the infinite baffle - klippel - the infinite the 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

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)

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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

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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

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Magnitude of transfer function H(f)

dB - [V

/ V ]

Frequency [Hz]

Magnitude

Magnitude response

KLIPPEL

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0

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100

150

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Phase of transfer function H(f)

[d eg

]

Freq uency [H z]

Phase

Phase response

Distance > 1 m

KLIPPEL

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0,0

0,5

1,0

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Stimulus (t) vs time

[V]

Time [ms]

Stimulus (t)

Shaped Stimulus

KLIPPEL

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0

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Sound Pressure spectrum Signal 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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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 ?

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