the infinite baffle - klippel - the infinite the infinite baffle loudspeaker measurement
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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