Vector network analyzer measurements of frequency fluctuations in aluminum nitride contour-mode resonators

As part of the current drive to engineer minitureized monolithic high performance microelectromechanical enabled oscillators there is a need for further study of frequency fluctuations in microelectromechanical resonators. To facilitate this we consider the measurement of frequency fluctuations using a vector network analyzer and demonstrate the utility of this approach using an aluminum nitride contour-mode resonator. We examine a generalized quasi-static model as well as a more detailed dynamic model and compare one- and two-port measurement setups.