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In this paper the theory of microstrip Yagi-Uda arrays is considered. An integral equation is derived for the current distribution on the exciter, reflector, and parasitic elements of the array which is printed on a grounded dielectric substrate. The integrand involves improper Sommerfeld type integrals which are solved by analytic-numeric techniques via a principal value integration along the real axis. In this manner the integral equations can be solved for the current distribution by the Galerkin method. Some results for the design of printed Yagi-Uda arrays are discussed.