The infinite baffle - Klippel - The infinite baffle.pdfThe infinite baffle loudspeaker measurement...

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


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)


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.


Road Map

1) Half Space Measurement

2) Near Field Measurements

3) Holographic Approach

4) Examples


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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Measurement of Far-Field Response

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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

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Magnitude of transfer function H(f)

dB - [V

/ V]

Frequency [Hz]

Magnitude

Magnitude response

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Phase of transfer function H(f)

[deg

]

Freq uency [H z]

Phase

Phase response

Distance > 1 m

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Stimulus (t) vs time

[V]

Time [ms]

Stimulus (t)

Shaped Stimulus

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Sound Pressure spectrumSignal at IN2

dB - [V] (rm

s)

Frequency [Hz]

Signal lines Noise floor

Noise floor

Sound pressure spectrum

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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


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


• 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


Diffraction from baffle edges (2)


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


Diffraction from baffle edges (3)


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


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)


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


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


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:


How to find the required Order N ?

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0

100 1k 10k

f in Hz

Fitting E

rror

in d

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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


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


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


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


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


Baffle Symmetry symmetry axis 𝜗 = 90°


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


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


• 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


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


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f in Hz

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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

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0 10 20 30 40 50 60 70 80 90 100

h(t

)

t in ms


Measurement Results

500Hz

Sound pressure response can be extrapolated to any point outside the scanning surface

Sensitivity

Sound Power Directivity Index

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Directivity Index

Dir

ectiv

ity In

dex

/ dB

f / Hz

Speaker 1 Speaker 2

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Radiated Sound Power

dB S

ound

Pow

er

f / Hz

Speaker 1 Speaker 2

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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


Measurement Results

2 kHz

500Hz

8.5 kHz 14 kHz

2 kHz

6 kHz

6 kHz 8.5 kHz 14 kHz

3D Directivity


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


baffle

2xPhi + Baffle Symmetry 2 symmetry axis 𝜑 = 𝜑𝑠, 𝜑 = 𝜑𝑠 + 90° and 𝜗 = 90°


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


Rotational + Baffle Symmetry


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°


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


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


1 Point Measurement with Correction Curves Loudspeakers with similar geometry

100 1k 10k

f in Hz

measured response (Dut + room)

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100

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Reference Measurement (Full Scan) Single Point Measurement with correction curves

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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


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


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

The infinite baffle - Klippel - The infinite baffle.pdfThe infinite baffle loudspeaker measurement...

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