A modified transmission line model is proposed for input impedance analysis of a square microstip antenna with single-circularly-polarized. Alog-periodic arrangement with microstrip antenna (LPMA) which consists of 3 resonant element ($3\times1$) is designed for broadband operation ranging from 11.2 GHz to 12.4 GHz, based on this pro- posed model from transmission line model. Aplanar array ($3\times4$array), in which 4sets of the above LPMA are in the same plane, is fabricated for high gain X-band satellite communication antennas. The optimum spacing between each LPMA is determined using computer simulation for the minimum bariation of far field pattern and null. This $3\times4$array has a measured values of gain greater than 8dBi, VSWR les then 2.3, and bandwidth greater than 7% respectively.