Because loudspeaker drivers are electro-mechano-acoustical transducers, their parameters may be measured from physical domains other than the electrical domain. A method has been developed by the authors to determine moving-coil loudspeaker parameters through the use of acoustical measurements. The technique utilizes a plane wave tube and the two-microphone transfer function technique to measure acoustical properties of a baffled driver under test (DUT). Quantities such as the reflection and transmission coefficients of the DUT are first measured. Driver parameters are then extracted from the measurements using curve-fitting techniques and theoretical solutions to equivalent circuits of the composite system. This paper discusses the acoustical measurement apparatus, system modeling, and a comparison of acoustically measured parameters to those measured using common electrical techniques. Parameters derived from the various methods are also compared to reference parameters to establish bias errors. 0. GLOSSARY OF SYMBOLS B Magnetic flux density in the driver gap Bl Motor strength, the product of B and l c Speed of sound in air MS C Compliance of driver suspension c f Cutoff frequency for the first cross mode of the plane wave tube 0 f In vacuo resonance frequency of driver s f Free-air resonance frequency of driver l Length of voice coil in magnet air gap VC L Inductance of driver voice coil MD M Moving mass of driver diaphragm assembly ANDERSON AND LEISHMAN ACOUSTICAL MEASUREMENT OF LOUDSPEAKERS AES 115TH CONVENTION, NEW YORK, NEW YORK, 2003 OCTOBER 10-13 2 MS M Moving mass of driver diaphragm assembly including air load B p Blocked sound pressure from source driver i p Sound pressure incident upon driver t p Sound pressure transmitted through driver ES Q Electrical quality factor MS Q Mechanical quality factor TS Q Total system quality factor MS R Mechanical resistance of driver suspension VC R DC resistance of driver voice coil S Cross-sectional area of plane wave tube D S Effective radiating surface area of driver TL Transmission loss U Volume velocity, particle velocity multiplied by surface area AS V Volume of air having the same acoustic compliance as the driver suspension i W Sound power incident upon driver t W Sound power transmitted through driver E X Electrical reactance of driver’s electrical system M X Mechanical reactance of driver’s mechanical system MT X Mechanical reactance of termination impedance AR Z Acoustic radiation impedance seen by source driver AT Z Acoustic impedance of termination translated up to the back of the driver diamphram E Z Electrical impedance of the driver’s voice coil M Z Mechanical impedance of the driver’s mechanical system BB M Z , Mechanical impedance of a black box MT Z Mechanical termination impedance translated up to the back of the driver diaphragm 0 ρ Density of air τ Sound power transmission coefficient CC τ Closed circuit transmission coefficient of driver under test OC τ Open circuit transmission coefficient of driver under test ω Angular frequency, in rad/s

An Acoustical Measurement Method for the Derivation of Loudspeaker Parameters

DERIVATION OF MOVING-COIL LOUDSPEAKER PARAMETERS USING PLANE WAVE TUBE TECHNIQUES Brian E. Anderson Department of Physics and Astronomy Master of Science Small-signal moving-coil loudspeaker driver parameters are traditionally derived through electrical impedance measurement techniques. These parameters are commonly called Thiele/Small parameters, after Neville Thiele and Richard Small who are credited with developing industry-standard loudspeaker modeling techniques. However, because loudspeaker drivers are electro-mechano-acoustical transducers, it should be possible to measure their parameters in physical domains other than the electrical domain. A method of measuring loudspeaker parameters from the acoustical domain will be developed. The technique uses a plane wave tube to measure acoustical properties of a baffled driver under test. Quantities such as the transmission loss through the driver are measured for a driver placed in the tube using the two-microphone transfer-function technique. Models have been developed to curve fit the resulting data, from which small-signal loudspeaker parameters are subsequently derived. This thesis discusses the acoustical measurement theory, apparatus, and system modeling methods (via equivalent circuits). It also compares measured parameters to those derived using electrical techniques. Parameters derived from both approaches are compared with reference values to establish bias errors. Sequential measurements are also compared to reveal random errors in the derivation processes.

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Derivation of Moving-Coil Loudspeaker Parameters Using Plane Wave Tube Techniques

The parameters of moving-coil loudspeaker drivers are typically determined using direct electrical excitation and measurement. However, as electro-mechano-acoustical devices, their parameters should also follow from suitable mechanical or acoustical evaluations. This paper presents the theory of an acoustical method of excitation and measurement using normal-incidence sound transmission through a baffled driver as a plane-wave tube partition. Analogous circuits enable key parameters to be extracted from measurement results in terms of open and closed-circuit driver conditions. Associated tools are presented that facilitate adjacent field decompositions and derivations of sound transmission coefficients (in terms of driver parameters) directly from the circuits. The paper also clarifies the impact of nonanechoic receiving tube terminations and the specific benefits of downstream field decompositions.

Evaluation of moving-coil loudspeaker and passive radiator parameters using normal-incidence sound transmission measurements: theoretical developments.

Simulation of Loudspeaker Crossover Filters with a Digital Signal Processor

This article presents an inverse method for estimating the electromechanical parameters of a moving-coil loudspeaker with or without the eddy current and suspension creep effects. With known voice-coil displacement, voice-coil current, and stimulus signal as inputs, four calculation procedures for the direct problem, adjoint problem, sensitivity problem, and conjugate gradient method are involved in inversely solving the unknown electromechanical parameters. The proposed method features high efficiency in solving the direct problem through a hybrid spline difference method. It requires a small number of iterations for the computational algorithm, while offering excellent accuracy in parameter estimations. Analysis results demonstrate small differences between the estimated and measured electromechanical parameters under a variety of stimulus signals, excitation times, and initial guesses. The results are also confirmed by experimental measurements. These results indicate that the proposed method has a strong potential for estimating the electromechanical parameters of moving-coil loudspeakers.

An inverse method for estimating the electromechanical parameters of moving-coil loudspeakers

This paper proposes an estimation method for the system parameters in the low-frequency range of the direct-radiator loudspeaker system. The system parameters considered in this paper are defined by the elements in the electrical and mechanical equivalent circuit in the low-frequency range. In previous estimations of the system parameters, the impedance measurement was required for the driver speaker in the free space or in the standard box. On the other hand the proposed method can provide estimations for the system parameters, including the proper additional air mass and the effective volume of the box for the driver speaker and the passive radiator (drone cone or port), only by the measurement of the system impedance. Consequently, it is a practically useful method. The estimation is made by minimizing (optimizing) the evaluation function by the nonlinear optimization, which is composed of the square sum of the difference between the measured and calculated impedances at the voice-coil terminals of the driver speaker at a finite number of discrete frequencies. Eight kinds of methods are examined for efficient estimation. By computer simulation and two examinations, the validity and usefulness of the method are indicated. Since the method can provide estimations of the true system parameters, it can present effective means for the system design.

Takaharu Ai

Papers

Estimation method of direct-radiator loudspeaker system parameters in low-frequency range by nonlinear optimization technique