A Case Study of Nelder Mead Simplex Optimization Algorithm: Trade-Offs of Sprienski Fractal Bowtie Antenna Parameters

Duygu Nazan Gençoğlan

doi:10.21605/cukurovaumfd.1459378

Research Article

A Case Study of Nelder Mead Simplex Optimization Algorithm: Trade-Offs of Sprienski Fractal Bowtie Antenna Parameters

Year 2024, Volume: 39 Issue: 1, 73 - 84, 28.03.2024

Duygu Nazan Gençoğlan

https://doi.org/10.21605/cukurovaumfd.1459378

Abstract

In this study, tri-band antenna design adapted for wireless communication, Internet of Things (IoT) and RFID systems is examined. The simulation results indicate that the proposed antenna has three distinct frequency bands. Band 1 (lower band) covers the frequency range of 1.64-1.78 GHz with a resonance frequency of 1.7 GHz. Band 2 covers the range of 3.06-3.9 GHz with a resonance frequency of 3.4 GHz with a high gain of 10 dBi and a radiation efficiency of 92% for long-range communication. Band 3 radiates from 6.25 to 7.6 GHz with a resonance frequency of 6.62 GHz, which is suitable for higher-frequency applications. The antenna design is simulated and analyzed regarding S11, VSWR, gain, radiation efficiency, and bandwidth. Especially, Band 2 (mid-band) provides notable performance, with its 10 dBi gain and 92% efficiency, which makes the proposed antenna an ideal structure for high-data-rate, long-distance communication systems, and 5G (midband) applications. This study also employs the Nelder-Mead Simplex algorithm to observe the optimization of the physical parameters of the proposed antenna via multiple objective functions. The optimization results outlines that longer the arm length of the proposed antenna causes to decrease the resonance frequency of Band 3. Addition to this, the gain is higher with the lower arm length except for the arm length of 90.467 mm and flare angle of 64.77o. That’s, the trade-off condition occurs between minimum return loss and gain. At this point, it can be concluded from this optimization algorithm results that each objective function should be evaluated separately due to this trade-off condition.

Keywords

Antenna, Algorithm, Fractal, High gain, Optimization, Sprienski

References

1. Li, D., Mao, J., 2014. Coplanar Waveguide‐Fed Koch‐Like Sided Sierpinski Hexagonal Carpet Multifractal Monopole Antenna. IET Microwaves. Antennas&Amp; Propagation, 8(5), 358-366.
2. Ramalakshmi, G., Rao, P.M., 2019. Performance Characteristics of Modified Sierpinski Fractal Antenna for Multiband Applications. International Journal of Recent Technology and Engineering (IJRTE), 8(2), 2194-2200.
3. Shi, Y., Zhang, X., Qiu, Q., Gao, Y., Huang, Z., 2021. Design of Terahertz Detection Antenna with Fractal Butterfly Structure. IEEE Access, 9, 113823-113831.
4. Mishra, P., Pattnaik, S., Dhaliwal, B., 2017. Square-Shaped Fractal Antenna Under Metamaterial Loaded Condition for Bandwidth Enhancement. Progress in Electromagnetics Research C, 78, 183-192.
5. Desai, A., Upadhyaya, T., Patel, R., Bhatt, S., Mankodi, A., 2018. Wideband High Gain Fractal Antenna for Wireless Applications. Progress in Electromagnetics Research Letters, 74, 125-130.
6. Dahiya, A., Anand, R., Sindhwani, N., Kumar, D., 2021. A Novel Multi-Band High-Gain Slotted Fractal Antenna Using Various Substrates for X-Band and Ku-Band Applications. Mapan, 37(1), 175-183.
7. Tripathi, S., Mohan, A., Yadav, S., 2014. Ultra‐Wideband Antenna Using Minkowski‐Like Fractal Geometry. Microwave and Optical Technology Letters, 56(10), 2273-2279.
8. Dwivedi, R., Kommuri, U., 2018. Compact High Gain UWB Antenna Using Fractal Geometry and UWB‐AMC. Microwave and Optical Technology Letters, 61(3), 787-793.
9. Islam, M., Islam, M., Samsuzzaman, M., Faruque, M., Misran, N., 2015. Microstrip Line‐Fed Fractal Antenna with a High-Fidelity Factor for UWB Imaging Applications. Microwave and Optical Technology Letters, 57(11), 2580-2585.
10. Kubacki, R., Czyżewski, M., Laskowski, D., 2018. Minkowski Island and Crossbar Fractal Microstrip Antennas for Broadband Applications. Applied Sciences, 8(3), 334.
11. Mohanamurali, R., Shanmuganantham, T., 2012. Sierpinski Carpet Fractal Antenna for Multiband Applications. International Journal of Computer Applications, 39(14), 19-23.
12. Tripathi, S., Mohan, A., Yadav, S., 2014. Hexagonal Fractal Ultra‐Wideband Antenna Using Koch Geometry with Bandwidth Enhancement. IET Microwaves Antennas & Propagation, 8(15), 1445-1450.
13. Dhaliwal, B., Pattnaik, S., Boparai, J., 2014. A Cross‐Stitch Geometry‐Based Multiband Fractal Antenna. Microwave and Optical Technology Letters, 56(3), 667-671.
14. Azari, A., Rowhani, J., 2008. Ultra-Wideband Fractal Microstrip Antenna Design. Progress in Electromagnetics Research C, 2, 7-12.
15. McKinnon, K.I., 1998. Convergence of the Nelder-Mead Simplex Method to A Nonstationary Point. SIAM Journal on Optimization, 9(1), 148-158.
16. Barton, R.R., Ivey Jr, J.S., 1996. Nelder-Mead Simplex Modifications for Simulation Optimization. Management Science, 42(7), 954-973.
17. Nelder, J.A., Mead, R., 1965. A Simplex Method for Function Minimization. Computer Journal, 7, 308-313.
18. Lagarias, J.C., Reeds, J.A., Wright, M.H., Wright, P.E., 1998. Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions. SIAM Journal on Optimization, 9(1), 112-147.
19. Mohsin, A., Alsmadi, Y.M., Uppal, A.A., Gulfam, S.M., 2021. A Modified Simplex Based Direct Search Optimization Algorithm for Adaptive Transversal FIR Filters. Science Progress, 104(2), 1-19.
20. Gao, F., Han, L., 2010. Implementing the Nelder-Mead Simplex Algorithm with Adaptive Parameters. Computational Optimization and Applications, 51(1), 259-277.
21. Musafer, H., Mahmood, A., 2018. Dynamic Hassan Nelder Mead with Simplex Free Selectivity for Unconstrained Optimization. IEEE Access, 6, 39015-39026.
22. Chang, J., Liao, S., Wu, S., Lin, C., 2015. A Hybrid of Cuckoo Search and Simplex Method for Fuzzy Neural Network Training. 2015 IEEE 12th International Conference on Networking, Sensing and Control, 13-16.
23. Li, Q.W.X., 2011. Application of İmproved Genetic Algorithm in Practical Medical Image Registration. International Journal of Digital Content Technology and Its Applications, 5(10), 60-67.
24. Xu, S., Zou, X., Liu, W., Wang, X., Zhu, H., Zhao, T., 2010. Research of Particle Swarm Optimization Algorithm Based on Nelder-Mead Simplex and Its Application on Partial Discharge Parameter Recognition. 2010 IEEE International Power Modulator and High Voltage Conference, 719-722.
25. Mistry, K.K., Lazaridis, P.I., Zaharis, Z.D., Akinsolu, M.O., Liu, B., Xenos, T.D., Prasad, R., 2019. Time and Frequency Domain Simulation, Measurement and Optimization of Log-Periodic Antennas. Wireless Personal Communications, 107, 771-783.
26. Mahmoud, K., 2010. Design Optimization of a Bow-Tie Antenna for 2.45 GHz RFID Readers Using A Hybrid BSO-NM Algorithm. Progress in Electromagnetics Research, 100, 105-117.
27. Barman, B., Chatterjee, D., Caruso, A.N., 2021. Probe-Location Optimization in A Wideband Microstrip Patch Antenna Using Genetic Algorithm, Particle Swarm and Nelder-Mead Optimization Methods. In 2021 International Applied Computational Electromagnetics Society Symposium (ACES), 1-3.
28. Montaser, A.M., Mahmoud, K.R., Elmikati, H.A., 2011. Slotted Bow-Tie Antenna Design for RFID Readers Using Hybrid Optimization Techniques. In 2011 28th National Radio Science Conference (NRSC), 1-8.
29. Liu, J., Zhao, Z., Yang, K., Liu, Q.H., 2014. A Hybrid Optimization for Pattern Synthesis of Large Antenna Arrays. Progress in Electromagnetics Research, 145, 81-91.
30. Rao, L.Y., Tsai, C.J., 2018, August. 8-Loop Antenna Array in the 5 Inches Size Smartphone for 5G Communication the 3.4 GHz-3.6 GHz Band MIMO Operation. In 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 1995-1999.
31. Kumar, L., Nath, V., Reddy, B.V.R., 2023. Triple-Band Stub Loaded Patch Antenna with High Gain for 5G Sub-6 GHz, WLAN and WIMAX Applications Using DGS. Facta Universitatis, Series: Electronics and Energetics, 36(2), 171-188.
32. Karthikeyan, M., Sitharthan, R., Ali, T., Pathan, S., Anguera, J., Shanmuga Sundar, D., 2022. Stacked T-Shaped Strips Compact Antenna for WLAN and WIMAX Applications. Wireless Personal Communications, 1-14.
33. Elkorany, A.S., Mousa, A.N., Ahmad, S., Saleeb, D.A., Ghaffar, A., Soruri, M., Limiti, E., 2022. Implementation of A Miniaturized Planar Tri-Band Microstrip Patch Antenna for Wireless Sensors in Mobile Applications. Sensors, 22(2), 667.
34. Patel, U., Parekh, M., Desai, A., Upadhyaya, T., 2021. Wide Slot Tri‐Band Antenna for Wireless Local Area Network/World‐Wide İnteroperability for Microwave Access Applications. International Journal of Communication Systems, 34(12), 1-10.
35. Ahmad, H., Zaman, W., Bashir, S., Rahman, M., 2020. Compact Triband Slotted Printed Monopole Antenna for WLAN and WIMAX Applications. International Journal of RF and Microwave Computer‐Aided Engineering, 30(1), 1-8.
36. Pandya, A., Upadhyaya, T. K., Pandya, K.,2021. Tri-Band Defected Ground Plane Based Planar Monopole Antenna for Wi-Fi/WIMAX/WLAN Applications. Progress in Electromagnetics Research C, 108, 127-136.
37. Chowdhury, M.Z.B., Islam, M.T., Rmili, H., Hossain, I., Mahmud, M.Z., Samsuzzaman, M., 2022. A Low‐Profile Rectangular Slot Antenna for Sub‐6 GHz 5G Wireless Applications. International Journal of Communication Systems, 35(17), 1-14.
38. Sajith, K., Jose, J., Sweety, T.J., Arun, T.R., Raj, R.K., 2022. SRR Inspired Multi-Layered Antenna for ISM and 5G Medical Applications. In 2022 8th International Conference on Signal Processing and Communication (ICSC), 196-199.
39. Gnanathickam, J., Thanusha, G., Moses, N., 2023. Design and Development of Microstrip Patch Antenna for 5G Application. In 2023 International Conference on Computer Communication and Informatics (ICCCI), 1-4.
40. Mushtaq, M.T., Shah, S.M.A., Munir, S., Hussain, M., Iqbal, J., Khan, U.H., 2022. Dual Band Microstrip Semicircular Slot Patch Antenna for WLAN and WIMAX Applications. Radioengineering, 31(3), 407.
41. Wang, E., Liu, X., Chang, H., 2023. Wideband Circular Polarized Fractal Antenna for RFID/WiMAX/WLAN Applications. Progress in Electromagnetics Research Letters, 111, 111-120.

Nelder Mead Simpleks Optimizasyon Algoritması Üzerine Bir Durum Çalışması: Sprienski Fraktal Bowtie Anten Parametrelerinin Ödünleşimleri

Year 2024, Volume: 39 Issue: 1, 73 - 84, 28.03.2024

Duygu Nazan Gençoğlan

https://doi.org/10.21605/cukurovaumfd.1459378

Abstract

Bu çalışmada, kablosuz iletişim, nesnelerin interneti ve RFID sistemleri için uyarlanmış üç bantlı anten tasarımı incelenmiştir. Simülasyon sonuçları, önerilen antenin üç farklı frekans bandına sahip olduğunu göstermektedir. Bant 1 (alt bant), 1.7 GHz rezonans frekansı ile 1.64-1.78 GHz frekans aralığını kapsar. Bant 2, 3.06 GHz’ten başlayan 3.9 GHz de sonlanan çalışma bant aralığına sahiptir. Ayrıca, bant-2 için wn yüksek kazanç değeri 10 dBi ve radyasyon verimliliği 92% olarak tespit edilmiştir. Bant 3, daha yüksek frekanslı uygulamalar için uygun olan 6.62 GHz rezonans frekansı ile 6.25 -7.6 GHz arasında yayılır. Anten tasarımı, S11, VSWR, kazanç, radyasyon verimliliği ve bant genişliği açısından simüle edilmiş ve analiz edilmiştir. Özellikle, Bant 2 (orta bant), 10 dBi kazancı ve %92 verimliliği ile kayda değer bir performans sağlar, bu da önerilen anteni yüksek veri hızı, uzun mesafeli iletişim sistemleri ve 5G (orta bant) uygulamaları için ideal bir yapı haline getirmektedir. Bu çalışma da aynı zamanda, önerilen antenin fiziksel parametrelerinin optimizasyonunu çoklu objektif fonksiyonlar aracılığıyla gözlemlemek için Nelder-Mead Simplex algoritmasını kullanılmıştır. Optimizasyon sonuçları, önerilen antenin kol uzunluğunun artması Bant 3'ün rezonans frekansının azalmasına neden olduğunu özetlemektedir. Buna ek olarak, kol uzunluğu küçüldükçe gain artmaktadır. Ancak 90.467 mm'lik kol uzunluğuna ve 64.77o'lik açıya sahip olan antende bu özelliğin tersi durum olduğu tespit edilmiştir. Bu noktada, bu optimizasyon algoritması sonuçlarından, bu ödünleşim koşulu nedeniyle her bir amaç fonksiyonunun ayrı ayrı değerlendirilmesi gerektiği sonucuna varılmıştır.

Keywords

Anten, Algoritma, Fraktal, Yüksek Kazanç, Optimizasyon, Sprienski

References

1. Li, D., Mao, J., 2014. Coplanar Waveguide‐Fed Koch‐Like Sided Sierpinski Hexagonal Carpet Multifractal Monopole Antenna. IET Microwaves. Antennas&Amp; Propagation, 8(5), 358-366.
2. Ramalakshmi, G., Rao, P.M., 2019. Performance Characteristics of Modified Sierpinski Fractal Antenna for Multiband Applications. International Journal of Recent Technology and Engineering (IJRTE), 8(2), 2194-2200.
3. Shi, Y., Zhang, X., Qiu, Q., Gao, Y., Huang, Z., 2021. Design of Terahertz Detection Antenna with Fractal Butterfly Structure. IEEE Access, 9, 113823-113831.
4. Mishra, P., Pattnaik, S., Dhaliwal, B., 2017. Square-Shaped Fractal Antenna Under Metamaterial Loaded Condition for Bandwidth Enhancement. Progress in Electromagnetics Research C, 78, 183-192.
5. Desai, A., Upadhyaya, T., Patel, R., Bhatt, S., Mankodi, A., 2018. Wideband High Gain Fractal Antenna for Wireless Applications. Progress in Electromagnetics Research Letters, 74, 125-130.
6. Dahiya, A., Anand, R., Sindhwani, N., Kumar, D., 2021. A Novel Multi-Band High-Gain Slotted Fractal Antenna Using Various Substrates for X-Band and Ku-Band Applications. Mapan, 37(1), 175-183.
7. Tripathi, S., Mohan, A., Yadav, S., 2014. Ultra‐Wideband Antenna Using Minkowski‐Like Fractal Geometry. Microwave and Optical Technology Letters, 56(10), 2273-2279.
8. Dwivedi, R., Kommuri, U., 2018. Compact High Gain UWB Antenna Using Fractal Geometry and UWB‐AMC. Microwave and Optical Technology Letters, 61(3), 787-793.
9. Islam, M., Islam, M., Samsuzzaman, M., Faruque, M., Misran, N., 2015. Microstrip Line‐Fed Fractal Antenna with a High-Fidelity Factor for UWB Imaging Applications. Microwave and Optical Technology Letters, 57(11), 2580-2585.
10. Kubacki, R., Czyżewski, M., Laskowski, D., 2018. Minkowski Island and Crossbar Fractal Microstrip Antennas for Broadband Applications. Applied Sciences, 8(3), 334.
11. Mohanamurali, R., Shanmuganantham, T., 2012. Sierpinski Carpet Fractal Antenna for Multiband Applications. International Journal of Computer Applications, 39(14), 19-23.
12. Tripathi, S., Mohan, A., Yadav, S., 2014. Hexagonal Fractal Ultra‐Wideband Antenna Using Koch Geometry with Bandwidth Enhancement. IET Microwaves Antennas & Propagation, 8(15), 1445-1450.
13. Dhaliwal, B., Pattnaik, S., Boparai, J., 2014. A Cross‐Stitch Geometry‐Based Multiband Fractal Antenna. Microwave and Optical Technology Letters, 56(3), 667-671.
14. Azari, A., Rowhani, J., 2008. Ultra-Wideband Fractal Microstrip Antenna Design. Progress in Electromagnetics Research C, 2, 7-12.
15. McKinnon, K.I., 1998. Convergence of the Nelder-Mead Simplex Method to A Nonstationary Point. SIAM Journal on Optimization, 9(1), 148-158.
16. Barton, R.R., Ivey Jr, J.S., 1996. Nelder-Mead Simplex Modifications for Simulation Optimization. Management Science, 42(7), 954-973.
17. Nelder, J.A., Mead, R., 1965. A Simplex Method for Function Minimization. Computer Journal, 7, 308-313.
18. Lagarias, J.C., Reeds, J.A., Wright, M.H., Wright, P.E., 1998. Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions. SIAM Journal on Optimization, 9(1), 112-147.
19. Mohsin, A., Alsmadi, Y.M., Uppal, A.A., Gulfam, S.M., 2021. A Modified Simplex Based Direct Search Optimization Algorithm for Adaptive Transversal FIR Filters. Science Progress, 104(2), 1-19.
20. Gao, F., Han, L., 2010. Implementing the Nelder-Mead Simplex Algorithm with Adaptive Parameters. Computational Optimization and Applications, 51(1), 259-277.
21. Musafer, H., Mahmood, A., 2018. Dynamic Hassan Nelder Mead with Simplex Free Selectivity for Unconstrained Optimization. IEEE Access, 6, 39015-39026.
22. Chang, J., Liao, S., Wu, S., Lin, C., 2015. A Hybrid of Cuckoo Search and Simplex Method for Fuzzy Neural Network Training. 2015 IEEE 12th International Conference on Networking, Sensing and Control, 13-16.
23. Li, Q.W.X., 2011. Application of İmproved Genetic Algorithm in Practical Medical Image Registration. International Journal of Digital Content Technology and Its Applications, 5(10), 60-67.
24. Xu, S., Zou, X., Liu, W., Wang, X., Zhu, H., Zhao, T., 2010. Research of Particle Swarm Optimization Algorithm Based on Nelder-Mead Simplex and Its Application on Partial Discharge Parameter Recognition. 2010 IEEE International Power Modulator and High Voltage Conference, 719-722.
25. Mistry, K.K., Lazaridis, P.I., Zaharis, Z.D., Akinsolu, M.O., Liu, B., Xenos, T.D., Prasad, R., 2019. Time and Frequency Domain Simulation, Measurement and Optimization of Log-Periodic Antennas. Wireless Personal Communications, 107, 771-783.
26. Mahmoud, K., 2010. Design Optimization of a Bow-Tie Antenna for 2.45 GHz RFID Readers Using A Hybrid BSO-NM Algorithm. Progress in Electromagnetics Research, 100, 105-117.
27. Barman, B., Chatterjee, D., Caruso, A.N., 2021. Probe-Location Optimization in A Wideband Microstrip Patch Antenna Using Genetic Algorithm, Particle Swarm and Nelder-Mead Optimization Methods. In 2021 International Applied Computational Electromagnetics Society Symposium (ACES), 1-3.
28. Montaser, A.M., Mahmoud, K.R., Elmikati, H.A., 2011. Slotted Bow-Tie Antenna Design for RFID Readers Using Hybrid Optimization Techniques. In 2011 28th National Radio Science Conference (NRSC), 1-8.
29. Liu, J., Zhao, Z., Yang, K., Liu, Q.H., 2014. A Hybrid Optimization for Pattern Synthesis of Large Antenna Arrays. Progress in Electromagnetics Research, 145, 81-91.
30. Rao, L.Y., Tsai, C.J., 2018, August. 8-Loop Antenna Array in the 5 Inches Size Smartphone for 5G Communication the 3.4 GHz-3.6 GHz Band MIMO Operation. In 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 1995-1999.
31. Kumar, L., Nath, V., Reddy, B.V.R., 2023. Triple-Band Stub Loaded Patch Antenna with High Gain for 5G Sub-6 GHz, WLAN and WIMAX Applications Using DGS. Facta Universitatis, Series: Electronics and Energetics, 36(2), 171-188.
32. Karthikeyan, M., Sitharthan, R., Ali, T., Pathan, S., Anguera, J., Shanmuga Sundar, D., 2022. Stacked T-Shaped Strips Compact Antenna for WLAN and WIMAX Applications. Wireless Personal Communications, 1-14.
33. Elkorany, A.S., Mousa, A.N., Ahmad, S., Saleeb, D.A., Ghaffar, A., Soruri, M., Limiti, E., 2022. Implementation of A Miniaturized Planar Tri-Band Microstrip Patch Antenna for Wireless Sensors in Mobile Applications. Sensors, 22(2), 667.
34. Patel, U., Parekh, M., Desai, A., Upadhyaya, T., 2021. Wide Slot Tri‐Band Antenna for Wireless Local Area Network/World‐Wide İnteroperability for Microwave Access Applications. International Journal of Communication Systems, 34(12), 1-10.
35. Ahmad, H., Zaman, W., Bashir, S., Rahman, M., 2020. Compact Triband Slotted Printed Monopole Antenna for WLAN and WIMAX Applications. International Journal of RF and Microwave Computer‐Aided Engineering, 30(1), 1-8.
36. Pandya, A., Upadhyaya, T. K., Pandya, K.,2021. Tri-Band Defected Ground Plane Based Planar Monopole Antenna for Wi-Fi/WIMAX/WLAN Applications. Progress in Electromagnetics Research C, 108, 127-136.
37. Chowdhury, M.Z.B., Islam, M.T., Rmili, H., Hossain, I., Mahmud, M.Z., Samsuzzaman, M., 2022. A Low‐Profile Rectangular Slot Antenna for Sub‐6 GHz 5G Wireless Applications. International Journal of Communication Systems, 35(17), 1-14.
38. Sajith, K., Jose, J., Sweety, T.J., Arun, T.R., Raj, R.K., 2022. SRR Inspired Multi-Layered Antenna for ISM and 5G Medical Applications. In 2022 8th International Conference on Signal Processing and Communication (ICSC), 196-199.
39. Gnanathickam, J., Thanusha, G., Moses, N., 2023. Design and Development of Microstrip Patch Antenna for 5G Application. In 2023 International Conference on Computer Communication and Informatics (ICCCI), 1-4.
40. Mushtaq, M.T., Shah, S.M.A., Munir, S., Hussain, M., Iqbal, J., Khan, U.H., 2022. Dual Band Microstrip Semicircular Slot Patch Antenna for WLAN and WIMAX Applications. Radioengineering, 31(3), 407.
41. Wang, E., Liu, X., Chang, H., 2023. Wideband Circular Polarized Fractal Antenna for RFID/WiMAX/WLAN Applications. Progress in Electromagnetics Research Letters, 111, 111-120.

There are 41 citations in total.

Details

Primary Language	English
Subjects	Electronics, Sensors and Digital Hardware (Other), Antennas and Propagation
Journal Section	Articles
Authors	Duygu Nazan Gençoğlan 0000-0001-5014-9514
Publication Date	March 28, 2024
Submission Date	October 26, 2023
Acceptance Date	March 28, 2024
Published in Issue	Year 2024 Volume: 39 Issue: 1

Cite

APA	Gençoğlan, D. N. (2024). A Case Study of Nelder Mead Simplex Optimization Algorithm: Trade-Offs of Sprienski Fractal Bowtie Antenna Parameters. Çukurova Üniversitesi Mühendislik Fakültesi Dergisi, 39(1), 73-84. https://doi.org/10.21605/cukurovaumfd.1459378

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