An analysis and design theory of an aperture-coupled cavity-fed back-to-back microstrip directional coupler is presented for the efficient and optimized design. For this purpose, an equivalent network is developed, and simple but accurate calculations of circuit element values are described. Design equations of the coupler are derived based on the equivalent circuit. In order to determine various structural design parameters, the evolutionary hybrid optimization method based on the genetic algorithm and Nelder-Mead method is invoked. As a validation check of the proposed theory and optimized design method, a 10 dB directional coupler was designed and fabricated. The measured coupling was 10.3 dB at 3 GHz, and the return loss and isolation were 31.8 dB and 30.5 dB, respectively. The directional coupler also showed very good quadrature phase characteristics. Good agreements between the measured and the design specifications fully validate the proposed network analysis and design procedure.