A non-galerkin spatial-domain approach for efficient calculation of the dispersion characteristics of microstrip lines

In the analysis of dispersion characteristics of microstrip lines, spectral domain approaches has been preferred as opposed to the spatial domain calculations since the spatial domain Green´s functions corresponding to the microstrip structure require the numerical evaluation of inverse Fourier transform integrals which are computationally expensive. However as demonstrated in Bernal, J. et al, (2000), the discrete complex image representation of the spatial domain Greenpsilas functions eliminates the need for the evaluation of numerical integrals and renders the spatial domain method to be more efficient compared to the spectral domain approach. When the discrete complex image method (DCIM) is used, the matrix entries of the eigenvalue problem involve double integrations in the spatial domain. One of them is the convolution integral with the basis function, the other one is the inner product integral with the testing function to impose the boundary conditions. In case a Galerkin approach with basis functions satisfying the edge conditions on the conducting strips is preferred as in Bernal, J. et al, (2000), these integrals need to be evaluated numerically. However, if a non-Galerkin approach with pulse type testing functions is adopted, one of the integrals could be evaluated analytically and a single numerical integration is required. In this paper, the non-Galerkin method is utilized and the accuracy of the method is demonstrated by comparing the results of dispersion characteristics to the ones found in the literature.