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

Dalibor L Sekulic,Zivorad Mihajlovic,Miljko V Sataric,Natasa M Samardzic

doi:10.3390/electronics10182278

Dalibor L Sekulic, Zivorad Mihajlovic + Show 2 more

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https://doi.org/10.3390/electronics10182278

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Journal: Electronics	Publication Date: Sep 17, 2021
Citations: 11	License type: CC BY 4.0

Affiliation: University of Novi Sad

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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.

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For electrical engineers, nonlinearity and dispersion are generally undesirable, but a nonlinear transmission line (NLTL) can balance these two effects to generate soliton-like pulses
It is obvious that a bright soliton is formed, preserving its shape, which is in good agreement with our theoretical predictions since the product of the dispersion and nonlinearity coefficients is positive for the parameters of the NLTL and the bright soliton should occur
We have reported analytical, numerical, and experimental results of propagation characteristics of soliton waves in the lossy NLTL, loaded periodically with linear series inductors and shunt varactors used as nonlinear capacitors

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Nonlinearity and dispersion are generally undesirable, but a nonlinear transmission line (NLTL) can balance these two effects to generate soliton-like pulses. The first one uses a ladder network of repeating lumped inductors and capacitors, where the inductors or capacitors are nonlinear in their response to current or voltage, respectively [1,2,3]. For experimental research, this implementation of the equivalent NLTL circuit is most common in which special diodes (varactors or Schottky diodes) are used as nonlinear capacitors placed in shunt form [4]

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