Growth-rate function for the nonlinear analysis of the transient dynamics of microwave oscillators

Suárez, Almudena; Sancho, Sergio; Ramírez, Franco

doi:10.1109/mwsym.2016.7540302

Cited by 5 publications

(10 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To extend the numerical model in order to account for the build-up transient, the preliminary work [19], [20] presents the derivation of a first-order envelope-domain equation from a single observation node. The model relies on a full extraction of an outer-tier admittance function ( , ) Y V  from HB, which depends on the excitation amplitude V and frequency .…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Transient Dynamics of Microwave Oscillators

Sancho

Suárez

Ramírez

et al. 2019

IEEE Trans. Microwave Theory Techn.

Self Cite

View full text Add to dashboard Cite

A semi-analytical method for the global prediction and understanding of the transient dynamics of oscillator circuits is presented. It covers both the linear and nonlinear transient stages, which are related with the circuit generalized eigenvalues, here introduced for the first time. The transient model relies on the application of the implicit-function theorem to the harmonicbalance system, in order to derive a reduced-order nonlinear differential equation from a given observation node. This requires the extraction of a nonlinear admittance function, depending on the voltage excitation and oscillation frequency, which is done with a forcing auxiliary generator. The linearization of this admittance function for each excitation amplitude provides a sequence of linear ordinary differential equations, describing the system dynamics in the vicinity of each point of the transient trajectory, which can be reconstructed from the expression of the solution increment at each time step. The sequence of differential equations provides a set of generalized eigenvalues, responsible for the acceleration or deceleration of the oscillation growth and capable to detect spurious transient frequencies. The concept of escape time, or time required by the transient trajectory to go through a certain interval of amplitude values, is also introduced, for the first time to our knowledge. The method has been successfully applied to analyze the transient dynamics of several FET oscillators, including dual-frequency oscillators and switched oscillators.

show abstract

Section: Introductionmentioning

confidence: 99%

Analysis of the Transient Dynamics of Microwave Oscillators

Sancho

Suárez

Ramírez

et al. 2019

IEEE Trans. Microwave Theory Techn.

Self Cite

View full text Add to dashboard Cite

show abstract

“…At the primary Hopf bifurcations, the oscillation condition is fulfilled with zero amplitude. The parameter boundaries for oscillation at  d and  h can be obtained with the aid of an AG [1]- [6], which is an independent voltage source at the frequency  AG in series with an ideal bandpass filter at the same frequency. In the circuit in Fig.…”

Section: Dual-frequency Oscillatormentioning

confidence: 99%

“…In the last years, numerous efforts [1]- [6] have been devoted to the development of novel analysis and synthesis tools for oscillator circuits, intended to be applied in combination with the harmonic-balance (HB) method [7]- [8]. In fact, HB suffers from a number of shortcomings when dealing with autonomous circuits, mostly due to the fact that it is insensitive to the stability properties of the solution, generated and extinguished through bifurcation phenomena [8].…”

Section: Introductionmentioning

confidence: 99%

“…Here a bifurcation-analysis technique is provided to accurately determine the parameter values leading to each oscillation. The second methodology addresses the prediction of the oscillator transient [6], highly relevant in mobile communications [11]- [13], where a fast oscillation start-up reduces the power consumption. A regular oscillator transient is also essential in envelope-modulation systems and radar.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New methodologies for the analysis and synthesis of oscillator circuits

Suárez¹,

Pontón²,

Sancho³

et al. 2018

2018 IEEE MTT-S Latin America Microwave Conference (LAMC 2018)

Self Cite

View full text Add to dashboard Cite

Advances in the analysis and synthesis of oscillator circuits, using harmonic balance (HB), are presented. They rely on the use of auxiliary generators, which can be introduced into the HB software to impose mathematical conditions or to extract a realistic oscillator model. In particular, a bifurcation-detection technique, for the accurate design of dual-frequency oscillators, and a semi-analytical function, for the prediction of oscillation transients, are described. In dual-frequency oscillators, each oscillation must be the only stable solution in a certain parameter interval. This is ensured through the calculation of two distinct primary-Hopf bifurcation loci, which should give rise to disjoint parameter regions. Conditions for the physical observability of concurrent oscillations are also given. With respect to the transient prediction, both the linear and nonlinear stages are considered. The analysis is based on the derivation of outer-tier semi analytical equation, from which a growth rate function is identified, which, unlike ordinary simulations, is not constrained to particular initial values. The methods have been applied to two FET-based oscillator circuits that have been manufactured and measured, obtaining good agreement with the simulation results.

show abstract

“…The recent works [13], [14] present a methodology to extract a reduced-order nonlinear model of a single oscillator, which is able to predict the build-up transient. The model relies on the application of the implicit function theorem to the HB system, in order to derive a reduced-order nonlinear differential equation at the observation node.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Transient Dynamics of Coupled-Oscillator Systems

Sancho

Suárez

Ramírez

2020

2020 IEEE/MTT-S International Microwave Symposium (IMS)

Self Cite

View full text Add to dashboard Cite

A realistic reduced-order formulation of systems containing several transistor-based oscillators, such as coupledoscillator networks, is presented. The formulation is able to predict the oscillation build-up and other transient effects for the first time to our knowledge. The individual oscillator models are constructed from a nonlinear admittance function extracted from circuit-level harmonic-balance simulations. These models are used to derive a nonlinear differential-equation system able to describe the transient behavior of the entire structure. For illustration, the method has been applied to a coupled-oscillator system at 5 GHz, obtaining very good agreement with circuit-level envelope transient (when applicable) and with measurements.

show abstract

Growth-rate function for the nonlinear analysis of the transient dynamics of microwave oscillators

Abstract: Index Terms -microwave oscillator, frequency-domain analysis.

Cited by 5 publications

References 8 publications

Analysis of the Transient Dynamics of Microwave Oscillators

Analysis of the Transient Dynamics of Microwave Oscillators

New methodologies for the analysis and synthesis of oscillator circuits

Analysis of the Transient Dynamics of Coupled-Oscillator Systems

Contact Info

Product

Resources

About