Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2023. ¹1

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DOI: https://doi.org/10.30898/1684-1719.2023.1.1

GENERALIZED IMPEDANCE METHOD

FOR CALCULATION REFLECTION AND PASSAGE OF WAVES

THROUGH MULTI-LAYER STRUCTURE.

PART 1. SUCCESSIVE CALCULATION OF IMPEDANCES

AND AMPLITUDES

I.V. Antonets^{1}, V.G. Shavrov^{2}, V.I. Shcheglov^{2}

^{1 }Syktyvkar State University

167001, Russia, Syktyvkar, Oktyabr'skij pr-t, 55

^{2 }Kotelnikov IRE RAS, 125009, Russia, Moscow, Mokhovaya, 11, b. 7

The paper was received September 27, 2022.

Abstract.The algorithm for calculation of reflection and passage of single-dimension wave through multi-layer structure which is presented as the successive one to other uniform slides is proposed. On the basis solution of single-dimension wave equation for each slide as the parameter of slide it is established the wave number. It is proposed the conception of generalized impedance for single-dimension wave which consist of propagating wave velocity relation to the frequency of the same wave. It is proposed the conception of zero-impedance of uniform region of structure which is equal to inverse value of wave number in this region. The generalized impedance is presented in the product of zero-impedance to fraction which numerator is the sum of two special solutions of wave equation for this region and denominator is the difference of the same solutions. For the calculation of reflection and passage coefficients of wave by energy for the whole structure it is found two mechanisms successive calculation along the slides of structure – successive calculation of impedances and successive calculation of amplitudes. For the mechanism successive calculation of impedances it is proposed the conceptions of entrance and exit impedances of each separately slides. It is proposed the recurrence formula which allow to found the entrance impedance of preceding medium through the entrance impedance of following medium for anyone two neighbouring regions of structure. It is established the using of this formula proposed to found the entrance impedance in initial slide of structure from the entrance impedance in last slide of structure. In this case the successive calculation of impedances is made from the end of structure to its outset. For the mechanism of successive calculation of amplitudes it is found the system consisted of two recurrence formulas which allows to found the amplitudes of straight and backward directions in preceding medium through the amplitudes the same waves in following medium. It is proposed the scheme of step-by-step successive calculation which allows from the amplitude of initial falling wave found the amplitude of reflected and passage waves relative to structure as a whole. It is mentioned the possibility and proposed the formulas which allows to found the reflection and passage coefficients on energies for the structure as a whole. It is discussed the comparative characteristics of method successive calculation of impedances and successive calculation of amplitudes.

Key words:wave propagation, multi-layers structure, impedance.

Financing:The work was carried out within the framework of the state assignment of the Kotelnikov Institute of Radio Engineering and Electronics of the Russian Academy of Sciences.

Corresponding author:Shcheglov Vladimir Ignat'evich,vshcheg@cplire.ru

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For citation:Antonets I.V., Shavrov V.G., Shcheglov V.I. Generalized impedance method for calculation reflection and passage of waves through multi-layer structure. Part 1. Successive calculation of impedances and amplitudes.

Zhurnal radioelektroniki[Journal of Radio Electronics] [online]. 2023. ¹1. https://doi.org/10.30898/1684-1719.2023.1.1 (In Russian)