# Analysis and Design of Helmholtz Protector to Improve High-Frequency Response of Insert Earphone
## 1 Introduction  
With the rapid development of consumer products such as mobile phones, notebook computers, and MP4 players, earphones have been recognized as multifunctional assets to increase the convenience of consumer electronics. Based on the speaker driver type, there are MEMS speaker driver earphones [1], balanced armature speaker driver earphones [2], and dynamic speaker driver earphones [3].  
The present study focuses on dynamic speaker driver earphones. The earphone parts are shown in Figure 1. The Lorenz force is generated with an input current in the magnetic circuit. Then, the force contributes to the vibration of the diaphragm, which leads to sound radiation through the front chamber.  
Figure 1: Section view of earphone.  
To design and develop the earphone product, some previous studies have presented simulation methods. The finite element method has been used to analyze earphone performance [4]. According to the relationship between multi physics (electromagnetic, mechanical, and acoustic domains) and an equivalent circuit [5; 6], the lumped parameter method (LPM) can be used to analyze earphone performance [7; 8]. Based on the LPM, coupling between the headphone and the ear has been investigated in artificial ears and models. The influence of the back volume is taken into account [9]. A model of a dynamic driver in an enclosure has been developed using lumped-parameter analysis and analogous circuits [10]. In addition, the properties of porous materials have been investigated to determine their influence on the SPL of an insert earphone [11]. The acoustic structure (volume of front chamber, volume of back chamber duct radius, and length) has been optimized by making use of annealing optimization [12]. To determine the performance of an insert earphone, the target curve for an insert earphone has been defined [13; 14].  
The parameters of the dynamic speaker driver in previous studies [5; 6; 7; 8; 9; 10; 11; 12] were obtained from experiments, so that it is impossible to use these parameters to design a new earphone structure without samples. The first novelty of the present work is the identification of parameters in the analysis tool with respect to the dimensions and material properties. In this way, each dimension and each material property of an earphone can be varied to determine their influence on earphone performance. The second novelty involves analysis and design of a Helmholtz detector based on the proposed analysis tool and identified parameters. It is a challenge to match with the target curve from 7 k to 10 k because the mismatch is generated by the resonance of the ear canal. In other words, they will always exist if there is an ear canal. The paper focuses on the high-frequency response improvement from 7 k to 10 k by reducing the mismatch caused by the ear canal. The designed Helmholtz detector can reduce the peak value of SPL from 7 k to 10 k and improve the earphone high-frequency response.  
The main content of this paper is as follows. First, the electromagnetic, mechanical, and acoustic domains are described by the LPM, which makes use of an equivalent circuit. Second, based on the dimensions and material properties, the electromagnetic and mechanical domain parameters are identified by FEM. The acoustic parameters are determined from the acoustic component dimension. These parameters are treated as input information for simulation. Then, based on the simulation, a Helmholtz detector is designed and simulated to improve the SPL. Finally, the earphone sample is manufactured. The SPL simulation result is matched with the experimental result. With the use of a Helmholtz detector, the high-frequency response is improved.