Periodic solutions of Toda lattice in loop nonlinear transmission line

Ballantyne, Gary J.; Gough, P.T.; Taylor, D.P.

doi:10.1049/el:19930407

Cited by 15 publications

(4 citation statements)

References 1 publication

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“…For the stability analysis of the coupled system, a small instantaneous perturbation is considered, which will gives rise to the following increments of the state variables: (12) Next, Kirchoff's laws are applied to the perturbed system. When doing so, the exponentials of the phase variables are approached as (13) It is also taken into account that the complex-frequency increment gives rise to a time-derivative operator [29]- [32], so the perturbed system can be written (14) where superindexes and indicate real and imaginary parts and the following functions have been defined and .…”

Section: Stability Analysis Of the Coupled-oscillator Systemmentioning

confidence: 99%

“…The soliton is a solitary wave that maintains its shape while travelling through the NLTL at a constant speed [9]. Some previous works [1], [12]- [16] have demonstrated the possibility to obtain an autonomous soliton generator by suitably loading an active element with an NLTL (reflection configuration) [14], [15] or by using the NLTL as the feedback block of an amplifier [1], [16]. This provides a periodic pulsed waveform, with no need of an input periodic signal.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Two Coupled NLTL-Based Oscillators

Pontón

Suárez

2014

IEEE Trans. Microwave Theory Techn.

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A system of two coupled oscillators based on nonlinear transmission lines (NLTL) is proposed for pulsed-shaping applications. The maximum propagation frequency through the NLTL is calculated and optimized with a realistic numerical method. With additional design considerations, this is used to increase the waveform steepening capabilities of the NLTL and obtain an oscillator based on the shockwave concept. Coupling two of these oscillators with slightly different characteristics various pulse shapes can be achieved through composition of the individual waveforms. The coupled-system behavior is understood with the aid of a new reduced-order formulation, which takes into account the differences between the oscillator elements. The formulation is extended for stability and phase-noise analysis. It provides valuable insight into the impact of the individual oscillator characteristics on the coupled-system dominant poles and unsymmetrical stable phase-shift range. It also explains the variation of the spectral density with the phase shift, as well as the mechanisms for the phase noise corners observed when increasing the offset frequency. A more realistic analysis of the coupled system is also carried out with the conversion-matrix approach, using cyclostationary noise sources. The analysis and design techniques have been applied to several prototypes at 0.8 GHz.Index Terms-Nonlinear transmission line (NLTL), oscillator, phase noise, stability. 0018-9480

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Section: Stability Analysis Of the Coupled-oscillator Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of Two Coupled NLTL-Based Oscillators

Pontón

Suárez

2014

IEEE Trans. Microwave Theory Techn.

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“…• Case I-Saturating amplifier: Consider the case where a standard saturating, non-inverting amplifier is used in the soliton oscillator [ Fig Ballantyne et al [19], [20] indeed implemented such a system, where a periodic train of solitons was seen. With minor ( 2%) changes to loop parameters such as gain, however, multiple pulses appeared in the oscillator and collided with one another, causing once again oscillation instabilities [ Fig.…”

Section: B Oscillation Instability Mechanismsmentioning

confidence: 99%

“…This shows the lack of robustness, reproducibility, and controllability in the soliton oscillator using the linear amplifier. This second case suggests that the saturation reduction is a necessary but not a sufficient condition to stabilize the oscilla- [19], [20].…”

Section: B Oscillation Instability Mechanismsmentioning

confidence: 99%

On the Self-Generation of Electrical Soliton Pulses

Ricketts

Sun

et al. 2007

IEEE J. Solid-State Circuits

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The nonlinear transmission line is a structure where short-duration pulses called electrical solitons can be created and propagated. By combining, in a closed-loop topology, the nonlinear line and a special amplifier that provides not only gain but also mechanisms to tame inherently unruly soliton dynamics, we recently constructed the first electrical soliton oscillator that self-generates a stable, periodic train of electrical soliton pulses (Ricketts et al., IEEE Trans. MTT, 2006). This paper starts with a review of this recently introduced circuit concept, and then reports on new contributions, i.e., further experimental studies of the dynamics of the stable soliton oscillator and a CMOS prototype demonstrating the chip-scale operation of the stable soliton oscillator. Finally, we go to the opposite end of the spectrum and present a numerical study showing the possibilities that deliberate promotions of the unruly soliton dynamics in the closed-loop topology can produce chaotic signals.

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Ultra-Wideband Analogue Channels Using Solitions

Arnold

Ultra-Wideband Short-Pulse Electromagnetics 4

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Periodic solutions of Toda lattice in loop nonlinear transmission line

Cited by 15 publications

References 1 publication

Analysis of Two Coupled NLTL-Based Oscillators

Analysis of Two Coupled NLTL-Based Oscillators

On the Self-Generation of Electrical Soliton Pulses

Ultra-Wideband Analogue Channels Using Solitions

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