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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 (<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, 4
Road Map
1) Half Space Measurement
2) Near Field Measurements
3) Holographic Approach
4) Examples
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)
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10 100 f in Hz
infinite baffle closed Box
vented box
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L in d
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The infinite baffle – loudspeaker measurement in half space, 7
Measurement of Far-Field Response
KLIPPEL
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-90
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-50
-40
-30
1 2 5 10 20 50 100 200 500 1k 2k 5k 10k 20k
Voltage Spectrum at TerminalsVoltage Speaker 1
dB - [V]
(rms)
Frequency [Hz]
Signal lines Noise floor
Noise floor
Voltage spectrum
Complex transfer function
)(
)()(
jU
jPjH
FT
KLIPPEL
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50 100 200 500 1k 2k 5k 10k
Magnitude of transfer function H(f)
dB - [V
/ V]
Frequency [Hz]
Magnitude
Magnitude response
KLIPPEL
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-100
-50
0
50
100
150
50 100 200 500 1k 2k 5k 10k
Phase of transfer function H(f)
[deg
]
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
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0
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5 10 20 50 100 200 500 1k 2k 5k 10k 20k
Sound Pressure spectrumSignal at IN2
dB - [V] (rm
s)
Frequency [Hz]
Signal lines Noise floor
Noise floor
Sound pressure spectrum
KLIPPEL
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0
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500
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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 (<100 Hz)
• baffle cannot be rotated to measure 3D directivity
• limited baffle size
(baffle is not infinite)
• measurement in full anechoic
room
The infinite baffle – loudspeaker measurement in half space, 9
• 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
Diffraction from baffle edges
© 1999-2014 Linkwitz Lab - http://www.linkwitzlab.com/diffraction.htm
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
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-35
-30
-25
-20
-15
-10
-5
0
100 1k 10k
f in Hz
Fitting E
rror
in d
B
Fitting error as a function of the maximum order N
The measurement system determines
automatically:
optimum order N of the wave expansion
total number of the measurement points
measurement time
N=0 N=1 N=2 N=5 N=10
-20dB = 1%
N=1 N=0 N=2 N=5 N=10
Directivity at 2kHz:
Target
Sufficient accuracy
Low fitting error
The infinite baffle – loudspeaker measurement in half space, 19
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)
Z-Axis
R-Axis
Phi-Axis
Microphone
DUT
Measurement Hardware
Near Field Scanner
The infinite baffle – loudspeaker measurement in half space, 20
How to realize the scanning for 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
out
in
or 4 -Scan 2 -Scan
measure on two
hemispherical surfaces
in front the baffle
measure on two
complete surfaces
around the baffle
2 -scan provides a perfect half space measurement – Infinite baffle
✔
out
in
The infinite baffle – loudspeaker measurement in half space, 21
Symmetry assumption
How can symmetry assumption applied to wave expansion?
Solution : Use symmetry properties of basis functions
Symmetries ?
A reflected sound wave can be modelled by a
mirror sound source.
The total sound field is axes symmetrical to
the reflection plane
Sound reflection on a plate S
S‘
Symmetry
The infinite baffle – loudspeaker measurement in half space, 22
No symmetry
Number of Coefficients:
𝐽 = 𝑁 + 1 2
Condition for used Spherical harmonics: All orders used
N
n=0
n=2
m=0 m=2 m=-2
Full set of basis function required
The infinite baffle – loudspeaker measurement in half space, 23
Baffle Symmetry symmetry axis 𝜗 = 90°
Number of Coefficients:
𝐽 =𝑁 + 1 𝑁 + 2
2
Only use basis functions that satisfy the symmetry condition
baffle
N
n=0
n=2
m=0 m=2 m=-2
𝜗 = 0°
𝜗 = 90° 𝜗 = −90°
Condition for used Spherical harmonics: n-m is an uneven number
𝑛 − 𝑚 ≠ 2𝑠 |𝑠 ∈ ℤ
Half Space Measurement
The infinite baffle – loudspeaker measurement in half space, 24
Scanning Process
How to determine the position of 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)
X ✔ ✔
Diagnostics (Which point is wrong?)
X X ✔
TEST FAILED Please measure Initial Point 3 again!
• moving the microphone to initial points in front of the baffle
• all points have the same distance to the baffle
Requirements: • Baffle position must be detected
d
The infinite baffle – loudspeaker measurement in half space, 25
• Use a smaller baffle in the center
of the Near Field Scanner
• Position Baffle outside the Near Field Scanner
(norm baffle – IEC 602648-5))
Measurement Setup
Scanning Process
The same hardware can be used to measure in front of the baffle
The infinite baffle – loudspeaker measurement in half space, 26
3rd Step: Extrapolation of the Sound Pressure
Ss
region of validity
S1
Loudspeaker
characteristics
)( fC
COEFFICIENTS BASIS FUNCTIONS
),( rB f+
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
between the input signal u(t) and the sound pressure output
p(t,r) at measurement point r at a distance r=| r –rref | from the
reference point rref which is larger than the validity radius a
)(),(),( fffH CrBr
Reconstructed
Transfer Function
),( rfHIndependent of
the loudspeaker at any point outside the
scanning surface
Region of
validity
The infinite baffle – loudspeaker measurement in half space, 28
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f in Hz
SP
L in d
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Measurement Results
Direct sound is
separated from room
reflections at the
measurement surface
Direct Sound
Measured Sound
Room Reflections
Holographic
Sound Separation
Sound Separation
by time windowing
Direct Sound Reflections
Field Separation
KLIPPEL
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h(t
)
t in ms
The infinite baffle – loudspeaker measurement in half space, 29
Measurement Results
500Hz
Sound pressure response can be extrapolated to any point outside the scanning surface
Sensitivity
Sound Power Directivity Index
KLIPPEL
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Directivity Index
Dir
ectiv
ity In
dex
/ dB
f / Hz
Speaker 1 Speaker 2
KLIPPEL
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Radiated Sound Power
dB S
ound
Pow
er
f / Hz
Speaker 1 Speaker 2
KLIPPEL
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10 2 10 3 10 4
Sensitivity
dB S
PL
/ V
f / Hz
Speaker 1 on axis at r=10m referenced to 1m and 2.83V Speaker 2
Contour Plots
The infinite baffle – loudspeaker measurement in half space, 30
Measurement Results
2 kHz
500Hz
8.5 kHz 14 kHz
2 kHz
6 kHz
6 kHz 8.5 kHz 14 kHz
3D Directivity
The infinite baffle – loudspeaker measurement in half space, 31
baffle
Condition for used Spherical harmonics: 𝑚 ≥ 0 and 𝑛 − 𝑚 ≠ 2𝑠 |𝑠 ∈ ℤ Symmetry Condition between 𝑚 > 0 and 𝑚 < 0
𝑅𝑠 =𝐶𝑚𝑛
𝐶−𝑚𝑛= −1 𝑚+1 sin 𝑚𝜑𝑠 + 𝑖 cos 𝑚𝜑𝑠
2
Number of Coefficients: for even orders N = 0,2,4,6, …
𝐽 =𝑁
2+ 1
2
for uneven orders 𝑁 = 1,3,5, …
𝐽 =𝑁
2+ 1
2
−1
4
1xPhi + Baffle Symmetry symmetry axis 𝜑 = 𝜑𝑠 and 𝜗 = 90°
N
n=0
n=2
m=0 m=2
RS
The infinite baffle – loudspeaker measurement in half space, 32
baffle
2xPhi + Baffle Symmetry 2 symmetry axis 𝜑 = 𝜑𝑠, 𝜑 = 𝜑𝑠 + 90° and 𝜗 = 90°
Number of Coefficients:
𝐽 =𝑁
2+ 1
𝑁
4+ 1
only even 𝑁 = 0,2,4,6, …
Condition for used Spherical harmonics: 𝑚 ≥ 0
𝑛 − 𝑚 ≠ 2𝑠 𝑛 = 2𝑠 | 𝑠 ∈ ℤ
Symmetry Condition between 𝑚 > 0 and 𝑚 < 0
𝑅𝑠 =𝐶𝑚𝑛
𝐶−𝑚𝑛= −1 𝑚+1 sin 𝑚𝜑𝑠 + 𝑖 cos 𝑚𝜑𝑠
2
N
n=0
n=2
m=0 m=2
The infinite baffle – loudspeaker measurement in half space, 33
Rotational + Baffle Symmetry
Number of Coefficients:
𝐽 =𝑁
2+ 1
only even N:
𝑁 = 0,2,4,6, …
Condition for used Spherical harmonics: 𝑚 = 0
𝑛 = 2𝑠 , 𝑠 ∈ ℕ+
baffle
N
n=0
n=2
m=0 m=2
no phi dependency + sym. axis 𝜗 = 90°
The infinite baffle – loudspeaker measurement in half space, 34
Number of Coefficients vs. Order and Symmetry
N No Symmetry Baffle Symmetry 1x Phi+baffle 2x phi+baffle rotational+baffle
0 1 1 1 1 1
5 36 21 12 6 3
10 121 66 36 21 6
15 256 136 72 36 8
20 441 231 121 66 11
25 676 351 182 91 13
30 961 496 256 136 16
For order 30 100% 52% 27% 14% 2%
Measurement time can be minimized using symmetry assumptions
t 3-4h <3min 1h
The infinite baffle – loudspeaker measurement in half space, 35
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
PROBLEMS:
• 1 point is insufficient for
holografic processing
• No field separation
• No far field extrapolation
Single Point measurement in non-
anechoic room
• complete Scan in
the near field of a
DUT with similar
geometry (in the
same room)
room
Near field
Near field
response
+ Extrapolated
far field +
correction curve
for extrapolation room correction curve
room
Direct sound near field
Near field
The infinite baffle – loudspeaker measurement in half space, 36
1 Point Measurement with Correction Curves Loudspeakers with similar geometry
100 1k 10k
f in Hz
measured response (Dut + room)
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90
100
SP
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Reference Measurement (Full Scan) Single Point Measurement with correction curves
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f in Hz
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Single Point Measurement (Speaker 1 + Room)
extrapolation
room correction
room correction curve
correction curve for extrapolation
far field r=6m
free field r=0.5m
corrected response
(free field)
extrapolated far field r=6m
The infinite baffle – loudspeaker measurement in half space, 37
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, 80
LECTURE INVITATION SOUND QUALITY OF AUDIO SYSTEMS
March 07th to 09th, 2016
Presented by: Prof. Dr. Wolfgang Klippel
Institute of Acoustics and Speech Communication,
Dresden University of Technology, Germany