Title :
Modelling non-linearities in a MEMS square wave oscillator
Author :
Agrawal, Deepak K. ; Woodhouse, Jim ; Seshia, Ashwin A.
Author_Institution :
Dept. of Eng., Univ. of Cambridge, Cambridge, UK
Abstract :
The modelling of the non-linear behaviour of MEMS oscillators is of interest to understand the effects of non-linearities on start-up, limit cycle behaviour and performance metrics such as output frequency and phase noise. This paper proposes an approach to integrate the non-linear modelling of the resonator, transducer and sustaining amplifier in a single numerical modelling environment so that their combined effects may be investigated simultaneously. The paper validates the proposed electrical model of the resonator through open-loop frequency response measurements on an electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. A square wave oscillator is constructed by embedding the same resonator as the primary frequency determining element. Measurements of output power and output frequency of the square wave oscillator as a function of resonator bias and driving voltage are consistent with model predictions ensuring that the model captures the essential non-linear behaviour of the resonator and the sustaining amplifier in a single mathematical equation.
Keywords :
frequency measurement; micromechanical resonators; numerical analysis; oscillators; silicon; MEMS square wave oscillator; electrical model; electrically addressed flexural silicon MEMS resonator; limit cycle behaviour; mathematical equation; motional amplitudes; nonlinearity modelling; open-loop frequency response measurements; phase noise; single numerical modelling environment; sustaining amplifier; transducer; Equations; Frequency measurement; Mathematical model; Micromechanical devices; Oscillators; Power generation; Resonant frequency;
Conference_Titel :
Frequency Control Symposium (FCS), 2012 IEEE International
Conference_Location :
Baltimore, MD
Print_ISBN :
978-1-4577-1821-2
DOI :
10.1109/FCS.2012.6243674