The present paper is devoted to the investigation of lossless transmission lines terminated by a nonlinear load with an interval of negative differential resistance and in series connected conductance. In contrast of almost all paper when i=f(u), here the case u=f(i) is considered. A general method of reducing the mixed problem to an initial value problem for neutral system on the boundary is presented. Sufficient conditions for the existence-uniqueness of an oscillatory solution are formulated. This is achieved by introducing an appropriate operator acting on suitable function space whose fixed point is an oscillatory solution of the initial value problem.
Cite this paper
Angelov, V. G. (2017). Oscillatory Solutions of Lossless Transmission Lines Terminated by Nonlinear Resistance and in Series Connected Inductance. Open Access Library Journal, 4, e3884. doi: http://dx.doi.org/10.4236/oalib.1103884.
Nagumo, J. and Shimura, M. (1961) Self-Oscillation in a Transmission Line with a Tunnel Diode. Proceedings of the IRE, 49, 1281-1291. https://doi.org/10.1109/JRPROC.1961.287920
Shimura, M. (1967) Analysis of Some Nonlinear Phenomena in a Transmission Line. IEEE Transactions on Circuit Theory, 14, 60-68. https://doi.org/10.1109/TCT.1967.1082648
Martín, F. (2015) Artificial Transmission Lines for RF and Microwave Applications. Wiley Series in Microwave and Optical Engineering. https://doi.org/10.1002/9781119058403
Kalaga, S. and Yenumula, P. (2016) Design of Electrical Transmission Lines: Structures and Foundations. CRC Press. https://doi.org/10.1201/9781315755687