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

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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	µF	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 Z	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	cm²	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 C_MS is the linear compliance and f_s  is the driver resonance frequency. There is a straight forward interpretation of the creep factor . The quantity 100%   indicates the decrease of the compliance C_MS(f_s) in percentages at low frequencies. For a frequency one decade below the resonance frequency f_s  the compliance C_MS(f_s) 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

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. 

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. 

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).

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.

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. 

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