## 3 Equivalent Circuit of Microspeker
\begin{array}{l}Z_{m}=R_{m}+j\omega m_{m}+\frac{1}{j\omega C_{m}}\\ Z_{eb}=R_{e}+j\omega L_{e}+\frac{R_{2}-j\omega L_{2}}{R_{2}+j\omega L_{2}}\\ Z_{ag}=R_{ag}+j\omega m_{ag}\\ Z_{Car1}=\frac{1}{j\omega C_{Car1}},Z_{Ca1h1}=\frac{1}{j\omega C_{Ca1}}\\ Z_{uh1}=\frac{R_{ab1}+j\omega m_{ah1}}{N_{ai1}},Z_{ap1}=\frac{R_{ap1}}{N_{ap1}} \\ Z_{a\text{-}rad1}=\left(\frac{1}{R_{a\text{-}rad1}}+\frac{1}{j\omega m_{a \text{-}rad1}}\right)^{-1}\\ Z_{a\text{-}rad2}=\left(\frac{1}{R_{a\text{-}rad2}}+\frac{1}{j\omega m_{a \text{-}rad2}}\right)^{-1}\end{array}  \tag{1}\]  
All symbols have their usual meaning. \(Z_{m}\) is the mechanical impedance of the diaphragm (assuming it as a simple spring-mass-dashpot system), \(R_{m}\) is the mechanical resistance, \(m_{m}\) is the mechanical mass, and \(C_{m}\) is the mechanical compliance of the diaphragm. The blocked electrical impedance, \(Z_{eb}\) is modeled as a series combination of the electrical inductance of VC (\(L_{e}\)) and electrical resistance of VC (\(R_{e}\)), along with the addition of a parallel combination of resistance due to eddy current (\(R_{2}\)) and inductance induced at high frequency (\(L_{2}\)). The acoustic impedance of the small duct/port/tube along with the cavity is modeled analogously to the \"Helmholtz Resonator\" as a series combination of acoustic mass (\(m_{a}\)) and acoustic resistance (\(R_{a}\)). Thus, \(Z_{ag}\) is the acoustic impedance  
Figure 3: Schematic diagram of microsp-peaker on the barrier in an anechoic chamber. of the air gap below the diaphragm, and \(Z_{ah1}\) is the effective acoustic impedance of the vent, such that \(N_{ah1}\) is the number of vents. The acoustic impedance of the cavity (\(Z_{Ca}\)) is calculated by the compliance of cavity (\(C_{a}\)), volume of cavity (\(V_{c}\)), density of air (\(\rho_{0}\)), and speed of sound in air (\(c\)). Thus, \(Z_{Ca1}\) represents the acoustic impedance of cavity below the diaphragm and \(Z_{Chh1}\) represents the acoustic impedance cavity due to all vents. Finally, the acoustic cloth covered all vents, so \(Z_{ap1}\) represents the acoustic impedance of acoustic cloth, by considering the number of vents (\(N_{ah1}\)). For more details, readers can refer to our group's earlier works [31; 32; 33; 34; 35]. Further, ECM circuit has to be simplified by removing transformers to form a typical three loop circuit to solve it according to Kirchhoff's voltage law. Loops are driven by velocities \(v_{1}\), \(v_{2}\), and \(v_{3}\), respectively, and can be represented by  
\[ \begin{bmatrix}\frac{e_{g}Bl}{Z_{eb}}\\ 0\\ 0\end{bmatrix} =\mathbf{Z}\cdot \begin{bmatrix}v_{1}\\ v_{2}\\ v_{3}\end{bmatrix}  \tag{2}\]  
where the impedance matrix \(\mathbf{Z}\) is given by  
\[\mathbf{Z}= \begin{bmatrix}\hat{B}&-A^{2}Z_{Car1}&0\\ -A^{2}Z_{Car1}&\hat{C}&-A^{2}Z_{Chh1}\\ 0&-A^{2}Z_{Chh1}&\hat{D}\end{bmatrix}  \tag{3}\]  
and  
\[ \begin{array}{l}\hat{B}=\frac{(Bl)^{2}}{Z_{eb}}+Z_{m}+A^{2}\Big{(}Z_{a-rad1}+ \frac{1}{2}Z_{ag}+Z_{Car1}\Big{)}\\ \hat{C}=A^{2}\Big{(}Z_{Car1}+\frac{1}{2}Z_{ag}+\frac{1}{2}Z_{ah1}+Z_{Chh1}\Big{)} \\ \hat{D}=A^{2}\Big{(}Z_{Chh1}+\frac{1}{2}Z_{ah1}+Z_{ap1}+Z_{a-rad2}\Big{)}\end{array}  \tag{4}\]  
The diaphragm velocity \(v_{1}\) can be obtained by  
\[v_{1}= \begin{bmatrix}1&0&0\\ 0\end{bmatrix} \cdot\mathbf{Z}^{-1}\cdot \begin{bmatrix}1\\ 0\\ 0\end{bmatrix} \cdot\Big{(}\frac{e_{g}Bl}{Z_{eb}}\Big{)} \tag{5}\]  
Finally, the sound pressure \(p\) can be obtained by  
\[p(r)=-j\rho_{0}\omega Av_{1}\bigg{(}\frac{e^{-j\kappa r}}{2\pi r}\bigg{)} \tag{6}\]  
where \(r\) (=10 cm, see Figure 3) is the distance of the microphone from the microspeaker. Finally, the sound pressure level of the microspeaker is the pressure level of the sound measured in decibels (dB) and abbreviated dBSPL. On axis SPL can be obtained by  
\[SPL=20\log_{10}\bigg{(}\frac{p(r)}{p_{ref}}\bigg{)} \tag{7}\]  
where \(p_{ref}\) is the reference sound pressure in air, \(2\times 10^{-5}\) N/m\({}^{2}\) (0.00002 Pa). The \(p_{ref}\) is the lowest sound pressure possible for human hearing.