SYSTEMATIZATION OF THE FORMULAS OF THE RESONANT FERRITE ISOLATOR LOSS
DOI:
https://doi.org/10.15588/1607-3274-2022-1-2Keywords:
ferrite isolator, isolator ratio, direct loss, reverse loss, frequency properties, electrodynamics, verification, circular polarization, waveguide field distribution.Abstract
Context. The problem is to systematize and improve the models of a resonance ferrite isolator in the rectangular waveguide for the antenna-feeder devices, generating, receiving, measuring microwave equipment containing ferrite decoupling devices: ferrite isolators and circulators.
Objective. The goal of the work is to verify the formula for the losses of the resonant ferrite isolator in the direct and reverse directions, as well as the isolator ratio.
Method. The research method of the work is a critical analysis of literary sources, which was carried out, but did not bring the desired results, since it did not allow to verify the correctness of the derivation of the formula [17]. Therefore, a number of hypotheses were put forward, what the formula might mean. The difficulty lay in the presence in the formula of the product of trigonometric functions that can be attributed to frequency properties, which was taken as an initial hypothesis, which was not subsequently confirmed. The check included transformation of formulas using mathematical physics in terms of microwave electrodynamics, trigonometry and algebra. The beginning was the formula of the classics [16], similar to the formula of [18], accepted without proof. As it is known, for the main type of wave in a rectangular waveguide, the components of the magnetic field strength, obtained as a solution to the wave equation under the boundary conditions inherent in a rectangular waveguide. One component of the magnetic field strength is along the direction of wave propagation, and the second one is in the transverse direction in the section of the waveguide are proportional to the trigonometric functions cosine and sine with the same arguments. The equality of the two components of the strengths is traditionally uses to find the plane of circular polarization where to place the ferrite isolator, and so the authors use this proportionality to trigonometric functions in their derivation, namely the formulas of trigonometric functions of a double angle, the basic trigonometric identity sine squared plus cosine squared is equal to one for replacing the propagation constants with trigonometric functions, this allows to get rid of radicals in the formulas, these radicals in the formula are due to the phenomenon of dispersion in a rectangular waveguide. The rest of the manipulations with the formula are the reduction of similar terms.
Results. There was obtained analytical expressions for the losses of the resonant ferrite isolator in the forward and reverse directions, as well as the isolator ratio by strict mathematical transformations. There was performed such transformations. The ratios of the longitudinal propagation constant to the transverse propagation constant are replaced by the ratios of the trigonometric functions sine and cosine, since they are continuous as opposed to tangents and cotangents. Such a transformation allows to avoid square roots in the formula for the losses of the ferrite isolator in the forward and reverse directions, which are associated with the presence of dispersion in the waveguide, as in the formula for wavelength in the waveguide. The conversion is based on microwave electrodynamics. The formulas are used for the distribution of fields in a rectangular waveguide for the main type of wave. Further transformations consist in taking the common factor out of brackets and other arithmetic transformations.
Conclusions. Тhrer was obtained results partially coincide with the well-known [17], the derivation of the formula [17] was obtained for the first time, the studies carried out allowed us to reject the hypothesis that the product of cosines and sines in the loss formula of a ferrite isolator is a frequency characteristic, it appears as a result of arithmetic transformations. To take into account the frequency range, it is used that there is circular polarization at the middle frequency, there will also be circular polarization at the extreme frequency of the range, but the plane of circular polarization will shift in comparison with the position of the plane of circular polarization at the middle frequency. That is, a peculiar system of two equations is obtained with respect to two positions of the polarization plane relative to the wide side of the rectangular waveguide section. The scientific novelty consists in systematization and generalization of the formulas of the loss of the resonance ferrite isolator, the connection between the formulas from different literature sources, both foreign and domestic, is proved, which saves time for researchers of ferrite isolators for the verification of the formula. The practical significance. It may be useful for teaching purposes and in optimization of the ferrite isolator design.
References
Fuller A. B. Ferrites at microwave frequencies, IEEE electromagnetic wave series, London: Peter Peregrinus Ltd, 1987. Vol. 23, 256 p. DOI: 10.1049/PBEW023E
Kord A., Sounas D. L., Alu A. Microwave nonreciprocity, Proceedings of the IEEE, 2020, No. 108, pp. 1728–1758. DOI: 10.1109/JPROC.2020.3006041
Tong W., Wang J., Qui T. et al. Magnetically tunable ferriteloaded waveguide isolator based on magnetic photonic crystals, Progress in Electro-magnetic Research Symposium (PIERS), Shanghai, 8–11 August, 2016, pp. 409–412. DOI: 10.1109/PIERS.2016.773435
Yao J., Yang F., Li C. et al Modeling of a Ku-Band Rectangular Ferrite-Loaded Waveguide Based on Left-Handed Metamaterial, Progress In Electromagnetics Research, 2016, Vol. 51, pp. 71–81. DOI:10.2528/PIERM16082301
Sanada A., Caloz C., Itoh T. Characteristics of the composite right/left-handed transmission lines, IEEE Microwave and wireless components letters, 2004, Vol. 14(2), pp. 68– 70. DOI: 10.1109/LMWC.2003.822563
Okubo K., Kishihara M. A Study on Nonreciprocal CRLHTL Using Ferrite Volume Mode in Ferrite Loaded Rectangular Waveguide, IEEE Asia-Pacific Microwave Conference (APMC), 2019, pp. 1727–1729. DOI: 10.1109/APMC46564.2019.9038498
Mohammadi S., Ghalibafan J. Unbalanced CRLH behavior of ferriteloaded waveguide operated below cutoff frequency, Waves in Random and Complex Media, 2020, pp. 1–16. DOI: 10.1080/17455030.2020.1800133.
Mohammadi M., Kashani F. H., Ghalibafan J. A partially ferrite-filled rectangular wave-guide with CRLH response and its application to a magnetically scannable antenna, Journal of Magnetism and Magnetic Materials, 2019, Vol. 491, 165551, pp. 1–8. DOI: 10.1016/j.jmmm.2019.165551
Portela G., Dmitriev V., Zimmer D. Ferromagnetic resonance isolator based on a photonic crystal structure with terahertz vortices, Photonic Network Communications, 2020, No. 39, pp. 47–53. DOI: 10.1007/s11107-019-00871x
Dmitriev V., Zimmer D., Portela G. Vortex-based ferromagnetic resonance isolator in 2D photonic crystal waveguide, SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IMOC), 2017, pp. 1–5. DOI: 10.1109/IMOC.2017.8121044
Chaabane F., Benzina H., El Mir L., Tao J. Three- Dimensional Analysis of Ferrite-Loaded Waveguide Discontinuity by Transverse Operator Method Combined with ModeMatching Method, Progress In Electromagnetics Research, 2017, Vol. 53, pp. 1–8. DOI: 10.2528/PIERM16101703
Komissarova E. V., Krekhtunov V. M., Rusov Y. S. Analysis of a fast-acting waveguide ferrite phase shifter with longitudinal magnetization phasing structure, ITM Web of Conferences, 2019, pp. 1–6. DOI: 10.1051/itmconf/20193006013
Abdelaal M. A., Shams S. I., Kishk A. A. Rectangular Waveguide Differential Phase Shifter Based on Horizontal Ferrite Tiles: Accurate Model for Full- Band Operation, IEEE Access, 2019, Vol. 7, pp. 23766–23778. DOI: 10.1109/ACCESS.2019.2899567
Yao H. Y., Chang W. G., Chang L. W., Chang T. H. Theoretical and experimental investigation of ferrite-loaded waveguide for ferrimagnetism characterization, Progress In Electromagnetics Research, 2019, No. 90, pp. 195–208. DOI:10.2528/PIERC18102602
Marvasti M., Rejaei B. Formation of hotspots in partially filled ferrite-loaded rectangular waveguides, Journal of Applied Physics, 2017, Vol. 122, 233901, pp. 1–9. DOI: 10.1063/1.5008616
Mikaelyan A. L. Teoriya i primeneniye ferritov na sverkhvysokikh chastotakh. M. L., Gosenergoizdat, 1963, 664 p
Vamberskiy M. V., Abramov V. P., Kazantsev V. I. Konstruirovaniye ferritovykh razvyazyvayushchikh ustroystv SVCH. Moscow, Radio i svyaz’, 1982, 136 p.
Laks B., Batton K. Per. s angl. pod red. A. G. Gurevicha Sverkhvysokochastotnyye ferrity i ferrimagnetiki. Moscow, Mir, 1965, 676 p.
Microwave Physics and Techniques Lecture 14 Ferrite Materials [Elektronnij resurs], 2003, Rezhim dostupu do resursu, antena.fe.unilj.si/literatura/VajeVT/Cirkulator/stara/Lecture14.pdf
Zaichenko O., Galkin P., Zaichenko N., Miroshnyk M. Sixport Reflectometer with Kalman Filter Processing of Sensor Signals, Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (TCSET), 2020, pp. 55–58. DOI: 10.1109/TCSET49122.2020.235390
Zaichenko O., Galkin P., Zaichenko N. Six-Port Refectometer Model with Accounting on Sensors Mutual Impedance, IEEE Ukrainian Microwave Week (UkrMW), 2020, pp. 639–642. DOI: 10.1109/UkrMW49653.2020.9252666
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 O. B. Zaichenko, N. Ya. Zaichenko
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Creative Commons Licensing Notifications in the Copyright Notices
The journal allows the authors to hold the copyright without restrictions and to retain publishing rights without restrictions.
The journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles.
The journal allows to reuse and remixing of its content, in accordance with a Creative Commons license СС BY -SA.
Authors who publish with this journal agree to the following terms:
-
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC BY-SA that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
-
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
-
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
