KLIPPEL ANALYZER SYSTEM

Linear Parameter Measurement (LPM)

Using Fixed Mmd Method

 

 




Driver Name:

SS 9

Driver Comment:

Measurement:

LPM subwoofer Fixed Mmd

Measurement Comment:

Date:

07/21/07

Time:

19:37:16


Comments

Measured BL was lower than included datasheet. Data gives 11.67 measured value is 10.37. Note that Klipple measurement does correlate with the Scan-Speak frequency response sensitivity of 80.2 @2.83 volts.

 




MEASUREMENT TECHNIQUE

A paper detailing the measurement methods used can be found at: Fast and Accurate Linear Parameter Measurement

Testing on the woofer was performed using the Fixed Mmd method. This yields by far the most accurate results for compliance values. The measurement module identifies the electrical and mechanical parameters (Thiele-Small parameters) of electro-dynamical transducers. The electrical parameters are determined by measuring terminal voltage u(t) and current i(t) and exploiting the electrical impedance Z(f)=U(f)/I(f). Furthermore the suspension creep of the driver is identified giving more accuracy of the loudspeaker model at low frequencies.

Measurement Results

Linear electrical and mechanical parameters

The measurement module determines the components (Thiele-Small Parameters) of the linear loudspeaker model below describing the small signal behaviour of the driver.

The table below shows the electrical and mechanical parameters of the linear driver model, the derived parameters (resonance frequency, loss factors etc.) and the parameter of the suspension creep factor. 

 

 

   

 Name 

 Value 

 Unit 

 Comment 

 Electrical Parameters 

   

   

   

 Re 

 6.10 

 Ohm 

 electrical voice coil resistance at DC 

 Krm 

 0.0711 

   

 WRIGHT inductance model 

 Erm 

 0.38 

   

 WRIGHT inductance model 

 Kxm 

 0.0134 

   

 WRIGHT inductance model 

 Exm 

 0.64 

   

 WRIGHT inductance model 

 Cmes 

 997 

 F 

 electrical capacitance representing moving mass 

 Lces 

 32.73 

 mH 

 electrical inductance representing driver compliance 

 Res 

 62.25 

 Ohm 

 resistance due to mechanical losses 

 fs 

 27.9 

 Hz 

 driver resonance frequency  

   

 Mechanical Parameters 

   

   

   

 (fixed Mmd) 

   

   

   

 Mms 

 107.289 

 g 

 mechanical mass of driver diaphragm assembly including air load and voice coil 

 Rms 

 1.729 

 kg/s 

 mechanical resistance of total-driver losses 

 Cms 

 0.304 

 mm/N 

 mechanical compliance of driver suspension 

 Kms 

 3.29 

 N/mm 

 mechanical stiffness of driver suspension 

 Bl 

 10.37 

 N/A 

 force factor (Bl product) 

   

 Loss factors 

   

   

   

 Qtp 

 1.043 

   

 total Q-factor considering all losses 

 Qms 

 10.865 

   

 mechanical Q-factor of driver in free air considering Rms only 

 Qes 

 1.064 

   

 electrical Q-factor of driver in free air considering Re only 

 Qts 

 0.969 

   

 total Q-factor considering Re and Rms only 

   

 Vas 

 23.1708 

 l 

 equivalent air volume of suspension  

 n0 

 0.045 

 % 

 reference efficiency (2 pi-radiation using Re)  

 Lm 

 78.76 

 dB 

 characteristic sound pressure level (SPL at 1m for 1W @ Re) 

 Lnom 

 79.94 

 dB 

 nominal sensitivity (SPL at 1m for 1W @ Zn) 

   

 rmse

 7.02 

 % 

 root-mean-square fitting error of driver impedance Z(f) 

   

 Series resistor 

 0.00 

 Ohm 

 resistance of series resistor 

 Mmd (fixed) 

 105.290 

 g 

 Mmd value specified by the user 

 Sd 

 232.00 

 cm 

 diaphragm area 


Suspension creep factor

Some loudspeaker suspension materials exhibit significant creep (continued slow displacement under sustained force) in their dynamic behaviour. Therefore the traditional low-frequency loudspeaker model is expanded to incorporate suspension creep by replacing the simple linear compliance by the dynamic transfer function [1].

 where CMS is the linear compliance and  fs  is the driver resonance frequency. There is a straight forward interpretation of the creep factor . The quantity 100%   indicates the decrease of the compliance CMS(fs) in percentages at low frequencies. For a frequency one decade below the resonance frequency fs  the compliance CMS(fs) is decreased by  100% .

 [1] Knudsen, M. H. and Jensen, J. G. Low-frequency loudspeaker models that include suspension creep. J. Audio Eng. Soc., Vol. 41, No. 1 / 2, 1993


Electrical Impedance

The two figures below show the magnitude and the phase response of  the measured and estimated transfer function Z(f)= U(f)/I(f) where U is the terminal voltage and I is the current. The solid curve is the ratio of the measured spectra  U(f), I(f) while the thin curve is the impedance of the linear driver equivalent circuit using the linear model and the identified electrical parameters shown

 

Magnitude of electric impedance Z(f)

Phase of electric impedance Z(f)

 

 


Displacement Transfer Function

The figure below shows the magnitude of  the measured and estimated transfer function Hx(f)= X(f)/U(f) between the voice coil displacement X and the terminal voltage U. The solid black curve is the ratio of the measured spectra  X(f), U(f) while the thin black curve is the transfer function based on the linear driver equivalent circuit using the identified electrical and mechanical parameters as well as the creep parameter. The dashed red curve is based on the conventional model without considering the creep factor.  

 
Magnitude of transfer function Hx(f)= X(f)/U(f)

 


Spectra of measurement signals

Voltage Spectrum

The diagram shows the multi-tone spectrum of the voltage at the terminals. The blue lines represent the fundamental components excited by the stimulus. The black noise floor lines represent the residual measurement noise caused by the voltage sensor. If the grey noise + distortions exceeds the residual noise floor we see the distortions generated by the nonlinearities of the power amplifier. This information is important for assessing the distortion of the speaker in the current, displacement and sound pressure below.   

 Spectrum U(f) of voltage at speaker terminals


Current Spectrum

The diagram below shows the multi-tone spectrum of the current at the terminals. The red lines represent the fundamental components excited by the stimulus. Note the notch of the spectrum at the resonance frequency of the driver. The black noise floor lines indicate the residual noise caused by the measurement system (current sensor). If the grey noise + distortions lines exceeds the residual noise floor we see the distortions generated by the nonlinearities of the speaker (assuming that the power amplifier is sufficiently linear). 

 

Spectrum I(f) of current at speaker terminals

 


Displacement Spectrum

The diagram below shows the multi-tone spectrum of the voice coil displacement measured with the laser sensor. The violet lines represent the fundamental components excited by the stimulus. Note the 12 dB/octave decay of the displacement spectra above the resonance frequency of  the laser. The black noise floor lines indicate the measurement noise caused by the resolution of the used Laser Sensor Head. Increasing the number of averaging will further reduce the residual noise line. If the grey noise + distortions exceeds the residual noise floor we see the distortions generated by the nonlinearities of the speaker. These components are independent on the number of averaging. 

 

Spectrum X(f) of voice coil displacement










Sound Pressure Spectrum

The diagram shows the multi-tone spectrum of the sound pressure measured with the microphone. The green lines represent the fundamental components excited by the stimulus.The black noise floor lines indicate the ambient noise during the measurement. The grey noise + distortions are the nonlinear distortion components generated by the speaker. 

 
Spectrum p(f) of microphone signal










Signal Characteristics

The table below summarizes important statistical characteristics (peak values, head rooms, SNR ratio, ) of the state variables (voltage, current, displacement and sound pressure). This information is helpful for assessing the working point of the driver (Small - Large Signal Domain) and to detect any malfunction operation (microphone or laser not connected). 

 

 

   

 Name 

 Value 

 Unit 

 Comment 

 HINT : 

   

   

 Reduce Fmax to 20* fs to improve impedance fitting 

   

 U pp 

 2.37 

 V 

 peak to peak value of voltage at terminals 

 U ac 

 0.30 

 V rms 

 AC part of voltage signal 

 U dc 

 -0.00 

 V 

   

 U head 

 47.2 

 dB 

 digital headroom of voltage signal 

 U SNR+D 

 44.1 

 dB 

 ratio of signal to noise+distortion in voltage signal  

 fu noise 

 1.1 

 Hz 

 frequency of noise+distortion maximum in voltage signal 

   

 I pp 

 0.28 

 A 

 peak to peak value of current at terminals 

 I ac 

 0.04 

 A rms 

 AC part of current signal 

 I dc 

 -0.00 

 A 

   

 I head 

 51.7 

 dB 

 digital headroom of current signal 

 I SNR+D 

 21.4 

 dB 

 ratio of signal to noise+distortion in current signal  

 fi noise 

 27.5 

 Hz 

 frequency of noise+distortion maximum in current signal 

   

 X pp 

 0.60 

 mm 

 peak to peak value of displacement signal 

 X ac 

 0.09 

 mm rms 

 AC part of displacement signal 

 X dc 

 0.02 

 mm 

   

 X head 

 50.2 

 dB 

 digital headroom of displacement signal 

 X SNR+D 

 20.9 

 dB 

 ratio of signal to noise+distortion in displacement signal  

 fx cutoff 

 77.3 

 Hz 

 frequency of highest valid line in displacement signal 

   

 p pp 

 0.02 

 mV 

 peak to peak value of microphone signal 

 p ac 

 0.00 

 mV rms 

 AC part of microphone signal 

 p head 

 111.0 

 dB 

 digital headroom of microphone signal 

 p sum level 

 -11.4 

 dB 

 sum level of microphone signal 

 p mean level 

 -49.4 

 dB 

 mean level of microphone signal 

   

 f sample 

 6000 

 Hz 

 sample frequency 

 N stim 

 16384 

 number of samples 

 stimulus length