Nonlinear Dispersive Waves and Parametric Interaction in the Transmission Line

Tutomu KAWATA; Jun-ichi SAKAI; Hiroshi INOUE

Nonlinear Dispersive Waves and Parametric Interaction in the Transmission Line

Tutomu KAWATA, Jun-ichi SAKAI, Hiroshi INOUE

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The phenomena of the wave propagation in a nonlinear transmission line are analyzed theoretically by the derivative expansion method. Each section of this line is constructed with a series inductor L₁ and the shunt circuit consisting of a seriesed L₂ - C₂ element and a nonlinear capacitor C (V) in which V is a line voltage. There exist two modes; L.F. mode propagating in the frequency range 0ωω_t and H.F. mode in the range ω_pω, where (L₂ C₂)¹ and (1C₂/C(0)). In the strongly dispersive region the asymptotic behavior of the nonlinear waves is described by the nonlinear Schrödinger equation and by the Korteweg-de Vries equation in the weakly dispersive region. Critical frequencies ω₁₀ and ω₂₀ (ω_pω₂₀ω₁₀) decompose the H.F. mode into three regions (1) ω_pωω₂₀, (2) ω₂₀ωω₁₀ and (3) ω₁₀ω. The resonant interaction between the L.F. mode and the H.F. mode occurs in the frequency ω₁₀, while the lowest order nonlinear interaction disappears in the frequency ω₂₀. In the regions (1), (3) and the L.F. mode the plane wave is stable under the wave modulation, while the plane wave is unstable in the region (2). We derive the basic equations describing the three wave interactions and find that the plane wave with a large amplitude becomes unstable through the parametric decay instability. The wave number and maximum growth rate of the excited waves are determined.

Publication: IEICE TRANSACTIONS on transactions Vol.E60-E No.7 pp.339-346

Publication Date: 1977/07/25

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Type of Manuscript: PAPER

Category: Circuits and Systems

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Tutomu KAWATA
Jun-ichi SAKAI
Hiroshi INOUE

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Tutomu KAWATA, Jun-ichi SAKAI, Hiroshi INOUE, "Nonlinear Dispersive Waves and Parametric Interaction in the Transmission Line" in IEICE TRANSACTIONS on transactions, vol. E60-E, no. 7, pp. 339-346, July 1977, doi: .
Abstract: The phenomena of the wave propagation in a nonlinear transmission line are analyzed theoretically by the derivative expansion method. Each section of this line is constructed with a series inductor L₁ and the shunt circuit consisting of a seriesed L₂ - C₂ element and a nonlinear capacitor C (V) in which V is a line voltage. There exist two modes; L.F. mode propagating in the frequency range 0ωω_t and H.F. mode in the range ω_pω, where (L₂ C₂)¹ and (1C₂/C(0)). In the strongly dispersive region the asymptotic behavior of the nonlinear waves is described by the nonlinear Schrödinger equation and by the Korteweg-de Vries equation in the weakly dispersive region. Critical frequencies ω₁₀ and ω₂₀ (ω_pω₂₀ω₁₀) decompose the H.F. mode into three regions (1) ω_pωω₂₀, (2) ω₂₀ωω₁₀ and (3) ω₁₀ω. The resonant interaction between the L.F. mode and the H.F. mode occurs in the frequency ω₁₀, while the lowest order nonlinear interaction disappears in the frequency ω₂₀. In the regions (1), (3) and the L.F. mode the plane wave is stable under the wave modulation, while the plane wave is unstable in the region (2). We derive the basic equations describing the three wave interactions and find that the plane wave with a large amplitude becomes unstable through the parametric decay instability. The wave number and maximum growth rate of the excited waves are determined.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e60-e_7_339/_p

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@ARTICLE{e60-e_7_339,
author={Tutomu KAWATA, Jun-ichi SAKAI, Hiroshi INOUE, },
journal={IEICE TRANSACTIONS on transactions},
title={Nonlinear Dispersive Waves and Parametric Interaction in the Transmission Line},
year={1977},
volume={E60-E},
number={7},
pages={339-346},
abstract={The phenomena of the wave propagation in a nonlinear transmission line are analyzed theoretically by the derivative expansion method. Each section of this line is constructed with a series inductor L₁ and the shunt circuit consisting of a seriesed L₂ - C₂ element and a nonlinear capacitor C (V) in which V is a line voltage. There exist two modes; L.F. mode propagating in the frequency range 0ωω_t and H.F. mode in the range ω_pω, where (L₂ C₂)¹ and (1C₂/C(0)). In the strongly dispersive region the asymptotic behavior of the nonlinear waves is described by the nonlinear Schrödinger equation and by the Korteweg-de Vries equation in the weakly dispersive region. Critical frequencies ω₁₀ and ω₂₀ (ω_pω₂₀ω₁₀) decompose the H.F. mode into three regions (1) ω_pωω₂₀, (2) ω₂₀ωω₁₀ and (3) ω₁₀ω. The resonant interaction between the L.F. mode and the H.F. mode occurs in the frequency ω₁₀, while the lowest order nonlinear interaction disappears in the frequency ω₂₀. In the regions (1), (3) and the L.F. mode the plane wave is stable under the wave modulation, while the plane wave is unstable in the region (2). We derive the basic equations describing the three wave interactions and find that the plane wave with a large amplitude becomes unstable through the parametric decay instability. The wave number and maximum growth rate of the excited waves are determined.},
keywords={},
doi={},
ISSN={},
month={July},}

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TY - JOUR
TI - Nonlinear Dispersive Waves and Parametric Interaction in the Transmission Line
T2 - IEICE TRANSACTIONS on transactions
SP - 339
EP - 346
AU - Tutomu KAWATA
AU - Jun-ichi SAKAI
AU - Hiroshi INOUE
PY - 1977
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E60-E
IS - 7
JA - IEICE TRANSACTIONS on transactions
Y1 - July 1977
AB - The phenomena of the wave propagation in a nonlinear transmission line are analyzed theoretically by the derivative expansion method. Each section of this line is constructed with a series inductor L₁ and the shunt circuit consisting of a seriesed L₂ - C₂ element and a nonlinear capacitor C (V) in which V is a line voltage. There exist two modes; L.F. mode propagating in the frequency range 0ωω_t and H.F. mode in the range ω_pω, where (L₂ C₂)¹ and (1C₂/C(0)). In the strongly dispersive region the asymptotic behavior of the nonlinear waves is described by the nonlinear Schrödinger equation and by the Korteweg-de Vries equation in the weakly dispersive region. Critical frequencies ω₁₀ and ω₂₀ (ω_pω₂₀ω₁₀) decompose the H.F. mode into three regions (1) ω_pωω₂₀, (2) ω₂₀ωω₁₀ and (3) ω₁₀ω. The resonant interaction between the L.F. mode and the H.F. mode occurs in the frequency ω₁₀, while the lowest order nonlinear interaction disappears in the frequency ω₂₀. In the regions (1), (3) and the L.F. mode the plane wave is stable under the wave modulation, while the plane wave is unstable in the region (2). We derive the basic equations describing the three wave interactions and find that the plane wave with a large amplitude becomes unstable through the parametric decay instability. The wave number and maximum growth rate of the excited waves are determined.
ER -