# Analysis and Identification of Nonlinear Acoustic Damping in Miniature Loudspeakers
## 1 Introduction  
It has been proven that nonlinear acoustic damping is a dominant nonlinearity in miniature loudspeakers and has a significant influence on their performance [1; 2; 3]. [PERSON] showed that the acoustic damping in ports is nonlinear and can generate distortion at the port resonance when describing the nonlinearities in micro-speakers [1]. [PERSON] et al. predicted the nonlinear resistance and distortion of miniature loudspeakers by considering the nonlinear acoustic damping caused by the gaps and orifices in a magnet system [2]. [PERSON] et al. analyzed the total harmonic distortion of miniature loudspeakers that are used in mobile phones and found that nonlinear acoustic damping can lead to significant harmonic distortions at both lower and higher frequency bands [3].  
While previous works have been devoted to the theoretical analysis of nonlinear acoustic damping and its influence on performance, less attention has been paid to the real measurement of the nonlinear acoustic damping in miniature loudspeakers. The nonlinearities of acoustic damping on orifices or resonators have been investigated theoretically and experimentally for many years in sound absorption theory [4; 5; 6; 7; 8; 9; 10; 11; 12]. [PERSON] measured the acoustic impedance of orifices under various particle velocities and found that the nonlinear resistance of the orifice is proportional to the velocity [4]. [PERSON] et al. investigated the nonlinear damping of perforated tubes using an extended impedance tube method and proposed a time-domain computational model to predict the acoustic behavior of perforated tube silencers [7]. [PERSON] et al. investigated the termination impedance of open-ended tubes at a high sound pressure level using a two-microphone method [8; 10]. It was found by the authors that the radius of the curvature of the edges of the open end of the tube has a crucial influence on the amplitude of nonlinear acoustic damping. Nonlinear acoustic damping can be obtained with accuracy using the measurement method used inthese works. However, the general measuring methods of the acoustic impedance used in these works, such as the standing-wave tube method and the impedance tube method, are not applicable in this scenario because the nonlinear acoustic damping in miniature loudspeakers is coupled with other nonlinearities in the entire loudspeaker system [3,13]. In this study, a measurement method based on nonlinear system identification was constructed to address this issue. The system identification method has been widely used in the electroacoustics industry to measure the nonlinear parameters of loudspeakers and miniature loudspeakers [14, 15, 16, 17]. Current research is limited to identifying the nonlinearities in the electrical and mechanical domains. To the best of our knowledge, no work to date has focused on identifying the nonlinearities in the acoustical domain. Thus, in this study, nonlinear acoustic damping was first theoretically analyzed and then coupled in an equivalent circuit method (ECM) model to describe the full dynamics of miniature loudspeakers. Based on the ECM model, nonlinear acoustic damping was identified using measured electrical data.  
The remainder of this paper is organized as follows: Section 2 summarizes the theoretical analysis of the nonlinear acoustic damping and establishes an ECM model of miniature loudspeakers with consideration of the nonlinear acoustic damping. In Section 3, a measurement method based on nonlinear system identification is proposed, and its implementation is introduced in detail to identify the nonlinear acoustic damping in miniature loudspeakers. Section 4 describes the experiments conducted to obtain the nonlinear acoustic damping and compares the results with theoretical calculations. Some discussion is presented in this section. Finally, conclusions are drawn in the last section.