## 2 Main Blocks for Wirelessly-Powered Cage System
### Spatial and Angular Misalignment between Tx and Rx Coils  
Spatial and angular misalignments and distance variation between Tx and Rx coils inside the wirelessly-powered cage happen quite frequently in practice as freely behaving animal subjects walk, sniff around, rear, and climb the walls of the cage. This will result in a significant reduction in the PTE and PDL, which might cause malfunctions in the mobile device which does not equip energy storage. The homogeneity of wireless coverage achieved by the Tx coil array alleviates the spatial misalignment as shown in Section 2.1.2, and the CLPC in Section 2.2[11; 13; 16] compensates the reduced power in the Rx against some angular misalignments or distance variations. However, the Rx coil rarely receives the wireless power from the Tx coil with maximum angular misalignment of 90\({}^{\circ}\). Therefore, the designer should consider the worst-case condition in the wirelessly-powered cage. The most common technique to address the angular misalignment with omnidirectional powering is to implement 3D Rx coils in x-, y-, and \(z\)-axis, as shown in Figure 10a[20]. The 3D Rx coil is composed of three individual Rx coils followed by each rectifier as shown in Figure 10b. For the nominal condition which angular misalignment is 0\({}^{\circ}\), the Rx\({}_{\mathrm{z}}\) coil mainly receives the power carrier from the Tx coils while Rx\({}_{\mathrm{x}}\) and Rx\({}_{\mathrm{y}}\) coils rarely receive the power. When the 3D Rx coil has large angular misalignments from the Tx coil, the received power in the Rx\({}_{\mathrm{x}}\) or Rx\({}_{\mathrm{y}}\) coil is increased depending on the misalignment axis to compensate the reduced power in the Rx\({}_{\mathrm{z}}\) coil. The 3D Rx coil can also be implemented by using the multiple resonator coils, \(L_{3}\), instead of multiple load coils, \(L_{4}\), as introduced in Figure 11[14]. As shown in Figure 11b, the multiple resonators are strongly coupled with \(L_{4}\), while the multiple resonators can receive the power against angular misalignment inside the cage. This technique only utilizes one rectifier resulting in the reduced circuit complexity compared to Figure 11b. Since these 3D Rx coils receive the inductive power from each direction, it provides better homogeneous PTE and PDL against the angular misalignments of the mobile device. However, the 3D Rx coil design in the mobile unit increases the volume compared to the conventional single planar Rx coil, resulting in the limited applications for tiny implants inside the animal body. Figure 10: **(a)** The design of the 3D Rx coil structure and (b) circuit diagrams in [20] to compensate for the angular misalignment of Rx coil. Instead of the 3D Rx coil, the new Tx coil configurations are studied to provide the homogeneous magnetic field along with \(x\)-, \(y\)-, and \(z\)-axis [21; 22]. The proposed architecture in Figure 12a [21] includes three layers of hexagonal planar spiral coil (hex-PSCs) array for homogeneous distribution of the PTE against angular misalignments. The individual Tx coil array generates power carriers with three phases (0\({}^{\circ}\), 120\({}^{\circ}\), 240\({}^{\circ}\)) as shown in Figure 12b, and provides both vertical and lateral magnetic fluxes at the same time over the entire powered 3D volume inside the cage. When the Rx coil is aligned with the Tx coil, the Rx coil can receive the power from the vertical magnetic flux. When the Rx coil has the angular misalignment against the Tx coil by 90\({}^{\circ}\), the lateral magnetic flux between the Tx coils mainly provides the power to the Rx, resulting in \(\sim\)4% PTE improvement compared to the conventional Tx coil array as shown in Figure 12b. In [22], the omnidirectional powering is achieved by two dipole coils using DQ rotating magnetic field.