This study investigated the lumped parameter method (LPM) and distributed parameter method (DPM) in the measurement of vibration and prediction of sound pressure levels (SPLs) produced by an electrostatic speaker with circular diaphragm. An electrostatic speaker with push-pull configuration was achieved by suspending the circular diaphragm (60 mm diameter) between two transparent conductive plates. The transparent plates included a two-dimensional array of holes to enable the visualization of vibrations and avoid acoustic distortion. LPM was used to measure the displacement amplitude at the center of the diaphragm using a scanning vibrometer with the aim of predicting symmetric modes using Helmholtz equations and SPLs using Rayleigh integral equations. DPM was used to measure the amplitude of displacement across the entire surface of the speaker and predict SPL curves. LPM results show that the prediction of SPL associated with the first three symmetric resonant modes is in good agreement with the results of DPM and acoustic measurement. Below the breakup frequency of 375 Hz, the SPL predicted by LPM and DPM are identical with the results of acoustic measurement. This study provides a rapid, accurate method with which to measure the SPL associated with the first three symmetric modes using semi-analytic LPM.
This study modeled the circular diaphragm of push-pull electrostatic speakers using electro-mechano-acoustical equivalent circuits to determine the frequency responses related to the average displacement and sound pressure of the diaphragm with respect to acoustic impedance effects. A laser vibrometer system was used to measure the displacement in the center of the circular diaphragms (60 mm and 65 mm in diameter) in optically transparent indium tin oxide (ITO) electrostatic speakers. The sound pressure levels (SPLs) were predicted using the average displacement of the diaphragm without resorting to sound field measurements or finite element analysis. The predicted SPL results were then compared to acoustic measurements. The results demonstrate that ITO plates are a practical tool for the measurement of displacement and the prediction of SPLs. When the proposed electrostatic speaker (65-mm-diameter diaphragm) design was applied to the over-ear electrostatic headphone, the SPL curve obtained from artificial ear measurements was similar to the preferred target curve of Harman International (Stamford, CT). This resulted in outstanding sound quality comparable to that of high-end commercial dynamic headphones.
This study modeled an elliptical diaphragm in a push-pull electrostatic speaker using the average displacement, specific impedance and equivalent radius to predict the frequency response in terms of sound pressure level (SPL). We also fabricated a prototype of an electrostatic speaker based on an elliptical diaphragm with fixed rim measuring 32 mm (semi-major axis) by 30 mm (semi-minor axis). The speaker was then used to analyze the frequency-response characteristics associated with resonance modes and displacement curves using the optical measurement, and obtain the SPL curves in an anechoic chamber using the acoustic measurements. The experiment results revealed that the predicted curves were in good agreement with the measured displacement and SPL curves. These curves of the electrostatic speaker were strongly affected by air radiation impedance. When our speaker was implemented in an over-ear electrostatic headphone, we obtained solid bass response and a frequency response typical of high-fidelity headphones.
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