In this paper, a unified SHE approach is proposed for the fundamental frequency modulated multilevel converters with unequal dc levels. Unlike the traditional SHE methods whose equations depend on the switching patterns, this approach unifies all the switching patterns into one group of equations and the inequality constraints on the switching angles are eliminated. In order to obtain all the possible switching angles and their corresponding switching patterns, a polynomial homotopy continuation (PHC) algorithm based method is proposed to solve this unified SHE equations. Experiments on an 11-level cascaded H-bridge (CHB) multilevel converter verify the correctness of this method.