2.1.1. Coil Optimization for Conventional Two-/Three-/Four-Coil Inductive Links

IMDs typically have a tight limitation in their size depending on the applications, resulting in the diameter limitation of Rx coil in the body. In contrast, the Tx coil in the wirelessly-powered cage has more size relaxation in its design. In the inductive link, the coil geometries should be carefully designed to achieve the efficient inductive coupling considering the load and coil separation. Figure 3 shows the physical and electrical configurations of a two-coil inductive link with geometrical parameters used for primary (*L*1) and secondary (*L*2) coils, where *d*in is inner diameter of each coil, *d*out 107

#### *2.1. Coil Design and Optimization*

#### 2.1.1. Coil Optimization for Conventional Two-/Three-/Four-Coil Inductive Links

IMDs typically have a tight limitation in their size depending on the applications, resulting in the diameter limitation of Rx coil in the body. In contrast, the Tx coil in the wirelessly-powered cage has more size relaxation in its design. In the inductive link, the coil geometries should be carefully designed to achieve the e fficient inductive coupling considering the load and coil separation. Figure 3 shows the physical and electrical configurations of a two-coil inductive link with geometrical parameters used for primary (*L*1) and secondary (*L*2) coils, where *d*in is inner diameter of each coil, *d*out is outer diameter of coils, *N* is number of turns, and *z* is the coil separation between *L*1 and *L*2 coils. The mutual inductance between Tx and Rx coils ( *M*12) is defined by *M*12 = *k* √ *L*1*L*2, where *k* is the coupling coe fficient of the two-coil link. *M*12 shows the ratio of magnetic flux common to both *L*1 and *L*2. *R*1 and *R*2 are the series resistance of the Tx and Rx coils, respectively. The quality factor ( *Q*) of each coil is defined by *Q* = <sup>ω</sup>*L*/*R*, where ω = <sup>2</sup>π*f* 0 and *f* 0 is the power carrier frequency. *Electronics* **2020**, *9*, x FOR PEER REVIEW 4 of 28 is outer diameter of coils, *<sup>N</sup>* is number of turns, and *z* is the coil separation between *L*1 and *L*2 coils. The mutual inductance between Tx and Rx coils ( *M*12) is defined by ܯଵଶ ൌ ݇ ඥܮଵܮଶ, where *k* is the coupling coefficient of the two-coil link. *M*12 shows the ratio of magnetic flux common to both *L*1 and *L*2. *R*1 and *R*2 are the series resistance of the Tx and Rx coils, respectively. The quality factor ( *Q*) of each coil is defined by *Q* <sup>=</sup> *<sup>Ν</sup>L/R*, where *<sup>Ν</sup> <sup>=</sup>*2*Δf*<sup>0</sup> and *f*0 is the power carrier frequency. 

**Figure 3.** Physical and electrical configurations in a two-coil inductive link. **Figure 3.** Physical and electrical configurations in a two-coil inductive link.

Although the two-coil inductive link has its optimized solution for highest PTE depending on a given set of *Q*1, *Q*2, and *k*12 based on [8], the optimized load resistance, *R*L,PTE, is sometimes far from the nominal target load resistance, *R*L, which is predefined in the IMD application. Therefore, the multi-coil solution such as three- or four-coil inductive links has been widely studied to provide the designer with more degrees of freedom to convert *R*L to *R*L,PTE and thereby maximize PTE, while they have a potential negative impact on the size-constrained applications. Figure 4 shows the two-, three-, and four-coil inductive links with the lumped circuit model. The PTE of two-, three-, and four-coil inductive links can be calculated based on the basic circuit theory found in [9]. Although the two-coil inductive link has its optimized solution for highest PTE depending on a given set of *Q*1, *Q*2, and *k*12 based on [8], the optimized load resistance, *<sup>R</sup>*L,PTE, is sometimes far from the nominal target load resistance, *R*L, which is predefined in the IMD application. Therefore, the multi-coil solution such as three- or four-coil inductive links has been widely studied to provide the designer with more degrees of freedom to convert *R*L to *<sup>R</sup>*L,PTE and thereby maximize PTE, while they have a potential negative impact on the size-constrained applications. Figure 4 shows the two-, three-, and four-coil inductive links with the lumped circuit model. The PTE of two-, three-, and four-coil inductive links can be calculated based on the basic circuit theory found in [9].

$$\begin{array}{c} \eta\_{2-\text{coll}} = \eta\_{23} = \frac{k\_{23}^2 Q\_2 Q\_{3\text{L}}}{1 + k\_{23}^2 Q\_{3\text{L}} Q\_{3\text{L}}} \cdot \frac{Q\_{3\text{L}}}{Q\_{3\text{L}}},\\ \eta\_{2-\text{coll}} = \eta\_{23} = \frac{1 + k\_{23}^2 Q\_2 Q\_{3\text{L}}}{1 + k\_{23}^2 Q\_2 Q\_{3\text{L}}} \cdot \frac{Q\_{3\text{L}}}{Q\_{\text{L}}}, \end{array} \tag{1}$$

$$\eta\_{3-\text{coll}} = \eta\_{23}\eta\_{34} = \frac{(k\_{23}^2 Q\_2 Q\_3)(k\_{34}^2 Q\_3 Q\_{4\perp})}{\Gamma(1 \pm \nu^2 \text{ cf\mu\text{A}} \text{ } \text{a} \text{ } \mu\text{s}^2 \text{ } \text{b} \text{ } 2 \text{ } \text{c} \text{ } \text{b} \text{ } \text{a} \text{ } \text{b} \text{ } \text{c})}, \frac{Q\_{4\perp}}{\alpha},\tag{2}$$

$$\eta\_{3-\text{coll}} = \eta\_{23} \eta\_{34} = \frac{\left[\left(1 + k\_{23}^2 Q\_4 \Theta\_{\text{2}} \xi\_2 \xi\_3\right) \left(k\_{34}^2 Q\_3 Q\_4 \right) k\_{34}^2 Q\_3 Q\_{4L}\right]}{\left[\left(1 + k\_{23}^2 Q\_2 Q\_3 + k\_{34}^2 Q\_3 Q\_{4L}\right) \left(1 + k\_{34}^2 Q\_3 Q\_{4L}\right)\right]} \cdot \frac{\left(\xi\right)}{Q\_L},\tag{2}$$

$$\begin{array}{c} \eta\_{4-\text{coll}} = \eta\_{12}.\eta\_{23}.\eta\_{34} \quad 1 \quad \omega\_{2} \sim \omega^{\star} \quad \text{ $\omega \sim \omega^{\star}$ }\\ = \frac{\eta\_{4-\text{coll}} - \eta\_{12}.\eta\_{23}^{\star}Q\_{1}Q\_{2}^{\star}(k\_{23}^{2}Q\_{2}Q\_{3})(k\_{34}^{2}Q\_{3}Q\_{4})}{\left[\left(1 + k\_{34}^{2}\right)\left(\left(1 + k\_{34}^{2}\right)Q\_{1}Q\_{3}\right)\omega + k\_{34}^{2}\eta\_{1}Q\_{2}Q\_{3}\right]\left(1 + k\_{34}^{2}Q\_{3}Q\_{3} + k\_{34}^{2}Q\_{4}Q\_{4}\right)} \cdot \frac{Q\_{4L}}{Q\_{1}}\tag{3} \\ \end{array} \tag{3}$$

ሾሺͳ݇ଵଶ ܳଵܳଶሻǤሺͳ݇ଷସ ܳଷܳସሻ݇ଶଷ ܳଶܳଷሿǤሾͳ݇ଶଷ ܳଶܳଷ ݇ଷସ ܳଷܳସሿ ܳ = (*k*212*<sup>Q</sup>*1*Q*2)(*k*223*<sup>Q</sup>*2*Q*3)(*k*234*<sup>Q</sup>*3*Q*4L) [(<sup>1</sup>+*<sup>k</sup>*212*<sup>Q</sup>*1*Q*2)·(<sup>1</sup>+*<sup>k</sup>*234*<sup>Q</sup>*3*Q*4L)+*k*223*<sup>Q</sup>*2*Q*3]·[<sup>1</sup>+*<sup>k</sup>*223*<sup>Q</sup>*2*Q*3+*<sup>k</sup>*234*<sup>Q</sup>*3*Q*4L]· *Q*4L *Q*L(3)

where *Q*3L and *Q*4L are the loaded quality factor, *Q*3L = *Q*3*Q*L/( *Q*3 + *Q*L) and *Q*4L = *Q*4*Q*L/( *Q*4 + *Q*L), in which the load quality factor, *Q*L = *<sup>R</sup>*L/*ΝL.* Note that the source output resistance, *R*S, is included in the driver coil resistance. The Equation (2) implies that the three-coil link gives the designers with an additional degree of freedom (*k*23) to adjust the reflected load onto *L*2 to be the optimal value, *R*L,PTE, compared to the two-coil link. The PTE of the three-coil inductive link is related with *k*23, *k*34, *Q*2, *Q*3, and *Q*4, for a given load condition. The four-coil link can provide an additional degree of freedom (*k*12) from the three-coil link for the impedance matching on the source side based on (3). Since the two-, three-, and four-coil inductive links have different strengths and weaknesses in the coupling coefficient (*k*), PDL, and coupling variations as summarized in Table 1, the designers can select the appropriate inductive link configuration depending on the specifications of the WPT system [9]. where *Q*3L and *Q*4L are the loaded quality factor, *Q*3L = *Q*3*Q*L/(*Q*3 + *Q*L) and *Q*4L = *Q*4*Q*L/(*Q*4 + *Q*L), in which the load quality factor, *Q*L = *R*L/ω*L.* Note that the source output resistance, *R*S, is included in the driver coil resistance. The Equation (2) implies that the three-coil link gives the designers with an 108

additional degree of freedom (*k*23) to adjust the reflected load onto *L*2 to be the optimal value, *<sup>R</sup>*L,PTE, compared to the two-coil link. The PTE of the three-coil inductive link is related with *k*23, *k*34, *Q*2, *Q*3, and *Q*4, for a given load condition. The four-coil link can provide an additional degree of freedom (*k*12) from the three-coil link for the impedance matching on the source side based on (3). Since the two-, three-, and four-coil inductive links have different strengths and weaknesses in the coupling coefficient (*k*), PDL, and coupling variations as summarized in Table 1, the designers can select the appropriate inductive link configuration depending on the specifications of the WPT system [ *Electronics* **2020**, *9*, x FOR PEER REVIEW 9]. 5 of 28 

**Figure 4.** The lumped circuit model for (**a**) two-coil, (**b**) three-coil, and (**c**) four-coil inductive links. **Figure 4.** The lumped circuit model for (**a**) two-coil, (**b**) three-coil, and (**c**) four-coil inductive links.


**Table 1.** Comparison between two-, three-, and four-coil inductive links. **Table 1.** Comparison between two-, three-, and four-coil inductive links.

The optimization procedures of two-, three-, and four-coil inductive links start with the design constrains imposed by the application and coil fabrication technology. The design constrains in the Rx defines the maximum outer diameter of coils in the IMD, and the coil fabrication technology indicates the minimum line width and line spacing. Depending on the application, the coil separation between *L*2 and *L*3 (*z*23), the nominal load resistance (*R*L), and the source resistance (*R*s) are also determined. In the two-coil optimization procedure, *k*23*Q*2*Q*3 should be maximized to achieve the maximum 2-coil based on (1). The optimum *k*23, *Q*2, and *Q*3 can be derived by the proper outer and inner diameter of Tx coil, inner diameter of Rx coil, and number of turns for Tx and Rx coils at given design constraints [8]. The three-coil link optimization procedure maximizes 23 and *Q*4 in (2), and additionally adjust *k*34 in the Rx to provide the maximum PTE, 3-coil. A more detailed flow chart is discussed in [9]. In this optimization procedure, the additional *L*3 coil in the Rx plays the role of an impedance-matching circuit, which can convert an arbitrary *<sup>R</sup>*L to *<sup>R</sup>*L,PTE for optimal PTE compared to the conventional two-coil link. In other words, the reflected load on the Tx can be adjustable for maximizing the PTE if the designer can choose the suitable *k*23 and *k*34 in the design of a three-coil link. As shown in Figure 5 which shows the exemplar designs of two- and three-coil inductive links, the three-coil link can maintain the maximum PTE by adjusting *k*34 while the two-coil link only reaches the optimal PTE for a specific *R*L = 200 ̛ [9]. The optimization procedures of two-, three-, and four-coil inductive links start with the design constrains imposed by the application and coil fabrication technology. The design constrains in the Rx defines the maximum outer diameter of coils in the IMD, and the coil fabrication technology indicates the minimum line width and line spacing. Depending on the application, the coil separation between *L*2 and *L*3 (*z*23), the nominal load resistance (*R*L), and the source resistance (*R*s) are also determined. In the two-coil optimization procedure, *k*23*Q*2*Q*3 should be maximized to achieve the maximum η2-coil based on (1). The optimum *k*23, *Q*2, and *Q*3 can be derived by the proper outer and inner diameter of Tx coil, inner diameter of Rx coil, and number of turns for Tx and Rx coils at given design constraints [8]. The three-coil link optimization procedure maximizes η23 and *Q*4 in (2), and additionally adjust *k*34 in the Rx to provide the maximum PTE, η3-coil. A more detailed flow chart is discussed in [9]. In this optimization procedure, the additional *L*3 coil in the Rx plays the role of an impedance-matching circuit, which can convert an arbitrary *R*L to *<sup>R</sup>*L,PTE for optimal PTE compared to the conventional two-coil link. In other words, the reflected load on the Tx can be adjustable for maximizing the PTE if the designer can choose the suitable *k*23 and *k*34 in the design of a three-coil link. As shown in Figure 5 which shows the exemplar designs of two- and three-coil inductive links, the three-coil link can maintain the maximum PTE by adjusting *k*34 while the two-coil link only reaches the optimal PTE for a specific *R*L = 200 Ω [9].

*Electronics* **2020**, *9*, x FOR PEER REVIEW 6 of 28

The four-coil link is sometimes very useful especially for large coil distance between the Tx and Rx and the large source impedance, *<sup>R</sup>*s, since it provides the additional degree of freedom on the Tx side. Therefore, the four-coil link is widely implemented in the high carrier frequency applications because *R*s in the PA is typically increased in the higher frequency. The four-coil link can tolerate the variations in *k*23 caused by the coil separation varying and maintain the high PTE by keeping *k*12 large. The four-coil link optimization maximizes the individual parameters of *k23Q2Q*3, *Q*1*, Q*4, *k*12 as similar in the two- and three-coil link optimization. Then, the optimal *k*34 is chosen to provide the maximum PTE as discussed in [9]. The optimization geometries of two-, three-, or four-coil links should satisfy the specific absorption rate (SAR) limit which can be verified by a field solver. If the resulted design cannot satisfy the SAR limit, the designer needs to modify the design constraints and perform the optimization procedure again. The segmented coil design in [10] helps to reduce the average SAR while the loss of the overall link is decreased by using a segmented Tx coil. In Figure 6, the segmented coil shows a more uniform E-field distribution compared to a normal coil with the same geometry, resulting in the reduced peak E-field. Therefore, more Tx power is allowable under the same tissue environment and SAR limit. The four-coil link is sometimes very useful especially for large coil distance between the Tx and Rx and the large source impedance, *R*s, since it provides the additional degree of freedom on the Tx side. Therefore, the four-coil link is widely implemented in the high carrier frequency applications because *R*s in the PA is typically increased in the higher frequency. The four-coil link can tolerate the variations in *k*23 caused by the coil separation varying and maintain the high PTE by keeping *k*12 large. The four-coil link optimization maximizes the individual parameters of *k23Q2Q*3, *Q*<sup>1</sup>*, Q*4, *k*12 as similar in the two- and three-coil link optimization. Then, the optimal *k*34 is chosen to provide the maximum PTE as discussed in [9]. The optimization geometries of two-, three-, or four-coil links should satisfy the specific absorption rate (SAR) limit which can be verified by a field solver. If the resulted design cannot satisfy the SAR limit, the designer needs to modify the design constraints and perform the optimization procedure again. The segmented coil design in [10] helps to reduce the average SAR while the loss of the overall link is decreased by using a segmented Tx coil. In Figure 6, the segmented coil shows a more uniform E-field distribution compared to a normal coil with the same geometry, resulting in the reduced peak E-field. Therefore, more Tx power is allowable under the same tissue environmentandSARlimit.The four-coil link is sometimes very useful especially for large coil distance between the Tx and Rx and the large source impedance, *<sup>R</sup>*s, since it provides the additional degree of freedom on the Tx side. Therefore, the four-coil link is widely implemented in the high carrier frequency applications because *R*s in the PA is typically increased in the higher frequency. The four-coil link can tolerate the variations in *k*23 caused by the coil separation varying and maintain the high PTE by keeping *k*12 large. The four-coil link optimization maximizes the individual parameters of *k23Q2Q*3, *Q*1*, Q*4, *k*12 as similar in the two- and three-coil link optimization. Then, the optimal *k*34 is chosen to provide the maximum PTE as discussed in [9]. The optimization geometries of two-, three-, or four-coil links should satisfy the specific absorption rate (SAR) limit which can be verified by a field solver. If the resulted design cannot satisfy the SAR limit, the designer needs to modify the design constraints and perform the optimization procedure again. The segmented coil design in [10] helps to reduce the average SAR while the loss of the overall link is decreased by using a segmented Tx coil. In Figure 6, the segmented coil shows a more uniform E-field distribution compared to a normal coil with the same geometry, resulting in the reduced peak E-field. Therefore, more Tx power is allowable under the same tissue environment and SAR limit.

Although previous studies provide the optimization of two-, three-, or four-coil inductive link [8,9], they only focus on the optimization procedure for fixed Tx and Rx coils that is not simply applicable for powering large arena in the cage. If the designer uses the large Tx coil around the cage, the overall PTE will significantly drop and show large variations depending on the location of the IMD. Several approaches have been studying to improve the PTE from Tx to Rx coils while maintaining the homogeneity of wireless power distribution. These approaches can be mainly Although previous studies provide the optimization of two-, three-, or four-coil inductive link [8,9], they only focus on the optimization procedure for fixed Tx and Rx coils that is not simply applicable for powering large arena in the cage. If the designer uses the large Tx coil around the cage, the overall PTE will significantly drop and show large variations depending on the location of the IMD. Several approaches have been studying to improve the PTE from Tx to Rx coils while maintaining the homogeneity of wireless power distribution. These approaches can be mainly Although previous studies provide the optimization of two-, three-, or four-coil inductivelink [8,9], they only focus on the optimization procedure for fixed Tx and Rx coils that is not simplyapplicable for powering large arena in the cage. If the designer uses the large Tx coil around the cage, the overall PTE will significantly drop and show large variations depending on the location of the IMD. 110

*Electronics* **2020**, *9*, 1999 Several approaches have been studying to improve the PTE from Tx to Rx coils while maintaining the homogeneity of wireless power distribution. These approaches can be mainly classified into two categories: modular design of coil array, as shown in Figure 7, and resonance-based multi-coil inductive link, as shown in Figure 8 in the following section. As shown in Figure 7b, the overall PTE distribution across the multi-layer Tx coil array has variations within ±24% of the average PTE. The higher PTE peaks are resulted from the Tx coils on layer 1, while the lower peaks are associated with the Tx coils in layers 2 and 3. On the one hand, the layer 1 is slightly closer to the Rx coil. On the other hand, the Tx coils in layers 2 and 3 are more overlapped and surrounded by other Tx coils. This condition leads to larger parasitic capacitance and resistance, resulting in the lower Q and PTE. Figure 7c shows the PDL distribution when the Rx is swept within the cage at the height of 70 mm. Thanks to the proposed configuration of multi-layer Tx coil array together with the CLPC mechanism, the PDL can be maintained at 20 mW with fluctuations of less than 2 mW. It should be noticed that one of the main disadvantages in this modular system is that one PA is required for each driving coil in the coil array, resulting in the increased complexity and cost of the Tx design. 

arena when the Rx is swept at the height of 70 mm with CLPC set at 20 mW [11,12].

whether to adopt a modular coil design or a specific coil design dedicated to a designated area.

the cage arena when the Rx is swept at the height of 70 mm with CLPC set at 20 mW [11,12].

 

The coupling between loosely coupled Tx and Rx coils is the dominant factor in determining the PTE of the four-coil inductive link. Since the size of the headstage is considerably smaller than the (**a**) (**b**) 

cubical headstage, as shown in Figure 8b.

the Tx resonators only

 

 the resonance frequency

**Figure 8.** The configuration of the resonance-based four-coil inductive link implemented in (**a**) the EnerCage-HC system [13] and (**b**) the EnerCage-HC2 system [14]. (**c**) Measured PTE when the headstage is swept inside the homecage at the heights of 4 cm, 8 cm, 12 cm, 16 cm, and 20 cm. **Figure 8.** The configuration of the resonance-based four-coil inductive link implemented in (**a**) theEnerCage-HC system [13] and (**b**) the EnerCage-HC2 system [14]. (**c**) Measured PTE when the headstageis swept inside the homecage at the heights of 4 cm, 8 cm, 12 cm, 16 cm, and 20 cm.

#### *2.2. Closed-Loop Power Control (CLPC)*  2.1.2. Coil Optimization for Inductive Links Implemented in Wirelessly-Powered Cages

Compared to the wireless power transmission system between the fixed Tx and Rx coils, as shown in Figure 1c, the Rx coil attached to the animal body continuously moves inside the wirelesslypowered cage resulting in the coupling variation between Tx and Rx coils. In addition, the power consumption in the mobile device is typically not constant for recording or stimulation operation. Therefore, CLPC, which can dynamically compensate for coupling distance and load variations due to animal movements and implant functions, is required to provide enough power for the mobile device [16]. When the mobile device receives more than enough power, the CLPC reduces the Tx power automatically to minimize the power dissipation on the Tx and the EM exposure on the animal subject, resulting in the improvement of wireless link efficiency and ensuring safety. The CLPC is typically composed of the data communication channel from the Rx to the Tx, the control unit, DC-DC converter, and the PA as shown in the exemplar design of Figure 9a. The rectifier voltage in the Rx, *V*rec, is monitored and sent to the Tx through the data communication channel which can be either near-field or far-field data communication. The control unit, such as a microcontroller, in the Tx collects the rectifier information through data demodulator block and determines whether the Rx receives enough power or not. If the Rx is not receiving sufficient power, the microcontroller controls the digital potentiometer to reduce the feedback voltage of DC-DC converter. Then, the DC-DC converter increases the PA supply voltage, *V*DD\_Tx, to increase the amount of transmitted power. Otherwise, the microcontroller adjusts the digital potentiometer to decrease *V*DD\_Tx if the Rx is receiving surplus power. Figure 9b shows the exemplar operation of CLPC in [16]. The CLPC starts to increase the transmitted power by increasing *V*DD\_Tx when the rat moved to low PTE areas or stood For the abovementioned two categories of inductive link configurations, the optimization method for each category is different. First, we talk about the optimization method for the inductive link incorporating Tx coil array [11,12]. Instead of having a single Tx coil, identical Tx coils are repeated and tiled at the bottom of the cage so that wireless power transmission covers the entire cage arena. One of the Tx coils, which is closest to the Rx, is activated, and together with the Rx coil forms a two-coil inductive link. Therefore, the optimization of the Tx coil and the Rx coil can refer to the optimization procedure of the conventional two-coil inductive link. Furthermore, other strategies in terms of the Tx coil array design are implemented to improve the homogeneous distribution of the electromagnetic (EM) field within the entire cage arena. As shown in Figure 7a, the effective area of a single Tx coil, where most of transmitted power are focalized, is located at the center of the Tx coil and has same distances from the edges of the Tx coil. The PTE drops at the boundaries of the adjacent Tx coils. Multi-layer Tx coil array is typically utilized to provide uniform power transmission over large areas. Instead of fully overlapping, one layer is shifted from the other layer, so that the point of intersection of every three adjacent coils is on the center of the coil in the previous layer, as shown in Figure 7a. With the configuration of multi-layer Tx coil array, the effective areas of the Tx coils cover the entire cage arena. Moreover, the Tx coil array should cover larger area than the cage arena so that the edges of the cage arena are still covered by the multi-layer Tx coil array for homogeneous wireless power transmission. As shown in Figure 7b, the overall PTE distribution across the multi-layer Tx coil array has variations within ±24% of the average PTE. The higher PTE peaks are resulted from the Tx coils on layer 1, while the lower peaks are associated with the Tx coils in layers 2 and 3. On the one hand, the layer 1 is slightly closer to the Rx coil. On the other hand, the Tx coils in layers 2 and 3 are more overlapped and surrounded by other Tx coils. This condition leads to larger parasitic capacitance and resistance, resulting in the lower Q and PTE. Figure 7c shows the PDL distribution when the Rx is swept within the cage at the height of 70 mm. Thanks to the proposed configuration of multi-layer Tx coil array together with the CLPC mechanism, the PDL can be maintained at 20 mW with fluctuations of less than 2 mW. It should be noticed that one of the main disadvantages in this modular system is that one PA is required for each driving coil in the coil array, resulting in the increased complexity and cost of the Tx design.

The other type of coil optimization is relevant to the inductive link incorporating Tx and/or Rx resonator, for instance the resonance-based four-coil inductive link implemented in the EnerCage-HC system families [13,14]. The key factor in determining the Tx resonator geometries in EnerCage-HC system is the compatibility with dimensions of the standard-sized rodent homecage and the maximum overlap with the Tx coil. Instead of having an array of identical Tx coils tiled at the bottom of the cage, in the EnerCage-HC system, multiple Tx resonators wrap around the cage to provide wireless power coverage of the entire cage (see Figure 8). In this case, optimizing the four-coil inductive link means increasing the minimum PTE within the homecage to ensure PDL is enough to keep the headstage on when the CLPC adjusts the Tx power, as opposed to maximizing PTE in the perfectly aligned regions in traditional coil optimization.

The coupling between loosely coupled Tx and Rx coils is the dominant factor in determining the PTE of the four-coil inductive link. Since the size of the headstage is considerably smaller than the homecage, the effective area of the Rx resonators should be maximized so that more Tx magnetic flux can pass through the Rx resonator, thereby improving the coupling between the Tx and Rx resonators. In [15], the Rx resonator wrap around the headstage, maximizing the area encompassed by the Rx resonator without enlarging the size of the headstage, as shown in Figure 8a. In [14], the largest possible area of the headstage is the diagonal planes of the headstage cube, therefore, the Rx resonators are tilting an angle of 25◦ compared to the horizontal plane in each four directions of the cubical headstage, as shown in Figure 8b.

Due to the large separation and size difference between the Tx and Rx structures, the Tx and Rx resonators are loosely coupled. Hence, a single target resonance frequency for this system can be set, regardless of the Rx location in the homecage. Additionally, because of the strong coupling among the Tx resonators, only one Tx resonator needs to be finely tuned to match the resonance frequency of the entire Tx structure with the target carrier frequency. Such practical and convenient characteristics are also applicable on the Rx resonators, which are also strongly coupled with each other.

Figure 8c shows the PTE distribution within the 3D volume of the cage. As we can see that while the center area has a weaker magnetic flux density, mutual coupling, and thereby lower PTE, the PTE measured at each height is more uniform, with smaller variations of less than 7%. Although the PTE reduces as the height increases, the deduction of the PTE is slowed, which is mainly credited to the enhancement of EM field by the Tx resonator at the top of the cage. Although the optimization procedures in [13,14] are only dedicated to the specific geometry of the cage, which is difficult to be extended for a large arena, these techniques show high and homogeneous PTE inside the standard geometry of cage. Besides, only one PA is needed, which can significantly simplify the design of the power Tx. Therefore, the designer needs to choose the coil design and optimization procedure whether to adopt a modular coil design or a specific coil design dedicated to a designated area.

#### *2.2. Closed-Loop Power Control (CLPC)*

Compared to the wireless power transmission system between the fixed Tx and Rx coils, as shown in Figure 1c, the Rx coil attached to the animal body continuously moves inside the wirelessly-powered cage resulting in the coupling variation between Tx and Rx coils. In addition, the power consumption in the mobile device is typically not constant for recording or stimulation operation. Therefore, CLPC, which can dynamically compensate for coupling distance and load variations due to animal movements and implant functions, is required to provide enough power for the mobile device [16]. When the mobile device receives more than enough power, the CLPC reduces the Tx power automatically to minimize the power dissipation on the Tx and the EM exposure on the animal subject, resulting in the improvement of wireless link efficiency and ensuring safety.

The CLPC is typically composed of the data communication channel from the Rx to the Tx, the control unit, DC-DC converter, and the PA as shown in the exemplar design of Figure 9a. The rectifier voltage in the Rx, *V*rec, is monitored and sent to the Tx through the data communication channel which can be either near-field or far-field data communication. The control unit, such as a microcontroller, in the Tx collects the rectifier information through data demodulator block and determines whether the Rx receives enough power or not. If the Rx is not receiving sufficient power, the microcontroller controls the digital potentiometer to reduce the feedback voltage of DC-DC converter. Then, the DC-DC converter increases the PA supply voltage, *V*DD\_Tx, to increase the amount of transmitted power. Otherwise, the microcontroller adjusts the digital potentiometer to decrease

*V*DD\_Tx if the Rx is receiving surplus power. Figure 9b shows the exemplar operation of CLPC in [16]. The CLPC starts to increase the transmitted power by increasing *V*DD\_Tx when the rat moved to low PTE areas or stood up resulting in the weak coupling from the Tx to Rx coils as shown in the inset t = 14,817 s. When the Rx coil was close to the Tx coil located the bottom of the homecage or high PTE areas as shown in the inset t > 14,817 s, the Rx receives more power than necessary resulting in the increase of rectifier voltage, *V*rec. Then, the CLPC immediately decreases the *V*DD\_Tx to reduce the transmitted power for the regulation of received Rx power. In the result, the Rx can always receive the constant power from the Tx regardless of any environmental variations during the experiment. *Electronics* **2020**, *9*, x FOR PEER REVIEW 10 of 28 up resulting in the weak coupling from the Tx to Rx coils as shown in the inset t = 14,817 s. When the Rx coil was close to the Tx coil located the bottom of the homecage or high PTE areas as shown in the inset t > 14,817 s, the Rx receives more power than necessary resulting in the increase of rectifier voltage, *V*rec. Then, the CLPC immediately decreases the *V*DD\_Tx to reduce the transmitted power for the regulation of received Rx power. In the result, the Rx can always receive the constant power from the Tx regardless of any environmental variations during the experiment. 

**Figure 9.** (**a**) Block diagram of CLPC in the two-coil inductive link, and (**b**) the experimental CLPC waveforms in the wirelessly-powered cage to compensate for the distance variation between Tx and Rx in transient caused by the animal movement [16]. **Figure 9.** (**a**) Block diagram of CLPC in the two-coil inductive link, and (**b**) the experimental CLPC waveforms in the wirelessly-powered cage to compensate for the distance variation between Tx and Rx in transient caused by the animal movement [16].

#### *2.3. Scalability for Wireless Coverage 2.3. Scalability for Wireless Coverage*

The animal experimental arena can be either a square standard cage or a specific shape with a larger area depending on the experimental purposes. Some wirelessly-powered cages are dedicated to the standard cage [13,16], which have an advantage in terms of compatibility with the standard racks of rodent cages in the animal facilities compared to the modular design for a specific shape. This compatibility is beneficial for longitudinal studies on multiple animals in separate standard cages resulting in the simultaneous and massive data collection from many animal subjects [15]. The modular designs can be easily extended for large area or specific shape [11,17,18] while the optimized wireless cages dedicated to the standard cage are hard to modify the wireless coverage. One of the important considerations for the scalability using the modular coil design is to choose the suitable method for tracking the Rx coil position because the modular coil design needs to select the nearest Tx coil to the Rx coil. If the modular system does not equip the tracking method, all the Tx coils in the array will be driven simultaneously, resulting in significant power loss. In [11], a small permanent magnet is attached to the mobile device, and the wirelessly-powered cage detects the mobile device using three-axis magnetic sensors to select the nearest Tx coil to the freely moving animal subject. The permanent magnet is also utilized in [18] for the Rx coil tracking, where a single Tx coil moves mechanically on XY-rails located at the bottom of the cage. However, in the WPT system, the performance of magnetic sensors might be degraded due to the strong magnetic fields inside the cage, resulting in not sufficient tracking resolution and quality. The optical animal tracking techniques are studied in [16,19] using an infrared range camera or The animal experimental arena can be either a square standard cage or a specific shape with a larger area depending on the experimental purposes. Some wirelessly-powered cages are dedicated to the standard cage [13,16], which have an advantage in terms of compatibility with the standard racks of rodent cages in the animal facilities compared to the modular design for a specific shape. This compatibility is beneficial for longitudinal studies on multiple animals in separate standard cages resulting in the simultaneous and massive data collection from many animal subjects [15]. The modular designs can be easily extended for large area or specific shape [11,17,18] while the optimized wireless cages dedicated to the standard cage are hard to modify the wireless coverage. One of the important considerations for the scalability using the modular coil design is to choose the suitable method for tracking the Rx coil position because the modular coil design needs to select the nearest Tx coil to the Rx coil. If the modular system does not equip the tracking method, all the Tx coils in the array will be driven simultaneously, resulting in significant power loss. In [11], a small permanent magne<sup>t</sup> is attached to the mobile device, and the wirelessly-powered cage detects the mobile device using three-axis magnetic sensors to select the nearest Tx coil to the freely moving animal subject. The permanent magne<sup>t</sup> is also utilized in [18] for the Rx coil tracking, where a single Tx coil moves mechanically on XY-rails located at the bottom of the cage. However, in the WPT system, the performance of magnetic sensors might be degraded due to the strong magnetic fields inside the cage, resulting in not su fficient trackingresolutionandquality.

 a Microsoft Kinect®. The Microsoft Kinect includes infrared depth (IR-3D) and red-green-blue (RGB-2D) cameras allowing animal tracking in both bright and dark conditions. Since the optical tracking method can obtain the information about both the Rx coil position and the animal subject behavior at a time, it is more beneficial than the permanent magnet sensing in terms of the additional analysis of animal locomotion and behavior. However, the optical cameras should be installed on the top of the cage with a few tens of centimeters. As such, the lid of the cage should not be closed during the experiment. As an alternative, the resonator-based cage design, which allows for automatic magnetic field localization, obviating the need for a tracking system or switching the coils, are introduced in [13–15,17]. In these systems, the multi-resonator coil arrangement around the cage, simply driven by The optical animal tracking techniques are studied in [16,19] using an infrared range camera or a Microsoft Kinect ®. The Microsoft Kinect includes infrared depth (IR-3D) and red-green-blue (RGB-2D) cameras allowing animal tracking in both bright and dark conditions. Since the optical tracking method can obtain the information about both the Rx coil position and the animal subject behavior at a time, it is more beneficial than the permanent magne<sup>t</sup> sensing in terms of the additional analysis of animal locomotion and behavior. However, the optical cameras should be installed on the top of the cage with a few tens of centimeters. As such, the lid of the cage should not be closed during the experiment. As an alternative, the resonator-based cage design, which allows for automatic magnetic field localization, obviating the need for a tracking system or switching the coils, are introduced in [13–15,17]. In these

a single LC-tank located at the bottom of the cage, can dynamically focus the magnetic field at the position of Rx coil. However, the parasitic resistance in multi-resonator coils still dissipates power all  the time regardless of the Rx coil position, resulting in the additional power loss compared to the switchable modular Tx coil design. 
