Nonlinear Losses in Electro-acoustical Transducers Wolfgang Klippel, Daniel Knobloch

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The Association of Loudspeaker Manufacturers & Acoustics International (ALMA) Nonlinear Losses in Electro-acoustical Transducers Wolfgang Klippel, Daniel

1 The Association of Loudspeaker Manufacturers & Acoustics International (ALMA) Nonlinear Losses in Electro-acoustical Transducers Wolfgang Klippel, Daniel Knobloch Institute of Acoustics and Speech Communication Dresden University of Technology KLIPPEL GmbH Klippel, Nonlinear Losses in Electro-acoustical Transducers, 1

2 Abstract The mechanical and acoustical losses considered in the lumped parameter modeling of electro-dynamical transducers may become a dominant source of nonlinear distortion in micro-speakers, tweeters, headphones and some horn compression drivers where the total quality factor Qts is not dominated by the electrical damping realized by a high force factor Bl and a low voice resistance Re. This paper presents a nonlinear model describing the generation of the distortion and a new dynamic measurement technique for identifying the nonlinear resistance R ms(v) as a function of voice coil velocity v. The theory and the identification technique are verified by comparing distortion and other nonlinear symptoms measured on micro-speakers as used in cellular phones with the corresponding behavior predicted by the nonlinear model. Klippel, Nonlinear Losses in Electro-acoustical Transducers, 2

3 Questions Addressed in This Paper Why do loudspeakers with low harmonic distortion produce significant intermodulations in audio signals? Why are nonlinear distortion generated by loudspeakers and amplifiers so different? Does each loudspeaker nonlinearity produce unique symptoms making an identification of the physical cause possible? Why is the measurement of the dc displacement more informative than the measurement of 2nd-order harmonics? What do even and odd-order distortions reveal? How do the distortion depend on the shape of the nonlinear curve? Why may loudspeakers with moving coil assembly become unstable at high amplitudes? Klippel, Nonlinear Losses in Electro-acoustical Transducers, 3

4 Generation of Signal Distortion Input Signal Measured Signal linear distortion nonlinear distortion disturbances Klippel, Nonlinear Losses in Electro-acoustical Transducers, 4

5 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 are compromised by size, weightand cost generate deterministic distortion which are predictable can be predicted by linear and nonlinear parameters some regular distortion improve perceived sound quality Klippel, Nonlinear Losses in Electro-acoustical Transducers, 5

6 Nonlinear Transducer Modeling Port nonlinearity Multiple Outputs Single Input Air compression Radiation Sound Propagation Room Acoustics p(r 1 ) u(t) Electromechanical Transducer x(t) Mechanoacoustical Transducer Radiation Sound Propagation Room Interference p(r 2 ) sound field Bl(x) Kms(x) Le(x) Le(i) Rms(v) i(t) Cone vibration Radiation Doppler effect Sound Propagation Room Interference Wave steepening p(r 3 ) linear Dominant nonlinearities nonlinear linear Klippel, Nonlinear Losses in Electro-acoustical Transducers, 6

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)

7 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, Nonlinear Losses in Electro-acoustical Transducers, 7

0 diplacement x mm restoring force F = Kms ( x) x displacement Kms(x) determined by

8 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, Nonlinear Losses in Electro-acoustical Transducers, 8

9 Voice Coil Inductance L e (x) Φ coil (-9 mm) Φ coil (+9 mm) 4.0 Le [mh] Without without shorting rings With with shorting rings Φ counter shorting ring voice coil displacement -9 mm 0 mm 9 mm x << Coil in X [mm] coil out ( L( x i) d ( x, i) d ) U ind = ϕ = 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, Nonlinear Losses in Electro-acoustical Transducers, 9

10 Nonlinear Mechanical Resistance R ms (v) v Air flow dome spider R ms (v) magnet gap woofer Pole piece v Air flow v R ms (v) depends on velocity v of the coil due to air flow and turbulences at vents and porous material (spider, diaphragm) microspeaker Klippel, Nonlinear Losses in Electro-acoustical Transducers, 10

11 Ranking List of Transducer Nonlinearities 1. Force Factor Bl(x) 2. Compliance C ms (x) tweeter 3. Inductance L e (x) 4. Flux Modulation of L e (i) 5. Mechanical Resistance R ms (v) 6. Nonlinear Sound Propagation c(p) 7. Doppler Distortion τ(x) 8. Flux Modulation of Bl(i) 9. Nonlinear Cone Vibration 10. Port Nonlinearity R A (v) 11. many others... microspeaker woofers microspeaker horns Klippel, Nonlinear Losses in Electro-acoustical Transducers, 11

12 Effects of the Dominant Nonlinearities 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 2 v + M ms dv dt = Bl( x) u( t) R e d ( L ( i, x) i) e dt + 2 i 2 dl e dx ( x) Nonlinear Restoring force Nonlinear damping Parametric Excitation Differentiated Flux Reluctance Force F m Klippel, Nonlinear Losses in Electro-acoustical Transducers, 12

13 Nonlinear Mechanical Resistance R ms (v) K ms 2 Bl( x) ( x) x + + Rms ( v) v + M ms R e Nonlinear Damping dv dt = Bl( x) d u( t) R e ( L ( i, x) i) e dt + 2 i 2 dle ( x) dx Source of distortion: Multiplication of velocity with a function of velocity This nonlinearity is important for microspeakers air compression drivers microphones headphones transducers with dominant mechanical damping 2 Bl( x) < Rms ( v) R e This nonlinearity is not relevant for woofers subwoofers midrange drivers (tweeters) transducers with dominant electrical damping 2 Bl( x) > Rms ( v) R e Klippel, Nonlinear Losses in Electro-acoustical Transducers, 13

14 Block-oriented Model of loudspeaker with R ms (v) under current drive current i Bl force F distortion band-pass fs v Velocity first-order differentiator s p sound pressure multiplier R ms (v)-r ms (0) v band-pass filtering s (0) s + M = L 1 * ( Bli ( Rms ( v) Rms (0)) v) nonlinear operation K ms + R ms ms s 2 Klippel, Nonlinear Losses in Electro-acoustical Transducers, 14

15 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, Nonlinear Losses in Electro-acoustical Transducers, 15

16 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(ε) 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 ε) 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 ε) High-pass (sound pressure p) Low-pass (displacement x) differentiator 1 differentiator 1 1 differentiator differentiator Klippel, Nonlinear Losses in Electro-acoustical Transducers, 16

17 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, Nonlinear Losses in Electro-acoustical Transducers, 17

18 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, Nonlinear Losses in Electro-acoustical Transducers, 18

19 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, Nonlinear Losses in Electro-acoustical Transducers, 19

20 Symptom of R ms (v): 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, Nonlinear Losses in Electro-acoustical Transducers, 20

21 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, Nonlinear Losses in Electro-acoustical Transducers, 21

22 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, Nonlinear Losses in Electro-acoustical Transducers, 22

23 Analysis of Intermodulation 2nd-order component 10 Bl(x) all nonlinearities Percent Doppler Bl(x) and Kms(x) is dominant source of THD below resonance L e (x) K ms (x) R ms (v) Frequency f 2 8 [khz] 9 10 Rms(v) and Kms(x) is dominant source of THD at resonance Klippel, Nonlinear Losses in Electro-acoustical Transducers, 23

24 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] Klippel, Nonlinear Losses in Electro-acoustical Transducers, 24

25 Symptoms of R ms (v) Summary Symptoms: Harmonics in SPL (maximal at resonance f s ) 3rd-order component is larger than 2nd-order distortion decrease by 18dB per octave to lower and higher frequencies compression of the fundamental at resonance no Xdc component Impact on Sound Quality: critical in micro-speaker (up to 20 %) Klippel, Nonlinear Losses in Electro-acoustical Transducers, 25

26 Summary Distortion, compression and other nonlinear symptoms in loudspeakers are predictable A block-oriented model comprising dynamic linear subsystems and static nonlinear subsystems explains the nonlinear distortion generation process The nonlinearities are part of of feed-back loop generating a complicated behavior The spectral and temporal properties of the distortion depend on the nonlinearity (curve shape and type), the linear pre- and post-shaping filters and the excitation signal Klippel, Nonlinear Losses in Electro-acoustical Transducers, 26

Klippel Non-Linear Test Results LSI (Large Signal Identification) Driver Name: ND90-8. Introduction. Nonlinear Parameters. Large Signal Modeling

Klippel Non-Linear Test Results LSI (Large Signal Identification) Driver Name: ND90-8 Introduction Large Signal Modeling At higher amplitudes, loudspeakers produce substantial distortion in the output