Acoustical Measurement of Sound System Equipment according ...21/E… · of Sound System Equipment...

KLIPPEL LIVE #9: Intermodulation Distortion, 1

Acoustical Measurement of Sound System Equipment

according IEC 60268-21

KLIPPEL LIVEa series of webinars presented by

Wolfgang Klippel


1. Modern audio equipment needs output based testing2. Standard acoustical tests performed in normal rooms3. Drawing meaningful conclusions from 3D output measurement4. Simulated standard condition at an evaluation point5. Maximum SPL – giving this value meaning 6. Selecting measurements with high diagnostic value7. Amplitude Compression – less output at higher amplitudes8. Harmonic Distortion Measurements – best practice9. Intermodulation Distortion – music is more than a single tone10. Impulsive distortion - rub&buzz, abnormal behavior, defects11.Benchmarking of audio products under standard conditions 12.Auralization of signal distortion – perceptual evaluation 13.Setting meaningful tolerances for signal distortion14.Rating the maximum SPL value for a product15.Smart speaker testing with wireless audio input

Previous Sessions


9th KLIPPEL LIVE:Intermodulation Distortion – music is more

than a single tone

Topics today:

• Physical causes for intermodulation distortion• Measurements according to IEC Standard 20268-21• Testing with a two-tone stimulus • Testing with a multi-tone complex• Interpretation of the results• Practical demos


Poll:

Do you evaluate the intermodulation distortion ?A. No 23%B. Yes, by listening to music 23%C. Yes, by using a two tone stimulus 33%D. Yes, by using a multi-tone complex 20%E. Yes, by other ways 0%


Bl-Distortion in Music

Undistorted music signal

High displacement required → signal below fs → bass signalIntermodulation with signal in audioband generate roughness when fs < 100 HzHigh impact on sound quality

Distortion generated by Bl(x) only

displacement

intermodulation

Harmonics

https://www.youtube.com/watch?v=pSTLM_vCAdU&feature=youtu.be


What causes the IM Distortion ?

pre-filterH1,1(f)

1st state variable

multiplier

distortion

fsVoltagesound

pressurehighpass

Static Nonlinearity

pre-filterH1,2(f)

post-filterH2(f)

2nd state variable

Generalized Signal Flow Modeldescribing a separated nonlinearity

The multiplication of two different state variables generates unique intermodulation distortion !


Causes for high IM-Distortion NONLINEARITY

INTERPRETATION

PRE-FILTER H1,1(f) (output)

PRE-FILTER H1,2(f) (output)

Stiffness Kms(x) of the suspension

restoring force Low-pass (displacement x)

Low-pass (displacement x)

Force factor Bl(x) electro-dynamical force Band-stop (current i)


nonlinear damping Band-pass (velocity v)


Inductance Le(x) self-induced voltage Band-stop (current i)


reluctance force Band-stop (current i)

Band-stop (current i)

Inductance Le(i) varying permeability Band-stop (current i)

Band-stop (current i)

Mechanical resistance Rms(v)

nonlinear damping Band-pass (velocity v)

Band-pass (velocity v)

Young’s modulus E(ε) of the material

cone vibration Band-pass (strain ε)

Band-pass (strain ε)

Speed of sound c(p) nonlinear sound propagation (wave steepening)

High-pass (sound pressure p)


Time delay τ(x) nonlinear sound radiation (Doppler effect)



Negligible THD

Negligible THD

Negligible THDf >2fs

Measurements of Intermodulation Distortion is important !

Nonlinearity

Interpretation

PRE-Filter H1,1(f)

(output)

PRE-Filter

H1,2(f)

(output)

Stiffness Kms(x) of the suspension

restoring force

Low-pass

(displacement x)

Low-pass

(displacement x)

Force factor Bl(x)

electro-dynamical force

Band-stop

(current i)

Low-pass

(displacement x)

nonlinear damping

Band-pass

(velocity v)

Low-pass

(displacement x)

Inductance Le(x)

self-induced voltage

Band-stop

(current i)

Low-pass

(displacement x)

reluctance force

Band-stop

(current i)

Band-stop

(current i)

Inductance Le(i)

varying permeability

Band-stop

(current i)

Band-stop

(current i)

Mechanical resistance Rms(v)

nonlinear damping

Band-pass

(velocity v)

Band-pass

(velocity v)

Young’s modulus E() of the material

cone vibration

Band-pass

(strain

Band-pass

(strain

Speed of sound c(p)

nonlinear sound propagation (wave steepening)

High-pass

(sound pressure p)

High-pass

(sound pressure p)

Time delay τ(x)

nonlinear sound radiation

(Doppler effect)

High-pass

(sound pressure p)

Low-pass

(displacement x)


Sparse but Comprehensive Stimulus

Stimuli

Single-Tone

Two-Tone

Multi-Tone

Noise AudioSignal

complexity

Spectral Analysis

Total Distortion2nd-order3rd-order

Amplitude Phase Intermodulation Distortion

Harmonics of the two tones


Intermodulation distortiongenerated by Two-tone Stimulus

difference tones summed tonesharmonics

frequency

Amplitude sound pressure spectrum

IntermodulationDistortion

3rd 3rd

nth

12 )1( fnf −−

nth

12 )1( fnf −+

2nd2nd

12 ff − 12 ff +

3rd2nd

12 f

nth

1nf

“bass tone”1f

“voice tone”2f

To simplify the identification of the components:• Keep large distance between the exciting tones f1 and f2


IM-Distortion (two-tone signal)Definitions according IEC 60268-21

Second-order Modulation

(FM + AM)2 1 2 1

22

( ) ( )20lg( )IMD

p f f p f fLp f

− + +=

Third-order Modulation

(FM + AM)2 1 2 1

32

( 2 ) ( 2 )20lg( )IMD

p f f p f fLp f

− + +=

Total Modulation Distortion

(FM+ AM)

2

2 1 2 11

1 22

( ) ( )( , ) 20lg

( )k

TIMD

p f kf p f kfL f f

p f=

− + + =

∑

The IEC 60268-21 uses relative measures (IMD component divided by carrier )The relative IMD are similar to the equivalent input distortion because the frequency distance |f2-f1|


Contribution of 2nd and 3rd-order Components to the total intermodulation distortion

KLIPPEL

-30

-25

-20

-15

-10

-5

0

5

4*102 6*102 8*102 103 2*103 4*103 6*103 8*103

Modulation distortion (U1=1 V)

dB

Frequency f1 [Hz]

Ld2 Ld3 Ldm (cumul)

Total modulation

3rd order2nd order


Sweeping the Two-Tone SignalHow to choose the frequencies ?

f1 f2

f1 f2

f1 f2

sweeping voice tone

sweeping bass tone

difference tone measurement

f1 f2

f2-f1=const.

f1=const.

f2=const.

Sweeping two tones f2/f1=const.

not very usefulExploit information for f2 ≠ f1 !!! f1

f2

20 kHz

20 kHz

20 Hz

20 Hz

f2/f1=const.


Poll:How do you set the frequencies of the two tones in the stimulus for the testing ?A. None 41%B. Fixed setting two tones (f1 > f2) 19%C. Sweeping the Bass tone f1 (fixed f2 > f1) 9%D. Sweeping the voice tone f2 (fixed f1 < f2) 25%E. Sweeping two tone sweep with constant

frequency ratio f2/f1=const 13%F. Other 0%


Setup for IMD in Sound Pressure bass sweep technique

Optimal Stimulus:Two-Tone stimulusVarying frequency of bass tone about resonance 0.5fs < f1 < 2fsConstant frequency of voice tone above resonance f2 =7fs

Requirement:2 sinusoidal generators, Spectrum analyzer

Bass tone f1

Loudspeaker~

FT

Microphone SpectrumAnalyzer

Amplifier

~voice tone f2

Amplitude response versus frequency f1 :

2nd-order IMD3rd –order IMD

frequency


Causes of IMD in Sound Pressure Output using bass sweep technique

Cone Vibration

L(i)

Bl(x)

L(x)

Doppler Effect

L(i)

Bl(x)

L(x)

L(i)

Cone Vibration

Doppler

IMD%

fs

30

f1bass tone

voice tonef2=10fsdistortion is minimal

above fs

IMD generated by voice displacement

Kms(x) negligible


Demo: Intermodulation Distortion2 tone stimulus with bass sweep

Tools of the KLIPPEL Analyzer: • 3D Distortion Measurement (DIS)

http://www.klippel.de/products/rd-system/modules/dis-3d-distortion-measurement.html


Measurement of IMD in Sound Pressure voice sweep technique

Optimal Stimulus:Two-Tone stimulusVarying frequency of voice tone above resonance 5fs < f2 < 20fsConstant frequency of bass tone below resonance f1 < 0.5fs

Requirement:ALMA Test CD, 2 tone generators, Spectrum analyzer, Microphone

Bass tone f1

Loudspeaker~

FT

Microphone SpectrumAnalyzer

Amplifier

~voice tone f2

Amplitude response versus frequency f1 :

2nd-order IMD3rd –order IMD

frequency


The Causes of IMD in Sound Pressure Outputvoice sweep technique

Cone Vibration (at maxima of AAL)

L(i) (rising with f2 )

Bl(x) independent of f2

L(x) (rising with f2 )

Doppler Effect (rising with f2 )

Bl(x)

L(x)

L(i)

Cone Vibration

Doppler

IMD%

f 220f s7f s

20 -

variable voice tone

fixedbass tonef2=0.5fs

independent of frequency

distinct frequencies

L(x) ,L(i) and Doppler

Bl(x)

Cone Vibration

Kms(x) negligible


Demo: Intermodulation Distortion2 tone stimulus with voice sweep




Sparse but Comprehensive Stimulus

Stimuli

Single-Tone

Two-Tone

Multi-Tone

Noise AudioSignal

complexity

Spectral Analysis

Time Domain Analysis EnvelopeCalculation

Phase Modulation

Amplitude Modulation

Total Distortion2nd-order3rd-order

Amplitude Phase Intermodulation Distortion

Harmonics of the two tones


Amplitude Modulationtwo-tone stimulus f1 < fs, f2 > fs

-5,0

-2,5

0,0

2,5

5,0

0,05 0,10 0,15 0,20 0,25 0,30

Sound pressure Pfar(t) in far field vs time

Pfar [

N / m^2

]

Time [s]

Pfar(t)

SymmetricalForce factor

Bl(x)

Cycle

peak

Rest positionKLIPPEL

0,51,01,52,02,53,03,54,04,55,0

-5 -4 -3 -2 -1 0 1 2 3 4 5

Bl(x)[N/A]

[mm] x BottomMean


-10,0

-7,5

-5,0

-2,5

0,0

2,5

5,0

7,5

10,0

0,08 0,09 0,10 0,11 0,12 0,13 0,14


Pfar [

N / m^2

]

Time [s]

without Doppler with Doppler

Phase (Frequency) Modulationcaused by Doppler Effect

-7,5

-5,0

-2,5

0,0

2,5

5,0

7,5

10,0

0,106 0,107 0,108 0,109 0,110 0,111 0,112 0,113


Pfar [

N / m^2

]

Time [s]

without Doppler with Doppler

Phase variation


Phase of Intermodulation Distortion

Amplitude Modulation Frequency Modulation(Phase Modulation)

variationof envelope

12 ff − 12 ff +

phase variation

1f 2f

Lamplitude spectrum

2f

in-phase

12 ff −12 ff +

90 degree phase shift

2f12 ff −

12 ff +


Audibility of Intermodulation DistortionJust-noticeable degree of amplitude modulation (AM) and just noticeable index of frequency modulation (FM) of a 1-kHz tone at 80 dB SPL, as a function of modulation frequency

„Bass tone“

Critical condition:modulation frequency of the „bass tone“ is sufficiently low (fB < 200Hz) the intermodulation

distortion are within a critical band rate

AM modulation (e.g. force factor distortion) are audible at 3 % and perceived as roughness

Threshold of FM modulation is 20 dB higher

Doppler distortion are not critical

„Voice tone“

fc = 1kHzLc = 80dB

100

%31.6

3.16

0.316

8 32 128 512

Modulation frequency fB

degr

ee o

f am

plitu

de m

odul

atio

n, m

inde

x of

freq

uenc

y m

odul

atio

n, n

AM

Zwicker, Fastl, 1999

FM


IM-Distortion (two-tone signal)Definitions according IEC 60268-21

Second-order Modulation

(FM + AM)2 1 2 1

22

( ) ( )20lg( )IMD

p f f p f fLp f

− + +=

Third-order Modulation

(FM + AM)2 1 2 1

32

( 2 ) ( 2 )20lg( )IMD

p f f p f fLp f

− + +=

Total Modulation Distortion

(FM+ AM)

2

2 1 2 11

1 22

( ) ( )( , ) 20lg

( )k

TIMD

p f kf p f kfL f f

p f=

− + + =

∑

Amplitude Modulation

(AM only)∑=

=K

kkE

KE

1][1

( )%100*

][21

2

E

EkEK

d

K

kAMD

∑=

−=

=100

lg20 AMDAMDd

L


Contribution of Amplitude Modulationto the total intermodulation distortion

KLIPPEL

-30

-25

-20

-15

-10

-5

0

5

4*102 6*102 8*102 103 2*103 4*103 6*103 8*103

Modulation distortion (U1=1 V)

dB

Frequency f1 [Hz]

AM distortion (Lamd) Ldm (cumul)

Total modulation

AM modulation(force factor, inductance, cone vibration)

Doppler


Demo: Amplitude Modulation2 tone stimulus with voice sweep




Intermodulation Measurement using a Two-Tone Stimulus

Disadvantages:• Frequency of excitation tones have to be set carefully

Advantages:• Simple generation (by using two sinusoidal generators)• Separation of noise and distortion• Easy to interpret• Good for loudspeaker diagnostics in R&D• Sensitive stimulus also for listening tests


Universal Stimuluscomplex, steady-state, like an organ tone

Single-Tone

Two-Tone

Multi-Tone

Noise AudioSignal

Spectral Analysis

complexity of the stimulus

sparse excitation

Amplitude and Phase response

Fundamental Components Multi-tone Distortion(harmonics, intermodulation)

some frequencies are not excited !!!


KLIPPEL

-50

-25

0

25

50

75

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

Spectrum p(f) of microphone signal

[dB]

Frequency [Hz]

Signal lines Noise + Distortions Noise floor

Signal level MTND

Multi-Tone Distortion (MTD)

MTD don‘t show the generation process in detail

„Fingerprint“ (good for quality control)

• distortion at fundamental frequencies• harmonic components• difference-tone components• summed tone components

intermodulation

DistortionfSparse multi-tone complex

Stimulus Output signal


Poll:Do you evaluate the distortion generated by a multi-tone stimulus ?

A. Yes 25%B. No 75%


Phase of the Excitation Tones is important !!

KLIPPEL

-20-15-10

-505

101520

0 50 100 150 200 250 300

Stimulus (t) vs time

[V]

Time [ms]

Stimulus (t)

Time signal (logarithmic sweep)

f

Phase spectrum

KLIPPEL

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

20

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

dB - [V] (rms

)

Frequency [Hz]

Curve 2

Amplitude spectrum

At any time there are multiple frequency components

interacting !!!

Intermodulation + Harmonics

At one time there is only one frequency component !!!

Harmonics only

KLIPPEL

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0

10

20

30

40

0 50 100 150 200 250 300

[V]

Time [ms]

Time Signal (Multi-tone complex)

f

Phase spectrum

KLIPPEL

-40

-35

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-20

-15

-10

-5

0

5

10

15

20

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

[dB] 0 dB = 1 V

Frequency [Hz]

Amplitude spectrum

random


Defined Properties of Multi-tone Stimulusaccording IEC 60268-21

Objective:- ensure comparability of the results measured by different instruments- easy to generate (by software implementation)- Modification of the stimulus should be possible (bandwidth , resolution R)

( ) NiwithfTT

f Ristarti ,...,12int1 / =⋅⋅=

=+ m

ii

mam

mod2

*21 π

ϕπϕ

( ) ( )∑=

+=N

iiii tffUtx

12cos)( ϕπ

Frequencies of the sparse line spectrum logarithmically spaced Pseudo-random phase

Amplitude spectrum

Max. Number of frequencies Seeds (a=48271, m=2

31-1 and ϕ1=1) Starting frequency

Duration(periodicity)

resolution


Interpretation of the Distortion

KLIPPEL

50

60

70

80

90

100

110

120

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

[dB]

Frequency [Hz]

Fundamental Multi-tone Distortion

Distortion

Fundamental

frequency of the spectral components

Total Harmonic Distortion (THD) Multi-tone Distortion

Sound pressure spectrum

KLIPPEL

50

60

70

80

90

100

110

120

130

50 100 200 500 1k 2k 5k

dB - [V] (rms)

Frequency [Hz]

Fundamental THD

Total Harmonic Distortion (THD)

FundamentalFundamental

frequency of the fundamental tone

THD

Benefit: Distance between fundamentals and distortions is meaningful for perceptualmasking


KLIPPEL

-80

-70

-60

-50

-40

-30

-20

-10

0

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

[dB]

Frequency [Hz]

MTND THD IMD

Multi-tone Distortion Measurementcompared with traditional THD, IMD

MTD

IMD:f1 = 50 Hz @15 V + sweep @ 3V

MTD:Multitone @ 15V

THD: sweep @ 15 V

600 Hz40 Hz 600 Hz

THD0.1 %

IMD10 %

1 %


The Causes of Multi-Tone DistortionKLIPPEL

50

60

70

80

90

100

110

120

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

[dB]

Frequency [Hz]

Fundamental Multi-tone Distortion

Distortion

Fundamental

resonance frequency Cone Vibration

L(i) (rising with frequency)

Bl(x) (independent of frequency)

Kms(x)

L(x) (rising with frequency)

Doppler (rising with frequency)

Kms(x)

Bl(x)

L(x)

L(i)

Cone Vibration

Doppler Effect

Rms(v)Rms(v)

frequency of the spectral component


Exercise: WooferAnalysis of Multi-tone Distortion

KLIPPEL

0

20

40

60

80

100

120

102 103

Spectrum sound pressure output

[dB

]

Frequency [Hz]

fundamental components

Bl(x)Kms(x)

Le(x)

Rms(v) Le(i)Bl(x)Kms(x)Le(x) Doppler Effect Cone Vibrationcauses:

total distortion

fs=60 Hz

out of band distortion

Le(i)


Exercise: MicrospeakerAnalysis of Multi-tone Distortion

KLIPPEL

30

40

50

60

70

80

90

100

110

120

130

Distortion Components

[dB]

Le(i)

fundamental components

20102 103 104

Frequency [Hz]

Bl(x)

Kms(x)

Le(x)

Rms(v) Le(i)Bl(x)Kms(x)Le(x) Doppler Effect Cone Vibrationcauses:

out of band distortiontotal distortion

Rms(v)

fs=600 Hz


Measurement of Multi-Tone Distortion

Disadvantages:• Amplitude and phase of stimulus have to be defined by standard• no separation of odd- and even-order distortion components• does not reveal the asymmetry of the nonlinearities• no separation of harmonics and intermodulation• fundamental components are also distorted

Advantages:• Considers intermodulation components• Audio-like signal • Separation of noise and distortion• fast (perfect for quality control)

This measurement is very powerful in loudspeaker diagnostics !


Demo. Multi-tone DistortionTool: Using a dedicated software module Multi-Tone Measurement (MTON) of the KLIPPEL Analyzer

http://www.klippel.de/products/rd-system/modules/mton-multi-tone-measurement.html


Discussion


Summary

• IM-Distortion give valuable diagnostic information not provided by harmonics

• IM-Distortion is the only symptom for L(x) nonlinearity (reduced by shorting rings)

• Multi-tone measurements gives a comprehensive fingerprint of all nonlinear distortion components

• Multi-tone testing shows the impact of the program material

• Two-tone stimulus gives more detailed information and is the most critical signal for listening


Open Questions

How to evaluate the irregular properties of the audio device ?

The next 10th KLIPPEL live webinar entitled Impulsive distortion - rub&buzz, abnormal behavior, defectswill address the points:• Need for special measurements more sensitive than the

human ear• What the Time-Frequency analysis shows• Inspecting the fine-structure of impulsive distortion in the

time domain • How to find the root cause of the irregular behavior• New solutions provided by IEC 60268-21


1. Modern audio equipment needs output based testing 2. Standard acoustical tests performed in normal rooms3. Drawing meaningful conclusions from 3D output measurement4. Simulated standard condition at a single evaluation point5. Maximum SPL – giving this value meaning6. Selecting measurements with high diagnostic value7. Amplitude Compression – less output at higher amplitudes8. Harmonic Distortion Measurements – best practice9. Intermodulation Distortion – music is more than a single tone10. Impulsive distortion - rub&buzz, abnormal behavior, defects

-- small break --11.Benchmarking of audio products under standard conditions (July 22nd)12.Auralization of signal distortion – perceptual evaluation 13.Setting meaningful tolerances for signal distortion14.Rating the maximum SPL value for product15.Smart speaker testing with wireless audio input

Next Section

Acoustical Measurement �of Sound System Equipment �according IEC 60268-21 Previous Sessions9th KLIPPEL LIVE:�Intermodulation Distortion – music is more than a single tone��Poll:Bl-Distortion in MusicWhat causes the IM Distortion ? Causes for high IM-DistortionSparse but Comprehensive Stimulus Intermodulation distortion�generated by Two-tone StimulusIM-Distortion (two-tone signal)�Definitions according IEC 60268-21Contribution of 2nd and 3rd-order Components �to the total intermodulation distortionSweeping the Two-Tone Signal�How to choose the frequencies ?Poll:Setup for IMD in Sound Pressure �bass sweep techniqueCauses of IMD in Sound Pressure Output �using bass sweep techniqueDemo: Intermodulation Distortion�2 tone stimulus with bass sweepMeasurement of IMD in Sound Pressure �voice sweep techniqueThe Causes of IMD in Sound Pressure Output�voice sweep techniqueDemo: Intermodulation Distortion�2 tone stimulus with voice sweepSparse but Comprehensive Stimulus Amplitude Modulation�two-tone stimulus f1 < fs, f2 > fs Phase (Frequency) Modulation�caused by Doppler EffectPhase of Intermodulation DistortionAudibility of Intermodulation DistortionIM-Distortion (two-tone signal)�Definitions according IEC 60268-21Contribution of Amplitude Modulation�to the total intermodulation distortionDemo: Amplitude Modulation�2 tone stimulus with voice sweepIntermodulation Measurement �using a Two-Tone Stimulus Universal Stimulus�complex, steady-state, like an organ toneMulti-Tone Distortion (MTD)Poll:Phase of the Excitation Tones is important !! Defined Properties of Multi-tone Stimulus�according IEC 60268-21 Interpretation of the DistortionMulti-tone Distortion Measurement�compared with traditional THD, IMDThe Causes of Multi-Tone DistortionExercise: Woofer�Analysis of Multi-tone DistortionExercise: Microspeaker�Analysis of Multi-tone DistortionMeasurement of Multi-Tone Distortion Demo. Multi-tone DistortionDiscussionSummaryOpen QuestionsNext Section

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Acoustical Measurement of Sound System Equipment according ...21/E… · of Sound System Equipment...

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