Sherwin Afshar

EECS Department, University of California, Berkeley

Technical Report No. UCB/EECS-2022-227

September 12, 2022

http://www2.eecs.berkeley.edu/Pubs/TechRpts/2022/EECS-2022-227.pdf

Micro electromechanical system (MEMS) based oscillators have become crucial for RF systems requiring high performing references with minimal power consumption. The combination of higher quality factor and low parasitic capacitances allows them to out-perform typical quartz crystal oscillators, capable of working at higher frequencies while providing excellent frequency stability with little power consumption. The key enabler for scaling capacitive transducer MEMS up in frequency while consuming less power is reducing the electrode-to-structure air gap, which drastically lowers the series motional resistance. Shrinking the air gap, however, worsens the linearity of a resonator, as higher order distortion causes “duffing” and gain expansion to a degree which can no longer be ignored. As the size of the gap approaches the displacement of the mechanical structure in resonance, these nonlinearities become more extreme and heavily effect the performance and behavior of oscillators. This work seeks to explain how capacitive transducer-based nonlinearities can affect the amplitude limiting of oscillators. The pierce oscillator is used throughout this work, which has been designed and taped out in TSMC 180nm. We first analyze the amplitude limiting of the quartz crystal pierce oscillator, where resonator nonlinearity can be ignored. The analysis is adjusted to meet the assumptions for a MEMS based oscillator, and verified with measurements of a crystal oscillator with added parasitic. A compact nonlinear MEMS resonator model is derived from equations and used to explain how transducer nonlinearities can cause hysteresis in the amplitude limiting of the pierce oscillator. This hysteresis has been measured in a pierce oscillator referenced to a 53 MHz polysilicon wineglass disk resonator, with 40 nm gap. The results show that the nonlinearities introduced by decreasing the transducer gap can reduce the power consumption of MEMS based oscillators, to a further degree than just reducing series motional resistance.

Advisors: Clark Nguyen

---

BibTeX citation:

@mastersthesis{Afshar:EECS-2022-227,
    Author= {Afshar, Sherwin},
    Title= {Influence of Capacitive Transducer Nonlinearities on the Amplitude Limiting of MEMS Based Oscillators},
    School= {EECS Department, University of California, Berkeley},
    Year= {2022},
    Month= {Sep},
    Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2022/EECS-2022-227.html},
    Number= {UCB/EECS-2022-227},
    Abstract= {Micro electromechanical system (MEMS) based oscillators have become crucial for RF systems requiring high performing references with minimal power consumption. The combination of higher quality factor and low parasitic capacitances allows them to out-perform typical quartz crystal oscillators, capable of working at higher frequencies while providing excellent frequency stability with little power consumption. The key enabler for scaling capacitive transducer MEMS up in frequency while consuming less power is reducing the electrode-to-structure air gap, which drastically lowers the series motional resistance. Shrinking the air gap, however, worsens the linearity of a resonator, as higher order distortion causes “duffing” and gain expansion to a degree which can no longer be ignored. As the size of the gap approaches the displacement of the mechanical structure in resonance, these nonlinearities become more extreme and heavily effect the performance and behavior of oscillators. This work seeks to explain how capacitive transducer-based nonlinearities can affect the amplitude limiting of oscillators.  
	The pierce oscillator is used throughout this work, which has been designed and taped out in TSMC 180nm. We first analyze the amplitude limiting of the quartz crystal pierce oscillator, where resonator nonlinearity can be ignored. The analysis is adjusted to meet the assumptions for a MEMS based oscillator, and verified with measurements of a crystal oscillator with added parasitic. A compact nonlinear MEMS resonator model is derived from equations and used to explain how transducer nonlinearities can cause hysteresis in the amplitude limiting of the pierce oscillator. This hysteresis has been measured in a pierce oscillator referenced to a 53 MHz polysilicon wineglass disk resonator, with 40 nm gap. The results show that the nonlinearities introduced by decreasing the transducer gap can reduce the power consumption of MEMS based oscillators, to a further degree than just reducing series motional resistance.},
}

EndNote citation:

%0 Thesis
%A Afshar, Sherwin 
%T Influence of Capacitive Transducer Nonlinearities on the Amplitude Limiting of MEMS Based Oscillators
%I EECS Department, University of California, Berkeley
%D 2022
%8 September 12
%@ UCB/EECS-2022-227
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2022/EECS-2022-227.html
%F Afshar:EECS-2022-227