This paper deals with the ellipse permanent magnet machines for the minimization of torque ripple based on electromagnetic field theory. On the basis of a magnetic vector potential and a two dimensional (2-D) polar system, analytical solutions for flux density due to permanent magnet (PM) and current are obtained. In particular, the analytical solutions for mathematical expressions of magnets with different circumferential thicknesses can be solved introducing improved magnetization modeling techniques. The analytical results are validated extensively be nonlinear finite element solutions, a reduction of torque ripple can be achieved.