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  • The infinite baffle – loudspeaker measurement in half space, 1

    2015, Klippel GmbH

    The infinite baffle loudspeaker measurement in half space

    by holographic near field scanning

    The infinite baffle – loudspeaker measurement in half space, 2

    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 2034 -2013)

    • 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 IEC60268-2014)

  • The infinite baffle – loudspeaker measurement in half space, 3

    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:

    1350 x 1650 mm), diffraction effects causes ripples in the frequency response.

    Especially for low frequency (

  • The infinite baffle – loudspeaker measurement in half space, 6

    Half Space Measurement Why transducers are measured in a Baffle?

    • 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

    Measurement Setup

    • Requires half space anechoic room

    • Loudspeaker is mounted in floor

    • Back volume is sufficient large

    (negligible compression)

    35

    40

    45

    50

    55

    60

    65

    70

    75

    80

    85

    90

    95

    10 100 f in Hz

    infinite baffle closed Box

    vented box

    S P

    L i n d

    B

    The infinite baffle – loudspeaker measurement in half space, 7

    Measurement of Far-Field Response

    KLIPPEL

    -130

    -120

    -110

    -100

    -90

    -80

    -70

    -60

    -50

    -40

    -30

    1 2 5 10 20 50 100 200 500 1k 2k 5k 10k 20k

    Voltage Spectrum at Terminals Voltage Speaker 1

    dB - [V]

    (rm s)

    Frequency [Hz]

    Signal lines Noise floor

    Noise floor

    Voltage spectrum

    Complex transfer function

    )(

    )( )(

     

    jU

    jP jH 

    FT

    KLIPPEL

    55

    60

    65

    70

    75

    80

    85

    90

    95

    50 100 200 500 1k 2k 5k 10k

    Magnitude of transfer function H(f)

    dB - [V

    / V ]

    Frequency [Hz]

    Magnitude

    Magnitude response

    KLIPPEL

    -150

    -100

    -50

    0

    50

    100

    150

    50 100 200 500 1k 2k 5k 10k

    Phase of transfer function H(f)

    [d eg

    ]

    Freq uency [H z]

    Phase

    Phase response

    Distance > 1 m

    KLIPPEL

    -1,0

    -0,5

    0,0

    0,5

    1,0

    0 250 500 750 1000 1250

    Stimulus (t) vs time

    [V]

    Time [ms]

    Stimulus (t)

    Shaped Stimulus

    KLIPPEL

    -20

    -10

    0

    10

    20

    30

    40

    50

    60

    70

    80

    5 10 20 50 100 200 500 1k 2k 5k 10k 20k

    Sound Pressure spectrum Signal at IN2

    dB - [ V] (rm

    s)

    Frequency [Hz]

    Signal lines Noise floor

    Noise floor

    Sound pressure spectrum

    KLIPPEL

    -300

    -200

    -100

    0

    100

    200

    300

    400

    500

    600

    0 1 2 3 4 5 6 7 8

    Impulse response h(t)

    [V / V]

    left:0.875 Time [ms] right:4.958

    Measured Windowed

    Impulse

    response windowing

  • The infinite baffle – loudspeaker measurement in half space, 8

    Half Space Measurement Practical Limitation

    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 (

  • The infinite baffle – loudspeaker measurement in half space, 10

    Diffraction from baffle edges (2)

    © 1999-2014 Linkwitz Lab - http://www.linkwitzlab.com/diffraction.htm

    Circular baffles

    Squared baffles

    plate diameter 3 inch plate diameter 6 inch

    Sound pressure response shows distinct peak and dips at multiples of the half wave length

    Ripples are reduced by the squared shape of the baffle

    plate diameter 12 inch

    plate size 3 inch squared plate size 6 inch squared plate size 12 inch squared

    The infinite baffle – loudspeaker measurement in half space, 11

    Diffraction from baffle edges (3)

    © 1999-2014 Linkwitz Lab - http://www.linkwitzlab.com/diffraction.htm

    Rectangular baffles

    Normalized Baffle (IEC 60268-5)

    • rectangular baffle

    • transducer is positioned out of the

    center give addition reduction

    Conclusion:

    plate size 6x12 inch plate size 3x12 inch

    Using rectangular plates reduces the diffraction effects

  • The infinite baffle – loudspeaker measurement in half space, 13

    Short History on Near-Field Measurements

    Single-point measurement

    close to the source

    Don Keele 1974

    Klippel App Note 38,39

    On-axis

    Multiple-point measurement

    on a defined axis

    Ronald Aarts (2008)

    Scanning the sound field on

    a surface around the source

    . . . .

    Weinreich (1980), Evert Start (2000)

    Melon, Langrenne, Garcia (2009)

    Bi (2012)

    The infinite baffle – loudspeaker measurement in half space, 14

    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, 15

    2nd Step: Holographic Wave Expansion

    General solutions of the wave equation are

    used as basic functions in the expansion Total number of coefficients = (N+1)2

    monopole

    dipoles

    quadropoles

    )( fC

    COEFFICIENTS BASIS FUNCTIONS

    ),( rB f+

    Results

    3rd Step: Wave

    Extrapolation

    SCANNING

    DATA

    ),( rfH

    The infinite baffle – loudspeaker measurement in half space, 16

    Expansion into Spherical Waves

    tjm

    nn

    N

    n

    n

    nm

    in

    mn

    tjm

    nn

    N

    n

    n

    nm

    out

    mn

    eYkrhc

    eYkrhcrp

    

    

    ),()()(

    ),()()(),,,(

    )1(

    0

    ,

    )2(

    0

    ,

    

    

     

     

    Spherical

    Harmonics

    Hankel

    function of the

    second kind

    Coefficients

    incoming

    wave

    general solution of the wave

    equation in spherical coordinates

    region of validity

    surface

    sound source

    external sound source

    (ambient noise)

    external boundaries

    (walls) ),,,(),,,(),,,(  rprprp inout 

    outgoing

    wave

    incoming

    wave

    Spherical

    Harmonics

    Hankel

    function of the

    first kind

    Coefficients

    outgoing

    wave

    depending on frequency ω

    depending on

    distance r depending on

    angular direction

    + r0 ),,,( rp

    useful choice of the

    coordinate system results in

    three factors:

  • The infinite baffle – loudspeaker measurement in half space, 18

    How to find the required Order N ?

    -60

    -55

    -50

    -45

    -40

    -35

    -30

    -25

    -20

    -15

    -10

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