The topic of this thesis is to develop accurate and efficient CAD formulas for microstrip antennas and their arrays. The formulas are constructed based on the physical insight of the circuits, through the application of existing methods, commercial software, and the idea of Fuzzy EM.Analysis and design of large microstrip antenna array with the aid of software IE3D are investigated. The input impedance is obtained through the loading method, and antenna gain is accurately estimated through considering the losses on feed network. Stub tuning for impedance matching of the array is conducted, with the optimization of Genetic Algorithm combined with Neural Networks.The analysis and design based on full wave computations require large computer source and are time consuming. Therefore, accurate and efficient CAD formulas for microstrip antenna and its array are investigated.A successive approach method to solve the response of an irregularly shaped patch is developed. In this method, we starts from an ideal regular shaped patch, which could be easily analyzed by fast and accurate 2D modal expansions, the error is reduced by successive approach through adding the perturbation of cutting the corner, adding fringing field, and by applying Cauchy’s interpolation to eliminate instability, find wide band response.A CAD formula for this extension is derived from DC capacitor and is shown to be applicable for all practical thickness and permittivity er of the substrate. The fringe field effect is equivalently considered as an extension in size of an RF patch, either as resonator or as antenna. Resonant frequency of patch antenna on thick substrate is discussed. It is demonstrated that with the correct definition, our formula gives more accurate prediction compared to other existing formulas.A formula for mutual impedance between patch antennas is constructed based on the physics of the static near field and the radiation far field of the couplings. This leads to a synthetic asymptote form of separated variables of the center-to-center distance r and the azimuth angle . The formula is accurate and complete, with no restriction on the detailed structures of patch, feed and substrate. As its application, phased array and ultra low sidelobe array are analyzed.