Precise design of multilayer circuit using spectral domain and finite differences techniques

The design of multilayer directional couplers with septa is often done using the spectral domain technique. This consists in taking the Fourier transform of the boundary conditions and then expressing the charge distribution on the conductor, p_l, and the septum, p_s, as a function of G_ij, the Green´s function. The Galerkin optimization technique is then used to compute p_l and p _s as a summation of arbitrarily chosen basis functions. A proper choice of basis functions determines the precision and convergence of results. Presently, the choice of p_ln and p_sn is commonly done on an intuitive basis, which may result in imprecision of the impedance value. Since no technique has yet been developed for the optimization of p_ln and p_ls, the authors compute explicitly the charge distribution value, using the finite-difference method. These results are used to develop precise design curves for the multilayer coupler with septa. The methodology can also be applied to other multilayer circuits