# Analyzing the Nonlinear Performance of Miniature Loudspeakers in Consideration of the Creep Effect
## 3 Experimental Validation  
### Experimental Setup  
Experiments were conducted on three miniature loudspeaker samples to assess the effectiveness of the NL-C model. Figure 2 depicts the front views of the three samples. Based on the parameters of the loudspeaker samples measured using a Klippel R&D system (Klippel GmbH, Dresden, Germany), the nonlinear displacement waveforms and THD were predicted using the NL-C model and degraded NL-NC model and measured experimentally under the same nonlinear conditions after all the samples achieved a stable operating state. The predictions were then compared with the measurement values. The sample parameters used for the theoretical calculations were obtained from measurements using a Klippel R&D LPM system. The linear parameters \(R_{e}\), \(L_{e}\), and \(M_{m}\) were measured using the Klippel LPM module. These measurements also provided linear displacement data, which were used to derive \(K_{2}\) and \(R_{2}\) by fitting with a theoretical model, as reported in Ref. [16]. Notably, \(K_{2}\) and \(R_{2}\) were obtained under linear conditions and used for computation and prediction within the nonlinear model. The rationale for this approach is discussed in the subsequent section. The measured and fitted linear parameters of the three samples are presented in Table 1. The nonlinear parameters \(Bl\), \(K_{m}\), and \(R_{m}\) were measured using the Klippel LSI module, and the results are shown in Figure 3.  
Subsequently, the displacement waveforms were predicted using the state-space equations from the two models, as described in Section 2.3. The THD values were then predicted using Equation (14). The displacement waveforms and THD values under nonlinear conditions were measured as shown in Figure 4. The experimental setup for displacement measurement is depicted in Figure 4a. During the experiments, the samples were mounted on a laser measurement platform, with signal transmission and reception controlled by a laptop via an audio interface (Fireface UC, RME, Haimhausen, Germany). Two music clips containing rich low-frequency components were chosen as input signals, considering the dominant domain of the creep effect. Clip 01 was from the song \"Hotel California\" by the band The Eagles from their album \"Hotel California\". Clip 02 came from the song \"The Ferry\" by the singer [PERSON] featured on the album \"Folk Songs by [PERSON]\". These tracks are often used in audio assessments of low-frequency and dynamic performance. Each clip was excerpted to 30 s and sampled at 48 kHz. The root-mean-square (RMS) value \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Linear Parameters** & \(R_{e}\) & \(L_{e}\) & \(M_{m}\) & \(K_{2}\) & \(R_{2}\) \\ \hline
**[unit]** & **[Ohm]** & **[mH]** & **[g]** & **[N/mm]** & **[kg/s]** \\ \hline Sample A & 5.74 & 0.041 & 0.128 & 1.005 & 16.5 \\ Sample B & 6.96 & 0.050 & 0.121 & 1.103 & 15.0 \\ Sample C & 3.72 & 0.045 & 0.314 & 1.063 & 26.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Linear parameters of the samples. Figure 3: Nonlinear parameters of samples. Figure 2: Front views of the three miniature loudspeaker samples. of the input voltage was set at 2 V. The excitation signal was generated by the interface and delivered to the samples through a power amplifier (RMX 2450, QSC, Costa Mesa, CA, USA). Concurrently, the displacement signal was recorded using a laser probe (LK-G30, KEYENCE, Osaka, Japan) and fed back into the audio interface. This facilitated the acquisition of the displacement waveforms. The THD values of the miniature loudspeaker samples were evaluated in an anechoic chamber (5.8 m \(\times\) 4.8 m \(\times\) 2.9 m). As illustrated in Figure 4b, the samples were mounted on a baffle for the experimental procedures. The RMS value of the stepped sine input voltage was set at 2 V, and the frequency range was adjusted to 30-4000 Hz to ensure that the THD was evaluated across a broad frequency domain.