为满足柔性电子设备在宽频段和灵活性方面的性能需求，基于不同的分形结构，采用共面波导（CPW）馈电结构和阵列天线等技术，设计了三款不同应用频段的宽带柔性天线，工作内容如下：

（1）基于半圆分形结构设计了UWB宽带柔性天线。采用四阶半圆迭代嵌套分形结构作为辐射单元，通过不同分形半圆调节电长度，增加天线的工作谐振点，在接地板开槽提高天线的阻抗匹配特性，实现超宽带辐射，利用CPW馈电方式提高天线的集成性；天线的阻抗带宽为112.3%（2.98GHz-10.61GHz），带内峰值增益达到5.58dBi，在保持超宽带辐射性能的前提下，天线的弯曲半径可以达到13mm。

（2）基于圆切正方形分形结构设计了Sub-6G宽带柔性阵列天线。辐射单元采用五阶圆切正方形迭代嵌套分形结构，通过递归迭代形成自相似几何形态，使得电流路径在多个尺度上分布实现宽带特性，靠近馈线处开槽提高天线阻抗特性，利用CPW馈电方式提高天线的集成性；利用阵列天线的特性，将单元天线垂直正交放置，阵列天线的阻抗带宽为154.9%（0.67GHz-5.27GHz），端口隔离度大于24dB，带内峰值增益达到1.1dBi，天线在弯曲半径达到450mm时仍能保持稳定的辐射性能，工作频率覆盖了Sub-6G中n77、n78和n79等频段。

（3）基于Koch分形结构设计了5G毫米波宽带柔性阵列天线。以三阶Koch分形结构作为辐射单元，利用边缘结构增加高频辐射面积，通过槽线和CPW拓展天线频带宽度；在2×2结构阵列天线中添加耦合枝节提高各单元天线之间的隔离度，阻抗带宽为109.1%（16.41GHz-55.79GHz），端口隔离度大于20dB，带内峰值增益达到4.9dBi，天线的弯曲半径可以达到20mm，并且在5G毫米波段中能保持稳定的工作性能。

上述柔性天线在不同的柔性设备中均能保持稳定的超宽带性能、较高的增益和优良的隔离度，比吸收率满足FCC标准，为可柔性电子设备等应用场景提供有效通信保障。

To meet the performance requirements of flexible electronic devices in terms of wide frequency bands and flexibility, three different wideband flexible antennas were designed based on various fractal structures, utilizing coplanar waveguide (CPW) feeding structures and array antenna technologies. The work is as follows:

(1) Design of a UWB wideband flexible antenna based on semi-circular fractal structure. A fourth-order nested semi-circular iterative fractal structure was used as the radiating element. Different fractal semi-circles were employed to adjust the electrical length, increasing the antenna's resonant points. Slots were created in the ground plane to improve the antenna's impedance matching characteristics, achieving ultra-wideband radiation. CPW feeding was utilized to enhance antenna integration. The antenna achieved an impedance bandwidth of 112.3% (2.98GHz-10.61GHz), with an in-band peak gain of 5.58dBi. While maintaining ultra-wideband radiation performance, the antenna could be bent to a radius of 13mm.

(2) Design of a Sub-6G wideband flexible array antenna based on circle-cut square fractal structure. The radiating element employed a fifth-order circle-cut square iterative nested fractal structure. Through recursive iteration, self-similar geometric patterns were formed, distributing current paths across multiple scales to achieve wideband characteristics. Slots near the feed line improved the antenna's impedance properties, while CPW feeding enhanced integration. Utilizing array antenna characteristics, unit antennas were placed in vertical orthogonal arrangements. The array antenna achieved an impedance bandwidth of 154.9% (0.67GHz-5.27GHz), with port isolation greater than 24dB and an in-band peak gain of 1.1dBi. The antenna maintained stable radiation performance with a bending radius of 450mm, covering Sub-6G frequency bands including n77, n78, and n79.

(3) Design of a 5G millimeter-wave wideband flexible array antenna based on Koch fractal structure. A third-order Koch fractal structure was used as the radiating element, utilizing edge structures to increase high-frequency radiation area, and employing slot lines and CPW to extend the antenna's bandwidth. Coupling branches were added to the 2×2 structure array antenna to improve isolation between unit antennas. The antenna achieved an impedance bandwidth of 109.1% (16.41GHz-55.79GHz), with port isolation greater than 20dB and an in-band peak gain of 4.9dBi. The antenna could be bent to a radius of 20mm while maintaining stable performance in the 5G millimeter-wave band.

The aforementioned flexible antennas maintained stable ultra-wideband performance, relatively high gain, and excellent isolation in various flexible devices. The specific absorption rate met FCC standards, providing effective communication assurance for flexible electronic device applications.

[1] K. S. Patil and E. Rufus. A review on antennas for biomedical implants used for IoT

based health care[J]. Sensor Review, 2020, 40(2): 273-280.

[2] Commission F C. Revision of part 15 of the commission's rules regarding ultra-wide band transmission systems: first report and order [S].Washington,DC:FCC,2002:2-48.

[3] Wu Z, Wu B, Su Z, et al. Development challenges for 5G base station antennas[C]//2018 International Workshop on Antenna Technology (iWAT). IEEE, 2018: 1-3.

[4] Dilli R. Analysis of 5G wireless systems in FR1 and FR2 frequency bands[C]//2020 2nd International Conference on Innovative Mechanisms for Industry Applications (ICIMIA). IEEE, 2020: 767-772.

[5] Singh G, Singh U. Triple band-notched UWB Antenna design using a novel hybrid optimization technique based on DE and NMR algorithms [J]. Expert Systems with Applications,2021,184:115299.

[6] Alani S, Zakaria Z, Saeidi T, et al. Microwave imaging of breast skin utilizing elliptical UWB antenna and reverse problems algorithm [J]. Micromachines, 2021, 12(6): 647.

[7] Yang B Q, YU Z Q, LAN J, et al. Digital beamforming-based massive MIMO transceiver for 5G millimeter-wave communications [J]. IEEE Transactions on Microwave Theory and Techniques, 2018, 66(7): 3403-3418.

[8] 段雅琼. 柔性可穿戴分形天线的研究[D]. 天津. 天津大学, 2018.

[9] Simorangkir R B V B, Kiourti A, Esselle K P. UWB wearable antenna with a full ground plane based on PDMS-embedded conductive fabric[J]. IEEE Antennas and Wireless Propagation Letters, 2018, 17(3): 493-496.

[10] Amir N F, Jusoh M, Isa M M, et al. A flexible UWB antenna for wearable technologies application[C]//2019 6th International Conference on Space Science and Communication (IconSpace). IEEE, 2019: 121-124.

[11] Elmobarak H A, Rahim S K A, Castel X, et al. Flexible conductive fabric/E‐glass fibre composite ultra‐wideband antenna for future wireless networks[J]. IET Microwaves, Antennas & Propagation, 2019, 13(4): 455-459.

[12] Awan W A, Naqvi S I, Hussain N, et al. A Miniaturized UWB Antenna for Flexible Electronics[C]//2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting. IEEE, 2020: 99-100.

[13] Hammoodi A I, Ali J K. Practical Bending studying on UWB pentagonal flexible antenna[C]//2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting. IEEE, 2020: 413-414.

[14] Desai A, Upadhyaya T, Patel J, et al. Flexible CPW fed transparent antenna for WLAN and sub‐6 GHz 5G applications[J]. Microwave and Optical Technology Letters, 2020, 62(5): 2090-2103.

[15] 张众贺, 张斌珍. 一款基于表面改性和 MEMS 工艺的超宽带柔性天线[J]. 现代电子技术, 2021, 44(17): 12-16.

[16] El Gharbi M, Martinez-Estrada M, Fernández-García R, et al. A novel ultra-wide band wearable antenna under different bending conditions for electronic-textile applications[J]. The journal of the Textile Institute, 2021, 112(3): 437-443.

[17] 陈沁文, 张斌珍, 段俊萍, 等. 一种超宽带柔性梯形环分形天线的设计[J]. 微纳电子技术, 2022, 59(04): 335-340+355.

[18] Rajesh G, Poonkuzhali R. A CPW fed flexible antenna for UWB Applications[C]//2023 2nd International Conference on Vision Towards Emerging Trends in Communication and Networking Technologies (ViTECoN). IEEE, 2023: 1-5.

[19] Josan S K, Dhaliwal B S, Maithani S. A Compact Flexible Crown Rectangular Fractal Antenna on low-cost PET substrate[C]//2022 IEEE Microwaves, Antennas, and Propagation Conference (MAPCON). IEEE, 2022: 1886-1890.

[20] Sidibe A, Takacs A, Dragomirescu D, et al. A novel polyimide flexible antenna design for S-band applications[C]//2022 16th European Conference on Antennas and Propagation (EuCAP). IEEE, 2022: 1-5.

[21] Afroz S, Al-Hadi A A, Azemi S N, et al. Dual band circular patch flexible wearable antenna design for sub-6 GHz 5G applications[C]//2022 IEEE International RF and Microwave Conference (RFM). IEEE, 2022: 1-4.

[22] Ahumada C, Kaschel H, Cordero S, et al. Flexible microstrip antenna for iot and 5g wireless systems[C]//2022 IEEE International Conference on Automation/XXV Congress of the Chilean Association of Automatic Control (ICA-ACCA). IEEE, 2022: 1-5.

[23] Suneesh S, Priya A S, Abirami K, et al. Design of Flexible and Wearable Antenna for 5G IoT Application[C]//2022 3rd International Conference on Smart Electronics and Communication (ICOSEC). IEEE, 2022: 402-407.

[24] Luo J, Jiang T, Liu L. A Design of Flexible Materials Microstrip Antenna[C]//2022 IEEE 5th International Conference on Electronic Information and Communication Technology (ICEICT). IEEE, 2022: 751-753.

[25] Sarkar D, Sen G. Detection of Breast Cancer using a Flexible Antenna at ISM Band[C]//2023 7th International Conference on Electronics, Materials Engineering & Nano-Technology (IEMENTech). IEEE, 2023: 1-6.

[26] Sidibe A, Takacs A, Dragomirescu D, et al. A Dual-Band and Flexible CPW-Fed Antenna for RF Energy Harvesting Applications[C]//2023 17th European Conference on Antennas and Propagation (EuCAP). IEEE, 2023: 1-5.

[27] Thaiwirot W, Hengroemyat Y, Kaewthai T, et al. Analysis of flexible dual-band microstrip patch antenna for wearable applications[C]//2023 Research, Invention, and Innovation Congress: Innovative Electricals and Electronics (RI2C). IEEE, 2023: 9-12.

[28] Tavares J, Loss C, Pinho P, et al. Flexible textile antenna for detection of 5G bandwidth in wearable systems[C]//2023 53rd European Microwave Conference (EuMC). IEEE, 2023: 673-676.

[29] Li E, Li X J, Seet B C, et al. Ink-printed flexible wideband dipole array antenna for 5G applications[J]. Physical Communication, 2020, 43: 101193.

[30] Jha K R, Jibran Z A P, Singh C, et al. 4-port MIMO antenna using common radiator on a flexible substrate for sub-1GHz, sub-6GHz 5G NR, and Wi-Fi 6 applications[J]. IEEE Open Journal of Antennas and Propagation, 2021, 2: 689-701.

[31] Gupta A, Kansal A, Chawla P. Design of a wearable MIMO antenna deployed with an inverted U-shaped ground stub for diversity performance enhancement[J]. International Journal of Microwave and Wireless Technologies, 2021, 13(1): 76-86.

[32] Sahoo B C, Al-Hadi A A, Azemi S N, et al. An UltraWideband Full Flexible 4 Elements DGS Based MIMO Antenna for Sub-6 GHz Wearable Applications[C]//2023 IEEE Microwaves, Antennas, and Propagation Conference (MAPCON). IEEE, 2023: 1-4.

[33] Jilani S F, Rahimian A, Alfadhl Y, et al. Low-profile flexible frequency-reconfigurable millimetre-wave antenna for 5G applications[J]. Flexible and Printed Electronics, 2018, 3(3): 035003.

[34] Jindal S, Sivia J S, Bindra H S. Defected ground based fractal antenna for S and C band applications[J]. Wireless Personal Communications, 2020, 110: 109-124.

[35] Lihua F. Design and Optimization of Plane Microstrip Fractal Antenna Based on Y Structure[C]//2020 IEEE MTT-S International Microwave Workshop Series on Advanced Materials and Processes for RF and THz Applications (IMWS-AMP). IEEE, 2020: 1-3.

[36] Amsaveni A, Bharathi M. Design and implementation of H-shaped fractal antenna for UWB applications[C]//2021 International Conference on Advancements in Electrical, Electronics, Communication, Computing and Automation (ICAECA). IEEE, 2021: 1-5.

[37] Lu Y, Jia J, He W. Design of Ka-Band Tree-Shaped Fractal Millimeter Wave Antenna[C]//2022 IEEE 5th International Conference on Electronics and Communication Engineering (ICECE). IEEE, 2022: 131-134.

[38] Rao N. Modified sierpinski and its use in fractal patch antenna for miniaturization and multiband behavior[C]//2022 IEEE Microwaves, Antennas, and Propagation Conference (MAPCON). IEEE, 2022: 1804-1809.

[39] Rishi R, Kumar Y. Fractal antenna design with slots for multiband applications[C]//2023 2nd International Conference on Advancements in Electrical, Electronics, Communication, Computing and Automation (ICAECA). IEEE, 2023: 1-6.

[40] Rao N. A Novel Parallelogram Shaped Microstrip Fractal Antenna For Home Automation using Smart Grid[C]//2023 IEEE Microwaves, Antennas, and Propagation Conference (MAPCON). IEEE, 2023: 1-6.

[41] Koniammal R, Ramesh G P, Naidu G G. Design a Multiband Frequency of Partial Defected Ground for Hexagonal Fractal Antenna[C]//2023 International Conference on Data Science and Network Security (ICDSNS). IEEE, 2023: 1-7.

[42] Beegum S F, Joseph M, Joyas S, et al. UHF Fractal Antenna for Space Applications[C]//2024 IEEE Wireless Antenna and Microwave Symposium (WAMS). IEEE, 2024: 01-03.

[43] Babu B R, Gullala D, Srinivas M, et al. Design and Analysis of Square Fractal Shaped Planar Antenna[C]//2024 IEEE Wireless Antenna and Microwave Symposium (WAMS). IEEE, 2024: 1-4.

[44] 孙洪泉.分形几何与分形插值[M]北京. 科学出版, 2011.

[45] Qiu Y, Jung Y H, Lee S, et al. Compact parylene‐c‐coated flexible antenna for WLAN and upper‐band UWB applications[J]. Electronics Letters, 2014, 50(24): 1782-1784.

[46] Simorangkir R B V B, Le D, Björninen T, et al. Washing durability of PDMS-conductive fabric composite: Realizing washable UHF RFID tags[J]. IEEE Antennas and Wireless Propagation Letters, 2019, 18(12): 2572-2576.

[47] Malek M A, Hakimi S, Rahim S K A, et al. Dual-band CPW-fed transparent antenna for active RFID tags[J]. IEEE Antennas and Wireless Propagation Letters, 2014, 14: 919-922.

[48] Yang H, Liu X, Fan Y. Design of broadband circularly polarized all-textile antenna and its conformal array for wearable devices[J]. IEEE Transactions on Antennas and Propagation, 2021, 70(1): 209-220.

[49] Nadeem I, Alibarhikenari M, BABAEIAN F, et al. A comprehensive survey on circular polarized antennas for existing and emerging wireless communication technologies[J/OL]. Journal of Physics D: Applied Physics, 2021, 55(3): 033002.

[50] Shafique K, Khawaja B A, Tarar M A, et al. A wearable ultra‐wideband antenna for wireless body area networks[J]. Microwave and Optical Technology Letters, 2016, 58(7): 1710-1715.

[51] Luo S, Wang D, Chen Y, et al. A compact dual-port UWB-MIMO antenna with quadruple band-notched characteristics[J]. AEU-International Journal of Electronics and Communications, 2021, 136: 153770.

[52] 李艳玲, 陈新伟, 苏晋荣. 具有三陷波特性的高隔离度紧凑型 UWB-MIMO 天线[J]. 测试技术学报, 2022, 36(1): 23-28.