Single-phase full-bridge transformerless topologies, such as the H5, H6, or the highly efficient and reliable inverter concept (HERIC) topologies, are commonly used for leakage current suppression for photovoltaic (PV) applications. The main derivation methodology of full-bridge topologies has been used based on both a DC-based decoupling model and an AC-based decoupling model. However, this methodology is not suited to the search for all possible topologies, and cannot verify whether they are inclusive. Part I of this paper will propose a new topology derivation methodology based on unipolar sinusoidal pulse width modulation (USPWM) to search all possible full-bridge topologies for leakage current suppression. First of all, a unified circuit model is proposed, instead of the DC- and AC-based models. Secondly, a mathematic method called the MN principle is then proposed to search for all possible topologies, and a derivation procedure is provided. It was verified that all existing topologies could be found using the proposed method; furthermore, seven new topologies were derived. The proposed topology derivation methodology is extended to search topologies under Double-Frequency USPWM (DFUSPWM). Twenty topologies under USPWM and four topologies under DFUSPWM have been derived.