D.G. Fomin¹, N.V. Dudarev², S.N. Darovskikh³

1–3  South Ural State University (National Research University) (Chelyabinsk, Russia)

One of the methods for reducing the dimensions of antenna-feeder devices is their printed version, where both radiating elements and elements of the antenna-feeder path that providing a required amplitude-phase distribution, can be implemented on one or several dielectric substrates of a vertical volume-modular structure. A symmetrical slot line is one of the basic elements for the implementation of printed antenna-feeder devices, the advantage of which is compactness and a significant reduction in dimensions due to the use of substrates with a high value of the relative permittivity. Nowadays numerical methods are the main methods for determining the electrodynamics parameters of a symmetrical slot line in the design of antenna-feeder devices. One of the known numerical methods is the finite element method in a three-dimensional formulation of the electrodynamics problem, implemented in the form of the ANSYS HFSS software. However, because of financial and computational limitations of its use, it becomes advisable to pay attention to the known analytical methods for solving the electrodynamics problem for radiating systems based on slot lines. Their accuracy in comparison with the numerical method is not known yet. This creates uncertainty in the use of analytical methods in the design of antenna-feeder devices, in the implementation of which a symmetrical slot line is used. This research has been carried out to solve the presented problem. The aim of this research is to show a comparative assessment of analytical and numeric methods for calculating the main electrodynamics parameters (impedance, wavelength, effective dielectric constant) of a symmetrical slot line.

The result of the research is the proof of the practical identity of the solution of the electrodynamics problem for a symmetrical slot line by both analytical and numerical methods. The main conclusions of the research are:

1. Electrodynamics parameters of a symmetrical slot line (impedance, effective dielectric constant, length of an electromagnetic wave propagating in the slot line) can be determined with high accuracy using analytical methods that do not require the use of expensive software for numerical solution of the electrodynamics problem.
2. The electrodynamics parameters obtained as a result of the calculation can be relevant in the design of printed antenna-feeder devices with slot radiating elements by the method of equivalent circuits. In this case, the theory of long transmission lines is used, and the radiation resistance is presented in the form of: 1) a lumped element or 2) the attenuation coefficient in the constant of propagation of an electromagnetic wave along the slot line. 

The calculation of the radiation resistance of a printed slot radiating elements can be performed in different ways and seems to be well studied.

Fomin D.G., Dudarev N.V., Darovskikh S.N. Comparison of the electrodynamics parameters values of a symmetrical slot line obtained by different methods. Radiotekhnika. 2021. V. 85. № 4. P. 138−146. DOI: https://doi.org/10.18127/j00338486-202104-15 (In Russian)

1. Kim J.P., Park W.S. Network modeling of an inclined and off-center microstrip-fed slot antenna. IEEE Transactions on Antennas and Propagation. 1998. V. 46. P. 1182–1188.
2. Ruyle J.E., Bernhard J.T. A wideband transmission line model for a slot antenna. IEEE Transactions on Antennas and Propagation. 2013. V. 61. № 3. P. 1407–1410.
3. Markov G.N. Antenny. L.: Gosudarstvennoe jenergeticheskoe izdatel'stvo. 1960 (In Russian).
4. Conh S.B. Slot line on a dielectric substrate. IEEE Transactions on Microwave Theory and Techniques. 1969. V. 17. № 10. P. 768–778.
5. Gupta K.C., Bhartia P., Garg R., Bahl I. Microstrip lines and slotlines. 2nd Ed. Norwood, MA: Artech House. 1996.
6. Vendik O.G., Danilov I.S., Zubko S.P. Modelirovanie volnovyh parametrov uzkoj shhelevoj linii peredachi na osnove sverhprovodjashhej plenki. Zhurnal tehnicheskoj fiziki. 1997. T. 67. № 9. S. 94–97 (In Russian).
7. Klyuev S.B., Nefyodov E.I., Potapov A.A. Symmetrical slot line with a dielectric insert in the slot. Journal of Physics: Conference Series. 2019. V. 1348. P. 1–5.
8. Knorr J.B., Kuchler K.D. Analysis of coupled slots and coplanar strips on dielectric substrates. IEEE Transactions on Microwave Theory and Techniques. 1975. V. 23. P. 541–548.
9. Liang G.C., Liu Y.W., Mei K.K. Full-wave analysis of coplanar waveguide and slotline using the time-domain finite-difference method. IEEE Transactions on Microwave Theory and Techniques. 1989. V. 37. P. 1949–1957.
10. Gvozdev V.I., Nefedov E.I. Ob#emnye integral'nye shemy SVCh. M.: Nauka. Glavnaja redakcija fiziko-matematicheskoj literatury. 1985 (In Russian).
11. Zavadil J.L. Slot transmission line. Monterey, California: Naval Postgraduate School. 1971.
12. Kostenetskiy P., Semenikhina P. SUSU Supercomputer resources for industry and fundamental science. 2018 Global Smart Industry Conference. IEEE. 2018. P. 1–7.