volume | PIER Journals

Abstract

The annular micro receiving coil (RC) holds promise in the wireless power supply for capsule endoscopy (CE). The equivalent series resistance (R_SR) of the RC plays a critical role in energy transmission efficiency. Calculating the R_SR is challenging because RC typically incorporates an embedded magnetic core. To overcome this challenge, this paper employs Dowell's method and the Bessel's method respectively to calculate R_SR. The analyzed RC consists of an annular core with two grooves and dual windings positioned within the grooves. The influence of the magnetic core on the R_SR is equivalently considered through the winding skin effect and core losses. We compared the simulated, calculated, and measured values of the R_SR, and found that: the error of Dowell's method becomes smaller when the groove spacing D_g > 4 mm, but fails to capture the influence of D_g on the R_SR. Conversely, Bessel's method effectively captures the influence of D_g but exhibits larger errors (2.09%~26.52%). Based on this finding, we propose a novel Bessel-modified Dowell's (BMD) method by integrating the framework of Dowell's method with a proximity-effect correction term from Bessel's method, which reduces the maximum calculation error to within 13.72%, facilitating rapid optimization of annular coils with embedded magnetic cores.

1. Flemming, Juliane and Silke Cameron, "Small bowel capsule endoscopy Indications, results, and clinical benefit in a University environment," Medicine, Vol. 97, No. 14, e0148, Apr. 2018.
doi:10.1097/MD.0000000000010148

2. Youssef, Fady F., Laurel L. Branch, Mark Kowalczyk, and Thomas J. Savides, "Endoscopic approaches for managing small intestinal disease," Annual Review of Medicine, Vol. 76, 155-165, Jan. 2025.
doi:10.1146/annurev-med-060123-120109

3. Zhao, K., Y. F. Yang, and J. P. Wang, "Clinical value of capsule endoscopy in small intestinal diseases," Zhonghua Nei Ke Za Zhi, Vol. 59, No. 2, 124-128, 2020.
doi:10.3760/cma.j.issn.0578-1426.2020.02.006

4. Cao, Qing, Runyi Deng, Yue Pan, Ruijie Liu, Yicheng Chen, Guofang Gong, Jun Zou, Huayong Yang, and Dong Han, "Robotic wireless capsule endoscopy: Recent advances and upcoming technologies," Nature Communications, Vol. 15, No. 1, 4597, May 2024.
doi:10.1038/s41467-024-49019-0

5. Khan, Sadeque Reza, Sumanth Kumar Pavuluri, Gerard Cummins, and Marc P. Y. Desmulliez, "Wireless power transfer techniques for implantable medical devices: A review," Sensors, Vol. 20, No. 12, 3487, Jun. 2020.
doi:10.3390/s20123487

6. Jiang, Bin, Yang-Yang Qian, Jun Pan, Xi Jiang, Yuan-Chen Wang, Jia-Hui Zhu, Wen-Bin Zou, Wei Zhou, Zhao-Shen Li, and Zhuan Liao, "Second-generation magnetically controlled capsule gastroscopy with improved image resolution and frame rate: A randomized controlled clinical trial (with video)," Gastrointestinal Endoscopy, Vol. 91, No. 6, 1379-1387, 2020.
doi:10.1016/j.gie.2020.01.027

7. Gao, Jinyang, Guozheng Yan, Zhiwu Wang, Shu He, Fei Xu, Pingping Jiang, and Dasheng Liu, "Design and testing of a motor-based capsule robot powered by wireless power transmission," IEEE/ASME Transactions on Mechatronics, Vol. 21, No. 2, 683-693, Apr. 2016.
doi:10.1109/tmech.2015.2497083

8. Khodaee, Zohreh, Mohammad Reza Zakerzadeh, and Mohammad Gafar Sedigh Damghanizadeh, "Enhancing capsule endoscopy with an orient-controllable internal actuation mechanism: Proof of concept," Mechatronics, Vol. 106, 103296, Apr. 2025.
doi:10.1016/j.mechatronics.2025.103296

9. Song, Zhibin, Wenjie Zhang, Wenhui Zhang, and Dario Paolo, "A novel biopsy capsule robot based on high-speed cutting tissue," Cyborg and Bionic Systems, Vol. 2022, Article ID 9783517, 2022.
doi:10.34133/2022/9783517

10. Sidhu, Mayenaaz, Neal Shahidi, Sunil Gupta, Lobke Desomer, Sergei Vosko, W. Arnout van Hattem, Luke F. Hourigan, Eric Y. T. Lee, Alan Moss, Spiro Raftopoulos, Steven J. Heitman, Stephen J. Williams, Simon Zanati, David J. Tate, Nicholas Burgess, and Michael J. Bourke, "Outcomes of thermal ablation of the mucosal defect margin after endoscopic mucosal resection: A prospective, international, multicenter trial of 1000 large nonpedunculated colorectal polyps," Gastroenterology, Vol. 161, No. 1, 163-170, Jul. 2021.
doi:10.1053/j.gastro.2021.03.044

11. Cui, Chang, Qiang Zhao, and Zhongjian Li, "Design of wireless power supply optimized structure for capsule endoscopes," Journal of Power Technologies, Vol. 96, No. 2, 101-109, 2016.

12. Dowell, P. L., "Effects of eddy currents in transformer windings," Proceedings of the Institution of Electrical Engineers, Vol. 113, No. 8, 1387-1394, 1966.
doi:10.1049/piee.1966.0236

13. Han, Ding, Renqing Wen, Guozheng Yan, Dahong Qian, Shuai Kuang, Pingping Jiang, and Zhiwu Wang, "Stable wireless power transfer system for capsule robot using three-dimensional hybrid transmitting coil pairs," IEEE Transactions on Power Electronics, Vol. 40, No. 6, 8824-8833, Jun. 2025.
doi:10.1109/tpel.2025.3535530

14. Hua, Dezheng, Lei Deng, Janusz Gołdasz, Xinhua Liu, Haiping Du, Grzegorz Królczyk, Weihua Li, and Zhixiong Li, "Functional capsule robots: A review of locomotion, pose, medical operation and wireless power transmission reported in 2018-2023," Smart Materials and Structures, Vol. 33, No. 7, 073002, 2024.
doi:10.1088/1361-665x/ad52d8

15. Gao, Jinyang, Jinshan Zhou, Changshun Yuan, Zenglei Zhang, Chen Gao, Guozheng Yan, Ruiqin Li, and Li Zhang, "Stable wireless power transmission for a capsule robot with randomly changing attitude," IEEE Transactions on Power Electronics, Vol. 38, No. 2, 2782-2796, Feb. 2023.
doi:10.1109/tpel.2022.3212699

16. Kuang, Shuai, Guozheng Yan, and Zhiwu Wang, "Optimization design for receiving coil with novel structure based on mutual coupling model in wireless power transmission for capsule endoscope," Energies, Vol. 13, No. 23, 6460, Jul. 2020.
doi:10.3390/en13236460

17. Elizondo, David, Ernesto L. Barrios, Alfredo Ursúa, and Pablo Sanchis, "Analytical modeling of high-frequency winding loss in round-wire toroidal inductors," IEEE Transactions on Industrial Electronics, Vol. 70, No. 6, 5581-5591, Jun. 2023.
doi:10.1109/tie.2022.3192689

18. Kutkut, N. H., "A simple technique to evaluate winding losses including two-dimensional edge effects," IEEE Transactions on Power Electronics, Vol. 13, No. 5, 950-958, 1998.
doi:10.1109/63.712319

19. Gao, Jinyang, Siyu Tian, Changshun Yuan, Ziyu Ma, Chen Gao, Guozheng Yan, Ruiqin Li, Qiulin Tan, and Li Zhang, "Design and optimization of a novel double-layer Helmholtz coil for wirelessly powering a capsule robot," IEEE Transactions on Power Electronics, Vol. 39, No. 1, 1826-1839, Jan. 2024.
doi:10.1109/tpel.2023.3321845

20. Gao, Jinyang and Guozheng Yan, "Design and implementation of a clamper-based and motor-driven capsule robot powered by wireless power transmission," IEEE Access, Vol. 7, 138151-138161, Sep. 2019.
doi:10.1109/access.2019.2941562

21. Jia, Zhiwei, Guozheng Yan, Zhiwu Wang, Hua Liu, et al. "Efficiency optimization of wireless power transmission systems for active capsule endoscopes," Physiological Measurement, Vol. 32, No. 10, 1561, Aug. 2011.
doi:10.1088/0967-3334/32/10/005

22. RamRakhyani, Anil Kumar, Shahriar Mirabbasi, and Mu Chiao, "Design and optimization of resonance-based efficient wireless power delivery systems for biomedical implants," IEEE Transactions on Biomedical Circuits and Systems, Vol. 5, No. 1, 48-63, Feb. 2011.
doi:10.1109/tbcas.2010.2072782

23. Yang, Zhi, Wentai Liu, and Eric Basham, "Inductor modeling in wireless links for implantable electronics," IEEE Transactions on Magnetics, Vol. 43, No. 10, 3851-3860, Oct. 2007.
doi:10.1109/tmag.2007.904189

24. Kazimierczuk, M., High-Frequency Magnetic Components, John Wiley & Sons, 2009.
doi:10.1002/9781118717806

25. Gao, J., et al. "Optimization of a powering coil onboard a dime-size inchworm-like robot for exploring the intestine," Journal of Shanghai Jiaotong University, Vol. 54, 152-159, Oct. 2020.

26. Abramowitz, Milton and Irene A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, Vol. 55, National Bureau of Standards, 2006.
doi:10.2307/2004284

Dr. Ruichen Qian

Dr. Chenzhi Lu

Dr. Zhixin Li

Dr. Xinyu Li

Dr. Kewei Zhu

Professor Jinyang Gao