Electrical Impedance
Characteristics:  KLIPPEL R&D System  KLIPPEL QC System 

Amplitude and phase response  LPM, TRF, MTON  IMP, SPLIMP, MSC 
Impedance measured by using a large signal model
 MSC 
The electrical input impedance is defined as transfer function Z(jω)= U(jω)/ I(jω) between the electrical signals at the terminals in the small signal domain where the transducer behaves sufficiently linear. The impedance is the basis for estimating the linear parameters (ThieleSmall parameters, lossy inductance parameters, viscoelastic parameters) of the lumped parameter model. The minimum of the impedance above the fundamental resonance is used for defining the nominal impedance of the speaker. The conventional measurement of the impedance requires a measurement in the small signal domain where the nonlinear distortion in voltage and current are negligible. Large signal measurement requires a nonlinear model of the speaker where the effect of the nonlinear distortion can be compensated and the linear impedance can be calculated.
Module  Comment 

TRF measures magnitude and phase response of the electrical impedance by using a sinusoidal sweep stimulus.  
LPM measures magnitude and phase response of the electrical impedance by using a multitone stimulus which ensures best SNR of voltage and current in the small signal domain. No smoothing of the curve is required.  
MultiTone Measurement (MTON)  MTON measures magnitude of the electrical impedance by using a multitone stimulus. Phase is available if transfer function is defined between voltage and current measurements.

Module  Comment 

 The IMP measure the magnitude and phase response of the electrical impedance at high speed using a sinusoidal sweep (chirp) with amplitude and sweep speed profile or using a multitone stimulus. The measurement has to be performed in the small signal domain where the effect of the transducer nonlinearities is negligible. 
Sound Pressure and Impedance Task (SPLIMP)  The SPLIMP measures the magnitude and phase response of the electrical impedance at high speed using a sinusoidal sweep (chirp) with amplitude and sweep speed profile. Limits can be applied. 
MSC measures the magnitude and phase response of the impedance also at high amplitudes by using an ultrashort multitone stimulus. The nonlinear distortion in the voltage and current are compensated by using the nonlinear parameters of the identified large signal transducer model.

Example:
Templates of KLIPPEL products
Name of the Template  Application 

LPM Microspeaker T/S (SP2)  Linear parameters of microspeakers using sensitive current sensor 2 
LPM Subwoofer T/S (Sp1)  Linear parameters of subwoofers using standard current sensor 1 
LPM Subwoofer T/S (Sp2)  Linear parameters of subwoofers using sensitive current sensor 2 
LPM Tweeter T/S (SP2)  Linear parameters of tweeters using sensitive current sensor 2 
LPM Woofer T/S (Sp1)  Linear parameters of woofers using standard current sensor 1 
LPM Woofer T/S (Sp2)  Linear parameters of woofers using sensitive current sensor 2 
LPM Woofer T/S added mass  Linear parameters of woofers using added mass method 
TRF Elect. Impedance (Sp 1)  Electrical impedance using the standard current sensor 1 
TRF Elect. Impedance (Sp 2)  Electrical impedance using the 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. SUBWOOFER (Sp1)  Comprehensive testing of subwoofers with a resonance 10 Hz < fs < 70 Hz using standard current sensor 1 
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 
Standards
Audio Engineering Society
AES2 Recommended practice Specification of Loudspeaker Components Used in Professional Audio and Sound Reinforcement
International Electrotechnical Commission
IEC 602685 Sound System Equipment, Part 5: Loudspeakers
IEC 62458 Sound System Equipment – Electroacoustic Transducers  Measurement of Large Signal Parameters
Papers and Preprints
W. Klippel, U. Seidel, “Fast and Accurate Measurement of Linear Transducer Parameters,” presented at the 110th Convention of the Audio Eng. Soc., Amsterdam, May 1215, 2001, Preprint 5308, J. of Audio Eng. Soc., Volume 49, No. 6, 2001 June, P. 526. (abstract)
J. Vanderkooy, “A Model of Loudspeaker Driver Impedance Incorporating Eddy Currents in the Pole Structure,” J. of Audio Eng. Soc., Volume 37, No. 3, pp. 119128, March 1989.
W. M. Leach, “Loudspeaker VoiceCoil Inductance Losses: Circuit Models, Parameter Estimation, and Effect on Frequency Response,“ J. of Audio Eng. Soc., Volume 50, No. 6, pp. 442450, June 2002.
J. R. Wright, “An Empirical Model for Loudspeaker Motor Impedance,“ J. of Audio Eng. Soc., Volume 38, No. 10, pp. 749754, October 1990.
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.
D. Clark, “Precision Measurement of Loudspeaker Parameters,“ J. of Audio Eng. Soc., Volume 45, pp. 129 – 140, (1997 March).
R. H. Small, “DirectRadiator Loudspeaker System Analysis,“ J. of Audio Eng. Soc., Volume 20, pp. 383 – 395 (1972 June).