## 4 Discussion  
Regarding the measurement results of mechanical impedance, it can be observed in the graph of Figure 9a that the downward-sloping region corresponds to elastic behavior, while the flat section represents resistive behavior. The mechanical impedance of the human ear cartilage obtained from Figure 9 gradually changed from a predominantly elastic behavior at low frequencies to a predominantly resistive behavior at above 2000 Hz. However, as described in the results, the phase above 2000 Hz and the modulus of mechanical impedance above 5000 Hz were not measured with sufficient accuracy. Future experiments are necessary to improve the accuracy. The average mechanical impedance of the human ear cartilage in the present study was approximately 5 dB lower than the pre-measured mechanical impedance of the concha auriculae over the entire bandwidth during the design of the coupler simulating the ear cartilage. The previous measurement method produced an ear-shaped shell for each subject for the attachment, which was in contact with a surface that matched the subject's ear shape. We believe that the smaller measurement result was due to the difference in the contact areas of the attachments. In this case, the vibrator is subjected to the mechanical impedance based on the contact area and the overall mechanical impedance of the coupler, which is connected in series downstream. When a CCHA is used, the contact area between the vibrator and the ear cartilage is several times larger than that of the present attachment. Considering this, the mechanical impedance of the coupler simulating ear cartilage is reasonable. Figure 10: (**a**) Measured sound pressure levels in the ear canal of 4 ears of 4 persons using human ear cartilage conduction. (**b**) (i) Sound pressure characteristics measured by the vibrator with the coupler simulating the ear cartilage. (ii) Sound pressure characteristics measured by the vibrator with an added mass of 1.5 g with a coupler simulating the ear cartilage. (iii) Average sound pressure characteristics for human ear cartilage conduction compiled from Figure 10a. Figure 10b shows that the sound pressure characteristics of the coupler simulating the ear cartilage and human cartilage conduction have a difference of approximately 10 dB below 500 Hz, although there is good agreement above 500 Hz. However, normal hearing is most sensitive in the frequency range of 300 to 4000 Hz. We assume that the coupler simulating the ear cartilage is sufficient for vibrator evaluations because it simulates the sound pressure characteristics of normal hearing within a sealed ear canal. Figure 11 shows the mechanical equivalent circuit of the concha auriculae using the obtained mechanical impedance of the ear cartilage. The acoustic impedance \(Z_{\text{A}}\) was negligible because it was sufficiently small. Figure 12 shows the calculated characteristics of the mechanical impedance (\(F(\omega)\)/\(\upsilon(\omega)\)) and the phase using the mechanical constants shown in the equivalent circuit. The blue lines in Figure 12 show the calculated characteristics. The grey plot in Figure 12 shows the average value of the measured ear cartilage from Figure 9. The mechanical constants shown in Figure 11 are consistent with the calculated and measured characteristics, which suggests that they are universal physical quantities of concha auriculae. These estimated results provide guidance for future developers of CCHAs. By representing the mechanical impedance when the vibrator is applied to the cartilage in an equivalent circuit, it can be utilized as a crucial design parameter when designing the vibrator and the associated CCHAs. The transducer developed for CCHAs is promising for open-air type hearing aids that do not seal the ear, not only for external auditory canal atresia, but also for slight  
Figure 11: Equivalent circuit estimation of the obtained mechanical impedance from the concha auriculae.