Mathematical Model of Multi-Frequency Piezoresonance Oscillation System

Alexander A. Zelensky; Sergey K. Pidchenko; Alla A. Taranchuk

doi:doi:10.11648/j.com.20130101.11

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Mathematical Model of Multi-Frequency Piezoresonance Oscillation System

Alexander A. Zelensky, Sergey K. Pidchenko, Alla A. Taranchuk

Published in Communications (Volume 1, Issue 1)

Published: 10 January 2013

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Abstract

The paper represents the basic model of multi-frequency piezoresonance oscillation system (MPOS) – the piezoresonance devices (PRD) core, which enables to study the processes of establishing multi-frequency oscillation mode and its stability. The basic structure of multi-channel multi-frequency PRD core, which is based on principles of filter schemes, is proposed, and the main designations are entered. The peculiarities of truncated differential equations for amplitude, phase and auto-bias voltage of MPOS for the quantity of simultaneously generated frequencies are examined. On the example of three-frequency mode of oscillation under polynomial approximation of transferable characteristics of active elements the characteristic cases of establishing oscillations in MPOS are represented. The area of a steady three-frequency oscillating behavior is defined and the assessment of time of establishment of oscillations and value of group runout of frequencies is made. Received results enable to form a new approach to construction of piezoresonance devices with controlled dynamics, which are represented in the form of adaptive controlled systems with predictive standard model and develop on its basis the new class of invariant to destabilizing disturbing PRD factors. On the basis of such approach there is the principle of using natural redundancy in multi-frequency basis of PRD core – multi-frequency oscillation system, which enables not only to synthesize the system with current identification of disturbing factors on basis of instruments of invariance theory, but also do the adaptation of PRD in accordance with their influences.

Published in	Communications (Volume 1, Issue 1)
DOI	10.11648/j.com.20130101.11
Page(s)	1-8
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Stabilization of Oscillations, Multi-Frequency Quartz Oscillatory System, Invariant Piezoresonance System

References

[1]	Barzhin V. (1972). Multiwave quartz crystal resonator - temperature sensor / V. Barzhin, A. Zelensky, F. Kolpakov [etc.] // Electronic Engineering. Ser. 10, Radiokomponenty. - 1972. - Issue. I, Moscow, Russia - pp. 54-57.
[2]	Rosati V. (1983). State of the art in crystal oscillators, present and future / V. Rosati [etc.] // MILCOM-83. Proc. IEEE Milit., – 1983. – V.2, – P. 386 – 390.
[3]	Petrov B. Selected Works / B. Petrov, v.1. - Moscow: Nauka, 1983. - 286 p.
[4]	Kolpakov F. Using multiparameter sensitivity piezoelectric resonators in measuring devices / F. Kolpakov // Electronic Engineering. Ser. Radiodetaly and radiokomponenty. - 1985.- Issue. 2 (59), Moscow, Russia - pp. 62-66.
[5]	Mourey M. (1985). New design of a dual-mode Quartz crystal oscillator / M. Mourey, J. Vaterkovski // Electronics Letters.–1985.–V.21.–№ 5. – pp. 184 –186.
[6]	Benjaminson A., Stallings S. (1989). A Microcomputer Compensated Crystal Oscillator using a Dual-Mode Resonator // Proc. of the 43rd Annual Symposium on Frequency Control, 1989, pp. 20-26.
[7]	Schodowski S. (1989). Resonator self-temperature-sensing using a dual-harmonic-mode crystal oscillator // Proc. of the 43rd Annual Symposium on Frequency Control, – 1989, pp. 2–7.
[8]	Filler R., Vig J. (1989). Resonators for the Microcomputer Compensated Crystal Oscillator // Proc. of the 43rd Annual Symposium on Frequency Control, 1989, pp. 8-15.
[9]	Besson R. (1993). A Dual-Mode Thickness-Shear Quartz Pressure Sensor / R. Besson, J. Boy, B. Glotin [etc.] // IEEE Transaction on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 40, No. 5, pp. 584-591, Sept. 1993.
[10]	Kosykh A., Abramson I., Bagaev V. (1994). Dual-mode Crystal Oscillators With Resonators excited on B- and C- modes // Proc. of the 48th Annual Symposium on Frequency Control, 1994, pp. 578-586.
[11]	Prokopenko V. (1994). Dual Frequency crystal oscillator /V. Prokopenko // Radiotehnika, Vol. 11, ISSN 0033-8486, Moscow, Russia, pp. 24 - 26.
[12]	Shmaly Y. (1995) . The modulation method of the precision quartz-crystal oscillators and standards frequency stabilization // Proc. of the 49th Annual Symposium on Frequency Control, 1995, pp. 579-589.
[13]	Tsarapkin D. (2000). Novel technique for dual-mode quartz oscillators // Frequency Control Symposium and Exhibition, 2000. Proceedings of the 2000 IEEE/EIA, 2000, pp. 425 – 429.
[14]	Oita T., Fukuda M., Nakamura A. [etc.]. (2004). Dual Mode SC-Cut Crystal Oscillator // 2004 IEEE International Ul-trasonics, Ferroelectrics, and Frequency Control Joint 50th Anniversary Conference, 2004, pp.436-442.
[15]	Stofanik V., Balaz I., Minarik M. (2007). Dual-Mode Crystal Oscillator with Simultaneous Excitation of Two Overtones in a Stress Compensated Quartz Resonator // Proceedings of the joint 2007 European Frequency and Time Forum and the 2007 IEEE International Frequency Control Symposium, 2007, pp. 227-229.
[16]	Kolpakov F., Pidchenko S. (2011). Theory and fundamentals implementation of invariant piezoresonance systems // Pub-lished by National Aerospace University (KhAI), ISBN 978-966-662-222-1, Kharkov, Ukraine.
[17]	Zelensky A., Pidchenko S. (2011). Principles of invariant piezoresonance oscillatory systems // 4th International Radio Electronic Forum (IREF’2011): Proceedings of the Interna-tional Conference ICTST’2011, October 18-21, Kharkov, Ukraine, Vol. 2, pp. 32-35.
[18]	Kolpakov F., Pidchenko S., Taranchuk A. (2008). Invariant piezoresonance oscillatory systems // Measuring and Com-puting Devices in Technological Processes, Vol. 1, Khmel-nitsky national university, ISSN 2219-9365, Khmelnitsky, Ukraine, pp. 174-190.
[19]	Pidchenko S., Taranchuk A. (2004). Identification of the thermal state of the crystal at the stage of oscillation // Ra-dioelectronic and computer system, Vol. 3, National Aerospace University (KhAI), ISSN 1814-4225, Kharkov, Ukraine, pp. 36-42.
[20]	Taranchuk A., Pidchenko S. (2005). Modelling of thermal processes in the piezoresonance sensors with modulated in-terelectrode gap // Khmelnitsky State University's bulletin, Vol. 1, Khmelnitsky national university, ISBN 978-966-330-114-3, Khmelnitsky, Ukraine, pp. 218-222.
[21]	Pidchenko S. Taranchuk A., Stetsyuk V. (2011). Mathe-matical modeling force-frequency characteristics of the quartz resonators // Radioelectronic and computer system, Vol. 2, National Aerospace University (KhAI), ISSN 1814-4225, Kharkov, Ukraine, pp. 27 – 31.
[22]	Zelensky A., Pidchenko S., Taranchuk A. (2012). Multifre-quency core structure of an invariant quartz oscillatory system //11th International Conference on "Modern Problems of Radio Engineering, Telecommunications and Computer Science" (TCSET’2012). Lviv-Slavske, Ukraine, 2012. –P. 125.
[23]	Kolpakov F., Pidchenko S., Hilchenko G. (1997). Features of setting process of the oscillations in the multi-channel multi-frequency crystal oscillator // Radiotehnika, Vol. 12, ISSN 0033-8486, Moscow, Russia, pp. 95 - 98.
[24]	Kolpakov F., Pidchenko S., Hilchenko G. (1999). Minimiza-tion of settling time of oscillations in multi-channel mul-ti-frequency crystal oscillator // Radiotehnika, Vol. 2, ISSN 0033-8486, Moscow, Russia, pp. 42 - 44.
[25]	Pidchenko S., Kolpakov F., Akulinichev A. (2000). Analysis of the characteristics of multi-frequency controlled crystal oscillator // Measuring and Computing Devices in Technol-ogical Processes, Vol. 3, Khmelnitsky national university, ISSN 2219-9365, Khmelnitsky, Ukraine, pp. 70-75.
[26]	Kolpakov F., Pidchenko S. (1999). Syntheses of many- channel multifrequency quartz crystal oscillators with reduced (shortened) time of adjusting oscillations // Zarubejnaya radioelectronica, Vol. 11, ISSN 0373-2428, Moscow, Russia, pp. 60 - 65.
[27]	Taranchuk A. , Pidchenko S., Opolska A. (2010). Utilization Features of the Mexanotron for Information Measurement Systems // Modern Problems of Radio Engineering, Tele-communication and Computer Science: Procedings of the Xth International Conference TCSET’2010. February 23-27, 2010. – Lviv-Slavske, Ukraine. – P. 358.
[28]	Taranchuk A., Pidchenko S. (2012). Design Methodology to Construct Information Measuring Systems Built on Piezo-resonant Mechanotrons with a Modulated Interelectrode Gap// Applied Measurement System. Published by InTech, ISBN 978-953-51-0103-1, Janeza Trdine 9, 51000 Rijeka, Croatia, 2012, pp. 229-258.
[29]	Taranchuk A., Pidchenko S., Mishan V. (2012). Frequen-cy-сompensated piezoresonance oscillator system with external MEMS control V. // 11th International Conference on "Modern Problems of Radio Engineering, Telecommuni-cations and Computer Science" (TCSET’2012). Lviv-Slavske, Ukraine, 2012. – P. 458.
[30]	Kolpakov F., Slavinsky S. (2004). The sphyg¬mogra¬phy measuring converter "pressure-fre¬quen¬cy" dynamic charac-teris¬tics examination // Measurement Sci¬ence Review, Vol. 4, Sect. 2, pp. 52-58.

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APA Style

Alexander A. Zelensky, Sergey K. Pidchenko, Alla A. Taranchuk. (2013). Mathematical Model of Multi-Frequency Piezoresonance Oscillation System. Communications, 1(1), 1-8. https://doi.org/10.11648/j.com.20130101.11

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ACS Style

Alexander A. Zelensky; Sergey K. Pidchenko; Alla A. Taranchuk. Mathematical Model of Multi-Frequency Piezoresonance Oscillation System. Communications. 2013, 1(1), 1-8. doi: 10.11648/j.com.20130101.11

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AMA Style

Alexander A. Zelensky, Sergey K. Pidchenko, Alla A. Taranchuk. Mathematical Model of Multi-Frequency Piezoresonance Oscillation System. Communications. 2013;1(1):1-8. doi: 10.11648/j.com.20130101.11

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@article{10.11648/j.com.20130101.11,
  author = {Alexander A. Zelensky and Sergey K. Pidchenko and Alla A. Taranchuk},
  title = {Mathematical Model of Multi-Frequency Piezoresonance Oscillation System},
  journal = {Communications},
  volume = {1},
  number = {1},
  pages = {1-8},
  doi = {10.11648/j.com.20130101.11},
  url = {https://doi.org/10.11648/j.com.20130101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.com.20130101.11},
  abstract = {The paper represents the basic model of multi-frequency piezoresonance oscillation system (MPOS) – the piezoresonance devices (PRD) core, which enables to study the processes of establishing multi-frequency oscillation mode and its stability. The basic structure of multi-channel multi-frequency PRD core, which is based on principles of filter schemes, is proposed, and the main designations are entered. The peculiarities of truncated differential equations for amplitude, phase and auto-bias voltage of MPOS for the quantity of simultaneously generated frequencies   are examined. On the example of three-frequency mode of oscillation under polynomial approximation of transferable characteristics of active elements the characteristic cases of establishing oscillations in MPOS are represented. The area of a steady three-frequency oscillating behavior is defined and the assessment of time of establishment of oscillations and value of group runout of frequencies is made. Received results enable to form a new approach to construction of piezoresonance devices  with controlled dynamics, which are represented in the form of adaptive controlled systems with predictive standard model and develop on its basis the new class of invariant to destabilizing disturbing PRD factors. On the basis of such approach there is the principle of using natural redundancy in multi-frequency basis of PRD core – multi-frequency oscillation system, which enables not only to synthesize the system with current identification of disturbing factors on basis of instruments of invariance theory, but also do the adaptation of PRD in accordance with their influences.},
 year = {2013}
}

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TY  - JOUR
T1  - Mathematical Model of Multi-Frequency Piezoresonance Oscillation System
AU  - Alexander A. Zelensky
AU  - Sergey K. Pidchenko
AU  - Alla A. Taranchuk
Y1  - 2013/01/10
PY  - 2013
N1  - https://doi.org/10.11648/j.com.20130101.11
DO  - 10.11648/j.com.20130101.11
T2  - Communications
JF  - Communications
JO  - Communications
SP  - 1
EP  - 8
PB  - Science Publishing Group
SN  - 2328-5923
UR  - https://doi.org/10.11648/j.com.20130101.11
AB  - The paper represents the basic model of multi-frequency piezoresonance oscillation system (MPOS) – the piezoresonance devices (PRD) core, which enables to study the processes of establishing multi-frequency oscillation mode and its stability. The basic structure of multi-channel multi-frequency PRD core, which is based on principles of filter schemes, is proposed, and the main designations are entered. The peculiarities of truncated differential equations for amplitude, phase and auto-bias voltage of MPOS for the quantity of simultaneously generated frequencies   are examined. On the example of three-frequency mode of oscillation under polynomial approximation of transferable characteristics of active elements the characteristic cases of establishing oscillations in MPOS are represented. The area of a steady three-frequency oscillating behavior is defined and the assessment of time of establishment of oscillations and value of group runout of frequencies is made. Received results enable to form a new approach to construction of piezoresonance devices  with controlled dynamics, which are represented in the form of adaptive controlled systems with predictive standard model and develop on its basis the new class of invariant to destabilizing disturbing PRD factors. On the basis of such approach there is the principle of using natural redundancy in multi-frequency basis of PRD core – multi-frequency oscillation system, which enables not only to synthesize the system with current identification of disturbing factors on basis of instruments of invariance theory, but also do the adaptation of PRD in accordance with their influences.
VL  - 1
IS  - 1
ER  -

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Author Information

Alexander A. Zelensky

N.E. Zhukovsky National Aerospace University ?KhAI?, Kharkov, Ukraine
Sergey K. Pidchenko

Khmelnitskiy National University, Khmelnitskiy, Ukraine
Alla A. Taranchuk

Khmelnitskiy National University, Khmelnitskiy, Ukraine

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APA Style

Alexander A. Zelensky, Sergey K. Pidchenko, Alla A. Taranchuk. (2013). Mathematical Model of Multi-Frequency Piezoresonance Oscillation System. Communications, 1(1), 1-8. https://doi.org/10.11648/j.com.20130101.11

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ACS Style

Alexander A. Zelensky; Sergey K. Pidchenko; Alla A. Taranchuk. Mathematical Model of Multi-Frequency Piezoresonance Oscillation System. Communications. 2013, 1(1), 1-8. doi: 10.11648/j.com.20130101.11

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AMA Style

Alexander A. Zelensky, Sergey K. Pidchenko, Alla A. Taranchuk. Mathematical Model of Multi-Frequency Piezoresonance Oscillation System. Communications. 2013;1(1):1-8. doi: 10.11648/j.com.20130101.11

Copy | Download

@article{10.11648/j.com.20130101.11,
  author = {Alexander A. Zelensky and Sergey K. Pidchenko and Alla A. Taranchuk},
  title = {Mathematical Model of Multi-Frequency Piezoresonance Oscillation System},
  journal = {Communications},
  volume = {1},
  number = {1},
  pages = {1-8},
  doi = {10.11648/j.com.20130101.11},
  url = {https://doi.org/10.11648/j.com.20130101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.com.20130101.11},
  abstract = {The paper represents the basic model of multi-frequency piezoresonance oscillation system (MPOS) – the piezoresonance devices (PRD) core, which enables to study the processes of establishing multi-frequency oscillation mode and its stability. The basic structure of multi-channel multi-frequency PRD core, which is based on principles of filter schemes, is proposed, and the main designations are entered. The peculiarities of truncated differential equations for amplitude, phase and auto-bias voltage of MPOS for the quantity of simultaneously generated frequencies   are examined. On the example of three-frequency mode of oscillation under polynomial approximation of transferable characteristics of active elements the characteristic cases of establishing oscillations in MPOS are represented. The area of a steady three-frequency oscillating behavior is defined and the assessment of time of establishment of oscillations and value of group runout of frequencies is made. Received results enable to form a new approach to construction of piezoresonance devices  with controlled dynamics, which are represented in the form of adaptive controlled systems with predictive standard model and develop on its basis the new class of invariant to destabilizing disturbing PRD factors. On the basis of such approach there is the principle of using natural redundancy in multi-frequency basis of PRD core – multi-frequency oscillation system, which enables not only to synthesize the system with current identification of disturbing factors on basis of instruments of invariance theory, but also do the adaptation of PRD in accordance with their influences.},
 year = {2013}
}

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TY  - JOUR
T1  - Mathematical Model of Multi-Frequency Piezoresonance Oscillation System
AU  - Alexander A. Zelensky
AU  - Sergey K. Pidchenko
AU  - Alla A. Taranchuk
Y1  - 2013/01/10
PY  - 2013
N1  - https://doi.org/10.11648/j.com.20130101.11
DO  - 10.11648/j.com.20130101.11
T2  - Communications
JF  - Communications
JO  - Communications
SP  - 1
EP  - 8
PB  - Science Publishing Group
SN  - 2328-5923
UR  - https://doi.org/10.11648/j.com.20130101.11
AB  - The paper represents the basic model of multi-frequency piezoresonance oscillation system (MPOS) – the piezoresonance devices (PRD) core, which enables to study the processes of establishing multi-frequency oscillation mode and its stability. The basic structure of multi-channel multi-frequency PRD core, which is based on principles of filter schemes, is proposed, and the main designations are entered. The peculiarities of truncated differential equations for amplitude, phase and auto-bias voltage of MPOS for the quantity of simultaneously generated frequencies   are examined. On the example of three-frequency mode of oscillation under polynomial approximation of transferable characteristics of active elements the characteristic cases of establishing oscillations in MPOS are represented. The area of a steady three-frequency oscillating behavior is defined and the assessment of time of establishment of oscillations and value of group runout of frequencies is made. Received results enable to form a new approach to construction of piezoresonance devices  with controlled dynamics, which are represented in the form of adaptive controlled systems with predictive standard model and develop on its basis the new class of invariant to destabilizing disturbing PRD factors. On the basis of such approach there is the principle of using natural redundancy in multi-frequency basis of PRD core – multi-frequency oscillation system, which enables not only to synthesize the system with current identification of disturbing factors on basis of instruments of invariance theory, but also do the adaptation of PRD in accordance with their influences.
VL  - 1
IS  - 1
ER  -

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