i-manager Publications

In Series Connected RCL-Elements Loaded on Lossy Transmission Lines without the Heaviside’s Condition

Vasil G. Angelov*

*Department of Mathematics, University of Mining and Geology “St. I. Rilski”, Sofia, Bulgaria.

Periodicity:April - June'2019
DOI : https://doi.org/10.26634/jmat.8.2.16649

Abstract

The main purpose of the present paper is to analyze the processes in a lossy transmission line terminated by in-series connected nonlinear RCL-loads. The distortion less propagation of the TEM-waves along the line under the Heaviside's condition has been investigated in a previous paper. Here we assume that the Heaviside condition is not satisfied. This leads to difficulties which can be overcome by a different type operator presentation of the mixed problem for the lossy transmission line. First, we formulate boundary conditions using the Kirchhoff's law, then transform the system in an operator form, and apply the fixed point method to obtain an existence-uniqueness theorem for a generalized solution. The uniqueness of solution is lost along the whole length of the line. Finally, we demonstrate the conditions of the main theorem on a typical example.

Keywords

Lossy transmission line, Nonlinear loads, Heaviside’s condition, Fixed point method.

How to Cite this Article?

Angelov, G. V. (2019). In Series Connected RCL-Elements Loaded on Lossy Transmission Lines without the Heaviside’s Condition. i-manager's Journal on Mathematics, 8(2), 1-14. https://doi.org/10.26634/jmat.8.2.16649

References

[1]. Angelov, V. G. (2013). A Method for Analysis of Transmission Lines Terminated by Nonlinear Loads. Nova Science Publishers, Incorporated.

[2]. Angelov, V. G. (2015). Josephson lossless transmission lines with nonlinear R-element. International Research Journal of Natural Sciences, 3(3), 59-79.

[3]. Angelov, V. G. (2016). Lossy Transmission Lines with Josephson Junction—Continuous Generalized Solutions. Communication in Applied Analysis, 20, 91-106.

[4]. Angelov, V. G., & Hristov, M. (2011). Distortionless lossy transmission lines terminated by in series connected RCL-loads. Circuits and Systems, 2(4), 297-310.

[5]. Chan, A. F. (2006). The Finite Difference Time Domain Method for Computational Electromagnetics. (Dissertation), University of Southern Queensland, Faculty of Engineering and Surveying.

[6]. Chua, L. O., & Lin, P. M. (1980). Machine Analysis of Electronic Circuits. Russian, Energy, Moscow.

[7]. Chua, L. O., Desoer, C. A., & Kuh, E. S. (1987). Linear and Nonlinear Circuits. McGraw-Hill Book Company, New York. https://doi.org/10.1002/bimj.4710300726

[8]. De Broglie, L. (1941). Problèmes de propagations guidées des ondes électromagnétiques (p. 6). Paris. https://doi.org/10.1090/S0002-9904-1952-09569-0

[9]. Dinakaran, C. (2015). Implementation of Shunt and Series FACTS Devices for Overhead Transmission Lines. International Electrical Engineering Journal (IEEJ), 6(8), 2009-2017.

[10]. Gaurav, Y., & Chauhan, R. K. (2016). Design of controllable dual-band bandpass filter using open loop triangular ring resonators loaded with stub coupled with transmission line. i-manager's Journal on Electronics Engineering, 7(2), 8-13. https://doi.org/10.26634/jele.7.2.11408.

[11]. Holt, C. A. (1963). Introduction to Electromagnetic Fields and Waves. John Wiley & Sons.

[12]. Jordan, E. C., & Balmain, K. G. (1968). Electromagnetic Waves and Radiating Systems, Second Edition. Prentice-Hall Inc.

[13]. Kalaga, S., & Yenumula, P. (2016). Design of Electrical Transmission Lines: Structures and Foundations. CRC Press.

[14]. Kapoor, G. (2019). Detection and classification of single line to ground boundary faults in a 138 kV six phase transmission line using Hilbert Huang transform. i-manager's Journal on Electrical Engineering, 12(3), 28-41. https://doi.org/10.26634/jee.12.3.15382.

[15]. Maas, S. A. (2003). Nonlinear Microwave and RF Circuits, 2^nd Ed., Artech House, Inc., Boston London.

[16]. Makwana, V. H., & Bhalja, B. R. (2016). Transmission Line Protection using Digital Technology, 1^st Ed. Springer.

[17]. Martin, F. (2015). Artificial Transmission Lines for RF and Microwave Applications. John Wiley & Sons. DOI:10.1002/9781119058403

[18]. Miamo, G., & Maffucci, A. (2001). Transmission Lines and Lumped Circuits: Fundamental and Applications, 2^nd Ed. Academic Press, New York.

[19]. Misra, D. K. (2004). Radio-frequency and Microwave Communication Circuits: Analysis and Design, 2^nd Ed. University of Wisconsin-Milwaukee. J. Wiley & Sons, Inc. DOI:10.1002/0471653764

[20]. Patil, N., & Behere, D. (2019). Performance analysis of PID and LQG control algorithms for antenna position control system. i-manager's Journal on Electrical Engineering, 13(1), 12-18. https://doi.org/10.26634/jee.13.1.16235

[21]. Raghuwanshi, S. K., Kumar, V., & Pandey, R. R. (2011). Guided and Leaky modes of a multilayer planar slab waveguide. i-manager's Journal on Electronics Engineering, 1(3), 14. https://doi.org/10.26634/jele.1.3.1421

[22]. Ramo, S., Whinnery, J. R., & Van Duzer, T. (1994). Fields and Waves in Communication Electronics. John Wiley & Sons.

[23]. Rosenstark, S. (1994). Transmission Lines in Computer Engineering. McGraw-Hill, Inc, New York, USA.

[24]. Ruikar, D. S. (2016). Electromagnetics and Transmission Lines. Nirali Prakashan.

[25]. Sharma, N., Sandhu, S., & Sharma, V. (2018). Analysis and Comparison of Rectangular Microstrip Patch Antennas with Omni-Directional Slotted Patch Antenna for Wireless Applications. i-manager's Journal on Communication Engineering and Systems, 7(2), 42-47. https://doi.org/10.26634/jcs.7.2.14105

[26]. Singh, R. (2013). Circuit Theory and Transmission Lines. McGraw Hill Education.

In Series Connected RCL-Elements Loaded on Lossy Transmission Lines without the Heaviside’s Condition

Abstract

Keywords

How to Cite this Article?

References

If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Options for accessing this content:

	North Americas,UK, Middle East,Europe		India	Rest of world
	USD	EUR	INR	USD-ROW
Pdf	35	35	200	20
Online	35	35	200	15
Pdf & Online	35	35	400	25