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In a piezoelectric energy harvesting (PEH) system, the dynamics and harvested power vary with different interface circuits connected. The impedance matching theory was regarded as the theoretical base for the harvested power optimization in the harmonically excited PEH systems. The previous literature started the impedance analyses based on the proposition that the harvested power is maximized when the output impedance of the piezoelectric transducer is matched by the input impedance of the harvesting circuit. Yet, retrospecting to the origin of the impedance matching theory, a philosophical problem is found with this proposition. Moreover, the definition, constraint, and composition of the equivalent impedance in the real (nonlinear) harvesting circuits were not clear as well. This paper clarifies these concepts and provides the impedance modeling and analysis for the PEH systems with different interface circuits, including standard energy harvesting, parallel synchronized switch harvesting on inductor, and series synchronized switch harvesting on inductor. The equivalent impedance network and corresponding mechanical schematics of a general PEH system are proposed. The difference between the PEH equivalent impedance network and the conventional impedance network is discussed. The harvested power is investigated based on this impedance analysis. The analytical results show good agreement with the experiments carried out on a base excited PEH device.