A time-frequency algorithm for the simulation of the initial transient response of oscillators

“…While numerous approaches have been developed over the years e.g. [1][2][3], each has its own merits and demerits. In this contribution, an asymptotic numeric method developed in e.g.…”

Section: Introductionmentioning

confidence: 99%

Simulation technique for RF oscillators

2011

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“…(2) are introduced in eq. (1), the orthogonality of the Fourier series leads to the following timefrequency equation in the harmonic components V k (t) [13][14][15][16][17]:…”

Section: A Envelope Transient Based On the Modified Nodal Approachmentioning

confidence: 99%

“…In [17], the transient of the freerunning oscillator was simulated by considering the autonomous frequency as a system unknown. In [19 -21], an auxiliary generator (AG) or probe is introduced in the circuit in order to avoid undesired convergence toward nonoscillating solutions.…”

Section: A General Considerationsmentioning

confidence: 99%

Application of the envelope-transient method to the analysis and design of autonomous circuits

Suárez¹,

Sancho²

2005

Int J RF and Microwave Comp Aid Eng

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ABSTRACT:The envelope transient enables a very efficient simulation of circuits with two different time scales, such as those that contain modulated signals (for example, amplifier or mixers), where an accurate prediction of intermodulation distortion is needed. The method has also been extended to oscillator analysis, where it requires additional techniques in order to avoid convergence to degenerate mathematical solutions, for which the circuit is not actually oscillating. It allows an efficient analysis of transients in these circuits and an accurate prediction of the phase-noise spectrum. This article presents an overview of the envelopetransient method and its most recent applications to the simulation of autonomous circuits, such as free and forced oscillators, frequency dividers, and phase-locked loops. Using this method, the operation bands of these circuits (which are delimited by qualitative stability changes or bifurcations) can be determined in a straightforward manner. This technique can also be applied to predict intermodulation distortion in self-oscillating mixers and to simulate the response of synchronized oscillators containing modulated signals. © 2005 Wiley Periodicals, Inc. Int J RF and Microwave CAE 15: 523-535, 2005.

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“…In FD simulations the circuit variables are conveniently expressed in terms of generalized Fourier series 5 , which permits to quickly have information about the steady state, skipping the transient evaluation (Kundert et al, 1990). Application of this principle in microwave circuit analysis gave rise to the Harmonic Balance (HB) method (Rizzoli & Neri, 1988;Rizzoli et al, 1992) and its extension to modulated signals, the Envelope Transient simulation (Brachtendorf et al, 1998;Ngoya et al, 1995, Ngoya & Larcheveque, 1996 which is a mixed TD/FD method.…”

Section: Introductionmentioning

confidence: 99%