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In this article, topology transformations of power converters are realized through the dual and isomorphic principles for both the planar and nonplanar circuits. The topology cycling phenomenon is discovered in the topology transformation process and investigated in the power electronics field for the first time. It fills the gap between the dual converter and isomorphic converter and reveals the fundamental relationships among various power converters (existing and/or future ones). By utilizing this new discovery, the operation analysis, modulation/control design, topology derivation can be facilitated in a more comprehensive way. Numerous examples with both theoretical and experimental verifications show the feasibility and versatility of this work.