Journal of Electroceramics

, Volume 35, Issue 1–4, pp 1–10 | Cite as

Losses in piezoelectrics derived from a new equivalent circuit

  • Weijia Shi
  • Husain N. Shekhani
  • Hui Zhao
  • Jie Ma
  • Yu Yao
  • Kenji Uchino


Miniaturization of piezoelectric devices such as ultrasonic motors, transformers, and sound projectors requires high power density maintained in the piezoelectric materials. During operation, heat generation due to material losses, however, hinders the realization of high power density. As a result, it is very important to understand the loss mechanisms in piezoelectric materials to successfully realize device miniaturization and at the same time maintain a good device performance. There are three fundamental losses in piezoelectric materials: dielectric, elastic, and piezoelectric. The first two components have been intensively investigated, whereas piezoelectric loss has not received much attention, which leaves some phenomena inexplicable. To verify its significance, in this paper, a new methodology has been presented to calculate the dielectric, elastic and piezoelectric losses based on a new equivalent circuit (EC) deduced from the revised Hamilton’s Principle. The improvement of the new methodology lies in the fact that all the three losses, including the piezoelectric loss, have been fully taken in consideration. The derivations and the calculation results indicate that the piezoelectric loss is not only non-negligible, but is also larger than other two components for hard PZT materials. The significance of the piezoelectric loss component has been therefore verified. During the above verification process, an elegant and concise measuring procedure of all the losses, including piezoelectric component, has been presented from an EC aspect for the first time. The calculation and measurement also indicate that the largest mechanical quality factor exists at a frequency between resonance and antiresonance, which may suggest a new optimal working frequency for piezoelectric devices from the loss reduction viewpoint.


Electromechanical system Equivalent circuit Hamilton’s principle Loss Piezoelectrics 



This work was supported by the funding of the China Scholarship Council (CSC).


  1. 1.
    G.E. Martin, Proc. of IEEE Ultrason. Symp., 613 (1974)Google Scholar
  2. 2.
    T. Ikeda, Fundamentals of Piezoelectric Materials Science (Ohm Publication, Tokyo, 1984), p. 83Google Scholar
  3. 3.
    Y. Zhuang, S.O. Ural, S. Tuncdemir, A. Amin, K. Uchino, Jan. J. Appl. Phys. 49, 021503 (2010)CrossRefGoogle Scholar
  4. 4.
    D. Damjanovic, T.R. Gururaja, S.J. Jang, L.E. Cross, Mat. Lett. 4, 414 (1986)CrossRefGoogle Scholar
  5. 5.
    Y. Zhuang, S.O. Ural, A. Rajapurkar, S. Tuncdemir, A. Amin, K. Uchino, Jan. J. Appl. Phys. 48, 041401 (2009)CrossRefGoogle Scholar
  6. 6.
    W.P. Mason, Proc. I.R.E. 23, 1252 (1935)CrossRefGoogle Scholar
  7. 7.
    D. Damjanovic, Ferroelect. 110, 129 (1990)CrossRefGoogle Scholar
  8. 8.
    N.W. Hagood IV, A.J. McFarland, IEEE Trans. Ultrason., Ferroelect., and Freq. Cont. 42, 210 (1995)CrossRefGoogle Scholar
  9. 9.
    N. Hagood, W. Chung, A.V. Flotow, J. Intell. Mat., Syst., and Struct. 1, 327 (1990)CrossRefGoogle Scholar
  10. 10.
    E.F. Crawley, K.B. Lazarus, AIAA J. 29, 944 (1990)CrossRefGoogle Scholar
  11. 11.
    K. Uchino, S. Hirose, IEEE Trans. Ultrason., Ferroelect., and Freq. Cont. 48, 307 (2001)CrossRefGoogle Scholar
  12. 12.
    R. Holland, E.P. EerNisse, IEEE Trans. Sonics Ultrason. 16, 173 (1969)CrossRefGoogle Scholar
  13. 13.
    W.G. Cady, Proc. I.R.E. 10, 83 (1922)CrossRefGoogle Scholar
  14. 14.
    K.H. Hӓrdtl, Ceram. Int. 8, 121 (2001)CrossRefGoogle Scholar
  15. 15.
    K. Uchino, J.H. Zheng, Y.H. Chen, X.H. Du, J. Ryu, Y. Gao, S. Ural, J. Mater. Sci. 41, 217 (2006)CrossRefGoogle Scholar
  16. 16.
    R. Holland, IEEE Trans. Sonics Ultrason. 14, 18 (1967)CrossRefGoogle Scholar
  17. 17.
    B. Richter, J. Twiefel, J. Wallaschek, in Energy Harvesting Technologies, ed. by S. Priya, D.J. Inman (Springer, New York, 2009), p. 114Google Scholar
  18. 18.
    IEEE Standard 177, (1966)Google Scholar
  19. 19.
    APC International, Ltd., Mackeyville, PA, (2013)Google Scholar
  20. 20.
    S.O. Ural, S. Tuncdemir, Y. Zhuang, K. Uchino, Jan. J. Appl. Phys. 48, 056509 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Weijia Shi
    • 1
  • Husain N. Shekhani
    • 2
  • Hui Zhao
    • 1
  • Jie Ma
    • 1
  • Yu Yao
    • 1
  • Kenji Uchino
    • 2
  1. 1.Control and Simulation Center, School of AstronauticsHarbin Institute of TechnologyHarbinChina
  2. 2.International Center for Actuators and Transducers, Materials Research InstitutePennsylvania State UniversityUniversity ParkUSA

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