Mathematical Modeling of Nonlinear Waves and Oscillations in Gyromagnetic Structures by Bifurcation Theory Methods

Makeeva, G. S.; Golovanov, O. A.; Pardavi‐Horváth, M.

doi:10.1163/156939306779274363

Cited by 10 publications

(8 citation statements)

References 2 publications

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“…Bifurcation theory is a powerful tool, since it provides a deep knowledge about the dynamics of nonlinear systems [24]. When the operation regime of a nonlinear circuit is near to a Hopf bifurcation point, an amplification phenomenon which affects to all the signals in the circuit is generated.…”

Section: Optimization Based On Bifurcation Controlmentioning

confidence: 99%

Optimization of the Synchronization Bandwidth of Rationally Synchronized Oscillators Based on Bifurcation Control

Fernández¹,

Hoeye²,

Vázquez³

et al. 2011

PIER

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Abstract-In this work, a nonlinear technique for the optimization of the synchronization bandwidth of Rationally Synchronized Oscillators (RSO) is presented. The circuit is forced to operate near a Hopf bifurcation point which is created around the frequency of the input reference signal. Under this operating regime, the reference signal is strongly amplified and the synchronization bandwidth of the circuit is considerably improved. A 5-3 GHz rationally synchronized oscillator has been optimized using the proposed method. The manufactured RSO provides a 5 MHz synchronization bandwidth with a reference signal power of −22 dBm, in good agreement with simulation results.

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Section: Optimization Based On Bifurcation Controlmentioning

confidence: 99%

Optimization of the Synchronization Bandwidth of Rationally Synchronized Oscillators Based on Bifurcation Control

Fernández¹,

Hoeye²,

Vázquez³

et al. 2011

PIER

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“…In this work, the conversion gain of the HSOM will be considerably improved through the application of a recently developed technique based on bifurcation analysis and control methods [4]. This technique combines the control of the harmonic content of the autonomous signal [3] with the careful selection of the HSOM operating regime, which will be established in the vicinity of a Hopf bifurcation point [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

New Non-Linear Approach for the Evaluation of the Linearity of High Gain Harmonic Self Oscillating Mixers

Fernández

Hoeye²,

Vázquez³

et al. 2012

PIER

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Abstract-In this work, the linearity of a high gain Harmonic Self Oscillating Mixer (HSOM) is analyzed. In order to obtain high conversion gain, the working point of the HSOM is established close to a Hopf bifurcation point. The traditional figures of merit used to characterize the linearity of conventional mixers cannot be directly applied to characterize the behavior of autonomous circuits, because of the influence of the input RF signal power on the autonomous signal parameters. The 1 dB compression point and the third order distortion will be analyzed as a function of the harmonic content and maximum gain of the circuit. From the collected data, the optimum harmonic content and the maximum conversion gain of the HSOM can be selected, for a particular application, in order to minimize the output IF signal distortion.

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“…Rizzoli and Lipparini proposed a general method for stability analysis of microwave circuits, but their method is very complex and difficult to implement [11][12][13]. Bifurcation is another tool for stability analysis of nonlinear circuits [14]. Based on the bifurcation theory, Suárez proposed a method for stability analysis.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Stability Analysis of Microwave Oscillators Using the Periodic Averaging Method

Vahdati¹,

Abdipour²

2008

PIER

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Abstract-In this paper an approach for stability analysis of microwave oscillators is proposed. Using the perturbation theory and averaging method, a theorem which relates the oscillation stability to the stability of the periodic average of the circuit's Jacobian is mentioned. Using this theorem, a criterion for oscillation stability is devised. The proposed criterion is applied to the stability analysis of a negative resistance diode oscillators and a Colpitts oscillator. This method is readily applicable to microwave CAD routines.

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Mathematical Modeling of Nonlinear Waves and Oscillations in Gyromagnetic Structures by Bifurcation Theory Methods

Cited by 10 publications

References 2 publications

Optimization of the Synchronization Bandwidth of Rationally Synchronized Oscillators Based on Bifurcation Control

Optimization of the Synchronization Bandwidth of Rationally Synchronized Oscillators Based on Bifurcation Control

New Non-Linear Approach for the Evaluation of the Linearity of High Gain Harmonic Self Oscillating Mixers

Nonlinear Stability Analysis of Microwave Oscillators Using the Periodic Averaging Method

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