Big Sound from Small Speakers Part 1 Wolfgang Klippel Institute of Acoustics and Speech Communication University of Technology Dresden, GmbH Email address: wklippel@klippel.de Big Sound from Small Speakers, 1 Abstract: This seminar focuses on modern methods for designing and manufacturing microspeakers and other small, light and costeffective loudspeakers reproducing the sound at high efficiency and sufficient sound quality as required in telecommunication, automotive, multi-media and other professional applications. The seminar gives an overview on physical modeling of loudspeakers in the large signal domain which is necessary to explain the relationship between geometry and the properties of the materials on the one side and the transfer behavior and the performance on the other side. Meaningful loudspeaker parameters (T/S, nonlinear and thermal) and other specifications (amplitude response, directivity, power) are discussed which allow a comprehensive description of the transducer. Prof. Klippel addresses the fundamentals of loudspeaker diagnostics which is important to interpret the measurement results and to localize the causes of the defects and to develop alternative design choices. Big Sound from Small Speakers, 2
Questions addressed in the Seminar: How to get the desired frequency response and directivity pattern? How to find the optimal geometry of the cone? How to measure the power handling? How to perform meaningful measurements in the large signal domain? How to find the optimal size of voice coil in the gap? Which loudspeaker nonlinearities are desired? How to get maximal power handling and acoustical output? How to get maximal bass out of a small enclosure? How to measure the power handling? What is a good and what is a bad speaker? How to select an optimal driver for loudspeaker system design? Big Sound from Small Speakers, 3 Loudspeakers are everywhere Cars Cellular phones Multimedia, Computers Hearing aids Home hifi reproduction Professional audio Active noise control Big Sound from Small Speakers, 4
Requirements on Modern Loudspeakers Small dimensions Low weight Low cost High output at low distortion Maximal efficiency Loud speakers are required Big Sound from Small Speakers, 5 List of Content Small Signal Modeling Lecture Assessing Small Signal Performance - Practical Workshop Large Signal Modeling Lecture Assessing Large Signal Performance - Practical Workshop Detection of Defective Speakers - Lecture Discussion Summary Big Sound from Small Speakers, 6
- Loudspeaker - a dynamic system Audio band Frequency 1 Hz 100 Hz 1 khz 20 khz heat transfer Creep Resonance Cone break up Time constant 1 h 1 s 10 ms 1 ms 0.05ms Length of sound wave 3 m 30 cm 15 mm lumped model useful CRL distributed model required Big Sound from Small Speakers, 7 Motor and Suspension Design Material parameters geometry u Motor F Vibration Big Sound from Small Speakers, 8 V Admittance Y(f) used in lumped parameter model inner cone edge FEA X(r) Cone s surface F(r) Radiation BEA Coupled Mechanic-acoustical analysis soundfield
Equivalent Circuit of a drive unit Impedance Type Analogy (Fu) Electrical domain Mechanical domain Electrical dc Resistance current Voltage I Impedance describing Lossy inductance U Re ZL(j) Back EMF Blv Bl v Bli compliance Cms(f) Mms Moving mass Rms Driving force Mechanical Losses Force factor Big Sound from Small Speakers, 9 Linear Lumped Paramters Basic parameters : dc resistance R e Voice coil Inductance L e (+ additional parameters describing impedance at higher frequencies) Moving mass M ms (with air load) Force factor Bl Mechanical resistance R ms Stiffness K ms of the suspension at f s Vicsco-elastic stiffness parameters ( creep factor lambda ) Effective Radiation Area S D Derived Parameters (Thiele/Small) ( T/S ): Resonance frequency f s ElectricalQ-factorQ es MechanicalQ factor Q ms Total Q-factor Q ts Equivalent box volume V as of mechanical stiffness Pass-band sensitity Important Time varying Big Sound from Small Speakers, 10
Creep Factor visco elastic behavior (creep)) of the suspension at low frequencies Magnitude of Transfer Function X(f)/U(f) very important for microspeakers [mm/v] 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 measured estimated without creep 10 1 10 2 10 3 10 4 Discrepancy to traditional modeling compliance increases for f << fs Creep model implemented in LPM LPM R e C ms (f) M ms R ms I U Z L (j) Blv Bl v Bli ( f ) C ms 1 log Cms 10 f f s Kundsen and Jensen, JAES 1993 Big Sound from Small Speakers, 11 Identification of Mechanical Parameters We need more information about the mechanical system Known Perturbation of Mechanical System (traditional technique ) Requires second measurement with additional mass or enclosure Based on impedance measurement No mechanical sensor required Time consuming Problems with mass attachment, box leakage Big Sound from Small Speakers, 12 Direct Measurement of a Mechanical Signal Requires mechanical (acoustical) sensor (e.g. Laser) Only one measurement (fast) Driver in free air or in enclosure Reliable and reproducible data Can be applied to tweeters
Perturbation method: Sealed Test Box 1 Pro : Simple technique Cms is measured primarily Big Sound from Small Speakers, 13 Problems : Depends highlyon precise value of effective radiation area Sd Residual air volume(inside the transducer) can not be considered requires sealed diaphragm can not be used to measure mechanical mass without air load Time consuming Perturbation method: Added Mass 2 Pro: Simple technique Mms is measured primarily Problems : : can not be applied to tweeter and microspeakers Time consuming Mechanical Resistance or stiffness are assumed as frequency independent parameters Big Sound from Small Speakers, 14
Laser Technique Pro : Fast (one step technique) Simple to use Bl is measured primarily Most precise results Can be applied to most transducers Problems : Optical problems (angle, surface) Coil displacement is not axialsymmetrical Big Sound from Small Speakers, 15 Measurement in air or in vacuum? In Air Mms and Cms consider air load Useful input for system design Big Sound from Small Speakers, 16 In vacuum Mms and Cms consider mechanical elements only Useful for driver design and comparison with the weight of the loudspeaker parts
Effective Radiation Area S d very important for microspeakers Real surface area S Definition S d displacement air volume x r ds V ( ) S x x Mean voice coil displacement x C x( r) dr C dr Big Sound from Small Speakers, 17 How to Measure Radiation Area S d? Pistophone technique See Application note AN32 S d static air pressure p 0. closed volume V 0 V0 p p x 0 adiabatic coefficient Sound pressure p Displacement x Laser Microphone Big Sound from Small Speakers, 18
How to Measure Radiation Area S d? Differential method (sophisticated, precise) Displacement x 1 Sound pressure p 1 Displacement x 2 Sound pressure p 2 See Application note AN32 S d static air pressure p 0. V x p 2 0 p2 adiabatic coefficient Difference volume V x1 p 1 syringe (medical injection pump Big Sound from Small Speakers, 19 How to Measure Radiation Area S d? Laser Scanner Technique (precise,, robust) C Integration of x on curve C x C x( r) dr C dr S d V x x( r) ds S x Under klippel development Big Sound from Small Speakers, 20
How to Measure Radiation Area S d? Precise Technique III (using( Laser Scanner ) microspeaker woofer headphone Big Sound from Small Speakers, 21 Why is a precise measurement of S d important?? Effective Radiation Area S d S d determines the acoustical output sensitivity, efficiency affects the precision of the parameter measurement if the test box perturbation technique is used Moving mass Mms, force factor Bl and stiffness values Kms, compliance Cms Mms, BL, Kms, Cms Big Sound from Small Speakers, 22
10-1 10-2 10-3 10-4 4 Effective Coil Vibration Averaged Transfer Function between Displacement and Voltage Magnitude Transfer Function Hx(f)=X(r,f)/U(f) 1 2 3-15 -20 o Point 1 Point 2 o o Point 3 Laser Measurement gives three different transfer functions -25-30 -35 - -45 - -55 differences - -65 10 3 104 Displacement averaged over voice coil circumference mm/v averaged Hx(f) averaged Hx 310 10 Fitting of Mechanical Parameters Big Sound from Small Speakers, 23 - Loudspeaker - a dynamic system Audio band Frequency 1 Hz 100 Hz 1 khz 20 khz heat transfer Creep Resonance Cone break up Time constant 1 h 1 s 10 ms 1 ms 0.05ms Length of sound wave 3 m 30 cm 15 mm lumped model useful CRL distributed model required Big Sound from Small Speakers, 24
Measurements are the basis for loudspeaker diagnostics u Motor F inner cone edge V Vibration X(r) Cone s surface F(r) Radiation near field soundfield far field Electrical Measurement Mechanical Measurement Acoustical Measurement Z e (f)=u(f)/i(f) electrical H x (f)=x(f)/u(f) mechanical Lumped Parameters Big Sound from Small Speakers, 25 Cone Vibration + Geometry Far Field Response Distributed Parameters Cone Scanning Techniques Amplitude Olson,, 19 Amplitude+ phase + Doppler Interferometry (Polytech,, 1995) Amplitude + phase + geometry Triangulation Laser Scanner (Klippel, 2007) Frankort 1978 Intensity Velocity destribution on the cone Geometry Displacement Big Sound from Small Speakers, 26
New Tools for Loudspeaker Design Scanner Hardware Dedicated to loudspeakers Price effective Scanning geometry Many other applications Analyzer Software Visualization of cone vibration Prediction of sound pressure output Directivity Decomposition Big Sound from Small Speakers, 27 Automatic Scanning Process SCN Scanning System z phi r Mechanical scanning system with one rotational () and two linear actuators (r, z) The scanning starts at the outside rim and proceeds inwards Big Sound from Small Speakers, 28
Scanning Modes Profile Scan Explore Scan Detailed Scan Good for Radiation of axial-symmetrical Geometries only Good for Radiation all cones Rocking modes Scanning Time Good for Irregularities 8 min 1 hour 8 hours Big Sound from Small Speakers, 29 A Profile Scan is already useful! Profile Scan Detailed Scan 8 8 min 8 8 hours Big Sound from Small Speakers, 30
Measurement of Geometry High Precision < 10 m for 0 < z< 300 mm < 2.5 m for 5 mm < z < 5 mm Dual Measurement with correlation Automatic detection of optical errors Export in common formats ( such as *.txt, *.dxf) Big Sound from Small Speakers, 31 Visualization of Vibration Data 3D Animation Phase Distribution Big Sound from Small Speakers, 32 Cross-sectional Cut Amplitude Distribution
3937,5 Hz Analysis Software Tasks: Detect and suppress errors Animate vibration Make interpretation simpler Enhance information which are important for design Predict sound pressure output Big Sound from Small Speakers, 33 Vibration and Radiation Diagnostics needs complex vibration data + cone geometry Acoustical Characteristics (,,) (SPL, directivity, power,...) Drive Unit (woofer, tweeter,...) Geometry Vibration ANALYSIS Indications for acoustical improvement Mechanical Characteristics (AAL) Visual Animation Big Sound from Small Speakers, 34 Indications for mechanical improvement Modal & Decomposition Analysis
Checking Cone Vibration Do we have enough vibrational amplitude? On which cone part first break-up modes occur? Does the break-up modes gradually replace the piston mode? Do we have membran or bending modes? Big Sound from Small Speakers, 35 Accumulated Acceleration Level SPL [db] 90 Acceleration Level Rigid body modes Acceleration level Total sound Pressure level 30 100 1000 10000 a 2 (, c 0 a( j, r a) 2 r S a r c c r ) ds a j r a q AAL r (, ) (, a) 20log p o X j c db Weighted Sum of the accelaration amplitude Big Sound from Small Speakers, 36
How to perform modal analysis? Search for maxima in accumulated acceleration 0 aa( j) 2 i0 1 j / / i 2 i i 2 Sc i( rc ) dsc ra rc positive value 8296,9 Hz 90 85 AAL [db] 75 65 55 Acceleration Level 0 1 1 0.5 2 0.01 100 1000 10000 11109,4 Hz 13312,5 Hz 16289,1 Hz Big Sound from Small Speakers, 37? How to Specify the Radiator? Cone, Diaphragm and Surround 90 Acceleration Level 8296,9 Hz SPL [db] Rigid body modes Total sound Pressure level 11109,4 Hz 13312,5 Hz 30 100 1000 10000 loss factor Modal loss factor i of each mode i th -mode with i=1,2,... Natural frequency f i of the i th -mode with i=1,2,... Natural Funciton i (r c )of each mode i th -mode with i=1,2,... Loss factor of the material Young Young s Young s s E Modulus of the material () Geometry of the Radiator (shape, thickness,,..) Big Sound from Small Speakers, 38
??? Smooth SPL Response? Woofer A with paper cone Woofer B with magnesium cone SPL [db] SPL [db] 75 65 55 45 90 30 20 10 2 10 3 on -axis -30 degree +30 degree on -axis 10 2 10 3 10 4-30 degree +30 degree Woofer C with flat radiator on -axis 30 20-30 degree +30 degree 10 2 10 3 10 4 Big Sound from Small Speakers, 39 acceleration level? Sufficient Cone Vibration? SPL [db] 75 65 55 Total SPL Woofer A with paper cone : low Q factor of cone resonances SPL [db] 90 85 75 65 10 2 103 acceleration level Total SPL Woofer B with magnesium cone: natural modes cause high peaks in SPL 55 SPL [db] 90 30 10 2 10 3 10 4 acceleration level Total SPL 10 2 103 104 Woofer C with flat radiator dips are not visible in AAL AAL cause peak at 0.8 khz 0 Hz Big Sound from Small Speakers,
Sufficient Damping of the Material? Woofer C with flat radiator ACC [db] 90 85 75 65 Total Acceleration Level 10 2 10 3 10 4 Frequency [Hz] Read 3dB bandwidth in AAL i f i f i f i 8 0.1 Increase loss factor of material Big Sound from Small Speakers, 41? Where to apply additional damping? woofer C with flat radiator 90 Total Acceleration Level ACC [db] 85 75 65 10 2 10 3 10 4 Frequency [Hz] 820,3 Hz 12398,4 Hz Big Sound from Small Speakers, 42
? Where to apply additional damping? Woofer B Magnesium cone 90 85 AAL [db] 75 65 55 Acceleration Level 0 1 1 0.5 2 0.01 100 1000 10000 11109,4 Hz Rubber surround has sufficient losses Big Sound from Small Speakers, 43 Cone requires damping Finding Circumferential Modes Search for maxima in AAL of Circular or Quadrature Component 55 Radial Component AAL [db] 45 35 30 Big Sound from Small Speakers, 44 25 20 Circular Component 10 3 10 4
Decomposition into radial and circular components x total x rad x circ At 5 Hz Radial vibration mode Circular vibration mode Big Sound from Small Speakers, 45 causes Rub & Buzz Dominant Circumferential Modes? 90 SPL [db] 85 75 Acceleration Level Woofer C with flat radiator 65 55 Circular Component (Acceleration) 10 2 10 3 10 4 4 khz Big Sound from Small Speakers, 46
Decomposition into radial and circular components x total x rad x circ At 5 Hz Radial vibration mode Circular vibration mode causes Rub & Buzz Big Sound from Small Speakers, 47 How to find rocking modes? Woofer A with paper cone AAL [db] 75 65 55 45 35 30 Total AAL AAL of Quadrature Component 10 2 10 3 3 Hz Search for maximum in quadrature component in AAL at low frequencies Big Sound from Small Speakers, 48
? How to find irregular Vibrations? Aluminum diaphragm of a horn compression driver SPL [db] 85 75 65 Total (AAL) Circular (AAL) Search for maximum in quadrature or circular component of AAL 55 Quadrature (AAL) 45 10 3 104 6 khz Big Sound from Small Speakers, 49 Checking radiation problems Do we have a strong cancellation effect? Does the cancellation affect out-off axis points? Which cone part radiates sound? Does the size of radiating area decreases gradually? Big Sound from Small Speakers,
Prediction of Sound Pressure Rayleigh Rayleigh Integral Equation Total Sound Pressure Level 75 SPL [db] 65 55 10 3 10 4 Frequency [Hz] driver in infinite baffle good approximation for most angles short calculation time Big Sound from Small Speakers, 51? Smooth SPL Response? Woofer A with paper cone Woofer B with magnesium cone SPL [db] SPL [db] 75 65 55 45 90 30 20 10 2 10 3 on -axis -30 degree +30 degree on -axis 10 2 10 3 10 4-30 degree +30 degree Woofer C with flat radiator on -axis 30 20-30 degree +30 degree 10 2 10 3 10 4 Big Sound from Small Speakers, 52
Most important Results Example: headphone 90 Sound Pressure SPL @ 1m, 1V Power Level + 47 db @ 1V Accumulated Acceleration AAL Accumulated Acceleration (AAL) Rocking mode Directivity SPL on axis Power 30 10 1 10 2 10 3 10 4 Big Sound from Small Speakers, 53? Desired Directivity? 75 Sound Power Level SPL on-axis 30 20 Paper Cone 65 55 Woofer 45 A with paper cone Power [db] 10 2 103 power 10 Magnesium Cone 90 Sound Power Level SPL on-axis 85 0-10 -20 Flat Piston Power [db] 75 65 55 Woofer B with magnesium cone 45 SPL on-axis power -30 102 103 104 102 103 104 Power [db] Sound Power Level 90 85 75 65 55 Woofer 45 C with flat radiator SPL on-axis SPL on-axis power 35 30 102 103 104 Big Sound from Small Speakers, 54
? Desired Directivity? Directivity of SPL in the horizontal plane predicted for woofer C on -axis 30 20-30 degree +30 degree 10 2 10 3 10 4 0.9 khz. 330 0 30 1.1 khz. 330 0 30 1.4 khz. 330 0 30 300 300 300 2-10 90 2-10 90 2-10 90 2 120 2 120 2 120 210 1 1 210 1 1 210 1 1 Big Sound from Small Speakers, 55 Headphone Vibration 27 Hz 27Hz Asymmetrical Bending Mode Big Sound from Small Speakers, 56
Headphone Radiation 27 Hz 27Hz 0 330 30 + - + - 2 300-15 -10-5 90 2 120 210 1 1 Total Sound Pressure Level SPL [db] 30 20 10 3 104 Frequency [Hz] Big Sound from Small Speakers, 57? What causes the dips in SPL? Woofer C with flat radiator Compare Accumulated Acceleration (AAL) with sound pressure (SPL) 90 acceleration level SPL [db] Total SPL 30 102 103 104 There is enough vibration on the cone!! Radiation Problem Big Sound from Small Speakers, 58
Sound Pressure related Decomposition x total x in x anti x out quadrature of generates sound Reduces sound no sound Big Sound from Small Speakers, 59 X quadr ature X(,R i ) Reference phase I X(,R i ) How the decomposition works X in phase R Summation on all points no sound H(f,,R i,r j ) H(f,,R i,r j )-1 generates sound Contribution to sound pressure output at point r j I P(r j ) R Big Sound from Small Speakers,
Where is the sound radiated? Woofer C with flat radiator db - [V] (rms) 95 90 85 75 65 55 In-Phase Component Anti-Phase Component Cancellation frequencies 10 3 10 4 Frequency [Hz] Localization of the in-phase component Big Sound from Small Speakers, 61? How to Fix Acoustical Cancellation problems? - Area of in -phase component o node o INCREASE Target: Make in-phase component dominant Suppress anti-phase component Steps: 1. find location of in-phase component 2. use FEA to simulate behavior 3. (,, ) increase bending stiffness at this area (thickness, curvature, rips) Big Sound from Small Speakers, 62
Where is the sound radiated? Woofer A: Paper Cone SPL [db] 30 20 10 0 In-Phase Component Anti-Phase Component 10 2 10 3 In-phase component is dominant No acoustical cancellation In-phase component staysin the centre radiation area shrinks with frequency In-Phase Components 0.1 khz 0.7 khz 1 khz 1 khz 4 khz 10 khz Big Sound from Small Speakers, 63 : TIP: Reduction of effective cone area Breakup starts outside Outer ring area does not radiate significant sound () Inner part should radiate sound (in-phase component) 64 khz 2 khz 1 khz r b 0 Hz 3 khz 7 khz Big Sound from Small Speakers, 64
3937,5 Hz 3937,5 Hz Providing Input Data for FEA Finite Element Analysis E, Radiator (cone, diaphragm, panel) Material Parameters Drive Unit (woofer, tweeter,...) Geometry Vibration Modal & Decomposition Analysis Modal & Decomposition Analysis Predicted Víbration (accumulated level + shape) of total vibration of separated components Fitting Measured Víbration (accumulated level + shape) of total vibration of separated components Big Sound from Small Speakers, 65 Conclusion Displacement sensors + scanner + signal processing cost effective solution for loudspeakervibrometry Geometry + Vibration data is basis for analysis Interaction between vibration + radiation are important New decomposition techniquessimplifies interpretation Big Sound from Small Speakers, 66