PROPAGATION OF SOLITARY WAVES ON LOSSY NONLINEAR TRANSMISSION LINES

2009 ◽  
Vol 23 (01) ◽  
pp. 1-18 ◽  
Author(s):  
E. KENGNE ◽  
R. VAILLANCOURT
Keyword(s):  
Solitary Waves ◽  
Transmission Lines ◽  
Small Amplitude ◽  
Reductive Perturbation Method ◽  
Ginzburg Landau ◽  
Nonlinear Transmission Lines ◽  
Nonlinear Transmission ◽  
Long Wavelength ◽  
Reductive Perturbation ◽  
Ginzburg Landau Equations

We present a lossy nonlinear transmission RLC line and show how the coupled Ginzburg–Landau equations can be derived in the small amplitude and long wavelength limit using a standard reductive perturbation method and complex expansion. Soliton-like solution of the simplified equation was searched and the instability of a class of phase-winding solutions was explored.

scholarly journals Soliton Waves in Lossy Nonlinear Transmission Lines at Microwave Frequencies: Analytical, Numerical and Experimental Studies

Electronics ◽  
2021 ◽  
Vol 10 (18) ◽  
pp. 2278
Author(s):  
Dalibor L. Sekulic ◽  
Natasa M. Samardzic ◽  
Zivorad Mihajlovic ◽  
Miljko V. Sataric
Keyword(s):  
Transmission Lines ◽  
Experimental Studies ◽  
Reductive Perturbation Method ◽  
Nls Equation ◽  
Maximum Width ◽  
Nonlinear Transmission Lines ◽  
Microwave Frequencies ◽  
Nonlinear Transmission ◽  
Proposed Model ◽  
Loss Term

In this paper, we performed analytical, numerical and experimental studies on the generation of soliton waves in discrete nonlinear transmission lines (NLTL) with varactors, as well as the analysis of the losses impact on the propagation of these waves. Using the reductive perturbation method, we derived a nonlinear Schrödinger (NLS) equation with a loss term and determined an analytical expression that completely describes the bright soliton profile. Our theoretical analysis predicts the carrier wave frequency threshold above which a formation of bright solitons can be observed. We also performed numerical simulations to confirm our analytical results and we analyzed the space–time evolution of the soliton waves. A good agreement between analytical and numerical findings was obtained. An experimental prototype of the lossy NLTL, built at the discrete level, was used to validate our proposed model. The experimental shape of the envelope solitons is well fitted by the theoretical waveforms, which take into account the amplitude damping due to the losses in commercially available varactors and inductors used in a prototype. Experimentally observed changes in soliton amplitude and half–maximum width during the propagation along lossy NLTL are in good accordance with the proposed model defined by NLS equation with loss term.

scholarly journals Modulation of Pulse Train Using Leapfrogging Pulses Developed in Unbalanced Coupled Nonlinear Transmission Lines

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Koichi Narahara
Keyword(s):  
Solitary Waves ◽  
Transmission Lines ◽  
Pulse Train ◽  
Characteristic Impedance ◽  
Nonlinear Transmission Lines ◽  
Nonlinear Transmission ◽  
Resonant Interactions ◽  
The Difference ◽  
Nonlinear Solitary Waves ◽  
Leapfrogging Pulses

The leapfrogging pulses in two unbalanced electrical nonlinear transmission lines (NLTLs) with capacitive couplings are investigated for efficient modulation of a pulse train. Due to the resonant interactions, the nonlinear solitary waves in the NLTLs exhibit complementary behaviors of amplitudes and phases called leapfrogging. For maximizing resonance, both solitary waves should have a common average velocity. Sharing the common velocity, the characteristic impedance can still be freely designed for two coupled solitary waves. In this study, we characterize the leapfrogging pulses developed in unbalanced NLTLs having distinct characteristic impedance. Through the soliton perturbation theory and numerical time-domain calculations, it is found that both the leapfrogging frequency and the voltage variations of pulse amplitudes increase as the difference in the characteristic impedance becomes large. These properties can improve the on/off ratio of modulated pulse train.

Weakly Two-Dimensional Solitary Waves on Coupled Nonlinear Transmission Lines

2002 ◽  
Vol 19 (9) ◽  
pp. 1231-1233 ◽  
Author(s):  
Duan Wen-Shan ◽  
Hong Xue-Ren ◽  
Shi Yu-Ren ◽  
Lu Ke-Pu ◽  
Sun Jian-An
Keyword(s):  
Solitary Waves ◽  
Transmission Lines ◽  
Two Dimensional ◽  
Nonlinear Transmission Lines ◽  
Nonlinear Transmission

Picosecond Optical Switching Using RF Nonlinear Transmission Lines

2011 ◽  
Vol 29 (5) ◽  
pp. 666-669 ◽  
Author(s):  
David M. S. Johnson ◽  
Jason M. Hogan ◽  
Sheng-Way Chiow ◽  
Mark A. Kasevich
Keyword(s):  
Transmission Lines ◽  
Optical Switching ◽  
Nonlinear Transmission Lines ◽  
Nonlinear Transmission
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