Distortionless Lossy Transmission Lines Terminated by in Series Connected *RCL*-Loads

ABSTRACT

The paper deals with a lossy transmission line terminated at both ends by non-linear*RCL* elements. The mixed problem for the hyperbolic system, describing the transmission line, to an initial value problem for a neutral equation is reduced. Sufficient conditions for the existence and uniqueness of periodic regimes are formulated. The proof is based on the finding out of suitable operator whose fixed point is a periodic solution of the neutral equation. The method has a good rate of convergence of the successive approximations even for high frequencies.

The paper deals with a lossy transmission line terminated at both ends by non-linear

Cite this paper

nullV. Angelov and M. Hristov, "Distortionless Lossy Transmission Lines Terminated by in Series Connected*RCL*-Loads," *Circuits and Systems*, Vol. 2 No. 4, 2011, pp. 297-310. doi: 10.4236/cs.2011.24042.

nullV. Angelov and M. Hristov, "Distortionless Lossy Transmission Lines Terminated by in Series Connected

References

[1] M. Shimura, “Analysis of Some Nonlinear Phenomena in a Transmission Line,” IEEE Transactions on Circuit Theory, Vol. 14, No. 1, 1967, pp. 60-68. doi:10.1109/TCT.1967.1082648

[2] L. O. Chua and P.-M. Lin, “Machine Analysis of Electronic Circuits,” in Russian, Energy, Moscow, 1980.

[3] D. M. Pozar, “Microwave Engineering,” 2nd Edition, New York, Wiley, 1998.

[4] P. Chirlian, “Analysis and Design of Integrated Electronic Circuits,” Harper & Row, Publishers, Inc., New York, 1987.

[5] C. R. Paul, “Analysis of Multiconductor Transmission Lines,” Wiley-Interscience Publications, John Wiley & Sons, Hoboken, 1994.

[6] L. O. Chua, C. A. Desoer and E. S. Kuh, “Linear and Nonlinear Circuits,” McGraw-Hill Book Company, New York, 1987.

[7] A. H. Zemanian, “Hyperreal Waves on Transfinite, Terminated Distortionless and Lossless Transmission Lines,” International Journal of Circuit Theory and Applications, Vol. 33, No. 3, 2005, pp.183-193. doi:10.1002/cta.314

[8] S. Rosenstark, “Transmission Lines in Computer Engineering,” McGraw-Hill, Inc., New York, 1994.

[9] V. G. Angelov, “Transmission Lines Terminated by Series Nonlinear RLC-Loads,” Annual of the University of Architecture, Civil Engineering and Geodesy, Vol. 41, Sofia, 2000-2001, pp. 9-29.

[10] V. G. Angelov, “Lossy Transmission Lines Terminated by Nonlinear R-Loads with Exponential V-I Characteristics,” Journal Nonlinear Analysis, Vol. 8, No. 2, 2007, pp. 579-589.

[11] V. G. Angelov, “Periodic Regimes for Distortionless Lossy Transmission Lines Terminated by Parallel Connected RCL-Loads,” In: Transmission Lines: Theory, Types and Applications. Ser. Electrical Engineering Developments, Nova Science Publishers, New York, 2010.

[12] S. Grivet-Talocia, H. M. Huang, A. E. Rudehli, F. Canavero and I. M. Elfadel, “Transient Analysis of Lossy Transmission Lines: An Efficient Approach Based on the Method of Characteristics,” IEEE Transactions on Advanced Packaging, Vol. 27, No. 1, 2004, pp. 45-56. doi:10.1109/TADVP.2004.825467

[13] V. Rasvan, “Functional Differential Equations and One-Dimensional Distortionless Propagation,” Tatra Mountains Mathematical Publications, Vol. 43, 2009, pp. 215-228.

[14] K. L. Cooke and D. W. Krumme, “Differential—Difference Equations and Nonlinear Initial Boundary Value Problems for Linear Hyperbolic Partial Differential Equations,” Journal of Mathematical Analysis and Applications, Vol. 24, No. 2, 1968, pp. 372-387. doi:10.1016/0022-247X(68)90038-3

[15] A. D. Myshkis, “Linear Differential Equations with Retarded Arguments,” in Russian, Nauka, Moscow, 1972.

[16] M. A. Krasnoselskii, “The Shift Operator along the Trajectories,” in Russian, Moscow, 1970.

[17] Y. G. Borisovich, “Nonlinear Fredholm Mappings and Periodic Solutions of Functional Differential Equations,” in Russian, Proceedings of Mathematical Faculty, Vol. 10, 1973, pp. 12-25.

[18] V. G. Angelov, “Fixed Points in Uniform Spaces and Applications,” Cluj University Press, Cluj-Napoca, 2009.

[19] T. Dhaene and D. D. Zutter, “Selection of Lumped Models for Coupled Lossy Transmission Lines,” IEEE Transaction on Computer-Aided Design, Vol. 11, No. 7, 1992, pp. 805-815. doi:10.1109/43.144845

[20] S.Y. Lee, A. Konrad and R. Saldanha, “Lossy Transmission Line Transient Analysis by the Finite Element Method,” IEEE Transactions on Magnetics, Vol. 29, No. 2, 1993, pp. 1730-1732. doi:10.1109/20.250739

[21] Taflove and S. C. Hagness, “Computational Electromagnetics: The Finite-Difference Time-Domain Method,” 2nd Edition, Artech House, Boston, 2000.

[1] M. Shimura, “Analysis of Some Nonlinear Phenomena in a Transmission Line,” IEEE Transactions on Circuit Theory, Vol. 14, No. 1, 1967, pp. 60-68. doi:10.1109/TCT.1967.1082648

[2] L. O. Chua and P.-M. Lin, “Machine Analysis of Electronic Circuits,” in Russian, Energy, Moscow, 1980.

[3] D. M. Pozar, “Microwave Engineering,” 2nd Edition, New York, Wiley, 1998.

[4] P. Chirlian, “Analysis and Design of Integrated Electronic Circuits,” Harper & Row, Publishers, Inc., New York, 1987.

[5] C. R. Paul, “Analysis of Multiconductor Transmission Lines,” Wiley-Interscience Publications, John Wiley & Sons, Hoboken, 1994.

[6] L. O. Chua, C. A. Desoer and E. S. Kuh, “Linear and Nonlinear Circuits,” McGraw-Hill Book Company, New York, 1987.

[7] A. H. Zemanian, “Hyperreal Waves on Transfinite, Terminated Distortionless and Lossless Transmission Lines,” International Journal of Circuit Theory and Applications, Vol. 33, No. 3, 2005, pp.183-193. doi:10.1002/cta.314

[8] S. Rosenstark, “Transmission Lines in Computer Engineering,” McGraw-Hill, Inc., New York, 1994.

[9] V. G. Angelov, “Transmission Lines Terminated by Series Nonlinear RLC-Loads,” Annual of the University of Architecture, Civil Engineering and Geodesy, Vol. 41, Sofia, 2000-2001, pp. 9-29.

[10] V. G. Angelov, “Lossy Transmission Lines Terminated by Nonlinear R-Loads with Exponential V-I Characteristics,” Journal Nonlinear Analysis, Vol. 8, No. 2, 2007, pp. 579-589.

[11] V. G. Angelov, “Periodic Regimes for Distortionless Lossy Transmission Lines Terminated by Parallel Connected RCL-Loads,” In: Transmission Lines: Theory, Types and Applications. Ser. Electrical Engineering Developments, Nova Science Publishers, New York, 2010.

[12] S. Grivet-Talocia, H. M. Huang, A. E. Rudehli, F. Canavero and I. M. Elfadel, “Transient Analysis of Lossy Transmission Lines: An Efficient Approach Based on the Method of Characteristics,” IEEE Transactions on Advanced Packaging, Vol. 27, No. 1, 2004, pp. 45-56. doi:10.1109/TADVP.2004.825467

[13] V. Rasvan, “Functional Differential Equations and One-Dimensional Distortionless Propagation,” Tatra Mountains Mathematical Publications, Vol. 43, 2009, pp. 215-228.

[14] K. L. Cooke and D. W. Krumme, “Differential—Difference Equations and Nonlinear Initial Boundary Value Problems for Linear Hyperbolic Partial Differential Equations,” Journal of Mathematical Analysis and Applications, Vol. 24, No. 2, 1968, pp. 372-387. doi:10.1016/0022-247X(68)90038-3

[15] A. D. Myshkis, “Linear Differential Equations with Retarded Arguments,” in Russian, Nauka, Moscow, 1972.

[16] M. A. Krasnoselskii, “The Shift Operator along the Trajectories,” in Russian, Moscow, 1970.

[17] Y. G. Borisovich, “Nonlinear Fredholm Mappings and Periodic Solutions of Functional Differential Equations,” in Russian, Proceedings of Mathematical Faculty, Vol. 10, 1973, pp. 12-25.

[18] V. G. Angelov, “Fixed Points in Uniform Spaces and Applications,” Cluj University Press, Cluj-Napoca, 2009.

[19] T. Dhaene and D. D. Zutter, “Selection of Lumped Models for Coupled Lossy Transmission Lines,” IEEE Transaction on Computer-Aided Design, Vol. 11, No. 7, 1992, pp. 805-815. doi:10.1109/43.144845

[20] S.Y. Lee, A. Konrad and R. Saldanha, “Lossy Transmission Line Transient Analysis by the Finite Element Method,” IEEE Transactions on Magnetics, Vol. 29, No. 2, 1993, pp. 1730-1732. doi:10.1109/20.250739

[21] Taflove and S. C. Hagness, “Computational Electromagnetics: The Finite-Difference Time-Domain Method,” 2nd Edition, Artech House, Boston, 2000.