Nonlinear observer design based on immersion and invariance method: an insight to chaotic systems

Malekzadeh, Milad; Noei, Abolfazl Ranjbar

doi:10.1007/s40435-020-00670-7

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Extraction Of Oscillator Equations In General1

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2023

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“…We also assume that the polynomial function of degree 3 approximates (2), which is generally a correct assumption (Magierowski and Zukotynski, 2004; Kyamakya et al , 2009; Malekzadeh and Noei, 2021): …”

Section: Extraction Of Oscillator Equations In Generalmentioning

confidence: 99%

Closed-form and technology independent phase noise relation for LC oscillators

Moradnezhad

Naimi

2023

COMPEL

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Purpose The purpose of this paper is to find a closed relation for the phase noise of LC oscillators. Design/methodology/approach The governing equation of oscillators is generally a stochastic nonlinear differential equation. In this paper, a closed relation for the phase noise of LC oscillators was obtained by approximating the I–V characteristic of the oscillator with third-degree polynomials and analyzing its differential equation. Findings This relation expresses phase noise directly in terms of circuit parameters, including the sizes of the transistors and the bias. Next, for evaluation, the phase noise of the cross-coupled oscillator without tail current was calculated with the proposed model. In this approach, the obtained equations are expressed independently of technology by combining the obtained phase noise relation and gm/ID method. Originality/value A technology-independent method using the gm/ID method and the closed relationship is provided to calculate phase noise.

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