Open Access Open Access  Restricted Access Subscription Access
Relationships of contribution of expansion terms as function of angle for the first resonance frequency

Determination of biconical cavity eigenfrequencies using method of partial intersecting regions and approximation by rational fractions

M. V. Andreev, Oleg O. Drobakhin, D. Yu. Saltykov, N. B. Gorev, I. F. Kodzhespirova


The paper considers the problem of determining the eigenfrequencies of biconical cavity making it possible to simplify the eigenfrequency-based design of devices. We used the solving of the excitation problem for biconical cavity using the method of partial intersecting regions in combination with the collocation method. Based on the concept of the search of quasisolution for determining eigenfrequencies, it was proposed to apply the fractionally rational approximation of cavity response obtained as a result of solving the problem of resonator excitation. The efficiency of finding eigenfrequencies of biconical cavity was substantiated by using the fractionally rational approximation based on the chain fraction interpolation of cavity response calculated only at collocation points. Using the above approach, we have obtained the relationship of eigenfrequencies of azimuth-symmetric oscillations of biconical cavity as a function of the aperture angle, and the typing of lower azimuth-symmetric transverse electric modes of biconical cavity has been performed.


biconical cavity; eigenfrequency; method of partial intersecting regions; collocation method; quasisolution; fractionally rational approximation

Full Text:



Cullen, A.L. “Millimeter-wave open-resonator techniques,” Infrared and Millimeter Waves, v.10, p.233, 1983.

Afsar, M.N.; Button, K.J. “Millimeter-wave dielectric measurement of materials,” Proc. IEEE, v.73, n.1, p.131, 1985. DOI:

Kuzmichev, I.K.; Melezhik, P.N.; Poyedinchuk, A.Ye. “An open resonator for physical studies,” Int. J. Infrared Millimeter Waves, v.27, n.6, p.857, 2006. DOI:

Kuzmichev, I.K.; Popkov, A.Yu. “Resonant systems for measurement of electromagnetic properties of substances at V-band frequencies,” in: Emerging Microwave Technologies in Industrial, Agricultural, Medical and Food Processing. London: IntechOpen, 2018, Ch.3, p.27-53. URI:

Karpisz, T.; Salski, B.; Kopyt, P.; Krupka, J. “Measurement of dielectrics from 20 to 50 GHz with a Fabry-Pérot open resonator,” IEEE Trans. Microwave Theory Tech., v.67, n.5, p.1901, 2019. DOI:

Kovtun, Yu.V.; Pinos, I.B.; Ozerov, A.N.; Skibenko, A.I.; Skibenko, E.I.; Yuferov, V.B. “Microwave device on the basis of a barrel resonator for determining the average density and the density profile in plasma formations,” Ukrainian J. Phys., v.60, n.11, p.1101, 2015. DOI:

Rashidian, A.; Shafai, L.; Klymyshyn, D.; Shafai, C. “A fast and efficient free-space dielectric measurement technique at mm-wave frequencies,” IEEE Antennas Wireless Propag. Lett., v.16, p.2630, 2017. DOI:

Burtovoi, D.P.; Mironenko, V.L.; Tereshchenko, A.I. “Application of open cylindrical evanescent-mode resonator for investigating the dielectric properties of matter,” Izv. Vyssh. Ucheb. Zaved, Radioelek., v.13, n.9, p.1085, 1970.

Nagenthiram, P.; Cullen, A.L. “A microwave barrel resonator for permittivity measurements on dielectric rods,” Proc. IEEE, v.62, n.11, p.1613, 1974. DOI:

Andreev, M.V.; Drobakhin, O.O.; Privalov, Ye.N.; Saltykov, D.Yu. “Measurement of dielectric material properties using coupled biconical resonators,” Telecommun. Radio Eng., v.73, n.11, p.1017, 2014. DOI:

Alimov, A.A.; Radionov, A.A. “The open limit biconical resonator calculation,” Antennas, n.4, p.40, 2015. URI:

Katsenelenbaum, B.Z.; del Rio, L. Mercader; Pereyaslavets, M.; Ayza, M. Sorolla; Thumm, M. Theory of Nonuniform Waveguides: The Cross-Section Method. London: IEE, 1998. DOI:

Van’t Hof, J.P.; Stancil, D.D. “Eigenfrequencies of a truncated conical resonator via the classical and Wentzel-Kramers-Brillouin methods,” IEEE Trans. Microwave Theory Tech., v.56, n.8, p.1909, 2008. DOI:

Kuryliak, D.B.; Nazarchuk, Z.T.; Trishchuk, O.B. “Axially-symmetric TM-waves diffraction by sphere-conical cavity,” PIER B, v.73, p.1, 2017. DOI:

Kuryliak, D.B.; Sharabura, O.M. “Diffraction of axially-symmetric TM-wave from bi-cone formed by finite and semi-infinite shoulders,” PIER B, v.68, p.73, 2016. DOI:

Savin, K.G.; Golubeva, I.P.; Prokopenko, Yu.V. “Calculation of frequency and power characteristics of the composite metal-dielectric resonator using the method of partial regions,” Radioelectron. Commun. Syst., v.59, n.5, p.229, 2016. DOI:

Prokhoda, I.G.; Chumachenko, V.P. “The method of partial intersecting domains for the investigation of waveguide-resonator systems having a complex shape,” Radiophys. Quantum Electron., v.16, p.1219, 1973. DOI:

Hoppe, R.H.W.; Kuznetsov, Yu.A. “Overlapping domain decomposition methods with distributed Lagrange multipliers,” J. Numerical Math., v.9, n.1, p.285, 2001. DOI:

Drobakhin, O.O.; Zabolotnyy, P.I.; Privalov, Ye.N. “Approximate calculation of eigenfrequencies of biconical microwave cavities,” Radioelectron. Commun. Syst., v.56, n.3, p.127, 2013. DOI:

Andreev, M.V.; Drobakhin, O.O.; Saltykov, D.Yu.; Gorev, N.B.; Kodzhespirova, I.F. “Simple technique for biconical cavity eigenfrequency determination,” Radioelectron. Commun. Syst., v.60, n.12, p.555, 2017. DOI:

Andreev, M.V.; Drobakhin, O.O.; Saltykov, D.Yu. “Determination of the resonance frequency and the Q-factor of a half-disk dielectric resonator using fractional rational approximation,” Radio Phys. Radio Astron., v.18, n.4, p.362, 2013. URI:

© Radioelectronics and Communications Systems, 2004–2020
When you copy an active link to the material is required
ISSN 1934-8061 (Online), ISSN 0735-2727 (Print)
tel./fax +38044 204-82-31, 204-90-41