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 f1 f1 2f1 3f1 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.