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Application Notes Application Note Accurate Determination of Loudspeaker Parameters using Audio Analyzer Type 2012 and Laser Velocity Transducer Type 3544 by Søren Jønsson, Brüel & Kjær, Denmark A method to determine the parame- ters characterising low frequency, mid- range and high frequency loudspeaker units is presented. A laser velocity transducer is used to detect the veloc- ity of the diaphragm. All measure- ments are made with the loudspeaker in free air. The method uses an im- proved model of the loudspeaker and takes into account the frequency de- pendent behaviour of some of the ele- ments. It produces accurate results and is easy to implement compared with conventional methods. The proce- dure is fully automated using an au- tosequence program for the analyzer. The process of automation is discussed and results of a typical driver are in- cluded. 1. Introduction Over the last two decades, it has be- The method presented here is a ance. From these functions the loud- come almost an industrial standard compilation of the traditional method speaker parameters can be calculated. to measure the parameters of a loud- and the method introduced by Applying the post-processing capa- speaker by the method introduced by J. N. Moreno [6]. It uses an improved bilities of the analyzer to the meas- A.N. Thiele and Dr. Richard Small [1 model of the loudspeaker and takes ured data, it is shown how to correct & 2]. various non-linearities in frequency the loudspeaker parameters and ex- Since the method was introduced, into account. The method produces tract information about the frequency more research in loudspeaker model- accurate results regardless of the dependent behaviour of some of the ling has been made, (e.g., [3, 4 & 5], components in the equivalent circuit type of driver used. to mention some), and the measure- of the loudspeaker. The voltage across the driver termi- ment technique available with new Since this analysis implied a lot of electronic equipment has advanced nals, the current in the voice coil and arithmetic operations and calcula- tremendously. the velocity of the diaphragm are tions, an autosequence program for The technology of today makes it measured with the driver in free air. the analyzer was written. The scope possible to find a more accurate and The measured results are used to gen- of the automation process is discussed fast method to measure the parame- erate the two transfer functions: The and measurements of a typical driver ters of a loudspeaker. velocity to current ratio and the imped- are included. B Brüel & Kjær 7/6-'89 K 2. Loudspeaker equivalent C circuit R R R (ω)L(ω) MS g E ED VC I Vd MMS RMS Bl The model of a loudspeaker in free + + + + air used in this note is shown in E ∼ E Fig. 1. g s BlVd BlI The electrical and mechanical side is separated by a gyrator. A gyrator has the characteristics that viewed from one side, a dual of the network 920767/1e on the opposite side is seen. It allows Fig.1 Impedance type model of a loudspeaker in free air an impedance analogy to be used for the mechanical side of the circuit. This is a convenient approach, since the current V flowing through the eddy currents in the pole structure, of accuracy. As an example, for a typ- d as described in [3] and [4]. To obtain ical 10 inch woofer in free air, the components MMS, RMS and CMS on the mechanical side of the circuit is accurate results, the presence of mechanical radiation resistance at equivalent to the velocity of the dia- these elements are taken into ac- 100 Hz for both sides of the dia- phragm. The velocity is measured di- count. phragm is more than a 1000 times rectly with the laser velocity In the model, the radiation resist- smaller than the mechanical resist- transducer. ance is neglected while the radiation ance RMS of the suspension. On the electrical side, the compo- reactance is included as part of the The air load for the same woofer is ω ω nents RED( ) and LVC( ) represent moving mass (air load). only about 10 times smaller than the the frequency dependent behaviour of The radiation resistance is small mechanical mass MMD of the dia- the voice coil inductance due to the enough to be neglected without loss phragm and is therefore included. 3. Determination of the parameters 3.1 RE The DC resistance of the voice coil is measured with a precision bridge. 3.2 fs and QMS To find the resonance frequency and the mechanical Q of the driver, the measured velocity Vd of the dia- phragm is divided by the current I in the voice coil by postprocessing in the analyzer. The frequency response ob- tained has the characteristic shape seen in Fig. 2. An analysis of the equivalent cir- cuit in Fig. 1 shows that this response corresponds to the admittance of the mechanical system times a constant, namely the force factor Bl Fig.2 Magnitude and phase frequency responses for the ratio of diaphragm velocity to driver current. The cursor is placed at the resonant frequency in the phase curve Vd 1 ()jω = Bl I 1 jωM ++R MS MS ω j CMS 1 Comparing this to a general transfer ω = n (4) (1) function form G(s) expressed in terms MMSCMS ω of the resonance frequency n and and Rearranging and letting s = jω gives the quality factor Q ω n Q = (5) B V d 1 s s ()s = Bl ()= I M R Gs k (3) MS MS 1 ω s2 ++s 2 ++n ω2 where B is the – 3dB bandwidth M M C s s ω MS MS MS Q n around n. From the characteristics of (3) it (2) where k is the gain factor, yields follows that: 2 1. the resonance frequency of the driver is the frequency at which the magnitude of the velocity to current ratio is maximum and the corresponding phase is zero. 2. the mechanical Q of the driver, QMS can be calculated from (5). The velocity Vd and the current I are both present on the mechanical side of the equivalent circuit in Fig. 1. As it appears from equation (1), their ra- tio does not include any inductance or resistance from the voice coil, it only contains information about the mechanical properties of the driver. The resonance frequency and the me- chanical Q found from this ratio are therefore always accurate regardless of the type of driver unit. 3.3 QES QES can be calculated as in [2] Fig.3 Magnitude and phase of the total driver voice coil impedance. The cursor is placed in the phase curve at the resonance frequency obtained from the phase curve of the velocity QMS Q = (6) to current ratio in Fig.2. The phase difference of about 1 degree compared with Fig.2 is ES − caused by the inductance of the voice coil r0 1 where r0 is the ratio of voice-coil max- imum impedance to DC resistance given by Z ()ω VC s r = (7) 0 R ratio at resonance. The impedance is []Z ()jω − ()R + R ()ω E VC s RealPart E ED s obtained by dividing the measured Bl = V voltage across the driver terminals by d ()jω The definition of QES is the driver Q the current in the voice coil. See I s at f considering electrical resistance s Fig. 3. (11) only. A small error is therefore intro- At resonance Z is, according to VC To calculate Bl from (11) and QES duced when calculating r0 from (7), Fig. 1, given by since Z contains the reactance due from equation (8), the resistance VC ω to the voice-coil inductance. This ef- RED( s ) must be known. By initially Z ()jω = R + R ()ω ω fect can be removed by using the real VC s E ED s letting RED( s ) equal zero, however, estimates of Bl and QES can be ob- part of ZVC in (7) rather than the + jω L ()ω + R (9) magnitude. s VC s ES tained and used to calculate the rest Another error is introduced since of the parameters. and the velocity to current response ω ω Section 4 shows how RED( ) can be the electrical resistance RED( s ) in is given by Fig. 1 is not included in (7). As R determined, allowing a more correct ED estimation of the other parameters. is in series with RE, it will cause QES Vd 1 RES to rise. The value of QES calculated ()jω ==Bl (10) using (6) will therefore be lower than I s R Bl 3.5 MMS , RMS , and CMS MS Once Q , Q , Bl and R (ω ) are the actual QES of the driver. MS ES ED s known, the mechanical parameters of With both terms taken into ac- R is the resistance seen from the count, the following corrected expres- ES the loudspeaker can be calculated electrical side of the circuit in Fig. 1 from the following equations: sion for QES is obtained due to the mechanical resistance RMS. Q ()Bl 2 QMS It can be seen from (9) that the = ES Q = MMS (12) ES electrical resistance RES can be iso- ω ()R + R ()ω ()ω s E ED s ZVC lated from the total voice coil imped- s RealPart − 1 ance, by subtracting the DC R + R ()ω M ω E ED s resistance RE, the resistance due to MS s (8) ω R = the eddy currents RED( s ) and the MS Q (13) ω ω MS reactance of the voice coil s LVC ( s ).
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