Tunable Coil-Links for Multiple-Receiver Wireless Power Transfer System With Arbitrary Position and Power Division

This study demonstrates tunable coil links for a wireless power transfer system with arbitrarily-located multiple receivers and arbitrary power division between them. Both the Tx and Rx coils are composed of a main coil and an array of assistant coils loaded with varactors. By tuning the varactors to control the resonant characteristics of each assistant coil, the Tx coil can steer the near field, and the Rx coil can reconfigure its electrical size. Consequently, the proposed system maintains the high overall efficiency regardless of the position of the receivers and the power division ratio. For the verification, a two-receiver system at 6.78 MHz is designed and fabricated with a $2\times 1$ assistant coil array. A thorough investigation is performed for various cases, which include when the two receivers of the same size are located symmetrically with respect to the center of the Tx coil and two receivers of different sizes, located asymmetrically. For all cases, the overall efficiency is evaluated for various receiver locations and power division ratios when the tunable coil links are adopted on both Tx and Rx coils, only on either Tx or Rx coil. The conventional system provides the minimum transfer efficiency of 0% for symmetric case, as well as 12.8% for asymmetric case with respect to the receiver locations. On the other hand, results of the proposed system show minimum efficiency of 83.7% and 83.5% for symmetric and asymmetric case, respectively. More importantly, while the conventional system showed strong dependence not only on the Rx locations but also the power division ratio, the proposed system maintains the efficiency with little, if any, variation regardless of the two. For example, while the power division ratio is varied from 5:1 to 1:5, the proposed system remains a very high efficiency of up to 91.0% with only 0.3% variation.

Rxs, as well as the range of power division ratio between 82 them, which are the two most essential requirements in a 83 multiple-receiver WPT system. 84 Although the WPT system with tunable Tx and Rx coil 85 links provides the best performance, the asymmetric tun-86 able coil-link WPT system that adopts tunable coil links 87 at either Tx or Rx also provides outstanding performance. 88 Further, the tunable coil links can be applied even if the Rxs 89 have different size and/or are located asymmetrically. Hence, 90 the proposed tunable coil-link system can solve the limita-91 tions of multiple-receiver WPT systems with practical planar 92 structures. 93 The rest of this manuscript is organized as follows. 94 In Section II, the configuration and analysis of the proposed 95 system are presented. The effects of a tunable coil links with 96 arbitrary positions of Rxs and an arbitrary power division 97 to Rxs are investigated in Sections III and IV, respectively. 98 Section V provides the experimental results for the tunable 99 coil links. Two types of two-receiver systems are investigated; 100 first is the system with two Rxs of the same size that are 101 located symmetrically with respect to the center of the Tx 102 coil. The second is with two Rxs of different sizes, located 103 asymmetrically with respect to the center of the Tx coil. For 104 both systems, the performance is evaluated for various Rx 105 locations and power division ratios. Finally, for all cases, the 106 effect of tunable coil-link system is analyzed not only when it 107 is applied to both Tx and Rx coils, but also when it is adopted 108 to Tx coil and to Rx coils.

II. PROPOSED TUNABLE COIL-LINK SYSTEM
110 Figure 1 shows the proposed tunable coil-link WPT sys-111 tem with multiple receivers. For simplicity, the number of 112 receivers is set to two. The tunable coil links are composed 113 of one main coil and an array of assistant coils; a driving coil 114 (Tx D ) and assistant coils (Tx ai , i = 1, 2) in the Tx coil, a load 115 coil (Rx L ) and assistant coils (Rx ai , i = 1, 2) in the Rx coil. 116 Since the main coil and the assistant coils can be printed on 117 both sides of a substrate for planar-type coils, the increase in 118 the volume is minimized. For the Tx coil, only the driving coil 119 is driven and for the Rx coil, only the load coil is connected 120 directly with the load. 121 Each assistant coil in both Rx and Tx coils is loaded with 122 a varactor to control its resonant characteristics. However, its 123 effect is different for the two. For the Rx coil, the varactors 124   Therefore, in a multiple-receiver WPT system, the tunable 157 coil links applied to the Rx coil allows arbitrarily-positioned 158 receivers to maintain high overall transfer efficiency.

159
On the other hand, the varactors that load each assistant one receiver requires more power than the other in a two-170 receiver system. Then the varactors can be tuned such that 171 more flux is generated towards this receiver than the other, 172 i.e. the Tx coil is steered such that more power is transferred 173 to one receiver than the other.

174
This is illustrated in Fig. 3. In Fig. 3(a), the two varactors 175 in the two assistant coils are such that the currents induced 176 on both coils are identical. In this case, the same amount 177 of power is transferred wirelessly in the two regions divided 178 by the two assistant coils. However, when the varactors are 179 tuned such that the current on Tx a1 is much stronger than 180 Tx a2 , i.e. the resonant frequency of Tx a1 is close to that of 181 the driven signal while that of Tx a1 is far away from the 182 operating frequency, then a much larger amount of power 183 will be transferred in the left region than in the right, i.e. the 184 Tx coil will steer the power more to the left. Therefore, in a 185 multiple-receiver WPT system, the tunable coil links applied 186 to the Tx coil allows to steer the radiated power to maintain 187 high overall efficiency regardless of the power division ratio 188 between the multiple receivers. 189 In this work, the assistant coil array in the Tx coil is in 190 a 2 × 1 configuration. Thus the freedom of receiver positions 191 is only along the x axis. Further, the receivers are located 192 in the two WPT regions divided by the 2 × 1 assistant coil 193 array in the Tx, i.e. one in the +x side and the other on 194 the −x side. By increasing the size of the array, freedom in 195 the location of the receivers and/or the number of receivers 196 for simultaneous wireless power transfer can be increased. 197 For example, increasing the size of the assistant coil array in 198 the 2 × 2 configuration allows the Rx coils to have position 199 freedom in both x and y directions. The assistant coil array in the Rx coil is also in a 2 × 1 con-201 figuration. Therefore, the effective width of the coil can be 202 controlled along the x direction only. Similarly, by increasing 203 the array size to 2 × 2, both the width and length of the 204 coil can be controlled, at the cost of reduced Q and increased 205 system complexity.

206
For verification of the proposed tunable coil-link system, 207 the coils in Table 1 are designed and fabricated by printing 208 the driving and assistant coils on both sides of a 1.5-mm-thick 209 substrate (RF-35 from Taconic). Therefore, the increase in the

228
The proposed tunable coil-links system is an extremely ver-  The performance of the proposed system is investigated at a two-receiver system, the total transfer efficiency η is on both the Tx and Rx sides are tuned so that the power 251 division ratio between the two Rx coils is 1:1, i.e. |S 21 | 2 = 252 |S 31 | 2 for all cases. This is so that the effectiveness of the 253 proposed tunable coil links are verified from the location-free 254 perspective only. Finally, all simulated results are obtained by 255 post-processing the full-wave simulated results from ANSYS 256 HFSS [22]. The driving and load coils are adaptively matched 257 to provide a constant input power to the Tx coil regardless of 258 the location of Rx coils [23]. 259 The proposed coil system is a multi-coil system where 260 cross coupling between coils may have non-negligible effect 261 on the overall performance. Therefore, cross coupling is taken 262 into account in all simulations throughout the manuscript.

263
A. SYMMETRIC CASE 264 In the symmetric case, two Rx A coils of the same size 100 × 265 100 mm 2 are located symmetrically with respect to the center 266 of the Tx coil, i.e. D x = 0 in Fig. 1. The offset is set 267 to D x = 50 mm initially, and is increased up to 155 mm, 268 where the Rx coils fall completely outside the Tx coil. The 269 varactor on each assistant coil on both the Tx and Rx sides 270 are tuned so that the total transfer efficiency η is maximized 271 while maintaining |S 21 | 2 = |S 31 | 2 .
272 Figure 5 shows the simulated η of the proposed tunable 273 coil-link system at 6.78 MHz. For comparison, the total 274 transfer efficiency η of the conventional system composed of 275 only main coils is also shown. When the two coils are located 276 closely, i.e., when D x is small, both systems show virtually 277 the same performance with a very high η. For instance, when 278 D x = 55 mm, the simulated total transfer efficiencies are 279 97.9% and 98.3% for the proposed and the conventional 280 systems, respectively. However, as D x increases, a dramatic 281 decrease in the total efficiency is observed for the conven-282 tional system, which eventually reaches a transfer null at 283 D x = 109 mm. This is when the two coils are located such that 284 the net amount of magnetic flux passing through both coils in 285 the normal direction vanishes. Therefore, coupling vanishes 286 between the Tx and Rx coils, which results in zero transfer 287 efficiency. On the contrary, the proposed tunable coil-link 288  coil. This is verified by the two same 100 pF capacitances in 300 Table 2, and the transfer efficiency that is virtually the same as   is due to the asymmetry of the system: the two coils of 335 different sizes cannot be located at the transfer null point 336 simultaneously. However, it still suffers from transfer valleys, 337 with substantially low overall efficiency. Moreover, there are 338 two valleys in the simulated D x range. The first valley appears 339 at D x = 82 mm. This is when Rx #2 is located at D x + 340 D x = 102 mm, which is a transfer null point. Since Rx #2 341 cannot receive any power, Rx #1 must not receive any power 342 either in order to receive the same power, i.e. to satisfy the 343 condition |S 21 | 2 = |S 31 | 2 . However, the simulated efficiency 344 of 30.2% indicate that the two receivers are indeed receiving 345 non-zero amount of power. This means that although Rx #2 346 is located at a transfer null point, it still receives power not 347 from the Tx, but coupled from Rx #1.

348
A similar phenomenon occurs at D x = 109 mm where 349 Rx #1 is now located at the transfer null point. Nevertheless, 350 the conventional system suffers from rapid decrease in the 351 total transfer efficiency around the two points, which is as 352 low as 13%. On the other hand, the assistant coils in both the 353 Tx and Rx sides of the proposed system removes the transfer 354 valleys to maintain a very flat total transfer efficiency above 355 86.6% in the entire simulated D x range.

356
The values of all varactors for various offset D x is sum-357 marized in Table 3. Since it is an asymmetric system with 358 equal power division, the two varactors in the Tx coil require 359 different values to steer the generated magnetic field and 360 compensate for the difference in the size and location of 361 the two Rxs. A larger current is induced in the assistant 362 coil closer to the smaller coil to maintain the equal power 363 division. At D x = 55 mm, the assistant coil Tx a1 is open 364 circuited, as indicated by the varactor capacitance of 0 pF. 365 Since the larger Rx #1 have a larger coupling coefficient than 366 the smaller Rx #2, the assistant coil Tx a1 which transfers 367 power mostly to Rx #1 is turned off and Rx #1 receives power 368 only from the driving coil which is misaligned so that the 369 power division ratio of 1:1 is maintained.   conventional and the proposed system shows the highest over-416 all transfer efficiency η when R = 1:1, where the coupling 417 coefficient between the Tx and both Rxs are the same.

418
However, the total transfer efficiency for the conventional 419 system is η = 39.4%, which is substantially lower than that 420 of the proposed system η = 93.1%. Further, the situation 421 becomes worse as the power division ratio R is varied. As R is 422 tuned to 1:5, the conventional system suffers from a relatively 423 large 8.6% decrease in the overall transfer efficiency. This 424 is because the conventional system achieves power division 425 by adjusting the load impedances based on an impedance 426 matching network [17], [18], [19]. Because of the intentional 427 mismatch, lower efficiency is inevitable. On the other hand, 428 the proposed system maintains virtually the same total trans-429 fer efficiency, without any sacrifice in the transfer efficiency 430 regardless of the power division ratio.

431
The capacitance sets in Table 4 show important results. For 432 R = 1:1, the two capacitances in the Tx coil are the same. This 433 is to generate the same amount of magnetic flux in the two 434 WPT regions. Further, the capacitance conditions for both 435 Rxs are identical due to the equal power division. As R is 436 varied, the capacitances in the Tx coil must change to steer 437 the near field according to the R. However, the capacitances 438 remain the same in the Rxs, regardless of R, i.e. the optimal 439 effective size of Rx to maximize η does not change.   The conventional system shows a transfer valley at 462 D x = 109 mm. Since then Rx #1 is located at the transfer 463 null, the overall transfer efficiency must be η = 0%. However, 464 the smaller Rx #2, which is not located at the null, does 465 receive power from Tx, part of which is relayed to Rx #1. 466 Nevertheless, the overall efficiency is very low at 13% when 467 R = 1:1 due to the low efficiency of the power relay. As R 468 is tuned by controlling the impedance matching such that 469 Rx #2 receives more power than Rx #1 which is located at 470 the transfer null, the efficiency increases. For instance for 471 R = 1:5, the efficiency increases from 13% to 31.1%. This 472 is because the low-efficient power relay from Rx #2 to Rx #1 473 is not required as much. On the other hand, when R is tuned 474 such that the Rx #2 receives less power than the Rx #1, for 475 instance R = 5:1, more power must be relayed from Rx #2 to 476 Rx #1 since Rx #1 is located at the transfer null and cannot 477 receive any power directly from the Tx coil. Therefore, the 478 overall efficiency decreases even further to 8.3%, indicating 479 that both coils are receiving little power although to achieve 480 the power division ratio of 5:1.

481
On the other hand, the tunable coil links maintains a high 482 efficiency, which remains relatively constant regardless of 483 R. As R changes from 5:1 to 1:5, η changes from 91.3% to 484 87.3%. In contrast to the conventional system, the overall 485 efficiency is lower when Rx #2 receives more power than 486 when Rx #1 receives more power, although the difference is 487 small. This is natural because the Rx #2 is less efficient due 488 to the smaller size. Further, the fractional variation in η that 489 the proposed system exhibit as R varies from 5:1 to 1:5 is 490 only 5.9%, which is incomparable to that of 115.7% for the 491 conventional system. This indicates that besides showing a 492 high overall η, it is maintained regardless of R. 493 The capacitance conditions for the asymmetric case are 494 summarized in Table 5, which shows a very similar trend 495 as the symmetric case: adjustment of R is achieved with the 496 assistant coils in the Tx coil only.

499
For the experimental verification, the coils in Table 1 are 500 fabricated on a 1.52-mm Taconic RF-35 ( r =3.5) substrate. 501 As shown in Fig. 9, an acrylic fixture was used to fix the 502 vertical distance between the Tx and Rx coils at D z = 20 mm 503 and to position the Rx coils accurately.

504
To adjust the loaded capacitance on each assistant coil, 505 Infineon BBY66 was used. A total of four different cases 506 are measured; when the tunable coil links are adopted only 507 on the Tx coil, only on the Rx coils, and on both the Tx 508 coil and Rx coils. The last case is when the technique is 509 not applied on any side, which is the conventional case. 510 The S-parameters between the Tx and Rx coils were mea-511 sured using a ZNB8 VNA from ROHDE & SCHWARZ, 512 calibrated using a ZVZ135 kit. Measured S-parameters are 513 post-processed using the Agilent Advanced Design System 514 (ADS) to achieve optimal matching conditions for the 50-515 system at 6.78 MHz. 516 Figure 10 shows the measured and simulated η with respect 517 to the offset D x when the Rxs are symmetrical with the power 518 division ratio R = 1:1. For comparison, the measured results 519 of a conventional counterpart are provided. Simulated results 520 for all cases are also provided.

521
The measured total efficiency η of the conventional system 522 starts to decrease sharply at approximately D x = 105 mm, and 523 it shows a transfer null at D x = 109 mm. Therefore, the Rx 524 coils cannot receive power from the Tx around D x = 109 mm, 525 although the Rxs are still located within the Tx. However, the 526 WPT system with the proposed tunable coil links successfully 527 FIGURE 11. Measured (thick) and simulated (thin) total transfer efficiencies of asymmetric WPT systems according to D x with D x is 20 mm. that although the conventional system shows a very high 556 total efficiency of 95.9% at D x = 55 mm, it suffers from 557 two evident transfer valleys, the first one at D x = 82 mm 558 with η = 30.0% and the second one at D x = 109 mm with 559 η = 13.0%. The former is due to the smaller coil Rx B that is 560 located at the transfer null point, while the latter is because 561 the larger coil Rx A is located at the transfer null point.

562
Again, when the tunable coil links are on both sides and 563 when they are on the Rx coils show virtually the same per-564 formance, and maintains the total efficiency η extremely flat 565 above 82.0% in the entire range of D x tested. When tunable 566 coil links are on the Tx coil only, the efficiency is somewhat 567 lower than the previous two cases. However, this is only 568 around the valleys of the conventional system, and still shows 569 great compensation of the total efficiency that is higher than 570 75.4% in the entire range. As was the case for the symmetric 571 system, the assistant coils on the Rx coils play the dominant 572 role in the two-receiver asymmetric system with R = 1:1. Figure 12 shows the simulated and measured results of η 574 according to the R for the symmetric case, when two identical 575 VOLUME 10, 2022  Rx coils with 100×100 mm 2 sizes are located symmetrically 576 at D x = 108 mm, which is immediately next to the transfer 577 null. The conventional system suffers from η that is only 578 40.3% when R = 1:1, which reduces to 35.0% when R is tuned 579 to 5:1. However, the proposed system increases the efficiency 580 dramatically, and minimizes the degradation due to unequal 581 power division.

582
As R is tuned, the role of the tunable coil links on the Tx 583 coil becomes more important because they can steer the gen-  Figure 13 shows the total efficiency η with respect to R, 592 when two Rxs with different sizes in Table 1 are located 593 asymmetrically with D x = 109 mm and D x =20 mm. This is 594 the case when the larger Rx coil (Rx A ) is located at a transfer 595 null point. Again, the conventional system suffers from sub-596 stantial deterioration in the overall efficiency that is as low 597 as 7.9% when R = 5:1. Although the efficiency increases 598 as R is tuned, it is still very low at 30.3% when R = 1:5. 599 On the other hand, the tunable coil links, whether on the Rx 600 side only, Tx, side only, or on both sides, shows remarkably 601 high total efficiency with insignificant degradation in η due 602 to tuning of R. For all cases, the R = 5:1 case shows slightly 603 higher efficiency than the R = 1:5 case, since the steering of 604 Tx is more efficient when more power needs to be delivered 605 to the larger coil, than to the smaller, as discussed at the 606 end of Section IV. The measured results for the symmetric 607 and asymmetric cases with respect to R are summarized in 608 Table 7. Table 8 summarizes the recent state-of-the-art works on 610 multiple-device WPT systems, which all show successful 611 demonstration of wireless power transfer technology to mul-612 tiple receivers with different power division. For example, 613 the time-division management technique [16] can provide an 614 unlimited power division ratio. However, the freedom in the 615 location of the receivers is limited in most cases. This can be 616 overcome using repeaters [18], at the cost of increased system 617 complexity and reduced versatility.

618
On the other hand, the proposed WPT system maximizes 619 the freedom in the location of multiple receivers to allow high 620 efficiency even when the Rx coils fall completely outside the 621 Tx coil. Further, a very high transfer efficiency is maintained 622 with minimal variation even when the power division ratio is 623 tuned for Rx coils with different sizes. Moreover, even when 624 the tunable coil links adopted on either side, the performance 625 degradation is not significant, revealing the versatility of the 626 proposed system. Therefore, the proposed tunable coil links 627 are expected to be a strong candidate to develop a practical 628 multiple-device wireless charging system to provide a very 629 high efficiency regardless of the positions of the receivers, the 630 remaining battery capacity, and/or charging speed required. 631 The power capacity of the proposed system is dominated 632 by the power handling capacity of the varactors. Although 633 not shown in here, the performance degradation due to the 634 non-ideal varactors is negligible for low to medium input 635 However, the efficiency of conventional system becomes as 676 low as 7.9% with 117.3% variation. Based on a predetermined 677 criteria, the proposed system is capable of allocating the 678 power differently to a number of devices, but still maintain the 679 high efficiency. Verification of the proposed technique with 680 an increased array size to accommodate a lager number of 681 Rxs remains as a future work.