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Rectangular spiral coils are easier to implement in wireless power transfer (WPT) applications than circular spirals. Despite this fact, research into mutual coupling between rectangular spiral coils is insufficient. In this study, a new analytical model of mutual coupling is proposed, which converts a complex multi-turn rectangular spiral coil into a single-turn rectangular coil, simplifying calculation of the self-and mutual inductances. The mutual coupling between two different arbitrarily sized rectangular spiral coils with lateral misalignment and the rectangular cross-sections can be described accurately using this model. A series of experiments is carried out, the results of which agree well with the results of calculations. Finally, the effect of the number of turns in a coil on the coupling coefficient is discussed in order to determine the recommended number of turns. This research provides an effective tool for the design of a WPT system.

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Herein, a piezoelectric vibration energy harvester (PVEH) using liquid as an energy-capturing medium is proposed to simultaneously achieve ultralow frequency, low intensity, and multidirectional vibration energy harvesting in a horizontal plane, which is difficult to realize using traditional PVEHs. The proposed harvester comprises a cylindrical container with a certain liquid, a piezoelectric cantilever beam, ropes, and floater-lever arrays. The experimental results indicate that the proposed harvester with a single floater-lever can generate 9.8 μW under an ultralow frequency (2.6  Hz) and a low intensity vibration excitation (0.03 g), and the normalized power density is 8.89 μW/(cm3 g2 Hz). Under a multidirectional vibration excitation (360° in the horizontal plane) with frequencies below 3  Hz and an acceleration of 0.03 g, the two proposed harvesters with three and four floater-levers indicate a maximum output power (Pmax) deviation of 24.92% and 28.31%, respectively, and an angle bandwidth of 360° (using 2/2Pmax as the standard). All the experimental results indicate that the proposed PVEH is highly promising as an energy supply of wireless sensor networks distributed in ultralow frequency, low intensity, and multidirectional applications.