Large Signal Behavior of Micro-speakers. by Wolfgang Klippel, KLIPPEL GmbH ISEAT 2013

Transcription

1 Large Signal Behavior of Micro-speakers by Wolfgang Klippel, KLIPPEL GmbH Institute of Acoustics and Speech Communication Dresden University of Technology ISEAT 2013 Klippel, Modeling of Micro-speakers, 1

2 Scope of the Paper diaphragm coil pole plate magnet backplate microspeakers 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? Klippel, Modeling of Micro-speakers, 3

3 Generation of Signal Distortion Input Signal Measured Signal Input Signal Measured Signal H(s)-1 Regular Nonlinearities Defects linear distortion nonlinear distortion Rub&Buzz and other irregular distortion Noise Klippel, Modeling of Micro-speakers, 4

4 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 Regular Nonlinearities generate deterministic distortion which are predictable are related with the design (geometry and material ) are compromised by size, weight and cost Klippel, Modeling of Micro-speakers, 5

5 Force Factor Bl(x) back plate magnet pole plate Bl(x) determined by Φ dc Magnetic field distribution Height and overhang of the coil B-field Optimal voice coil position coil F F Bl( x) i U Bl( x) v pole piece displacement 0 mm x Electro-dynamical driving force Voice coil current Back EMF Voice coil velocity 5.0 N/A Bl(x) << Coil in X mm coil out >> Klippel, Modeling of Micro-speakers, 7

6 Stiffness K ms (x) of Suspension K 6 N/mm 5 total suspension F F x 4 3 x 2 1 spider surround diplacement x mm restoring force F Kms ( x) x displacement Kms(x) determined by suspension geometry impregnation adjustment of spider and surround Klippel, Modeling of Micro-speakers, 8

7 Voice Coil Inductance L e (x) Φ coil (-9 mm) Φ coil (+9 mm) 4.0 Le [mh] With with shorting rings Without without shorting rings Φ counter shorting ring voice coil displacement -9 mm 0 mm 9 mm x << Coil in X [mm] coil out >> d ( x, i) d L( x) i U ind dt dt Reluctance force 2 i ( t) dl( x) F rel 2 dx Differentiated Magnetic flux L e (x) determined by geometry of coil, gap, magnet optimal size and position of short cut ring Klippel, Modeling of Micro-speakers, 9

8 非線性機械阻 R ms (v) Nonlinear Mechanical Resistance R ms (v) v Air flow dome spider R ms (v) magnet gap woofer Pole piece v Air flow coil microspeaker v pole plate magnet diaphragm backplate 機械阻語音圈的速度有關, 這是由於氣體在管或多孔材料間的流動與擾動 ( 彈波, 振膜 ) R ms (v) depends on velocity v of the coil due to air flow and turbulences at vents and porous material (spider, diaphragm) Klippel, Modeling of Micro-speakers, 10

9 換能器非線性特性的排名 Ranking List of Transducer Nonlinearities tweeter 1. 磁力轉換因數 Force Factor Bl(x) 2. 順性 Compliance Cms(x) 3. 電感 Inductance Le(x) 4. 磁通調變 Flux Modulation Le(i) 5. Mechanical Resistance Rms(v) 6. 非線性聲傳播 Nonlinear Sound Propagation c(p) 7. 多普勒失真 Doppler Distortion (x) 8. 非線性振膜振動 Nonlinear Cone Vibration 9. 洩音孔的非線性 Port Nonlinearity RA(v) 10. 其他 many others... microspeaker 低音揚聲器 woofers microspeaker 號角揚聲器 horns Klippel, Modeling of Micro-speakers, 11

10 主導非線性影響 Effects of the Dominant Nonlinearities R e (T v) L e(x,i) F m (x,i) M ms R ms(v) K ms(x) -1 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) Flux Modulation L e (i) K ms ( x) x R ms ( v) Bl( x) R e 2 v M ms dv dt Bl( x) u( t) R e d L e ( i, x) i dt 2 i 2 dl e dx ( x) Nonlinear damping 非線性阻尼 Parametric excitation Differentiated Flux 磁阻力 Reluctance Force Klippel, Modeling of Micro-speakers, 12

11 通用訊號流模型 - 描述一不同揚聲器的非線性 Generalized Signal Flow Model describing a separated loudspeaker nonlinearity distortion added to the input post-shaping Voltage distortion fs highpass sound pressure postshaping post-filter H 2 (f) 1st state variable pre-filter H 1,1 (f) Static Nonlinearity preshaping multiplier 2nd state variable pre-filter H 1,2 (f) feed-back loop Klippel, Modeling of Micro-speakers, 15

12 The Particularities of Each Nonlinearity NONLINEARITY INTERPRETATION PRE-FILTER H 1,1 (f) (output) PRE-FILTER H 1,2 (f) (output) POST-FILTER H 2 (f) Stiffness K ms (x) of the suspension restoring force Low-pass (displacement x) Force factor Bl(x) electro-dynamical force Band-stop (current i) nonlinear damping Band-pass (velocity v) Inductance L e (x) self-induced voltage Band-stop (current i) reluctance force Band-stop (current i) Inductance L e (i) varying permeability Band-stop (current i) Mechanical resistance R ms (v) Young s modulus E() of the material Speed of sound c(p) Time delay τ(x) nonlinear damping cone vibration nonlinear sound propagation (wave steepening) nonlinear sound radiation (Doppler effect) Band-pass (velocity v) Band-pass (strain High-pass (sound pressure p) High-pass (sound pressure p) Low-pass (displacement x) Low-pass (displacement x) Low-pass (displacement x) Low-pass (displacement x) Low-pass (displacement x) Band-stop (current i) Band-pass (velocity v) Band-pass (strain High-pass (sound pressure p) Low-pass (displacement x) differentiator 1 differentiator 1 1 differentiator differentiator micro-speaker Klippel, Modeling of Micro-speakers, 16

13 藉由基頻成份耦合各個非線性間的影響 Interaction Between Nonlinearities coupling via fundamental component Le(i) Bl(x) Cms(x) Le(x) Rms(v) Force (fundamental component) electrical input current voice coil displacement voice coil velocity Feedback to the nonlinearities Klippel, Modeling of Micro-speakers, 17

14 Using the Loudspeaker as Sensor to identify Motor and Suspension Nonlinearities Stimulus Noise, Audio signals (music, noise) V A Multi-tone complex Power amplifier Voltage & current Speaker Nonlinear Digital processing System Identification unit State Variables peak displacement during measurement voice coil temperature eletrical input power, Linear Parameters T/S parameters at x=0 Box parameters fb,qb Impedance at x=0 Nonlinear Parameters nonlinearities Bl(x), Kms(x), Cms(x), Rms(v), L(x), L(i) Voice coil offset Suspension asymmetry Maximal peak displacement (Xmax) Thermal Parameters Thermal resistances Rtv, Rtm Thermal capacity Ctv, Ctm Air convection cooling Klippel, Modeling of Micro-speakers, 18

15 利用 LSI 進行模擬 Model used in LSI 假設 Assumptions: 電動換能器 Electro-dynamical transducer 機械共振器 Mechanical resonator (2 nd -order system LSI Woofer and LSI Tweeter) 附加共振器 Additional resonator (4 th -order system in LSI Woofer Box) 四個非線性 Four nonlinearities: Bl(x), L(x), Kms(x), L(i) (LSI Woofer, LSI Woofer Box) 四個非線性 Four nonlinearities: Bl(x), L(x), Kms(x), Rms(v) (LSI Tweeter) 代表阻抗 L(i)+L(x) represents impedance Z(f,i,x) 磁力轉換因數也反映了磁場交流磁通量的影響 Bl(x) also reflects influence of magnetic ac-flux Klippel, Modeling of Micro-speakers, 19

16 Nonlinear Parameter Identification Microspeaker K ms N/mm 1,25 1,00 in air Bl(x) N/A 0,6 0,5 in air 0,012 Le mh 0,008 in vacuum in air 0,4 0,75 0,50 in vacuum 0,3 0,2 in vacuum 0,006 0,004 0,25 0,1 0,002 0,00-0,3-0,2-0,1 0,0 0,1 0,2 0,3 X mm 0,0-0,3-0,2-0,1 0,0 0,1 0,2 0,3 X mm 0,000-0,3-0,2-0,1 0,0 0,1 0,2 0,3 X mm 0,16 R ms (v) kg/s 0,12 0,10 0,08 0,06 0,04 0,02 in air in vacuum DISTORTION caused by AIR VACUUM K ms (x) 28% 36 % Bl(x) 20 % 17 % L e (x) 2% 2% R ms (v) 45% 6% 0,00-2,0-1,5-1,0-0,5 0,0 0,5 1,0 1,5 2,0 V m/s Klippel, Modeling of Micro-speakers, 20

17 Agreement Measured and predicted peak and bottom displacement mm 0,4 X linear model measured 0,2 0,1 nonlinear model 0,0-0,1-0,2 GENERATION OF A DC COMPONENT -0,3-0, Frequency f khz] COMPRESSION OF THE FUNDAMENTAL COMPONENT Klippel, Modeling of Micro-speakers, 21

18 Analysis of Peak and Bottom Displacement 0,4 X L(x) Bl(x) mm 0,2 0,1 nonlinear model 0,0 Bl(x) and Kms(x) gemerate dccomponent -0,1-0,2-0,3 R ms (v) K ms (x) -0, Frequency f khz] Rms(v) causes compression of the fundamental at resonance component caus Klippel, Modeling of Micro-speakers, 22

19 DC Displacement of the Voice Coil measured by a single tone 0,015 0,010 Bl(x) rest position Bl maximum X mm 0,005 0,000-0,010-0,015 L e (x) R ms (v) -0,020-0,025 predicted softer side of the suspension -0,030-0,035 measured -0,040 K ms (x) Frequency f khz Klippel, Modeling of Micro-speakers, 23

20 Analysis of THD Total Harmonic Distortion predicted 35 Percent K ms (x) Bl(x) and Kms(x) is dominant source of THD below resonance Bl(x) measured 10 5 L e (x) R ms (v) Frequency f khz Rms(v) and Kms(x) is dominant source of THD at resonance Klippel, Modeling of Micro-speakers, 24

21 Analysis of Intermodulation 2nd-order component Bl(x) is the dominant source of 2nd-order IMD 10 Bl(x) all nonlinearities Percent Doppler 1 K ms (x) L e (x) 0.1 R ms (v) Frequency f 2 8 [khz] varying frequency f constant frequency f 1 =700 Hz Klippel, Modeling of Micro-speakers, 25

22 Analysis of Intermodulation 3rd-order component Bl(x) distortions are independent of frequency 10 Percent Bl(x) all nonlinearities Kms(x) distortions are falling with displacement 1 K ms (x) L e (x) R ms (v) Rms(v) distortions are falling falling with 6dB per octave inductance distortions are negligible Doppler distortions are negligible 0.1 Doppler Frequency f 1 [khz] varying frequency f 1 constant frequency f 2 =700 Hz Klippel, Modeling of Micro-speakers, 26

23 Nonlinear Symptoms of R ms (v) Harmonics in SPL (maximal at resonance f s ) 3rd-order component is larger than 2nd-order distortion decreas by 18dB per octave to lower and higher frequencies Intermodulation decreasing by 6dB/octave Compression of the fundamental at resonance no Xdc component Klippel, Modeling of Micro-speakers, 27

24 Summary variation of the (mechanical) resistance Rms(v) versus velocity is a dominant nonlinearity in microspeakers caused by turbulences in air leaks (disappears in vacuum) contributes significantly to harmonic distortion at resonance (high impact on sound quality) dominant compression of the amplitude at resonance (important for mechanical protection systems) Klippel, Modeling of Micro-speakers, 29

25 Many Thanks! Klippel, Modeling of Micro-speakers, 30