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In order to reduce the thrust ripple of linear servo system, a double-sided air core permanent magnet linear servo motor with trapezoidal shape permanent magnets (TDAPMLSM) is proposed in this paper. An analytical model of the motor for predicting the magnetic field in the air-gap at no-load is introduced. This model is derived based on the equivalent magnetization intensity method, and its accuracy is validated by using the results obtained from the finite-element method. The key dimensions that affect the air-gap magnetic field are analyzed based on the analytical model, and the design is optimized by using genetic algorithm. A thrust ripple reduction of 70.6% is achieved by optimization. The proposed analytical model may be used for a quick and reliable design and design optimization of the TDAPMLSM.