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Numerical Solution of Transmission Line PDEs Using Finite Difference

Year 2023, Issue: 49, 94 - 99, 31.03.2023
https://doi.org/10.31590/ejosat.1261908

Abstract

Transmission lines refer to a variety of electrical structures that transfer information or energy typically in the form of carrying electromagnetic waves. Examples of transmission lines include coaxial cables, telephone wires, microstrips, and optical fibers. Understanding the transmission and distribution of the electromagnetic waves across the line is critical for matching the load with the generator to deliver the energy or information with minimum losses. The flow of electromagnetic waves across the line is described based on the voltage and current using Partial Differential Equations (PDEs). In this paper we apply the Central Space Central Time (CSCT) finite difference numerical method to solve the transmission line PDEs. We present the numerical solution of the waveforms and compare it with the analytical solution to evaluate the accuracy of this numerical method in solving the transmission line problem. It is found that the numerical solution of the voltage waveform is very near the analytical result with small error margin. However, while the numerical solution of the current shows the same waveform as the analytical one, there is some quite significant error in the magnitude. The error is found to result from the fact that the waveform of the numerical solution has some phase shift from that of the analytical solution. Adjusting the phase shift of the current waveform results in having good agreement between numerical and analytical results.

Supporting Institution

Qatar National Research Fund

Project Number

GSRA8-L-2-0523-21052

References

  • Daafouz, J., Tucsnak, M., & Valein, J. (2014). Nonlinear control of a coupled PDE/ODE system modeling a switched power converter with a transmission line. Systems & Control Letters, 70, 92–99. https://doi.org/10.1016/j.sysconle.2014.05.009
  • Davoli, F., Kourogiorgas, C., Marchese, M., Panagopoulos, A., & Patrone, F. (2018). Small satellites and CubeSats: Survey of structures, Architectures, and protocols. International Journal of Satellite Communications and Networking, 37(4), 343–359. https://doi.org/10.1002/sat.1277
  • Korzeniewska, E., & Krawczyk, A. (2019). 5G technology as the succesive stage in the history of Wireless Telecommunication. 2019 IEEE International Conference on Modern Electrical and Energy Systems (MEES). https://doi.org/10.1109/mees.2019.8896516
  • Transmission line theory. (2009). The Transmission-Line Modeling Method. https://doi.org/10.1109/9780470546659.ch2
  • Ulaby, F. T., & Ravaioli, U. (1994). Fundamentals of Applied Electromagnetics. Pearson.
  • Wang, D., Chen, D., Song, B., Guizani, N., Yu, X., & Du, X. (2018). From IOT to 5G I-IOT: The next generation IOT-based intelligent algorithms and 5G technologies. IEEE Communications Magazine, 56(10), 114–120. https://doi.org/10.1109/mcom.2018.1701310

Sonlu Fark Kullanarak İletim Hattı PDE'lerinin Sayısal Çözümü

Year 2023, Issue: 49, 94 - 99, 31.03.2023
https://doi.org/10.31590/ejosat.1261908

Abstract

İletim hatları, tipik olarak elektromanyetik dalgalar taşıma biçiminde bilgi veya enerji aktaran çeşitli elektrik yapılarını ifade eder. İletim hatlarına örnek olarak koaksiyel kablolar, telefon kabloları, mikro şeritler ve optik fiberler verilebilir. Elektromanyetik dalgaların hat boyunca iletimini ve dağıtımını anlamak, enerjiyi veya bilgiyi minimum kayıpla iletmek için yükü jeneratörle eşleştirmek için kritik öneme sahiptir. Hat boyunca elektromanyetik dalgaların akışı, Kısmi Diferansiyel Denklemler (PDE'ler) kullanılarak voltaj ve akıma dayalı olarak tanımlanır. Bu yazıda, iletim hattı PDE'lerini çözmek için Merkezi Uzay Merkezi Zaman (CSCT) sonlu farklar sayısal yöntemini uyguluyoruz. Dalga biçimlerinin sayısal çözümünü sunuyoruz ve bu sayısal yöntemin iletim hattı problemini çözmedeki doğruluğunu değerlendirmek için analitik çözümle karşılaştırıyoruz. Gerilim dalga biçiminin sayısal çözümünün, küçük hata payı ile analitik sonuca çok yakın olduğu bulunmuştur. Bununla birlikte, akımın sayısal çözümü analitik olanla aynı dalga biçimini gösterse de, büyüklükte oldukça önemli bazı hatalar vardır. Hatanın, sayısal çözümün dalga biçiminin analitik çözümden bir miktar faz kaymasına sahip olmasından kaynaklandığı bulunmuştur. Mevcut dalga formunun faz kaymasını ayarlamak, sayısal ve analitik sonuçlar arasında iyi bir uyum sağlar.

Project Number

GSRA8-L-2-0523-21052

References

  • Daafouz, J., Tucsnak, M., & Valein, J. (2014). Nonlinear control of a coupled PDE/ODE system modeling a switched power converter with a transmission line. Systems & Control Letters, 70, 92–99. https://doi.org/10.1016/j.sysconle.2014.05.009
  • Davoli, F., Kourogiorgas, C., Marchese, M., Panagopoulos, A., & Patrone, F. (2018). Small satellites and CubeSats: Survey of structures, Architectures, and protocols. International Journal of Satellite Communications and Networking, 37(4), 343–359. https://doi.org/10.1002/sat.1277
  • Korzeniewska, E., & Krawczyk, A. (2019). 5G technology as the succesive stage in the history of Wireless Telecommunication. 2019 IEEE International Conference on Modern Electrical and Energy Systems (MEES). https://doi.org/10.1109/mees.2019.8896516
  • Transmission line theory. (2009). The Transmission-Line Modeling Method. https://doi.org/10.1109/9780470546659.ch2
  • Ulaby, F. T., & Ravaioli, U. (1994). Fundamentals of Applied Electromagnetics. Pearson.
  • Wang, D., Chen, D., Song, B., Guizani, N., Yu, X., & Du, X. (2018). From IOT to 5G I-IOT: The next generation IOT-based intelligent algorithms and 5G technologies. IEEE Communications Magazine, 56(10), 114–120. https://doi.org/10.1109/mcom.2018.1701310
There are 6 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Amr Zeedan 0000-0003-2880-8573

Arslan Ayari 0000-0002-8663-886X

Project Number GSRA8-L-2-0523-21052
Early Pub Date March 25, 2023
Publication Date March 31, 2023
Published in Issue Year 2023 Issue: 49

Cite

APA Zeedan, A., & Ayari, A. (2023). Numerical Solution of Transmission Line PDEs Using Finite Difference. Avrupa Bilim Ve Teknoloji Dergisi(49), 94-99. https://doi.org/10.31590/ejosat.1261908