The infinite baffle loudspeaker measurement in half space by holographic near field scanning

Transcription

1 The infinite baffle loudspeaker measurement in half space by holographic near field scanning 2015, Klippel GmbH The infinite baffle loudspeaker measurement in half space, 1 Comprehensive 3D-Directivity Data Required: Professional Stage and PA Equipment Accurate complex directivity data in the far-field is required for room simulations and sound system installations (line arrays) Home Audio Application Specification for 360 degree polar measurements (CEA ) Studio Monitor Loudspeakers Professional reference loudspeakers need a careful evaluation in the near-field Handheld Personal Audio Devices The near-field response generated by laptops, tablets, smart phones, etc. is more important than the far field response (considered in new proposal IEC ) The infinite baffle loudspeaker measurement in half space, 2

2 Abstract To measure loudspeakers under standardized conditions, the device is usually mounted in a baffle, which avoids the acoustical shortcut between front and backward sound and enables a measurement without the influence of an enclosure. Because of practical limitation of the baffle size (normalized baffle: 13 x 16 mm), diffraction effects causes ripples in the frequency response. Especially for low frequency (<100 Hz) the measurement is very inaccurate, because of both insufficient damping of the measurement room and limited dimensions of the baffle. A solution of the know problems is the holographic approach, using spherical harmonics and Hankel functions to identity the sound pressure in the near field. Due to the measurement on multiple layers, both room reflections and diffraction can be separated from the direct sound of the device. Thus, the holographic technique provides full 3D radiation data, measured in a normal room (e.g. workshop), without the problems of a non-infinite baffle. The infinite baffle loudspeaker measurement in half space, 3 Road Map 1) Half Space Measurement 2) Near Field Measurements 3) Holographic Approach 4) Examples The infinite baffle loudspeaker measurement in half space, 4

3 SPL in db db - [V / V] db - [V] (rms) [V] 1,0 0,5 0,0-0,5-1,0 Magnitude Stimulus (t) Stimulus (t) vs time k 2k 5k 10k Frequency [Hz] Time [ms] [V / V] db - [V] (rms) [deg] Phase k 2k 5k 10k Freq uency [H z] Half Space Measurement Why transducers are measured in a Baffle? infinite baffle vented box closed Box Reliable and standardized measurement of the acoustical output of a transducer Measure Transducer without the influence of an enclosure (e.g. compression effects, box resonances) prevent acoustic short cut f in Hz Measurement Setup Requires half space anechoic room Loudspeaker is mounted in floor Back volume is sufficient large (negligible compression) The infinite baffle loudspeaker measurement in half space, 6 Measurement of Far-Field Response Shaped Stimulus Distance > 1 m Voltage Spectrum at Terminals Voltage Speaker 1 Sound Pressure spectrum Signal at IN Signal lines Noise floor Signal lines Noise floor Voltage spectrum Noise floor k 2k 5k 10k 20k Frequency [Hz] Impulse response h(t) Sound pressure spectrum Noise floor k 2k 5k 10k 20k Frequency [Hz] Measured Impulse response Windowed windowing -200 Magnitude of transfer function H(f) left:0.875 Time [ms] right:4.958 Phase of transfer function H(f) FT Magnitude response P( j ) H ( j ) U ( j ) Complex transfer function The infinite baffle loudspeaker measurement in half space, 7 Phase response

4 Half Space Measurement Practical Limitation limited baffle size (baffle is not infinite) measurement in full anechoic room Problems: Acoustic short cut for low frequencies (measurement range limited) Diffraction effects from the edges of the baffle anechoic rooms are insufficiently damped for low frequencies (<100 Hz) baffle cannot be rotated to measure 3D directivity The infinite baffle loudspeaker measurement in half space, 8 Diffraction from baffle edges wave length is smaller than the dimension of the baffles Sound source radiates into halfspace (2 ) delayed reflections from baffle edges cause ripples in the sound pressure output Example Measurement of a 38mm driver in free air mounted in circular baffle mounted in rectangular baffle The infinite baffle loudspeaker measurement in half space, Linkwitz Lab -

5 Diffraction from baffle edges (2) Circular baffles plate diameter 3 inch plate diameter 6 inch plate diameter 12 inch Sound pressure response shows distinct peak and dips at multiples of the half wave length Squared baffles plate size 3 inch squared plate size 6 inch squared plate size 12 inch squared Ripples are reduced by the squared shape of the baffle The infinite baffle loudspeaker measurement in half space, Linkwitz Lab - Diffraction from baffle edges (3) Rectangular baffles plate size 6x12 inch plate size 3x12 inch Using rectangular plates reduces the diffraction effects Conclusion: Normalized Baffle (IEC ) rectangular baffle transducer is positioned out of the center give addition reduction The infinite baffle loudspeaker measurement in half space, Linkwitz Lab -

6 Short History on Near-Field Measurements Single-point measurement close to the source Multiple-point measurement on a defined axis Scanning the sound field on a surface around the source On-axis.... Don Keele 1974 Klippel App Note 38,39 Ronald Aarts (2008) Weinreich (1980), Evert Start (2000) Melon, Langrenne, Garcia (2009) Bi (2012) The infinite baffle loudspeaker measurement in half space, 13 Measurements in the Near Field Advantages: High SNR Amplitude of direct sound much greater than room reflections providing good conditions for simulated free field conditions Minimal influence from air properties (air convection, temperature deviations) Disadvantages: Not a plane wave Velocity and sound pressure are out of phase 1/r law does not apply, therefore, no sound pressure extrapolation into the far-field (holographic processing required) Solution: Holographic Approach 1. Measurement of sound pressure distribution 2. Holographic post-processing of the measured data (wave expansion) 3. Extrapolation of the sound pressure at any point in the far and near field The infinite baffle loudspeaker measurement in half space, 14

7 2nd Step: Holographic Wave Expansion SCANNING DATA H ( f, r) + BASIS FUNCTIONS B( f, r) COEFFICIENTS C( f ) monopole dipoles quadropoles Results General solutions of the wave equation are used as basic functions in the expansion Total number of coefficients = (N+1) 2 3rd Step: Wave Extrapolation The infinite baffle loudspeaker measurement in half space, 15 Expansion into Spherical Waves region of validity surface r 0 p( r, ) + sound source external boundaries (walls) general solution of the wave equation in spherical coordinates p( r, ) p ( r, ) p ( r, ) p( r, ) out outgoing wave Coefficients outgoing wave N n out cn, m n 0 m n ( ) h N n in cn, m( n 0 m n Coefficients incoming wave Hankel function of the second kind (2) n ) h (1) n in incoming wave ( kr) Y ( ) e m n m n Spherical Harmonics j t ( kr) Y ( ) e Hankel function of the first kind j t Spherical Harmonics external sound source (ambient noise) useful choice of the coordinate system results in three factors: depending on frequency ω depending on distance r depending on angular direction The infinite baffle loudspeaker measurement in half space, 16

8 Fitting Error in db How to find the required Order N? Fitting error as a function of the maximum order N N=0 N=1 N=2 N=5 N= The measurement system determines automatically: optimum order N of the wave expansion total number of the measurement points measurement time Low fitting error -20dB = 1% -55 Directivity at 2kHz: k 10k f in Hz Target N=0 N=1 N=2 N=5 N=10 Sufficient accuracy The infinite baffle loudspeaker measurement in half space, 18 Measurement Hardware DUT Z-Axis Microphone Phi-Axis R-Axis Moving the microphone Advantages: Facilitate heavy loudspeakers (hanging on a crane) Constant DUT interaction in the room during the scan (required in a non-anechoic environment) Accurate positioning of Mic Minimum gear within the scanning surface (only a platform and a pole) Near Field Scanner The infinite baffle loudspeaker measurement in half space, 19

9 How to realize the scanning for the baffle? 4 -Scan or 2 -Scan in out measure on two complete surfaces around the baffle in out measure on two hemispherical surfaces in front the baffle Advantages: + sound separation can compensate room effects + non-anechoic measurement Disadvantages - acoustical short cut and diffractions cannot be separated (internal sources) - Not applicable for large baffle (scanning surface is very large) Advantages: + acoustic short cut and diffractions are outside the scanning surface and can be separated by sound separation + Perfect half-space measurement + transducer can be measured in smaller baffles Particularities: baffle must be larger than the scanning surface Symmetry assumptions required 2 -scan provides a perfect half space measurement Infinite baffle The infinite baffle loudspeaker measurement in half space, 20 Symmetry assumption Sound reflection on a plate S A reflected sound wave can be modelled by a mirror sound source. The total sound field is axes symmetrical to the reflection plane S Symmetry How can symmetry assumption applied to wave expansion? Solution : Use symmetry properties of basis functions Symmetries? The infinite baffle loudspeaker measurement in half space, 21

10 No symmetry Condition for used Spherical harmonics: All orders used Number of Coefficients: J = N n=0 m=-2 n=2 m=0 m=2 N Full set of basis function required The infinite baffle loudspeaker measurement in half space, 22 Half Space Measurement Baffle Symmetry symmetry axis θ = 90 Condition for used Spherical harmonics: n-m is an uneven number n m 2s s Z Number of Coefficients: n=0 baffle θ = 90 θ = 90 J = N + 1 N θ = 0 n=2 m=-2 m=0 m=2 Only use basis functions that satisfy the symmetry condition The infinite baffle loudspeaker measurement in half space, 23 N

11 Scanning Process Requirements: Baffle position must be detected How to determine the position of the baffle? d moving the microphone to initial points in front of the baffle all points have the same distance to the baffle How much initial points are required? No. of Initial Points 3 Points 4 Points 5 Points Plane position Self Validation (check residual error) Diagnostics (Which point is wrong?) X X X TEST FAILED Please measure Initial Point 3 again! The infinite baffle loudspeaker measurement in half space, 24 Scanning Process The same hardware can be used to measure in front of the baffle Measurement Setup Position Baffle outside the Near Field Scanner (norm baffle IEC )) Use a smaller baffle in the center of the Near Field Scanner The infinite baffle loudspeaker measurement in half space, 25

12 SPL in db h(t) rd Step: Extrapolation of the Sound Pressure COEFFICIENTS C( f ) Loudspeaker characteristics + BASIS FUNCTIONS B( f, r) Independent of the loudspeaker Reconstructed Transfer Function H ( f, r) at any point outside the scanning surface The coefficients C(f), the order N(f) depending on frequency f, the validity radius a and the general basic functions B(f,r) of the wave expansion describe the directional transfer function H ( f, r) B( f, r) C( f ) between the input signal u(t) and the sound pressure output p(t,r) at measurement point r at a distance r= r r ref from the reference point r ref which is larger than the validity radius a Region region of validity Ss S1 The infinite baffle loudspeaker measurement in half space, Measurement Results Field Separation Measured Sound Direct Sound Room Reflections Holographic Sound Separation Sound Separation by time windowing 100 1k 10k f in Hz Direct Sound Reflections Direct sound is separated from room reflections at the measurement surface t in ms The infinite baffle loudspeaker measurement in half space, 28

13 db Sound Power db SPL / V Directivity Index / db Measurement Results Sound pressure response can be extrapolated to any point outside the scanning surface Contour Plots Sensitivity Sensitivity Speaker 1 on axis at r=10m referenced to 1m and 2.83V Speaker f / Hz Sound Power Directivity Index Radiated Sound Power Directivity Index 90 Speaker 1 Speaker 2 16 Speaker 1 Speaker f / Hz 10 f / Hz The infinite baffle loudspeaker measurement in half space, 29 Measurement Results 3D Directivity 2 khz 6 khz 8.5 khz 14 khz 2 khz 6 khz 8.5 khz 14 khz The infinite baffle loudspeaker measurement in half space, 30

14 1xPhi + Baffle Symmetry symmetry axis φ = φ s and θ = 90 Condition for used Spherical harmonics: m 0 and n m 2s s Z Symmetry Condition between m > 0 and m < 0 R s = C mn C mn = 1 m+1 sin mφ s + i cos mφ s 2 baffle Number of Coefficients: for even orders N = 0,2,4,6, J = N R S n=0 for uneven orders N = 1,3,5, J = N m=0 n=2 m=2 The infinite baffle loudspeaker measurement in half space, 31 N 2xPhi + Baffle Symmetry 2 symmetry axis φ = φ s, φ = φ s + 90 and θ = 90 Condition for used Spherical harmonics: m 0 n m 2s n = 2s s Z Symmetry Condition between m > 0 and m < 0 R s = C mn C mn = 1 m+1 sin mφ s + i cos mφ s 2 Number of Coefficients: J = N N only even N = 0,2,4,6, n=0 baffle m=0 n=2 m=2 The infinite baffle loudspeaker measurement in half space, 32 N

15 Rotational + Baffle Symmetry no phi dependency + sym. axis θ = 90 Condition for used Spherical harmonics: m = 0 n = 2s, s N + Number of Coefficients: J = N n=0 baffle only even N: N = 0,2,4,6, m=0 n=2 m=2 N The infinite baffle loudspeaker measurement in half space, 33 Number of Coefficients vs. Order and Symmetry N No Symmetry Baffle Symmetry 1x Phi+baffle 2x phi+baffle rotational+baffle For order % 52% 27% 14% 2% 3-4h 1h <3min t Measurement time can be minimized using symmetry assumptions The infinite baffle loudspeaker measurement in half space, 34

16 SPL in db SPL in db Fast Near-Field Measurements 1 Measurement Point + Correction Curve Assumption: Loudspeakers of the same type with similar geometry have similar directivities Louspeaker are measured at the postition (microphone and DUT) in the room Single Point measurement in nonanechoic room room Near field Near field response Extrapolated + Near field + far field PROBLEMS: 1 point is insufficient for holografic processing No field separation No far field extrapolation room correction curve correction curve for extrapolation complete Scan in the near field of a DUT with similar geometry (in the same room) room Direct sound near field The infinite baffle loudspeaker measurement in half space, 35 1 Point Measurement with Correction Curves Loudspeakers with similar geometry Reference Measurement (Full Scan) Single Point Measurement with correction curves Single Point Measurement (Speaker 1 + Room) free field r=0.5m measured response (Dut + room) far field r=6m room correction corrected response (free field) room correction curve 60 extrapolated far field r=6m correction curve for extrapolation extrapolation k 10k f in Hz 100 1k 10k f in Hz The infinite baffle loudspeaker measurement in half space, 36

17 Summary Near-field scanning + holografic wave expansion + Field separation provides the following benefits: More information about the acoustical output Sound pressure at any point outside scanning surface (complete 2π space) Measurement can be performed in a normal room (e.g. workshop) Baffle diffractions are compensated (infinite baffle) Higher angular resolution with less measurement points measurement time can be minimized using symmetry assumption or correction curves No errors caused by turntable rotation Self-check by evaluating the fitting error Comprehensive data set without redundancy The infinite baffle loudspeaker measurement in half space, 37 LECTURE INVITATION SOUND QUALITY OF AUDIO SYSTEMS March 07 th to 09 th, 2016 Presented by: Prof. Dr. Wolfgang Klippel Institute of Acoustics and Speech Communication, Dresden University of Technology, Germany The infinite baffle loudspeaker measurement in half space, 80