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Transducer nonlinearities (curve shape)

Characteristics:

KLIPPEL R&D System

Force factor Bl(x) versus displacement x

LSI, PWT, SIM, AUR

Mechanical compliance Cms(x) versus displacement x

LSI, PWT, SIM, AUR, SPM

Mechanical stiffness Kms(x) versus displacement x

LSI, PWT, SIM, AUR, SPM

Incremental stiffness Kinc(x) versus displacement x

LSI, PWT

Inductance L(x,i) versus displacement x and current i

LSI, PWT, SIM, AUR

Mechanical resistance Rms(v) versus velocity v

LSI Tweeter

Force-deflection curve F(x)

CAL, SPM

Nonlinearities inherent in the loudspeaker determine the large signal performance, such as the maximal output, signal distortion and stability. The nonlinearities can be represented by lumped elements having parameters which vary with the internal state signal (current, displacement, velocity, pressure) shown as red elements in the equivalent circuit below.

 

 

The IEC standard 62458 defines the dominant nonlinearities and static, quasi-static, incremental and full dynamic methods of measurements. Only the full dynamic measurement operates the transducer under normal operation conditions and is able to detect all relevant large signal parameters, such as force factor Bl(x), stiffness Kms(x), compliance Cmx(x), inductance L(x), Rms(v) versus displacement x, current i and voice coil velocity v.

The nonlinear parameters can be represented as a nonlinear curve, such as the instantaneous force factor value Bl(x) versus x, or as a power series expansion providing full information for numerical simulation and prediction within the loudspeaker design.

Nonlinear parameters explain the generation of nonlinear distortion at high accuracy but are much easier to interpret than the result of a nonlinear distortion measurement.

Single-valued parameters are derived from the nonlinear characteristics. For example, the voice coil offset is a single-valued parameter derived from the symmetry point in the Bl(x) curve, expressed in mm. These values can be used for limit settings during the end-of-line testing and for the automatic control of the production process.

Ultra-fast measurements and long-term monitoring of the loudspeaker nonlinearities can be accomplished using special test signals or ordinary audio signals.

Dynamic measurement technique for transducer nonlinearities as defined in IEC standard 62458.
Dynamic measurement technique for transducer nonlinearities as defined in IEC standard 62458.

KLIPPEL R&D SYSTEM (development)

Module

Comment

Large Signal Identification (LSI Woofer, LSI Tweeter, LSI Box)

LSI measures the nonlinearities directly by using a nonlinear model adjusted adaptively to the device under test. A noise signal is used as stimulus, and the bandwidth is adjusted automatically to ensure the persistent excitation of the transducer. The permissible working range is automatically determined  by using a protection system. An optional laser sensor may be used to check the orientation of the voice coil movement (coil in or out) and to calibrate the mechanical parameters. There are three versions of LSI dedicated to woofers, tweeters and loudspeaker systems (transducer mounted in enclosure).    

Power Test (PWT)

PWT also provides full identification of the woofer’s lumped parameters using an arbitrary stimulus (music). In contrast to the LSI, the voltage and the working range is determined by the user.

Suspension Part Measurement (SPM)

SPM measures the nonlinear stiffness and compliance of spiders, suspensions, drones and passive radiators. The user can specify the working range which is defined by the target displacement, and the SPM adjusts the stimulus automatically. 

Large Signal Simulation (SIM)

SIM requires the transducer nonlinearities as input to predict the large signal performance. A curve editor is provided to import the parameter from LSI or any other finite element design tool or to synthesize the curves manually.

Auralization (AUR)

AUR requires the transducer nonlinearities for simulating the large signal performance in real time and to perform an auralization of the nonlinear distortion. The parameters are copied in a digital format from LSI to AUR module.

KLIPPEL QC SYSTEM (end-of-line testing)

Module

Comment

not available

Nonlinear curves are less suitable for end-of-line testing because pass/fail limits and process statistics (CPK, PPK) can not be applied to those curves.

Example:

The stiffness Kms(x) of the mechanical suspension is not constant but varies with displacement x generating significant distortion for spectral components below resonance.
The stiffness Kms(x) of the mechanical suspension is not constant but varies with displacement x generating significant distortion for spectral components below resonance.
The figure above illustrates the relationship between motor geometry (pole tips, size and position of the coil) and nonlinear force factor characteristic Bl(x) which is a function of voice coil displacement x. Instantaneous variation of the force factor Bl(x) modulates all signal components and generates a nonlinear excitation force F which contains significant intermodulation distortion in the audio band.
The figure above illustrates the relationship between motor geometry (pole tips, size and position of the coil) and nonlinear force factor characteristic Bl(x) which is a function of voice coil displacement x. Instantaneous variation of the force factor B

Templates of KLIPPEL products

Name of the Template

Application

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

Diagnost. MIDRANGE Sp1

Comprehensive testing of midrange drivers with a resonance 30 Hz < fs < 200 Hz using standard current sensor 1

Diagnost. RUB&BUZZ Sp1

Batch of Rub & Buzz tests with increased voltage (applied to high power devices)

Diagnostics MICROSPEAKER Sp2

Comprehensive testing of microspeakers with a resonance 100 Hz < fs < 2 kHz using sensitive current sensor 2

Diagnostics TWEETER (Sp2)

Comprehensive testing of tweeters with a resonance 100 Hz < fs < 2 kHz using sensitive current sensor 2

Diagnostics VENTED BOX SP1

Comprehensive testing of vented box systems using standard current sensor 1

Diagnostics WOOFER (Sp1)

Comprehensive testing of subwoofers with a resonance 30 Hz < fs < 200 Hz using standard current sensor 1

Diagnostics WOOFER Sp1,2

Comprehensive testing of subwoofers with a resonance 30 Hz < fs < 200 Hz using current sensor 1 and 2

Equivalent Input Dist. AN 20

Equivalent input distortion according Application Note AN 20

Force - Deflection Curve

Using the results from LSI, the force -deflection curve is calculated.

Separate suspension

Separated stiffness of surround and spider according to Application Note AN 2

SPM Suspension Part

Nonlinear stiffness of spiders and smaller cones based on ONE-SIGNAL Method

SIM closed box analysis

Maximal displacement, dc displacement, compression, SPL, distortion using large signal parameters imported from LSI BOX

SIM vented box analysis

Maximal displacement, dc displacement, compression, SPL, harmonic distortion using large signal parameters imported from LSI BOX

PWT 8 Woofers Param. ID Noise

Parameter identification of woofers using internal test signal (no cycling, no stepping)

PWT Woofer Param. ID MUSIC

Parameter Identification of Woofers

using external test signal (no ON/OFF cycling, no stepping)

PWT Woofer param. ID NOISE

Parameter Identification of Woofers

using internal test signal (no ON/OFF cycling, no stepping)

AUR auralization

Real-time auralization of the large signal performance

Standards:

  • IEC Standard IEC62458 Sound System Equipment – Electroacoustic Transducers - Measurement of Large Signal Parameters
  • IEC Standard IEC62459 Sound System Equipment – Electroacoustic Transducers – Measurement of Suspension Parts
  • AES2-1984 AES Recommended practice Specification of Loudspeaker Components Used in Professional Audio and Sound Reinforcement
  • IEC Standard IEC 60268-5 Sound System Equipment, Part 5: Loudspeakers




Papers and Preprints:


Paper: “Loudspeaker Nonlinearities. Causes, Parameters, Symptoms” undefined

 

Know-How Poster: “Loudspeaker Nonlinearities. Causes, Parameters, Symptoms” undefined

 

Paper: “Assessing the Large Signal Performance of Loudspeakers” undefined

 

Paper: “Large Signal Performance of Tweeters” undefined

 

Paper: “Measurement of Large Signal Parameters” undefined

W. Klippel, “Dynamic Measurement of Loudspeaker Suspension Parts,” J. of Audio Eng. Soc. 55, No. 6, pp. 443-459 (2007 June).

D. Clark, “Precision Measurement of Loudspeaker Parameters,“ J. of Audio Eng. Soc., Volume 45, pp. 129 – 140, (1997 March).

W. Klippel, “Measurement of Large-Signal Parameters of Electro-dynamic Transducer,” presented at the 107th Convention of the Audio Eng. Soc., New York, September 24-27, 1999, Preprint 5008.

M. Dodd, et al., “Voice Coil Impedance as a Function of Frequency and Displacement,” presented at the 117th Convention of the Audio Eng. Soc., 2004 October 28–31, San Francisco, CA, USA.

W. Klippel, et al. “Fast Measurement of Motor and Suspension Nonlinearities in Loudspeaker Manufacturing,” presented at the 127th Convention of the Audio Eng. Soc., 2009 October 9-12, New York, NY, USA.

R. H. Small, “Assessment of Nonlinearity in Loudspeakers Motors,” in IREECON Int. Convention Digest (1979 Aug.), pp. 78-80.

A. J. M. Kaizer, “Modeling of the Nonlinear Response of an Electrodynamic Loudspeaker by a Volterra Series Expansion,” J. of Audio Eng. Soc., Volume 35, pp. 421-433 (1987 June).

W. Klippel, “Dynamical Measurement of Non-Linear Parameters of Electro-dynamical Loudspeakers and their Interpretation”, J. of Audio Eng. Soc. 30 (12), pp. 944 - 955, (1990).

M. Knudsen, et al., “Determination of Loudspeaker Driver parameters Using a System Identification Technique,” J. of Audio Eng. Soc., Volume 37, No. 9.

W. Klippel, “Nonlinear Modeling of the Heat Transfer in Loudspeakers,” J. of Audio Eng. Soc. 52, Volume 1, 2004 January.