In this paper, an analytical model using equivalent magnetic circuits for the PMA-SynRG is presented. The lumped parameter model (LPM) is developed from machine geometry, stator winding and machine operating specifications. By the LPM, magnetic saturation of rotor bridges is incorporated into model and it provides effective means of predicting machine performance for a given machine geometry. The LPM is not as accurate as finite element analysis but the equivalent magnetic circuits provide fast means of analyzing electromagnetic characteristics of PMa-SynRG. It is the main advantage to find the initial design and optimum design. The initial design of PMa_RSG is performed by LPM model and FEM analysis, and the final PMA-RSG design is optimized and identified by FEM analysis considering actual machine design. The linear LPM and the nonlinear LPM are programmed using MATLAB and all of machine parameters are calculated very quickly. To verify justification of the proposed design of PMa-RSM, back-EMF is measured.