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The optimum design of the tapered slot antenna (TSA) profile and geometry is achieved through its modeling by a stepline terminated in free space intrinsic impedance. The impedance matching of the TSA input impedance (obtained by the transmission matrix properties) to the generator impedance is achieved by minimizing an error criterion constructed as the magnitude squared of the difference between the generator and input impedances over the desired bandwidth. The attenuation constant of the stepline is computed by the broadside radiation of TSA (which is an endfire antenna) and the longitudinal power flow. The spectral domain immitance approach is used to compute the broadside radiation, by first determining the electric field components in the slot by the Galerkin's method and then obtaining the equivalent magnetic surface current densities. The power flow in the endfire direction of TSA may be computed by the Poynting's vector in the substrate. The attenuation constant is calculated for various values of slot width. Finally, the minimization procedure gives the slotline widths and lengths.