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Distortion generated by force factor Bl(x)


Distortion generated by stiffness Kmx(x)


Distortion generated by inductance Le(x)


Distortion generated by inductance Le(i)


Voice coil displacement 


Voice coil temperature 


Voltage, current and input power


The auralization technique combines subjective testing and objective evaluation by using physical modeling, measurement and system identification techniques. The transfer path between stimulus and human ear is described by the large signal model comprising linear, nonlinear and thermal subsystem as shown below:



The nonlinear subsystem represents the motor and suspension system and considers the heat flow from the voice coil to the ambience. The nonlinear element is embedded by linear systems which represent the pre- and post-shaping of the signal due to the electrical, mechanical and acoustical elements which behave almost linearly. The parameters of the model can be varied and the impact on the perceived sound quality can be investigated in systematic listening tests. At the same time, the internal state variables (temperature, displacement, distortion, power) and the maximal acoustical output can be recorded. Both, subjective and objective information, are required to select between design choices and to find optimal performance-cost ratio.

KLIPPEL R&D SYSTEM (development)



Auralization Module (AUR)

AUR performs a large signal simulation and auralization of one drive unit in a two-way loudspeaker system.


The figure above shows the principle of the nonlinear Auralization Module (AUR). The linear, nonlinear and thermal parameters identified by the LSI module are exported to the digital model implemented in the hardware platform DA. An arbitrary test signal or any audio signal may be used as stimulus and the internal state variables and the output signal of the loudspeaker are predicted in real time. The AUR provides a mixing console where the ratio between linear signal component and the nonlinear distortion (from motor and suspension nonlinearities) can be varied by the user. The listener may listen to the output signal by using high-quality headphones or loudspeaker monitor systems. Blind testing and switching between two virtual examples (A/B comparison) are supported by AUR. The relative peak values of the distortion are measured and recorded over time. The linear signal and the separated distortion may be provided to a perceptual signal quality analyzer (PEAK) to predict the impact on the perceived sound quality.

Templates of KLIPPEL products

Name of the Template


AUR auralization

Real-time auralization of the large signal performance

LSI Tweeter Nonlin. Para Sp2

Tweeters with fs > 400 Hz at sensitive current sensor 2

LSI Headphone Nonlin. P. Sp2

Nonlinear parameters of headphones with fs < 300 Hz at sensitive current sensor 2

LSI Woofer Nonl. P. Sp1

Nonlinear parameters of woofers with fs < 300 Hz at standard current sensor 1

LSI Woofer Nonl.+Therm. Sp1

Nonlinear and thermal parameters of woofers with fs < 300 Hz at standard current sensor Sp1

LSI Woofer+Box Nonl. P Sp1

Nonlinear parameters of woofers operated in free air, sealed or vented enclosure with a resonance frequency fs < 300 Hz at standard current sensor Sp1

LSI Microspeaker Nonl. P. Sp2

Nonlinear parameters of microspeakers with fs > 300 Hz at sensitive current sensor 2


IEC Standard IEC 60268-5 Sound System Equipment, Part 5: Loudspeakers
AES2-1984 AES Recommended practice Specification of Loudspeaker Components Used in Professional Audio and Sound Reinforcement

Papers and Preprints

W. Klippel, “Speaker Auralization – Subjective Evaluation of Nonlinear Distortion,” presented at the 110th Convention of the Audio Eng. Soc., Amsterdam, May 12-15, 2001, Preprint 5310, J. of Audio Eng. Soc., Volume 49, No. 6, 2001 June, P. 526. (abstract)

W. Klippel, Tutorial “Loudspeaker Nonlinearities - Causes, Parameters, Symptoms,” J. of Audio Eng. Soc. 54, No. 10, pp. 907-939 (2006 Oct.).