Prediction of Speaker Performance at High Amplitudes

A new method is presented for the numerical simulation of the large signal performance of drivers and loudspeaker systems. The basis is an extended loudspeaker model considering the dominant nonlinear and thermal effects. The use of a two-tone excitation allows the response of fundamental, DC-component, harmonics, and intermodulation components to be measured as a function of frequency and amplitude. After measurement of the linear and nonlinear parameters, the electrical, mechanical, and acoustical state variables may be calculated by numerical integration. The relationship between large signal parameters and non-linear transfer behavior is discussed by modeling two drivers. The good agreement between simulated and measured responses shows the basic modeling, parameter identification, and numerical predictions are valid even at large amplitudes. The method presented reduces time-consuming measurements and provided essential information for quality assessment and diagnosis. The extended loudspeaker model also allows prediction of design changes on the large signal performance by changing the model parameters to reflect the driver design changes. The incorporation of nonlinear parameters into the loudspeaker model allows for optimization in both the small and large signal domains by model prediction. KLIPPEL PREDICTION OF SPEAKER PERFORMANCE 2 Introduction For many years linear models have been used for predicting and simulating the loudspeaker behavior [1-3]. Linear models assume a linear relationship between the input and output for any signal amplitude. However, a real speaker limits and distorts the output at higher amplitudes due to thermal and nonlinear mechanisms inherent in the driver, enclosure and radiation. Clearly, linear models fail at high amplitudes and are restricted to the small signal domain. However, assessing and improving the large signal performance becomes more and more an issue in loudspeaker design. Professional, multimedia, automotive and hi-fi applications require small, light-weight drivers manufactured at low cost generating the acoustical output at high efficiency and low distortion. New adequate tools are required for mastering the current challenges. This paper starts with a summary of the current state of large signal modeling and parameter identification. Then alternative ways for assessing the vibration and transfer behavior at high amplitudes are discussed. Traditional and new measurement techniques applied to the real speaker will be compared addressing the question about a suitable excitation signal. Alternatively, a numerical technique will be presented to predict the transfer functions using the identified model. The agreement between measured and predicted responses will be investigated on two example drivers. The relationship between the driver parameters and the resulting transfer responses will be discussed in detail to understand complicated effects such as the dynamic generation of a DC-component which shift the coil out of the gap. After understanding the mechanisms in the particular driver conclusions for practical improvements can be derived. Large Signal Modeling At first we give a short overview on the large signal modeling [411] of electro-dynamical drivers mounted in enclosures which considers the dominant driver nonlinearities and a simple model for the thermal mechanisms. State Variables The state of a speaker operated at low frequencies where the wavelength is large in comparison to the geometrical dimension can be described by using the following quantities x(t) displacement of the voice coil, v(t) velocity of the voice coil, i(t) the electric input current, u(t) the driving voltage at loudspeaker terminals, pbox(t) sound pressure in enclosure (AC-part), qP(t) volume velocity in port, prear(t) sound pressure in rear enclosure, pfar(t) sound pressure in the far field. Lumped Parameter Model The relationship between the state variables may be described by a lumped parameter model comprising a few number of elements characterized by parameter values. The number and kind of the lumped elements and the way how they are connected may be called the topology of our model. It is may be graphically represented as an electrical equivalent circuit as shown in Fig. 1. The speaker may be considered as a transducer coupling the electrical, mechanical and acoustical domain. In contrast to the traditional linear modeling some parameters are not constant but depend on instantaneous state variables.