Pub Date : 2006-06-04DOI: 10.1109/FREQ.2006.275480
F. Sthal, S. Galliou, P. Abbé, N. Franquet, X. Vacheret, P. Salzenstein, E. Rubiola, G. Cibiel
In this paper, the thermal stability characterization of crystal ovens used in a phase noise measurement system of ultra-low noise crystal resonators is proposed. This bench is dedicated to test 5 MHz and 10 MHz crystal devices packaged in HC40 enclosures. New double ovens have been designed to improve the ultimate noise floor of our carrier suppression bench. A brief description of the temperature environment and processing are given. In addition, experiments to measure the thermal stability of the oven control are given. These new crystal ovens present an Allan standard deviation of about 2-10-15 at 1 s in terms of relative frequency fluctuations
{"title":"Thermal characterization of crystal ovens used in phase noise measurement system","authors":"F. Sthal, S. Galliou, P. Abbé, N. Franquet, X. Vacheret, P. Salzenstein, E. Rubiola, G. Cibiel","doi":"10.1109/FREQ.2006.275480","DOIUrl":"https://doi.org/10.1109/FREQ.2006.275480","url":null,"abstract":"In this paper, the thermal stability characterization of crystal ovens used in a phase noise measurement system of ultra-low noise crystal resonators is proposed. This bench is dedicated to test 5 MHz and 10 MHz crystal devices packaged in HC40 enclosures. New double ovens have been designed to improve the ultimate noise floor of our carrier suppression bench. A brief description of the temperature environment and processing are given. In addition, experiments to measure the thermal stability of the oven control are given. These new crystal ovens present an Allan standard deviation of about 2-10-15 at 1 s in terms of relative frequency fluctuations","PeriodicalId":445945,"journal":{"name":"2006 IEEE International Frequency Control Symposium and Exposition","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127447981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-06-04DOI: 10.1109/FREQ.2006.275329
J. Levine
This tutorial reviews the subject of digital measurements of clocks and oscillators. It focuses primarily on the precision measurement of phase and the use of these measurements in estimating phase and frequency and common statistics such as the Allan deviation and the spectral density of phase. The subject matter includes direct counting, interpolating counters, dividers, heterodyne conversion, and dual-mixer systems. Biases in the measurements caused by aliasing and measurement quantization are evaluated. Analog techniques, which are used primarily to evaluate phase noise, are covered in a related tutorial.
{"title":"Tutorial Session 4A - Time and Frequency Transfer","authors":"J. Levine","doi":"10.1109/FREQ.2006.275329","DOIUrl":"https://doi.org/10.1109/FREQ.2006.275329","url":null,"abstract":"This tutorial reviews the subject of digital measurements of clocks and oscillators. It focuses primarily on the precision measurement of phase and the use of these measurements in estimating phase and frequency and common statistics such as the Allan deviation and the spectral density of phase. The subject matter includes direct counting, interpolating counters, dividers, heterodyne conversion, and dual-mixer systems. Biases in the measurements caused by aliasing and measurement quantization are evaluated. Analog techniques, which are used primarily to evaluate phase noise, are covered in a related tutorial.","PeriodicalId":445945,"journal":{"name":"2006 IEEE International Frequency Control Symposium and Exposition","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130202556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-06-04DOI: 10.1109/FREQ.2006.275372
J. Le Floch, M. Tobar, D. Cros, J. Krupka
The Bragg reflection technique improves the Q-factor of a resonator by reducing conductor and dielectric losses by concentrating the field in the inner area of the cavity. In this paper, we present a general way of designing a high Q-factor Bragg resonator, using a simple model of non-Maxwellian equations. The method is a more general method, which allows us to design resonators of cylindrical geometry and arbitrary thicknesses for either the horizontal or cylindrical dielectric reflectors, which is often imposed by the manufacturer. In this work, we only consider cylindrical symmetric resonators operating in transverse electric mode (TE0,n,p), which only has the E 0 component made from low-loss single crystal dielectrics. The horizontal plates are of thickness 2.75 mm and radius 24.3 mm, and the rings are 31.8 mm high and of the same radius. The size of the cavity to obtain Bragg reflection may be calculated using the simple model, which is verified with rigorous method of lines analysis. When we fix the number of variation of E0 in r and z directions to the minimum (fundamental mode) we obtained an unloaded Q-factor of order 2times105 at 9.7 GHz in a single crystal sapphire resonator. Two other cavities were built to investigate Bragg confinement of higher order modes in the sapphire structure at 12.4 GHz with unloaded Q-factors of order 105. We also illustrate the general designing principles of a Bragg reflector with dielectric layers of arbitrary thicknesses using the simple model, with verification using the method of lines
{"title":"Simple Design Technique for High Q-factor Bragg Reflector Resonators with Reflectors of Arbitrary Thickness","authors":"J. Le Floch, M. Tobar, D. Cros, J. Krupka","doi":"10.1109/FREQ.2006.275372","DOIUrl":"https://doi.org/10.1109/FREQ.2006.275372","url":null,"abstract":"The Bragg reflection technique improves the Q-factor of a resonator by reducing conductor and dielectric losses by concentrating the field in the inner area of the cavity. In this paper, we present a general way of designing a high Q-factor Bragg resonator, using a simple model of non-Maxwellian equations. The method is a more general method, which allows us to design resonators of cylindrical geometry and arbitrary thicknesses for either the horizontal or cylindrical dielectric reflectors, which is often imposed by the manufacturer. In this work, we only consider cylindrical symmetric resonators operating in transverse electric mode (TE0,n,p), which only has the E 0 component made from low-loss single crystal dielectrics. The horizontal plates are of thickness 2.75 mm and radius 24.3 mm, and the rings are 31.8 mm high and of the same radius. The size of the cavity to obtain Bragg reflection may be calculated using the simple model, which is verified with rigorous method of lines analysis. When we fix the number of variation of E0 in r and z directions to the minimum (fundamental mode) we obtained an unloaded Q-factor of order 2times105 at 9.7 GHz in a single crystal sapphire resonator. Two other cavities were built to investigate Bragg confinement of higher order modes in the sapphire structure at 12.4 GHz with unloaded Q-factors of order 105. We also illustrate the general designing principles of a Bragg reflector with dielectric layers of arbitrary thicknesses using the simple model, with verification using the method of lines","PeriodicalId":445945,"journal":{"name":"2006 IEEE International Frequency Control Symposium and Exposition","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130366249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-06-04DOI: 10.1109/FREQ.2006.275421
Yanhui Wang, T. Liu, A. Stejskal, Y. N. Zhao, Jie Zhang, Zehuang Lu, R. Dumke, L. Wang, T. Becker, H. Walther
We report on the current status of the optical frequency standard based on a single 115In+ ion. A single indium ion is being trapped in a Paul-Strauble type trap and cooled in combination of Doppler cooling and sideband cooling to its lowest vibrational states. To interrogate the 1S0-3P0 clock transition with high accuracy we demonstrate a Hz-level laser system resonant to this transition. With the current setup we are able to achieve a measured linewidth of the clock transition of 260 Hz. The statistical uncertainty of the absolute frequency measurement is 3 times 10-13, limited mainly by our reference frequency standard
{"title":"Progress Toward an Optical Frequency Standard Based on a Single Indium Ion","authors":"Yanhui Wang, T. Liu, A. Stejskal, Y. N. Zhao, Jie Zhang, Zehuang Lu, R. Dumke, L. Wang, T. Becker, H. Walther","doi":"10.1109/FREQ.2006.275421","DOIUrl":"https://doi.org/10.1109/FREQ.2006.275421","url":null,"abstract":"We report on the current status of the optical frequency standard based on a single <sup>115</sup>In<sup>+</sup> ion. A single indium ion is being trapped in a Paul-Strauble type trap and cooled in combination of Doppler cooling and sideband cooling to its lowest vibrational states. To interrogate the <sup>1</sup>S<sub>0</sub>-<sup>3</sup>P<sub>0 </sub> clock transition with high accuracy we demonstrate a Hz-level laser system resonant to this transition. With the current setup we are able to achieve a measured linewidth of the clock transition of 260 Hz. The statistical uncertainty of the absolute frequency measurement is 3 times 10<sup>-13</sup>, limited mainly by our reference frequency standard","PeriodicalId":445945,"journal":{"name":"2006 IEEE International Frequency Control Symposium and Exposition","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131737847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-06-04DOI: 10.1109/FREQ.2006.275356
O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, G. Santarelli
The paper presents an ultra-stable fibre optic link which allows to transfer frequency reference signal between two research laboratories. The link is composed of two 43 km twin optical fibres of the Paris telecommunications network that rely the LPL to LNE-SYRTE. The stability of the transferred signal is degraded by mechanical vibration and temperature variation along the fibre. To correct these effects a compensation system has been developed who acts directly on the fibre length, with a variable optical delay line
{"title":"Fiber frequency dissemination with resolution in the 10-18 range","authors":"O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, G. Santarelli","doi":"10.1109/FREQ.2006.275356","DOIUrl":"https://doi.org/10.1109/FREQ.2006.275356","url":null,"abstract":"The paper presents an ultra-stable fibre optic link which allows to transfer frequency reference signal between two research laboratories. The link is composed of two 43 km twin optical fibres of the Paris telecommunications network that rely the LPL to LNE-SYRTE. The stability of the transferred signal is degraded by mechanical vibration and temperature variation along the fibre. To correct these effects a compensation system has been developed who acts directly on the fibre length, with a variable optical delay line","PeriodicalId":445945,"journal":{"name":"2006 IEEE International Frequency Control Symposium and Exposition","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116717954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-06-04DOI: 10.1109/FREQ.2006.275449
Babak Menbari, A. Suratgar
In this paper a low power-low voltage operational transconductance amplifier and capacitor (OTA-C) oscillator based on a CMOS transconductor is proposed. The frequency of proposed VCO is controlled by adaptive neural network. OTA-C uses output cross coupled and interpolation. In this paper, a frequency tuning circuit for VCOs is introduced, so that the final relationship between oscillating frequency and input voltage is fixed and independent of the non-idealities. The adaptive neural network is applied for control of nonlinear parameters. The circuit has been fabricated in a standard 0.13mum CMOS process. Simulation results show a frequency tuning range from 52 to 164 MHz. The circuit uses 2V power supply with maximum 1.8 mW power consumption
本文提出了一种基于CMOS晶体管的低功耗、低电压跨导运算放大器和电容振荡器。采用自适应神经网络控制压控振荡器的频率。OTA-C使用输出交叉耦合和插值。本文介绍了一种用于压控振荡器的频率调谐电路，使振荡频率与输入电压之间的最终关系是固定的，并且不受非理想性的影响。将自适应神经网络应用于非线性参数的控制。该电路采用标准的0.13 μ m CMOS工艺制造。仿真结果表明，频率调谐范围为52 ~ 164 MHz。电路采用2V电源，最大功耗1.8 mW
{"title":"A Low- Power Low-Voltage VCO with Wide Range Tuning Controlled by Adaptive Neural Network","authors":"Babak Menbari, A. Suratgar","doi":"10.1109/FREQ.2006.275449","DOIUrl":"https://doi.org/10.1109/FREQ.2006.275449","url":null,"abstract":"In this paper a low power-low voltage operational transconductance amplifier and capacitor (OTA-C) oscillator based on a CMOS transconductor is proposed. The frequency of proposed VCO is controlled by adaptive neural network. OTA-C uses output cross coupled and interpolation. In this paper, a frequency tuning circuit for VCOs is introduced, so that the final relationship between oscillating frequency and input voltage is fixed and independent of the non-idealities. The adaptive neural network is applied for control of nonlinear parameters. The circuit has been fabricated in a standard 0.13mum CMOS process. Simulation results show a frequency tuning range from 52 to 164 MHz. The circuit uses 2V power supply with maximum 1.8 mW power consumption","PeriodicalId":445945,"journal":{"name":"2006 IEEE International Frequency Control Symposium and Exposition","volume":"364 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114011032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-06-04DOI: 10.1109/FREQ.2006.275492
D. Gachon, G. Lengaigne, L. Gauthier-Manuel, V. Laude, S. Ballandras
Bulk acoustic waves excited in thin piezoelectric films have revealed their capabilities for addressing the problem of high frequency RF filters (above 1 GHz). In this paper, we propose an alternative to thin film deposition consisting in single crystal wafers bonded on a substrate (for instance silicon or glass) and thinned, allowing for plate thickness close to 10 mum. This has been achieved on 3 inches wafers and allows for an accurate selection of the wave characteristics. More, the properties of the piezoelectric material are found conform with tabulated values, enabling one to reliably design any passive signal processing device
{"title":"Development of high frequency bulk acoustic wave resonator using thinned single-crystal Lithium Niobate","authors":"D. Gachon, G. Lengaigne, L. Gauthier-Manuel, V. Laude, S. Ballandras","doi":"10.1109/FREQ.2006.275492","DOIUrl":"https://doi.org/10.1109/FREQ.2006.275492","url":null,"abstract":"Bulk acoustic waves excited in thin piezoelectric films have revealed their capabilities for addressing the problem of high frequency RF filters (above 1 GHz). In this paper, we propose an alternative to thin film deposition consisting in single crystal wafers bonded on a substrate (for instance silicon or glass) and thinned, allowing for plate thickness close to 10 mum. This has been achieved on 3 inches wafers and allows for an accurate selection of the wave characteristics. More, the properties of the piezoelectric material are found conform with tabulated values, enabling one to reliably design any passive signal processing device","PeriodicalId":445945,"journal":{"name":"2006 IEEE International Frequency Control Symposium and Exposition","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131562438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-06-04DOI: 10.1109/FREQ.2006.275427
S. Romisch, R. Lutwak
The chip-scale atomic clock (CSAC) requires a microwave source to interrogate the Cs ground-state hyperfine resonance in a scheme where the oscillator's frequency is half of the 9.2 GHz resonance frequency. This paper describes the design and implementation of a 4.6 GHz voltage-controlled oscillator (VCO) with relative frequency stability of 6.5middot10-9 for measurement times of 1 second. The tuning range has been measured to be larger than 4 MHz. The VCO is designed using a modified Colpitts circuit topology and has a power consumption of about 10 mW. Similar oscillators have been demonstrated which exhibit slightly lower power consumption but 5 times worse frequency stability (Brannon, 2005)
{"title":"Low-power, 4.6-GHz, Stable Oscillator for CSAC.","authors":"S. Romisch, R. Lutwak","doi":"10.1109/FREQ.2006.275427","DOIUrl":"https://doi.org/10.1109/FREQ.2006.275427","url":null,"abstract":"The chip-scale atomic clock (CSAC) requires a microwave source to interrogate the Cs ground-state hyperfine resonance in a scheme where the oscillator's frequency is half of the 9.2 GHz resonance frequency. This paper describes the design and implementation of a 4.6 GHz voltage-controlled oscillator (VCO) with relative frequency stability of 6.5middot10-9 for measurement times of 1 second. The tuning range has been measured to be larger than 4 MHz. The VCO is designed using a modified Colpitts circuit topology and has a power consumption of about 10 mW. Similar oscillators have been demonstrated which exhibit slightly lower power consumption but 5 times worse frequency stability (Brannon, 2005)","PeriodicalId":445945,"journal":{"name":"2006 IEEE International Frequency Control Symposium and Exposition","volume":"213 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121241574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-06-04DOI: 10.1109/FREQ.2006.275389
R. Boroditsky, J. Gomez, S. San-Pedro
Modern wireless communication equipment, point-to-point and point-to-multipoint microwave digital radios, radar equipment, microwave sources require high stability, low power consumption, and very low phase noise frequency sources in UHF band. Existing TCXO solutions can achieve -150 dBc/Hz phase noise floor at the carrier frequency of 100 MHz. The goal of this work was to create a 500 MHz TCXO with Stratum-3 stability performance (0.28 ppm over temperature, 4.6 ppm over all conditions), which can reach -155 dBc/Hz noise floor, -120 dBc/Hz at 1 KHz offset from the carrier, while providing +7 dBm of output power. The goal was accomplished by integrating in a small SMD package high performance, low frequency, Stratum-3 digitally compensated reference TCXO, low noise off-the-shelf phase locked loop (PLL) IC, and ultra low noise 500 MHz VCXO. The key solutions for this development besides solid digitally compensated TCXO design were optimization of the PLL circuit, and design of a VCXO. The VCXO is based on a 3rd overtone 100 MHz AT-cut crystal resonator with relatively high Q, passive band-pass filter, tuned on the fifth harmonic of the 100 MHz VCXO, and a free-running L-C oscillator, which is injection locked to the above mentioned fifth harmonic of the VCXO. The resulting device performance met all the stated goals and even somewhat exceeded the phase noise expectations. The sub-harmonic suppression was better than 50 dBc
{"title":"Ultra Low Phase Noise Stratum-3 TCXO with High Output Power","authors":"R. Boroditsky, J. Gomez, S. San-Pedro","doi":"10.1109/FREQ.2006.275389","DOIUrl":"https://doi.org/10.1109/FREQ.2006.275389","url":null,"abstract":"Modern wireless communication equipment, point-to-point and point-to-multipoint microwave digital radios, radar equipment, microwave sources require high stability, low power consumption, and very low phase noise frequency sources in UHF band. Existing TCXO solutions can achieve -150 dBc/Hz phase noise floor at the carrier frequency of 100 MHz. The goal of this work was to create a 500 MHz TCXO with Stratum-3 stability performance (0.28 ppm over temperature, 4.6 ppm over all conditions), which can reach -155 dBc/Hz noise floor, -120 dBc/Hz at 1 KHz offset from the carrier, while providing +7 dBm of output power. The goal was accomplished by integrating in a small SMD package high performance, low frequency, Stratum-3 digitally compensated reference TCXO, low noise off-the-shelf phase locked loop (PLL) IC, and ultra low noise 500 MHz VCXO. The key solutions for this development besides solid digitally compensated TCXO design were optimization of the PLL circuit, and design of a VCXO. The VCXO is based on a 3rd overtone 100 MHz AT-cut crystal resonator with relatively high Q, passive band-pass filter, tuned on the fifth harmonic of the 100 MHz VCXO, and a free-running L-C oscillator, which is injection locked to the above mentioned fifth harmonic of the VCXO. The resulting device performance met all the stated goals and even somewhat exceeded the phase noise expectations. The sub-harmonic suppression was better than 50 dBc","PeriodicalId":445945,"journal":{"name":"2006 IEEE International Frequency Control Symposium and Exposition","volume":"19 2-3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134179009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-06-04DOI: 10.1109/FREQ.2006.275358
Jianke Du, Xiaoying Jin, Ji Wang, Yun-ying Zhou
Propagation of SH waves in a circular cylindrical layered piezoelectric structure with initial stress is investigated analytically, the governing equations of the coupled waves are reduced to Bessel equation and Laplace equation. The boundary conditions are assumed that the displacements, shear stress, electric potential, and electric displacements are continuous across the interface between the layer and the substrate together with the traction free at the surface of the layer. The electrically open and short conditions at cylindrical surface are adopted to solve the problem. The phase velocity is numerically calculated for the electric open and short cases, respectively, for different thickness of the layer and wave number. The effect of the initial stress on the phase velocity and the electromechanical coupling factor are discussed in detail for piezoelectric ceramics PZT-5H. The authors find that the initial stress has an important effect on the SH wave propagation in a circular cylindrical layered structure
{"title":"SH Waves in a Circular Cylindrical Layered Piezoelectric Structure with Initial Stress","authors":"Jianke Du, Xiaoying Jin, Ji Wang, Yun-ying Zhou","doi":"10.1109/FREQ.2006.275358","DOIUrl":"https://doi.org/10.1109/FREQ.2006.275358","url":null,"abstract":"Propagation of SH waves in a circular cylindrical layered piezoelectric structure with initial stress is investigated analytically, the governing equations of the coupled waves are reduced to Bessel equation and Laplace equation. The boundary conditions are assumed that the displacements, shear stress, electric potential, and electric displacements are continuous across the interface between the layer and the substrate together with the traction free at the surface of the layer. The electrically open and short conditions at cylindrical surface are adopted to solve the problem. The phase velocity is numerically calculated for the electric open and short cases, respectively, for different thickness of the layer and wave number. The effect of the initial stress on the phase velocity and the electromechanical coupling factor are discussed in detail for piezoelectric ceramics PZT-5H. The authors find that the initial stress has an important effect on the SH wave propagation in a circular cylindrical layered structure","PeriodicalId":445945,"journal":{"name":"2006 IEEE International Frequency Control Symposium and Exposition","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121727000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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