M.V. Davidovich – Dr.Sc.(Phys.-Math.), Professor, 

Department «Radioengineering and Electrodynamics», Saratov State University named after N.G. Chernyshevsky E-mail: DavidovichMV@info.sgu.ru

On the basis of the tensor Green’s functions obtained by the mode matching technique, and by the integral equation for the current on the meander located on the substrate in a rectangular screen, the meander slow wave system is considered. Using this equation and the related functional, the dispersion equation for the slow wave system in the form of a narrow meander on the substrate is obtained. In disregard of the transverse current on the meander the dispersion is considered, which allows to implement a fast algorithm for calculating of the dispersion. The considered model takes into account the losses on the meander in the form of imposing impedance conditions and in the substrate, taken into account by the introduction of complex permittivity. Numerical results are obtained on the basis of iteration.

A rigorous method is proposed for determining the variance and loss in a meander type ZS on a substrate in a screen. The method allows you to determine all the components of the fields and, accordingly, the coupling resistance. For a simple model, an analytical control is obtained. The rows included in it can be analytically summarized. ZS has a mirror plane of symmetry, due to which the frequency band of the main mode increases compared to ZS of the «symmetrical comb» type. The DP, the dispersion in the MPL, and the plasmon effect lead to an increase and narrowing of the band in which the deceleration changes slightly. Therefore, it is advisable to use dielectrics with a low DP or ZS of the «weighted meander» type. In the latter case, the problem of locking the beam is removed.

1. Davidovich M.V., Bushuev N.A., Altshuler E.Yu. Matematicheskoe modelirovanie zamedlyayushchei sistemy tipa «meandr v pryamougolnom ekrane» dlya korotkovolnovykh LBVO. Fizika volnovykh protsessov i radiotekhnicheskie sistemy. 2012. T. 15. № 2. S. 37‒41. (In Russian).
2. Benedik A.I., Rozhnyov A.G., Ryskin N.M., Sinitsyn N.I., Torgashov G.V., Shalaev P.D. Razrabotka planarnykh zamedlyayushchikh sistem na dielektricheskikh podlozhkakh dlya priborov vakuumnoi mikroelektroniki millimetrovogo i submillimetrovogo diapazonov. Radiotekhnika. 2016. № 7. S. 47‒52. (In Russian).
3. Markov G.T., Chaplin A.F. Vozbuzhdenie elektromagnitnykh voln. M.: Radio i svyaz. 1986. 296 s. (In Russian).
4. Davidovich M.V. Dis. … dokt. fiz.-mat. nauk. Saratov. 2000. 480 s. (In Russian).
5. Davidovich M.V. Iteratsionnye metody resheniya zadach elektrodinamiki. Saratov: Izd-vo Saratovskogo un-ta. 2014. 240 s. (In Russian).
6. Nikolskii V.V. Klass matematicheskikh modelei elektrodinamicheskikh sistem s chastichno ekranirovannymi granitsami. Radiotekhnika i elektronika. 1977. T. 22. № 4. S. 657‒669. (In Russian).