Highly accurate and numerically stable computations of double-layer coaxial waveguides

Purpose: The purpose of this study is to develop and investigate a fast and accurate algorithm for the modeling of characteristic impedance of double-layer coaxial waveguides. Design/methodology/approach: This paper presents the newly developed numerically stable analytical formula for calculation of the characteristic impedance of double-layer coaxial conductor and its elements such as resistance, inductance, capacitance and conductance per unit length. The formula contains modified scaled Bessel functions. The results of the developed analytical formula were compared with results obtained from the axis-symmetric 2D and 3D finite element method (FEM) simulations, using three different solvers. Findings: The proposed method shows a good agreement between results obtained with the new fast and stable analytical model and particular FEM models, selected depending on frequency range. The relative difference between characteristic impedance calculated using the new analytical method and obtained from chosen FEM method for discussed frequency range is less than 0.1 per cent which proves the correctness of the new analytical formula. Noteworthy is the fact that the relative difference of the resistance computed using the developed analytical method and obtained with Maxwell FEM solver for the frequency in range from 1 Hz to 10 MHz is less than 0.01 per cent. The presented work shows that when the calculations are performed over wide frequency range, it is necessary to use more than one solver, especially when the wavelength is comparable with dimensions of the conductor. The computation time of the new analytical model is much shorter than the computation time of FEM. Originality/value: An efficient, numerically stable algorithm for computation of characteristic impedance of a double-layer coaxial conductor (waveguide).