hz] Effects like creep and leakage may increase displacement at low frequencies by more than 100% Various models available (e.g. Ritter, Knudsen) but may not be valid down to DC Effects vary with time through aging, climate, position etc. Very difficult to model reliably 69

57 Summary Most of the nonlinear transducer behavior can modeled with static nonlinearities DC components are caused by nonlinearities as well as time varying effects Modeling the displacement at far below the audio band is difficult Need to avoid signal components below the audio band 70

58 Nonlinear Adaptive Enclosure z(t) Audio Processing w(t) Amplifer u(t) Woofer p(t) Parameter memory M P[n] Parameter Identification i(t) Questions addressed in this section: How is the structure of a nonlinear adaptive controller How to cope with time varying effects, DC components etc. 71

59 Nonlinear Structure amplifier transducer audio signal Alignment Thermal Protection Mechanical Protection Equalization Linearization Active parameters Transducer mirror symmetry H(f,r 1 ) p(r 1 ) sound field z Nonlinear System - u D u u D Nonlinear System H(f,r ) H(f,r 3 ) p(r ) p(r 3 ) synthesized distortion generated distortion structure derived from loudspeaker modeling Feed forward structure is stable for any set of parameters Interpretable state variables (displacement, velocity,..) 7

60 Requirements for Distortion Reduction p dist (t) Original distortion Residual distortion synthesized distortion t Equal amplitude 180 degree phase shift 73

61 Bl [N/ A] DC Coupled Amplifiers 4,0 3,5 3,0,5,0 1,5 1,0 0,5 -Xprot < X < Xprot Bl (-X) Force factor Bl (X) 00:7:35 Xbottom < X < Xpeak KL IPPEL 0, X [mm] Compensating asymmetric nonlinearities requires a DC signal at the loudspeaker terminals Driving the speaker into the Bl-maximum might be beneficial for efficiency and maximum AC-displacement 74

62 Avoiding DC Displacement by Linearization Bl(x) Visco-elastic behavior Cms(x) DC Force Cms(f) DC Displacement Le(x) Leaky Enclosures Feedback to the nonlinearities Linearization suppresses generation of DC force No components below the audio band avoid need for modelling displacement far below the audio band 75

63 Bl [N/A] Problem: Variation of Loudspeaker Parameters pole plate voice coil pole plate voice coil magnet Influence of Gravity magnet [N/m] Suspension Stiffness Force Factor ,5 Motor 3500, Load induced aging, fatigue over time 1,5 Voice coil offset 000 1, , displacement x [mm] 0, << Coil in X [mm] coil out >> 76

64 Adaptive Feedback Audio ler Voltage Sound Pressure Feedback of Parameters Parameters Depend on type of transducer Vary from unit to unit Vary slowly over time ( aging) Depend on climate (temperature, humidity) Depend on stimulus (no model for visco-elasticity) Adaptive adjustment required! 77

65 Voice Coil Offset Key Idea: Freezing the updating of particular parameters which vary slowly due to aging, fatigue and ambience Introducing a voice coil offset x off (t) describing the fast variation of the nonlinear parameters Estimating (permanently) the voice coil offset x off (t) from voltage and current for any AUDIO INTPUT (including single tone) L( x) N i0 l i x x off t i Bl( x) N i0 b i x x off t i K ms ( x) K ms (0) N i1 k i x x off t i 4.0 Le [mh] With shorting rings Without shorting rings x off t << Coil in X [mm] coil out >> Inductance L(x) Bl(x) 6 N/A x off t displacement x mm Force factor Bl(x) K 6 N/mm x off displacement t x mm Stiffness K ms (x) Properties of the voice coil offset x off (t): May be interpreted as a fast varying parameter or an additional state variable Contains spectral components below the audio band (0.1 < f < 5 Hz) 78

66 Adaptive Parameter Identification considering voice coil offset x off (t) Enclosure z(t) Audio Processing w(t) Amplifer u(t) Woofer p(t) P[n-1] Leakage Memory M P[n] x off (t) Parameter Identification i(t) Parameters P: Slowly time varying Slow learning speed is sufficient Updating requires persistent excitation Can be stored in memory Used as starting values after powering Voice coil offset x off (t): Time varying High learning speed Permanent updating required Not stored in memory Initialized to zero after powering 79

67 Active Loudspeaker Protection amplifier transducer audio signal Alignment Thermal Protection Mechanical Protection Equalization Linearization Requirements Reliable Protection of the transducer Generating a maximum of sound output Generating a minimum of distortion and artifacts Causing minimum or no latency in the audio signal Easy adjustment (tuning) to the transducer Coping with time variant loudspeaker properties 8

68 Active Loudspeaker Protection audio signal Alignment HP Equalization Linearization amplifier voltage current transducer initial transducer parameters Thermal Protection Mechanical Protection Memory transducer parameters Parameter Identification displacement voice coil temperature State Predictor Prerequisites 1. Permanent information on the transducer s state variables Temperature of voice coil and magnet Voice coil displacement (anticipated peak value). Limits describing maximum load permissible for the particular transducer Maximum voice coil and magnet temperature Maximum peak displacement 83

69 Protection System based on adaptive nonlinear modeling and control Linearization Stabilization transducer w(t) audio signal Attenuator (High-pass) DELAY Attenuator (High-pass) v(t-τ ) Nonlinear z(t) voltage v(t) displacement x rel (t) Mechanical Attenuation current Linear Model P nlin (t) parameters Nonlinear Adaptive Model 84

70 Alignment amplifier transducer audio signal Alignment Thermal Protection Mechanical Protection Equalization Linearization z(t) H tot (f) p(t) z(t) H equ (f) z (t) H lin (f) p(t) audio source z(t) Equalization z (t) Linearization Stabilization p(t) sound output amplifier transducer User Target value Automatic Alignment P[n] Parameter Identification The (transducer + mirror filter) has a linear overall transfer response and the identified loudspeaker parameter can be used for Automatic alignment to a desired target function (e.g. Butterworth for vented boxes) Compensation for varying parameters (aging, fatigue, climate changes, air load,...) Diagnostic information for system optimization (e.g. port velocity) 86

71 Poles-Zeros Cancellation The mirror filter compensates for the effect of the nonlinear and time-varying parameters and provides a linearized overall system with constant transfer function H lin (f) An additional pre-filter with the transfer function H equ (f) may be used to align the transducer to a desired target response H tot (f) Filter replaces poles of the identified system by the poles of the target system H tot = H equ H lin = N equ D equ N lin D lin = N lin D equ desired poles linearized loudspeaker system cancellation with N equ = D lin 87

72 Automatic Alignment of a Closed-box System Alignment of closed-box system with 4 th order filter Attenuation at low frequencies Extended bass response Align a transducer to a given enclosure (volume) Extend the frequency response of your system (< octaves) Maximal sound pressure output for minimum displacement No perfect match of transducer and enclosure necessary Enclosure design is decoupled from transducer design process Compensation of production variances, aging, fatigue 88

73 Layers in the Signal Processing Chain amplifier transducer audio signal Alignment Thermal Protection Mechanical Protection Equalization Linearization Subsequent adjustment of linear transfer behavior Protected against any kind of hazardous input signal Linear and time - invariant system irrespective of climate, aging and operating range Rely on each other 90

74 Demo Setup AMP Output Real Time Spectrum Analyzer Amplifier Klippel Platform Input Monitor 91

75 AMP AMP Audio Signal Flow Klippel Platform Woofer Channel IN1 Crossover Decimation Alignment ler Interpolation OUT1 yes Delay Line Mix Chann els? OUT Tweeter Channel Tweeter Audio Source Woofer 9

76 Evaluating an Adaptive led Loudspeaker System Evaluation of distortion compensation Evaluating the predicted displacement Comparison between different control techniques 93

77 Evaluation of Linearization Simple Approach: Comparing generated distortion with and without linearization in sound pressure z Active parameters Nonlinear System mirror symmetry - u D u u D Transducer Nonlinear System H(f,r 1 ) H(f,r ) H(f,r 3 ) p(r 1) sound field p(r ) p(r 3) synthesized distortion generated distortion Evaluation of linearization gives a fast indication of the overall performance Are the identified parameters correct? Is the adaptive updating working? 94

78 Single and Two Tone Measurement Amplitude X DC fundamental HD HD 3 fundamental IMD IMD IMD 3 IMD3 Simple Measurement Measures steady state behavior Not music-like harmonics difference tones summed tones f 1 0 f f 1 f -f 1 f +f 1 3f 1 f -f 1 f +f 1 frequency bass sweep: 0.5f s f 1 f s f = 0 f s voice sweep: f 1 = 0.5 f 5f s s f 0f s 95

79 [Percent] [Percent] [Percent] [Percent] Harmonic and Intermodulation Distortion Closed box 1liter aligned to 50Hz LINEAR CONTROL 3rd-order Signal at IN1 NONLINEAR CONTROL Linear KLIPPEL 30 5 NONLINEAR CONTROL nd-order Harmonics Signal at IN1 LINEAR CONTROL Linear KLIPPEL Nonlinear 10 Nonlinear Frequency [Hz] Frequency [Hz] Relative second-order intermodulation distortion ( d ) Signal at IN1 NONLINEAR LINEAR CONTROL 4 KLIPPEL Linear *10 4*10 6*10 8* Frequency f1 [Hz] Relative third-order intermodulation distortion ( d3 ) Signal at IN1 NONLINEAR CONTROL LINEAR CONTROL 40 KLIPPEL Linear *10 4*10 6*10 8* Frequency f1 [Hz] 96

80 IN1 [V] IN1 [V] [Percent] [Percent] Intermodulation Distortion Vented box without alignment Relative second-order intermodulation distortion ( d ) Signal at IN1 NONLINEAR LINEAR KLIPPEL OFF Relative third-order intermodulation distortion ( d3 ) Signal at IN1 NONLINEAR CONTROL LINEAR OFF KLIPPEL 10 5 Nonlinear Nonlinear 0 *10 4*10 6*10 8* Frequency f1 [Hz] 0 *10 4*10 6*10 8* Frequency f1 [Hz] 0,15 0,10 0,05 0,00-0,05-0,10 IN1 (t) Waveform IN1 f1 = Hz U1 = 0.40 V OFF KLIPPEL The bass tone at 50 Hz intermodulates the 1kHz tone 0,15 0,10 0,05 0,00-0,05-0,10 IN1 (t) Waveform IN1 f1 = Hz U1 = 0.40 V Nonlinear -0,15-0, Time [ms] -0, Time [ms] 97

81 [db] Multi-Tone Measurement Stimulus Spectrum p(f) of microphone signal Signal lines Noise + Distortions Noise floor Signal level Output signal MT ND 75 KLIPPEL 50 f Sparse multi-tone complex 5 0 Distortion Music-like signal Good for quick testing of overall performance k k 5k 10k 0k Frequency [Hz] distortion at fundamental frequencies harmonic components difference-tone components summed tone components 98

82 [mm] Multi-Tone Measurement 6 Woofer in 5l Box Aligned to 40Hz Spectrum U(f) of voltage at speaker terminals Signal level linear Noise + Distortion linear Signal level linear Signal level nonlinear Signal level nonlinear Noise + Distortion nonlinear 0,5 KLIPPEL Alignment KLIPPEL Compensation of Le 0,0 Spectrum X(f) of voice coil displacement Compensation of compression [db] 0 db = 1 v Synthesized Distorion 0,15 0, , Frequency [Hz] 0,00 *10 1 4*10 1 6*10 1 8* *10 Frequency [Hz] 99

83 [db] Multi-Tone Measurement 70 6 Woofer in 5l Box Aligned to 40Hz Spectrum p(f) of microphone signal Signal level linear Noise + Distortion linear Signal level nonlinear Noise + Distortion nonlinear KLIPPEL Distortion Compensation 30 Modal distortion Frequency [Hz] 100

84 p[pa] [db] Tone Burst Measurement 1 Burst Response Time Domain IN1 (Mic) - f = 50 Hz - U =.51 V Sound pressure referenced to 1 m in Full space (4 pi) environment Measured - U =.51 V Bandpassed: U =.51 V Window KLIPPEL Increasing Voltage Maximum Burst Response Spectrum IN1 (Mic) - f = 50Hz Distortion / Noise Threshold Maximal Level Curve: U = 1.41 V Curve above threshold: U = 1.58 V KLIPPEL Compare to limits ,1 0, 0,3 t[sec] Frequency [Hz] Measurement according to CEA010 Applying short burst signals with increasing voltage to the transducer Maximum SPL with distortion below defined threshold Measurement of impulsive behavior 101

85 p[dbspl] (0dB = 0uPa) Tone Burst Measurement Woofer in 5l Box no alignment Peak Value of IN1 (Mic) vs. Frequency and Voltage Sound pressure referenced to 1 m in Full space (4 pi) environment without control with conrol KLIPPEL *10 1 6*10 1 8* Frequency [Hz] 10

86 Evaluating the Predicted Displacement audio signal Alignment HP Equalization Linearization amplifier voltage current transducer initial transducer parameters Thermal Protection Mechanical Protection Memory transducer parameters Parameter Identification displacement voice coil temperature State Predictor Mechanical transducer protection relies on predicted displacement Displacement prediction relies on linearization Comparison to laser measurement 103

87 [mm] Accuracy of the Modelled Displacement 1,0 0,8 0,6 Non-Adaptive Linear Modeling Voice coil displacement 01:07:06 Xpeak Xbottom x min (laser) x max (laser) KLIPPEL 0,4 0, 0,0-0, -0,4-0,6-0,8-1,0 predicted by a linear model with fixed parameters transducer measured by laser sensor Discrepancy t [sec] Linear modeling can not describe the displacement at high amplitudes and can not cope production variance and other time variant processes (aging, climate) 104

88 [mm] Accuracy of the Modelled Displacement 1,0 0,8 0,6 0,4 0, Adaptive Linear Modeling (ALM) Voice coil displacement 01:01: Xpeak Xbottom x min (laser) x max (laser) KLIPPEL 0,0-0, -0,4-0,6-0,8 predicted by a linear model transducer measured by laser sensor -1, t [sec] Linear modeling can not describe the displacement at high amplitudes 105

89 [mm] Accuracy of the Modelled Displacement Adaptive Nonlinear (ANC) 1,0 Voice coil displacement 00:49:33 Xpeak Xdc Xdcmax Xbottom x min (laser) x max (laser) x dc (laser) x offset KLIPPEL 0,5 offset identified and compensated by control 0,0-0,5 predicted by a linear system linearized transducer measured by laser sensor -1, t [sec] 106

90 Perceptive Evaluation of a Protection System Loudspeaker without protection Setup listening tests Evaluation at high signal levels might be difficult Utilize auralization techniques based on difference signals No differentiation between other effects and influence of protection system possible Stimulus Reference -1 db +1 db Test Loudspeaker in large signal domain with active protection - Sdis Auralization output 107

91 Conclusions Adaptive nonlinear control: Helps driving loudspeakers to their physical limits Minimizes effects of aging and external influences Adds new degrees of freedom and challenges to loudspeaker and system design 108