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The effects of saturation on torque production for non-salient, single-phase, permanent-magnet machines are studied in this paper. An analytical torque equation is proposed to predict the instantaneous torque with saturation effects. Compared to the existing methods, it is computationally faster and easier to calculate the torque using the analytical equation proposed. It can also handle arbitrary armature current waveforms and arbitrary flux linkage waveforms produced by the rotor permanent magnets. The results obtained by using the proposed torque equation are validated using finite-element results, and experimental results obtained on a prototype single-phase permanent-magnet machine.