Contribution à l’élaboration d’un modèle electromagnétique de supports de transmission non-uniformes

Abstract

With the development of telecommunications and the need for miniaturizing microwave circuits and components, the uniform transmission lines were replaced by non uniform transmission lines (LTNUs) in many applications. With the presence of discontinuities uneasy to model by traditional methods, these lines require powerful technique of design and modeling, especially for arbitrary shapes. In addition, due to the increase in the operation frequencies, it became necessary to predict the transient responses to directly estimate the performances of the microwave circuits over ultra wide frequency bands. On the other hand, the Meshless methods form a generic group of scientific computing schemes which was developed since the years 1970s to eliminate the drawbacks of a fixed discretization grid for the approximation of the problem equations. These methods have the advantages of arbitrary nodal distribution and conformal modeling of R.L.C.G parameters of NUTLs which require less computing costs than the traditional numerical methods. In this context we implemented the MATLAB codes for the analysis and the simulation of arbitrary non-uniform transmission lines in the time domain by three Meshless methods : the polynomial point interpolation method (PIM), the meshless method based on radial basis functions (RBF-MLM), and the radial point interpolation method (RPIM). To illustrate the superiority of these methods, such as the irregular discretiszation and the fast convergence rate, results comparisons for two distinct samples were held between the PIM, the RBF-MLM, the RPIM, the FDTD method, and the wavelet expansion method. These tests allow us to conclude that the RPIM converges quickly and provides the best compromise between the accuracy and the computing time.