## 1 Introduction
### Sound Quality Performance  
Apart from the design parameters as inputs of the model, the dependent variables, which are the sound performance of the earphone design, will be defined in order to formulate the simplified expression of the prediction. Essentially, six indicators, namely, total harmonic distortion (THD), power of output, range of frequency response, signal-to-noise ratio (SNR), impedance of the speaker, and headroom, were adopted in the formulation of the mathematical model, while these metrics are utilized in the evaluation of the sound performance of the designed earphone. Firstly, it is without any question that the expression of the original sound is one of the critical criteria for a sound system. Therefore, THD is found to be an important metric for evaluating the sound quality of designed earphones [14]. In essence, this factor quantifies the amount of distortion introduced by the earphone to the original signal, highlighting the contrast between the two. Therefore, a high-quality earphone should have low THD, indicating that it produces a faithful reproduction of the original signal [15]. To summarize, an earphone with high-quality sound should have a low THD rate. Earphone distortion rates are typically measured as a percentage of the total signal, with lower percentages indicating higher-quality sound reproduction. An excellent earphone system will have a distortion rate of less than 1%, while a moderately performing system will have a rate ranging from 1% to 5%. Conversely, a low-quality system may have a distortion rate as high as 10%. However, THD is not always a reliable metric for sound quality evaluation, as the nonlinear behavior of the human ear can limit its applicability, whereas the human sensation may have various sensitivities to sound with different loudness and frequency. Thus, reflecting the truth may be considered an evaluative dimension, but not a comprehensive scheme of quality measurement. Secondly, apart from the distortion, the power of output is another important metric for the evolution of sound quality that determines the loudness and bass capabilities of an earphone [16]. It is typically measured in watts or milliwatts and reflects the maximum power that the earphone can handle before it starts to attenuate with the inverse square law. While loudness may not be directly related to sound quality, a good earphone should have a high power of output, especially in the low-frequency range, to produce clear and powerful bass so that the original sound can be expressed. Thirdly, the range of frequency response [17] is a measure of an earphone's ability to reproduce different frequencies within the audible range [18]. The range of frequency response is typically measured in hertz (Hz) and indicates the range of frequencies that the earphone can produce [19; 20]. Therefore, a good earphone should have a wide range frequency range in order to take care of the special needs of some extremely sensitive users [21]. For a full-range earphone system, it is essential to have a range of frequency responses that can accurately reproduce sound across the entire audible range for humans [22; 23], which typically spans from 20 Hz to 20 kHz. Therefore, a high-quality full-range earphone system should be capable of responding to frequencies within this range. However, due to the physical limitations of earphones, they typically provide responses from 310 Hz to 12 kHz, with high-quality systems capable of a wider frequency range [24]. Fourthly, in addition to measuring distortion directly, the SNR is a crucial metric for evaluating earphone performance. It represents the ratio of the signal level to the noise level and is often used to determine the quality of the sound produced by the earphones. It is typically measured in decibels (dB) and indicates how much louder the signal is than the noise. A high-quality earphone should ideally have an SNR of 90 to 100 dB, indicating a low noise level and a clear, crisp sound.