Measurement of Equivalent Input Distortion AN 20 Application Note to the KLIPPEL R&D SYSTEM
Traditional measurements of harmonic distortion performed on loudspeakers reveal not only the symptoms of the nonlinearities but also the effect of linear loudspeaker parameters, radiation into the sound field and the interactions with the room. Thus, the interpretation and comparison of results are difficult if the acoustical conditions change. This problem can be solved by transforming the harmonic distortion measured in the sound pressure into equivalent distortion at the voltage input. The equivalent distortion is almost independent of the radiation, sound propagation, room acoustics and the linear properties of the sensor (Laser, microphone). The equivalent harmonic distortion are not only a minimal set of information but make it possible to predict the traditional harmonic distortion according (IEC standard) at any point r in the sound field by performing a simple filtering with a linear transfer function.
CONTENTS: Modeling ...... 2 Performing the Measurement ...... 5 Setup Parameters for the TRF Module ...... 6 Example ...... 6 Glossary of Symbols ...... 9 More Information ...... 9
updated April 4, 2012
Klippel GmbH www.klippel.de TEL: +49-351-251 35 35 Mendelssohnallee 30 [email protected] FAX: +49-351-251 34 31 01309 Dresden, Germany
AN 20 Equivalent Harmonic Distortion
Modeling
Loudspeaker Model H(f,r ) 1 p(r ) 1 sound field
H(f,r2) p(r ) u 2
Nonlinear H(f,r3) System p(r3) uD
The loudspeaker may be considered as a system having a single input at the terminals and multiple outputs in the sound field. The small amplitudes the signal flow between input U1 and output P(r) at point r may be represented by a linear transfer function H(f,r). In the large signal domain nonlinearities inherent in the loudspeaker produce distortion. Most of the nonlinearities are located in the electrical and mechanical domain where the signal flow is still one-dimensional. In this case the nonlinearities can be lumped into one system generating distortion UD which are added to the input signal U and then dispersed via the linear systems H(f, r) to any point in the far field.
Measurement Harmonic distortion are usually measured only at few points in the sound field to at one point in make practical performance feasible. After performing a spectral analysis the the sound reponses of the fundamental component P1(f) and the 2nd-harmonic component field P2(2f) and higher-order harmonics are measured versus excitation frequency f.
Nonlinear Generator u(t) System p(t)
FFT FFT
U(f) P(f) P1 P2 P3
f f f f 2f 3f 1 1 1 1
Application Note KLIPPEL R&D SYSTEM page 2 Equivalent Harmonic Distortion AN 20
Impulse response Impulse H(f)= Signal at IN1 / Stimulus Nonlinear Impulse response H(f)= Signal at IN1 / Stimulus Measured Windowed response Measured Windowed ZOOM KLIPPEL ZOOM KLIPPEL 0,75 10 0,50
5 0,25
0,00 0 -0,25 [V / V] [V / V]
-0,50 -5
-0,75
-10 -1,00
-1,25
0 500 1000 1500 2000 2500 1900 2000 2100 2200 2300 2400 2500 left:-227.000 Time [ms] right:1290.667 left:-162.667 Time [ms] right:1291.333
The Transfer Function Module (TRF) uses a sinusoidal sweep as excitation signal to separate the linear impulse response (0-0.2 s) from the nonlinear responses of 2nd, 3rd and higher (appear as peaks between 2 –2.5 seconds). Due to the diffuse field in the listening room both the linear and the nonlinear responses have a relatively long decay time. Thus, higher-order responses interfere with each other and can not completely be separated by using time windowing.
Fundamental + Harmonic distortion components Applying an FFT to the Amplitude Signal at IN1 Response windowed linear and nonlinear Fundamental 2nd Harmonic 3rd Harmonic 100 KLIPPEL impulse responses leads to 90 the magnitude of the nd fundamental P1(f), 2 -order 80 rd component |P2(2f)| and the 3 70 -order component |P3(3f)|. At 60 1 m distance from the 50 loudspeaker the diffuse field in dB - [V] dB - 40 the room generates significant
30 variation of the sound
20 pressure values.
10
0 50 100 200 500 1k Frequency [Hz]
Relative Harmonic distortion (relative) Signal at IN1 Harmonic Distortion in 2nd Harmonic 3rd Harmonic KLIPPEL the output 80 signal (IEC standard) 70 60
50
40 [Percent]
30
20
10
0 50 100 200 500 Frequency [Hz]
According to the IEC 60268 the nth-order harmonic distortion components generated by an excitation frequency f are referred to the rms amplitude of the total output signal P(f) and may be expressed in percent
P T (1) ()p n 1 2 d 100% , n > 1 with P pt() dt n t Pt T 0
Application Note KLIPPEL R&D SYSTEM page 3 AN 20 Equivalent Harmonic Distortion
or in dB
(2) d ()p ()p n , n > 1. Ln 20log 100%
This measure reflects the interactions between loudspeaker and room at the point r1 in the sound field. The sparse density of room modes generates fluctuations which vary with the measurement position r1.
Equivalent U , U , U Input 1 2 3 Distortion FFT
p(r) u+uD x H(f,r) H(f,r)-1 u
Nonlinear System FFT FFT uD
P1, P2, P3 U1, U2, U3
By performing a filtering of the input measured sound pressure signal with the inverse system function H(f)-1 , the effect of the radiation and room interactions can be compensated and the equivalent harmonic distortion
(3) Pn Pnf() U , n > 1 n Hnf() Hnf ()
can be calculated.
The transfer function can be calculated by
Pf(,)r (4) 11 Hf(,)r1 Uf1()
using the fundamental P1(f) and the input voltage U1(f).
Nonlinear Impulse response Nonlinear Impulse response H(f)= Signal at IN1 / Stimulus H(f)= Signal at IN1 / Stimulus Measured Windowed Measured Windowed 7,5 ZOOM KLIPPEL KLIPPEL 350 5,0
300 2,5
250 0,0
200 -2,5 [V / V]
[V / V] 150 -5,0 100
-7,5 50
-10,0 0
0 500 1000 1500 2000 2500 1950 2000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 left:-227.000 Time [ms] right:1290.667 left:-227.000 Time [ms] right:1290.667
Thus, the linear impulse response becomes close to an ideal Dirac impulse and the nonlinear impulse responses become much shorter because the effect of the room response is removed.
Application Note KLIPPEL R&D SYSTEM page 4 Equivalent Harmonic Distortion AN 20
Fundamental + Harmonic distortion components Absolute Signal at IN1 The "inverse filtering" of the measured fundamental and Equivalent Fundamental 2nd Harmonic 3rd Harmonic Distortion 0 KLIPPEL harmonic responses with the linear transfer function H(f,r1) Components -10 generates to the almost -20 constant linear transfer (voltage) nd -30 function U1(f) and 2 -order component U2(2f) and the -40 rd 3 -order component U3(3f). -50 dB - [V] - dB These curves describe the
-60 nonlinear distortion at the source and are almost -70 independent on the radiation, -80 sound propagation, room
-90 interactions and the 50 100 200 500 1k properties of the sensor. Frequency [Hz]
Harmonic distortion (relative) In an analogue way as in the Relative Signal at IN1 Distortion IEC standard the amplitude 2nd Harmonic 3rd Harmonic 6 of the nth-order harmonic KLIPPEL (Percent) distortion is referred to the 5 rms value of the total voltage signal.
4
3 [Percent]
2
1
0 50 100 200 500 Frequency [Hz]
Unf() (5) df()u ( ) n 100% n 222 Uf12( ) U (2 f ) U 3 (3 f ) ....
Assessing The large signal performance of loudspeakers can be more easily assessed by loudspeaker comparing the equivalent harmonic distortion in the input voltage because the influence system of the acoustical environment (room), distance and the sensor is minimal. It is also possible to predict the harmonic distortion at a preferred listening position (drivers seat) based on equivalent harmonic distortion (representing the loudspeaker) and the linear transfer function H(f) describing the room acoustics.
Performing the Measurement The following hardware and software is required Requirements Distortion Analyzer PC Software modules (TRF, dB-Lab) Sensor microphone (or laser) Power Amplifier (set gain to maximum) Setup Connect the terminals of the driver with SPEAKER 1. Switch the power amplifier between OUT1 and connector AMPLIFIER. Connect the microphone to input IN1,or connect a laser head to the connector LASER and adjust the laser beam to a white dot on the diaphragm. 1. Create a new database Preparation 2. Open the database within dB-Lab 3. Create a new object DRIVER based on the template Equivalent Input Dist. AN 20.
Application Note KLIPPEL R&D SYSTEM page 5 AN 20 Equivalent Harmonic Distortion 1. Adjust sensor. When using a microphone prefer a measurement point giving Measurement sufficient SNR (nearfield measurement or distance < 1m is preferable !!). 2. Start the measurement "1. TRF Small Signal Measurement". 3. Open Property Page IM/EXPORT in the measurement "1. TRF Small Signal Measurement" and select the transfer function "Fundamental + Total Phase". Press the button "Export to Clipboard". Select the measurement "2. TRF Equivalent Distortion". Open the Property Page PROCESSING and press button IMPORT under “Reference". Press the button "From Clipboard" to transfer data. 4. Open the Property Page STIMULUS of the measurement "2. TRF Equivalent Distortion". Adjust the voltage U of the stimulus in dBU according to the permissible load. Start the measurement. 5. Open the Result Window "Energy-Time Curve" and adjust the marker of the time window to separate the linear response from the nonlinear impulse responses (small spikes at later times).
Setup Parameters for the TRF Module
Template Create a new Object, using the object template Equivalent Input Dist. AN 20 in dB- Lab. If this database is not available you may generate an object TRF Equivalent Distortion AN 20 based on the general TRF module. 1. Generate an object Equivalent Input Dist. AN 20. 2. Assign to the object a measurement "1. TRF Small Signal Measurement" and "2. TRF Equivalent Distortion" based on the default TRF measurement. 3. Select "1. TRF Small Signal Measurement". Open the PP STIMULUS and set starting frequency Fmin= 20 Hz and Fmax =20kHz. Set resolution to 0.73 Hz. Set Voltage to 0 dBU at SPEAKER 1 Terminals. Select 16 times averaging. Open PP INPUT, select IN1 at Channel 1 and disable Channel 2. Open PP Processing and select “No Window”. 4. Select "2. TRF Equivalent Distortion ". Open the PP STIMULUS and set starting frequency Fmin= 20 Hz and Fmax =20kHz. Set resolution to 0.73 Hz. Set Voltage to 12 dBU or higher at SPEAKER 1 Terminals. Open PP INPUT, select IN1 at Channel 1 and disable Channel 2. Open PP Processing and use default setting of “Rectangular Window”. You may also modify the setup parameters according to your needs.
Example
fundamental Linear sound pressure
Amplitude 1 m distance 60 cm distance 30 cm distance nearfield
Response 110 KLIPPEL
100
90
80
70 dB - [mm] 60
50
40
30 50 100 200 500 1k Frequency [Hz]
The sound pressure response of a loudspeaker was measured at four positions (nearfield, 30 cm, 60 cm and 1 m distance). With rising distance the diffuse field in the room causes significant variations in the response (> 20 dB variation at 50 Hz) .
Application Note KLIPPEL R&D SYSTEM page 6 Equivalent Harmonic Distortion AN 20
2nd harmonic absolute Harmonic Signal at IN1 3rd harmonics absolute 1 m distance 60 cm distance 30 cm distance nearfield Signal at IN1 Distortion 90 1 m distance 60 cm distance 30 cm distance nearfield Components 90 80 KLIPPEL 85
70 80
75 60 70
65 50 dB - [V] dB
dB - [V] 60 40 55
50 30 45
20 40 50 100 200 500 1k 50 100 200 500 1k Frequency [Hz] Frequency [Hz]
The absolute sound pressure response of the 2nd and 3rd-order harmonics vary significantly within the sound field.
2nd harmonic distortion (IEC ) Relative Signal at IN1 3rd harmonics (IEC standard) Signal at IN1
30 cm distance 1 m distance nearfield 60 cm distance Harmonic 30 30 cm distance nearfield 60 cm distance 1 m distance KLIPPEL distortion in KLIPPEL 80 sound pressure 25 70
20 60
50 15 40 [Percent] [Percent]
10 30
20 5 10
0 0 50 100 200 500 50 100 200 500 Frequency [Hz] Frequency [Hz]
Calculating the 2nd and 3rd-order harmonic distortion in percent according to the standard IEC 60268 the variation of the fundamental are considered in the assessment of the distortion. However, there are substantial variations due to the interferences with the room modes.
Application Note KLIPPEL R&D SYSTEM page 7 AN 20 Equivalent Harmonic Distortion
2nd harmonics in voltage Equivalent Signal at IN1
1 m distance 60 cm distance 30 cm distance nearfield harmonic 0 distortion in KLIPPEL voltage -10
-20
-30 dB - [V] -40
-50
-60
50 100 200 500 1k Frequency [Hz] 3rd harmonic distortion in voltage Signal at IN1
nearfield 30 cm 60 cm 1 m distance 0 KLIPPEL -5
-10
-15
-20
-25 dB - [V]
-30
-35
-40
-45 50 100 200 500 1k Frequency [Hz]
nd rd The 2 and 3 -order harmonics measured at the point ri are filtered with the inverse -1 linear transfer function H(f,ri) to generate the equivalent harmonic distortion in the sound pressure input. If the nonlinearities are located in the electrical, mechanical and acoustical part before the sound disperses the equivalent harmonic distortion are independent of radiation, sound propagation and room interferences.
2nd order harmonics in voltage Equivalent Signal at IN1
1 m distance 30 cm distance 60 cm distance nearfield harmonic 5,0 KLIPPEL distortion in 4,5
voltage input 4,0
(in percent) 3,5
3,0
2,5
[Percent] 2,0
1,5
1,0
0,5
0,0 50 100 200 500 Frequency [Hz] 3rd harmonic in voltage Signal at IN1
60 cm distance 30 cm distance 1 m distance nearfield 7 KLIPPEL
6
5
4
3 [Percent]
2
1
0 50 100 200 500 Frequency [Hz]
The equivalent harmonic distortion may be referred to the total voltage signal and expressed in percent.
Application Note KLIPPEL R&D SYSTEM page 8 Equivalent Harmonic Distortion AN 20
Glossary of Symbols
H(f,r) linear transfer function between voltage and sound pressure at point r u voltage at terminals p(r) sound pressure at point r
P1(f) fundamental component in sound pressure versus excitation frequency f nd P2(2f) 2 -order harmonic component in sound pressure versus excitation frequency f rd P3(3f) 3 -order harmonic component in sound pressure versus excitation frequency f
U1(f) voltage at terminals versus excitation frequency f nd U2(2f) equivalent 2 -order harmonic component in voltage versus excitation frequency f rd U3(3f) equivalent 3 -order harmonic component in voltage versus excitation frequency f nd nd G2(f1,f2) 2 -order system function generating 2 -order harmonics rd rd G3(f1,f2,f3) 3 -order system function generating 3 -order harmonics (p) dn (f) nth-order harmonic distortion in the sound pressure output signal in percent (according to IEC 60268) (u) dn (f) equivalent nth-order harmonic distortion in the input voltage in percent
More Information W. Klippel, “Measurement of Equivalent Input Distortion Presented at the 115th Literature Convention of the Audio Eng. Society, 2003 October 10–13, New York, USA, Preprint 5913.
Related “TRF”, S7 Specification
Software User Manual for the KLIPPEL R&D SYSTEM.
updated April 4, 2012
Klippel GmbH www.klippel.de TEL: +49-351-251 35 35 Mendelssohnallee 30 [email protected] FAX: +49-351-251 34 31 01309 Dresden, Germany
Application Note KLIPPEL R&D SYSTEM page 9