Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Metrology and Measurement Systems

The Journal of Committee on Metrology and Scientific Instrumentation of Polish Academy of Sciences

4 Issues per year

IMPACT FACTOR 2016: 1.598

CiteScore 2016: 1.58

SCImago Journal Rank (SJR) 2016: 0.460
Source Normalized Impact per Paper (SNIP) 2016: 1.228

Open Access
See all formats and pricing
More options …
Volume 24, Issue 1


A New Approach to Measurement of Frequency Shifts Using the Principle of Rational Approximations

Fabian N. Murrieta-Rico
  • Corresponding author
  • 1) Posgrado en Física de Materiales, Centro de Investigación Cientifíca y Educación Superior de Ensenada, Carretera Ensenada-Tijuana 3918, Zona Playitas, 22860 Ensenada, B. C., Mexico
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Vitalii Petranovskii
  • 2) Universidad Nacional Autónoma de México, Centro de Nanociencias y Nanotecnología, Carretera Tijuana-Ensenada Km. 107, Pedregal Playitas, 22860 Ensenada, B. C., Mexico
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Oleg Y. Sergiyenko
  • 3) Universidad Autónoma de Baja California, Instituto de Ingeniería, Calle de la Normal S/N y Blvd. Benito Juárez Col. Insurgentes Este Mexicali B. C., Mexico
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Daniel Hernandez-Balbuena
  • 4) Universidad Autónoma de Baja California, Facultad de Ingeniería, Calle de la Normal S/N y Blvd. Benito Juárez Col. Insurgentes Este Mexicali B. C., Mexico
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Lars Lindner
  • 3) Universidad Autónoma de Baja California, Instituto de Ingeniería, Calle de la Normal S/N y Blvd. Benito Juárez Col. Insurgentes Este Mexicali B. C., Mexico
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-03-20 | DOI: https://doi.org/10.1515/mms-2017-0007


When a frequency domain sensor is under the effect of an input stimulus, there is a frequency shift at its output. One of the most important advantages of such sensors is their converting a physical input parameter into time variations. In consequence, changes of an input stimulus can be quantified very precisely, provided that a proper frequency counter/meter is used. Unfortunately, it is well known in the time-frequency metrology that if a higher accuracy in measurements is needed, a longer time for measuring is required. The principle of rational approximations is a method to measure a signal frequency. One of its main properties is that the time required for measuring decreases when the order of an unknown frequency increases. In particular, this work shows a new measurement technique, which is devoted to measuring the frequency shifts that occur in frequency domain sensors. The presented research result is a modification of the principle of rational approximations. In this work a mathematical analysis is presented, and the theory of this new measurement method is analysed in detail. As a result, a new formalism for frequency measurement is proposed, which improves resolution and reduces the measurement time.

Keywords: frequency measurement; rational approximations; sensors


  • [1] Filippov, P., Strizhak, P.E., Vlasenko, N.V., Kochkin, Y.N., Serebrii, T.G. (2014). Adsorption-Desorption Dynamics of Alcohols on H-Beta and H-CMK Zeolites Nanocrystallites Studied by Quartz Crystal Microbalance Method. Adsorption Science & Technology, 32(10), 807–820.CrossrefWeb of ScienceGoogle Scholar

  • [2] Afzal, N., Iqbal, A., Mujahid, Schirhagl. (2013). Advanced vapor recognition materials for selective and fast responsive surface acoustic wave sensors: A review. Analytica Chimica Acta, 787, 36 – 49.Google Scholar

  • [3] Arnau, A. (2008). Review of Interface Electronic Systems for AT-cut Quartz Crystal Microbalance Applications in Liquids. Sensors, 8(1), 370–411.Web of ScienceCrossrefGoogle Scholar

  • [4] Casteleiro-Roca, J.L., Calvo-Rolle, J.L., Meizoso-Lopez, M.C., Piñón-Pazos, A., Rodríguez-Gómez, B.A. (2014). New approach for the QCM sensors characterization. Sensors and Actuators A: Physical, 207, 1–9.Google Scholar

  • [5] Ishii, R., Naganawa, R., Nishioka, M., Hanaoka, T. (2013). Microporous organic-inorganic nanocomposites as the receptor in the QCM sensing of toluene vapors. Analytical sciences: the international journal of the Japan Society for Analytical Chemistry, 29, 283–289.Google Scholar

  • [6] Bhasker Raj, V., Singh, H., Nimal, A.T., Tomar, M., Sharma, M.U., Gupta, V. (2013). Effect of metal oxide sensing layers on the distinct detection of ammonia using surface acoustic wave (SAW) sensors. Sensors and Actuators B: Chemical, 187, 563–573.Google Scholar

  • [7] Kikuchi, M., Shiratori, S. (2005). Quartz crystal microbalance (QCM) sensor for CH3SH gas by using polyelectrolyte-coated sol-gel film. Sensors and Actuators B: Chemical, 108(1), 564–571.CrossrefGoogle Scholar

  • [8] Bein, T., Mo, S., Mintova, S., Valtchev, V., Schoeman, B., Sterte, J. (1997). Growth of silicalite films on pre-assembled layers of nanoscale seed crystals on piezoelectric chemical sensors. Advanced Materials, 9(7), 585–589.CrossrefGoogle Scholar

  • [9] Kirianaki, N.V., Yurish, S.Y., Shpak, N.O. (2001). Methods of dependent count for frequency measurements. Measurement, 29(1), 31–50.CrossrefGoogle Scholar

  • [10] Kalisz, J. (2003). Review of methods for time interval measurements with picosecond resolution. Metrologia, 41(1), 17.CrossrefGoogle Scholar

  • [11] Johansson, S. (2005). New frequency counting principle improves resolution. Frequency Control Symposium and Exposition. Proc. of the 2005 IEEE International, 628–635.Google Scholar

  • [12] Sergiyenko, O., Hernandez Balbuena, D., Tyrsa, V., Rosas Mendez, P.L.A., Rivas Lopez, M., Hernandez, W., Podrygalo, M., Gurko, A. (2011). Analysis of jitter influence in fast frequency measurements. Measurement, 44(7), 1229–1242.CrossrefWeb of ScienceGoogle Scholar

  • [13] Murrieta-Rico, F.N., Mercorelli, P., Sergiyenko, O.Y., Petranovskii, V., Hernández-Balbuena, D., Tyrsa, V. (2015). Mathematical modelling of molecular adsorption in zeolite coated frequency domain sensors. IFAC PapersOnLine, 48(1), 41–46.CrossrefGoogle Scholar

  • [14] Sergiyenko, O.Y. (2016). The mediant method for fast mass/concentration detection in nanotechnologies. International Journal of Nanotechnology, 13(1−3), 238–249.CrossrefWeb of ScienceGoogle Scholar

  • [15] Hernandez Balbuena, D., Sergiyenko, O., Tyrsa, V., Burtseva, L., Rivas Lopez, M. (2009). Signal frequency measurement by rational approximations. Measurement, 42(1), 136–144.CrossrefWeb of ScienceGoogle Scholar

  • [16] Murrieta-Rico, F.N., Yu, O., Sergiyenko, Petranovskii, V., Hernandez Balbuena, D., Lindner, L., Tyrsa, V., Rivas-Lopez, M., Nieto-Hipolito, J.I., Karthashov, V.M. (2016). Pulse width influence in fast frequency measurements using rational approximations. Measurement, 86, 67–78.CrossrefWeb of ScienceGoogle Scholar

  • [17] Jansson, P.A. (1998). Deconvolution of Images and Spectra. New York: J. Wiley & Sons.Google Scholar

  • [18] Yu, L., Ma, X., Wu, T., Ma, Y., Shen, D., Kang, Q. (2016). Monitor the Processes of Ice Film Disappearance under a Stimulant Convection Condition and Absorption Ethanol Vapor to Ice by a Quartz Crystal Microbalance. International Journal of Electrochemical Science, 11(4), 2595−2611.CrossrefGoogle Scholar

  • [19] Sasaki, I., Tsuchiya, H., Nishioka, M., Sadakata, M., Okubo, T. (2002). Gas sensing with zeolite-coated quartz crystal microbalances-principal component analysis approach. Sensors and Actuators B: Chemical, 86(1), 26−33.CrossrefGoogle Scholar

  • [20] Sauerbrey, G. (1959). Verwendung von schwingquarzen zur wägung dünner schichten und zur mikrowägung. Zeitschrift für physik, 155(2), 206−222.Google Scholar

  • [21] Boyes, W. (2009). Instrumentation Reference Book. Butterworth-Heinemann.Google Scholar

  • [22] Allan, D.W., Barnes, J.A. (1981). A modified “Allan variance” with increased oscillator characterization ability. Thirty Fifth Annual Frequency Control Symposium IEEE.Google Scholar

About the article

Received: 2016-05-18

Accepted: 2016-08-28

Published Online: 2017-03-20

Published in Print: 2017-03-01

Citation Information: Metrology and Measurement Systems, Volume 24, Issue 1, Pages 45–56, ISSN (Online) 2300-1941, DOI: https://doi.org/10.1515/mms-2017-0007.

Export Citation

© 2017 Polish Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in