METHOD FOR DETERMINING THE IMPEDANCE MATRIX OF A LINE WITH WAVE IMPEDANCE VARYING ALONG ITS LENGTH
DOI:
https://doi.org/10.18372/2310-5461.65.19930Keywords:
microwave, impedance, matrix, Riccati, line, transmission, calculation, nonuniformity, variability, methodAbstract
The paper investigates inhomogeneous transmission lines in microwave (MW) devices. The main challenges associated with the mathematical determination of such lines’ parameters are analyzed, particularly the difficulty of obtaining an exact solution to the telegraph equations in the general case. A method is proposed based on representing the solution of the Riccati equation as an analytical approximation, taking into account the characteristics of surface impedance. The derived expressions enable the direct determination of inhomogeneous transmission line parameters, simplifying the analysis of complex electromagnetic processes in MW devices.
Additionally, a study of limiting cases is conducted, particularly for a dielectric layer with constant wave impedance, allowing the derivation of compact analytical expressions for the elements of impedance and admittance matrices, confirming the efficiency of the proposed approach. Generalized formulas are obtained that are applicable to a wide range of inhomogeneous lines with arbitrary wave impedance variations.
It is demonstrated that the derived approximate formulas can be applied to the analysis and design of MW devices with irregular absorbing coatings. The proposed approach yields explicit analytical results, significantly simplifying the design of MW components with enhanced characteristics. It is established that, in the first approximation, the elements of the impedance and admittance matrices are determined by the integral of the surface impedance, making it possible to adapt the method to a broad class of inhomogeneous structures.
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