IEEE Journal of Solid-State Circuits · 2007 · 63 citations · 12 references
EngineeringPhysicsDifferential EquationsDynamical SystemsVibrationFrequency ResponseNonlinear DynamicsOscillatorsResonance In CircuitsResonant CircuitsResonant DynamicsNonlinear AnalysisNonlinear Oscillator AnalysisNonlinear OscillatorsPhase NoisePhase Noise AnalysisResonanceResonance FrequenciesResonator Quality Factor
An oscillator with a high-order (>2) resonator has multiple stable modes of oscillations. The stable modes for one such oscillator, having a fourth-order resonator, are found using a nonlinear analysis. By using a proper nonlinear active topology and tank component values, the fourth-order oscillator can generate either of the two distinct frequencies f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> or f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . A method is introduced to dynamically switch between the stable modes of oscillations. It is shown that the phase noise of this fourth-order oscillator, when generating only one of its resonant frequencies, is comparable to the phase noise of a second-order oscillator using the same active topology and resonator quality factor. Furthermore, the fourth-order oscillator has better phase noise and/or higher tuning range in VCO implementations compared to the commonly used switched resonator oscillators. The claims have been verified experimentally through an integrated oscillator prototype with f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> = 2.4 GHz and f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> = 4.7 GHz fabricated in a standard 0.18 mum CMOS technology. The oscillator draws 1.89 mA current of 1.8 V supply. The 1 MHz offset phase noises of the fourth-order oscillator for f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> = 2.4 GHz and f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> = 4.7 GHz are -122.4 dBc/Hz and -123.4 dBc/Hz, respectively.
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A simple model of feedback oscillator noise spectrum
D.B. Leeson · Proceedings of the IEEE · 1966 · 2.4K citations