Petri net is a mathematical and graphical tool used for analyzing the properties of parallel and concurrent system designs. Here, it is used for checking the process modeling of 4 × 4 Butler matrix fabricated on Rogers RO3210 and resonating in Ku band. Butler matrix is well suited for satellite and aircraft antenna applications as a feeding network for phase array systems. So, this basic feed design process of antennas is studied using Petri nets for better understating the designing process and removal of any deadlocks occurring during designing and feeding of antennas. It is accomplished by analyzing the behavioral and structural properties of Petri nets. A Butler matrix divides the power amplitude into four equal parts and provides a progressive phase difference of 45˚. Therefore, its components, 0 db coupler, 3 db coupler, and phase shifters, have also been designed and simulated. After designing the components, firstly these components are joined to form a matrix design which is simulated and fabricated in ANSYS HFSS. Secondly, the designed structure is analyzed for structural and behavioral properties using Petri net's graphical and mathematical properties. After analyzing the process, the feed design can be modified further according to user requirements, and deadlock can be removed by checking the difference between the simulated and measured results of design. Likewise, here the matrix has been compared and found to be following the same pattern. The overall size of the matrix is 5.58 × 7.43 cm2, which is further suitable for the user's feeding requirements and applications.
2. Kilani, M. B., M. Nedil, N. Kandil, and T. A. Denidni, "Design of conformal microstrip Butler matrix at 2.4 GHz," IEEE International Symposium on Antennas and Propagation, Chicago, 2012.
3. Alam, M. M., "Microstrip antenna array with four port Butler matrix for switched beam base station application," 12th International Conference on Computer and Information Technology (ICCIT), Dhaka, 2009.
4. Pandey, A. K., "Design of a compact high-power phased array for 5G FD-MIMO system at 29 GHz," Asia-Pacific Microwave Conference, New Delhi, 2016.
5. Babale, S. A., S. K. A. Rahim, O. Elijah, and S. I. Orakwue, "Two-dimensional beam-steering phased-array utilizing 2 × 2 Butler matrix," IEEE 3rd International Conference on Electro- Technology for National Development (NIGERCON), Owerri, Nigeria, 2017.
6. Ding, K., X. Fang, Y. Wang, and A. Chen, "Printed dual-layer three-way directional coupler utilized as 3 × 3 beamforming network for orthogonal three-beam antenna array," IEEE Antennas and Wireless Propagation Letters, Vol. 13, 911-914, 2014.
7. Solmain, I., A. Rydosz, S. Gruszczynki, and K. Wincza, "Three beam microstrip antenna arrays fed by 3×3 Butler matrix," 7th IEEE International Symposium on Microwave, Antenna, Propagation, and EMC Technologies (MAPE), Xi'an, China, 2017.
8. Djera, T., N. J. G. Fonseca, and K. Wu, "Design and implementation of a planar 4 × 4 Butler matrix in SIW technology for wide band high power applications," Progress In Electromagnetics Research B, Vol. 35, 29-51, 2011.
9. Zhai, Y., X. Fang, K. Ding, and F. He, "Miniaturization design for 8 × 8 Butler matrix based on back-to-back bilayer microstrip," International Journal of Antennas and Propagation, Vol. 2014, 1-7, 2014.
10. Rosati, G. and J. Munn, "Fast prototyping of an 8×8 Butler matrix beamforming network for 5G applications," International Conference on Electromagnetics in Advanced applications, (ICEAA), Verona, Italy, 2017.
11. Lei, S. and L. Jian, "Beam forming networks for triangular grid multi-beam array," IEEE International Conference on Microwave Technology & Computational Electromagnetics, Qingdao, China, 2013.
12. Zulkifli, F. Y., N. Chasanah, and E. T. Rahardjo, "Design of Butler matrix integrated with antenna array for beam forming," International Symposium on Antennas and Propagation (ISAP), Hobart, Australia, 2015.
13. Zhou, C., J. Fu, H. Sun, and Q. Wu, "A novel compact dual-band Butler matrix design," 3rd Asia-Pacific Conference on Antennas and Propagation, Harbin, China, 2014.
14. Lazovic, L., A. Jovanovic, B. Lutovac, and V. Rubezic, "The application of graph theory for the design of reconfigurable fractal antenna," 2016 24th Telecommunications Forum (TELFOR), Belgrade, Sweden, 2016.
15. Prakash, V., S. Kumawat, and P. Singh, "Circuital analysis of coaxial fed rectangular and U-slot patch antenna," International Conference on Computing, Communication and Automation (ICCCA2016), Greater, Noida, 2016.
16. Prakash, V., S. Kumawat, and P. Singh, "Design and analysis of full and half mode substrate integrated waveguide planar leaky wave antenna with continuous beam scanning in X-Ku band," Frequenz, Vol. 73, No. 5, 171-178, 2019.
17. Ren, H., B. Arigong, M. Zhou, J. Ding, and H. Zhang, "A novel design of 4×4 Butler matrix with relatively flexible phase differences," IEEE Antennas and Wireless Propagation Letters, Vol. 15, 1277-1280, 2016.
18. Wang, W., Z. Qu, Z. Shen, L. Lou, K. Tang, and Y. Zheng, "Design of broadband phased array antenna at X-band," 2017 Progress In Electromagnetics Research Symposium — Fall (PIERS — FALL), Singapore, Singapore, Nov. 19–22, 2017.
19. Chu, H. N. and T.-G. Ma, "An extended 4 × 4 Butler matrix with enhanced beam controllability and widened spatial coverage," IEEE Transactions on Microwave Theory and Techniques, Vol. 66, No. 3, 1301-1311, 2018.
20. Yao, Y.-L., F.-S. Zhang, and F. Zhang, "A new approach to design circularly polarized beam-steering antenna arrays without phase shift circuits," IEEE Transactions on Antennas and Propagation, Vol. 66, No. 5, 2354-2364, 2018.
21. Murata, T., "Petri nets: Properties, analysis and applications," Proceedings of the IEEE, Vol. 77, 541-580, 1982.
22. Kumawat, S. and G. N. Purohit, "Total span of farm workflow using Petri net with resource sharing," Int. J. Business Process Integration and Management, Vol. 8, 160-171, 2017.
23. Kumawat, S., "Weighted directed graph: A Petri Net based method of extraction of closed weighted directed Euler trail," International Journal of Services, Economics and management, Vol. 4, No. 3, 252-264, 2012.
24. Shareef, A. and Y. Zhu, "Effective Stochastic modelling of energy constrained wireless sensor networks," Journal Computer Network and Communication, 2012.
25. Di Martino, C., Resiliency assessment of wireless sensor networks: A holistic approach, Ph.D. Thesis, Federico II, University of Naples, Italy, 2009.
26. Yahya, B., J. Ben-Othman, L. Mokdad, and S. Diagne, "Performance evaluation of a medium access control protocol for wireless sensor networks using Petri Nets," HET-NET’s 2010, 335-354, 2010.
27. Gupta, S., S. Kumawat, and G. P. Singh, "Fuzzy Petri Net representation of fuzzy production propositions of a rule based system," Communications in Computer and Information Science, Springer CCIS, Advances in Computing and Data Sciences, 197-210, 2019.
28. Gupta, S., G. P. Singh, and S. Kumawat, "Petri Net recommender system to model metabolic pathway of polyhydroxyalkanoates," International Journal of Knowledge and Systems Science (IJKSS) IGI Global Editorial Discovery, Vol. 10, No. 2, 18, 2019.