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

Sekulić, Dalibor L.; Samardžić, Nataša; Mihajlović, Živorad; Satarić, M. V.

doi:10.3390/electronics10182278

Cited by 13 publications

(7 citation statements)

References 19 publications

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“…The interest in studies of discrete nonlinear electrical transmission lines, in particular of lossy nonlinear transmission lines, started some time ago, [ 32–34 ] but it became even more pronounced recently. [ 35–38 ] These studies should be seen in the general context of waves in strongly nonlinear discrete systems. [ 39–45 ]…”

Section: Introductionmentioning

confidence: 99%

“…[29][30][31] The interest in studies of discrete nonlinear electrical transmission lines, in particular of lossy nonlinear transmission lines, started some time ago, [32][33][34] but it became even more pronounced recently. [35][36][37][38] These studies should be seen in the general context of waves in strongly nonlinear discrete systems. [39][40][41][42][43][44][45] In our previous publication, [46] we considered shock waves in the continuous JTL with resistors, studying the influence of those on the shock profile.…”

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The Kinks, the Solitons and the Shocks in Series‐Connected Discrete Josephson Transmission Lines

Kogan

2022

Physica Status Solidi (b)

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The concept that in a nonlinear wave propagation system the various parts of the wave travel with different velocities and that wave fronts (or tails) can sharpen into shock waves is deeply imbedded in the classical theory of fluid dynamics. [1] The methods developed in that field can be profitably used to study signal propagation in nonlinear transmission lines. [2][3][4][5][6][7][8][9][10][11] In the early studies of shock waves in transmission lines, the origin of nonlinearity was due to nonlinear capacitance in the circuit. [12][13][14] Interesting and potentially important examples of nonlinear transmission lines are circuits containing Josephson junctions (JJ), [15] Josephson transmission lines (JTL). [16][17][18][19] The unique nonlinear properties of JTL allow to construct soliton propagators, microwave oscillators, mixers, detectors, parametric amplifiers, and analog amplifiers. [17][18][19] Transmission lines formed by JJ connected in series were studied from 1990s, though much less than transmission lines formed by JJ connected in parallel. [20] However, the former began to attract quite a lot of attention recently, [21][22][23][24][25][26][27][28] especially in connection with possible JTL traveling wave parametric amplification. [29][30][31] The interest in studies of discrete nonlinear electrical transmission lines, in particular of lossy nonlinear transmission lines, started some time ago, [32][33][34] but it became even more pronounced recently. [35][36][37][38] These studies should be seen in the general context of waves in strongly nonlinear discrete systems. [39][40][41][42][43][44][45] In our previous publication, [46] we considered shock waves in the continuous JTL with resistors, studying the influence of those on the shock profile. Now we want to analyze wave propagation in the discrete JTL, both lossless and lossy.The rest of the article is constructed as follows. In Section 2, we formulate the approximation to the circuit equations of the discrete lossless JTL. In Section 3, we formulate the quasicontinuum approximation and show the analogy between the problem of the running waves and the problem of equilibrium of an elastic rod in the potential field. In Section 4, by simplifying the approximation, we reduce the problem of the running waves to an effective mechanical problem, describing motion of a fictitious particle in a potential well, and study the profiles of the kinks and of the solitons. In Section 5, we consider specifically weak kinks and weak solitons. In Section 6, we discuss the effect of dissipation on the running waves in the discrete JTL. In Section 7, we formulate the modified quasicontinuum approximation and, on top of it, the simple wave approximation, which opens the way to conveniently study nonstationary waves in the JTL. In Section 8, we obtain the nonlinear dispersion law, and in Section 9, we study the modulation stability of the wavetrains. In Section 10, we briefly mention possible applications of the results obtained in the article and

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

The Kinks, the Solitons and the Shocks in Series‐Connected Discrete Josephson Transmission Lines

Kogan

2022

Physica Status Solidi (b)

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“…The interest in studies of discrete nonlinear electrical transmission lines, in particular of lossy nonlinear transmission lines, has started some time ago 32 , but it became even more pronounced recently 33,34 . These studies should be seen in the general context of waves in strongly nonlinear discrete systems [35][36][37][38][39][40] .…”

Section: Introductionmentioning

confidence: 99%

Shocks and solitary waves in series connected discrete Josephson transmission lines

Kogan¹

2022

Preprint

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“…The interest in studies of discrete nonlinear electrical transmission lines, in particular of lossy nonlinear transmission lines, has started some time ago [32][33][34] , but it became even more pronounced recently [35][36][37] . These studies should be seen in the general context of waves in strongly nonlinear discrete systems [38][39][40][41][42][43][44] .…”

Section: Introductionmentioning

confidence: 99%

The kinks, the solitons and the shocks in series connected discrete Josephson transmission lines

Kogan¹

2022

Preprint

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<div>We analytically study wave propagation in the discrete Josephson transmission lines (JTL), constructed from Josephson junctions (JJ) and capacitors. Our approach is based on the quasi-continuum approximation, which we discuss in details. The approximation allows to take into account the intrinsic dispersion in the discrete JTL. Due to competition between such dispersion and the nonlinearity, in the dissipationless JTL there exist running waves in the form of supersonic kinks and solitons. We also study the effect of dissipation in the system and find that in the presence of the resistors, shunting the JJ and/or in series with the ground capacitors, the only possible stationary running waves are the shock waves</div>

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

Cited by 13 publications

References 19 publications

The Kinks, the Solitons and the Shocks in Series‐Connected Discrete Josephson Transmission Lines

The Kinks, the Solitons and the Shocks in Series‐Connected Discrete Josephson Transmission Lines

Shocks and solitary waves in series connected discrete Josephson transmission lines

The kinks, the solitons and the shocks in series connected discrete Josephson transmission lines

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