# Analyzing the Nonlinear Performance of Miniature Loudspeakers in Consideration of the Creep Effect
## 1 Introduction  
Miniature loudspeakers are crucial sound-emitting components in mobile phones, headphones, and other portable audio devices. As the demand for compact portable audio devices with high sound output continues to grow, miniature loudspeakers increasingly operate under large signal conditions, leading to nonlinearities and consequent harmonic distortions. Additionally, with the requirements for good sound quality and the emergence of new near-ear open devices like AR/VR headsets, the nonlinear performance at low frequencies has also gained attention. Thus, investigating the nonlinear performance of miniature loudspeakers, including the low frequency range, is particularly significant. Theoretical models capable of accurately predicting nonlinear performance are needed to provide a foundation for displacement prediction, distortion compensation, and other performance enhancements.  
Previous studies have modeled and analyzed the nonlinear behavior of loudspeaker systems [1; 2; 3; 4]. [PERSON] expanded the widely employed lumped-parameter linear model into a nonlinear form [5; 6], delineated the principal nonlinear parameters of the loudspeaker system, and proposed methods for measuring these nonlinear parameters. [PERSON] also analyzed the harmonic distortion and other effects induced by nonlinearities. Subsequently, [PERSON] et al. numerically analyzed the nonlinear distortion in loudspeakers [7]. [PERSON] proposed a method for diagnosing speaker unit faults based on the measurement of nonlinear distortions [8]. However, these nonlinear models do not consider the creep effect, which is a typical viscoelastic property in the suspension systems of miniature loudspeakers.  
The creep effect refers to the gradual increase in deformation over time in the suspension system of a loudspeaker subjected to external forces [9]. As a result, displacement increases at low frequencies, which is an effect that is particularly evident in miniature loudspeakers with composite membranes. The models developed to evaluate the creep effect can mainly be classified into three types. The first type is the logarithmic empiricalmodel proposed by [PERSON] based on measurements and mathematical analysis [10; 11]. [PERSON] subsequently improved the empirical model [12] and integrated it into the testing of small-signal linear parameters. However, this type of model is only applicable to frequency domain analysis [13; 14], and it cannot be extended to time domain calculations. The second type of model involves the incorporation of the standard linear solid (SLS) model from linear viscoelastic mechanics into the small-signal analysis of loudspeakers while using Newtonian dashpots and Hookean springs to describe creep [15]. This model is applicable to both frequency and time domain analyses. However, most applications of this model are transfer-function-based frequency domain analysis [16; 17; 18; 19; 20], which is limited to the linear characteristics of the loudspeaker [16] and cannot be used for nonlinear calculations. The third type of model is the fractional derivative model, and existing research has demonstrated its applicability in describing the creep effect in loudspeaker systems [21]. Subsequent studies have also developed corresponding identification algorithms, providing methods for analyzing the nonlinear performance of loudspeaker systems based on this model [22]. Although this model allows for nonlinear analysis, it exhibits memory characteristics, is unable to run in real time, and demands high computational resources, thereby limiting its practical application for active control.  
To enable computationally efficient, real-time evaluations of the nonlinear performance of miniature loudspeakers in consideration of the creep effect, we extended the nonlinear model of miniature loudspeakers by incorporating the SLS model. The accuracy of the new nonlinear model incorporating creep was then assessed through comparison with experimental results.