A new lighting and enlargement on phase spectrogram （PS） and frequency spectrogram （FS） is presented in this paper. These representations result from the coupling of power spectrogram and short time Fourier transf...A new lighting and enlargement on phase spectrogram （PS） and frequency spectrogram （FS） is presented in this paper. These representations result from the coupling of power spectrogram and short time Fourier transform （STFT）. The main contribution is the construction of the 3D phase spectrogram （3DPS） and the 3D frequency spectrogram （3DFS）. These new tools allow such specific test signals as small slope linear chirp, phase jump case of musical signal analysis is reported. The main objective is to and small frequency jump to be analyzed. An application detect small frequency and phase variations in order to characterize each type of sound attack without losing the amplitude information given by power spectrogram展开更多
This article investigates the second overtone thickness-extensional(TE2)vibrations and associated mode-coupling behaviors in ZnO piezoelectric film bulk acoustic resonator(FBAR),utilizing its wave dispersion relation ...This article investigates the second overtone thickness-extensional(TE2)vibrations and associated mode-coupling behaviors in ZnO piezoelectric film bulk acoustic resonator(FBAR),utilizing its wave dispersion relation and the higher-order stress balance principle.By superimposing the general wave solutions of multiple eigenmodes within the frequency range of the TE2 mode,mode-coupling solutions for ZnO FBAR are constructed.The substitution of these mode-coupling solutions into the higher-order stress balance principle,as laterally weak boundary conditions,leads to the frequency spectrogram equation,determining the relationship between resonance frequency and plate length-to-thickness ratio.A modified algorithm that combines the bisection method and the complex modulus ratio method is developed to solve the dispersion equation and frequency spectrogram equation(namely a kind of 2D complex transcendental equations)accurately and efficiently.The obtained results indicate that the operational TE2 mode may couple to unwanted 3^(rd)thickness-shear,fundamental thickness-shear,and flexural modes.Moreover,the mode-coupling behaviors depend strongly on resonance frequencies and plate length-to-thickness ratio.The displacement distributions of total displacement components,alongside the main displacement com-ponents of all considered eigenmodes,clearly demonstrate the variety of coupling behaviors.According to the obtained frequency spectrograms,the desirable values of plate length-to-thickness ratio for a clean operating mode with very weak coupling intensity are determined.These findings are of vital importance for the understanding of the mode-coupling me-chanism in overtone thickness-extensional FBARs,which will facilitate the structural design and optimization of FBAR devices.展开更多
文摘A new lighting and enlargement on phase spectrogram （PS） and frequency spectrogram （FS） is presented in this paper. These representations result from the coupling of power spectrogram and short time Fourier transform （STFT）. The main contribution is the construction of the 3D phase spectrogram （3DPS） and the 3D frequency spectrogram （3DFS）. These new tools allow such specific test signals as small slope linear chirp, phase jump case of musical signal analysis is reported. The main objective is to and small frequency jump to be analyzed. An application detect small frequency and phase variations in order to characterize each type of sound attack without losing the amplitude information given by power spectrogram
基金supported by the National Natural Science Foundation of China(Grant Nos.12192210,12192211,12102183,12302200,and 12402192)the Natural Science Foundation of Zhejiang Province(Grant No.LD21A020001)+2 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20230873)the National Postdoctoral Program for Innovation Talents(Grant No.BX2021261)supported by the specialized research projects of Huanjiang Laboratory,Zhuji,Zhejiang Province.
文摘This article investigates the second overtone thickness-extensional(TE2)vibrations and associated mode-coupling behaviors in ZnO piezoelectric film bulk acoustic resonator(FBAR),utilizing its wave dispersion relation and the higher-order stress balance principle.By superimposing the general wave solutions of multiple eigenmodes within the frequency range of the TE2 mode,mode-coupling solutions for ZnO FBAR are constructed.The substitution of these mode-coupling solutions into the higher-order stress balance principle,as laterally weak boundary conditions,leads to the frequency spectrogram equation,determining the relationship between resonance frequency and plate length-to-thickness ratio.A modified algorithm that combines the bisection method and the complex modulus ratio method is developed to solve the dispersion equation and frequency spectrogram equation(namely a kind of 2D complex transcendental equations)accurately and efficiently.The obtained results indicate that the operational TE2 mode may couple to unwanted 3^(rd)thickness-shear,fundamental thickness-shear,and flexural modes.Moreover,the mode-coupling behaviors depend strongly on resonance frequencies and plate length-to-thickness ratio.The displacement distributions of total displacement components,alongside the main displacement com-ponents of all considered eigenmodes,clearly demonstrate the variety of coupling behaviors.According to the obtained frequency spectrograms,the desirable values of plate length-to-thickness ratio for a clean operating mode with very weak coupling intensity are determined.These findings are of vital importance for the understanding of the mode-coupling me-chanism in overtone thickness-extensional FBARs,which will facilitate the structural design and optimization of FBAR devices.
