The design of circuits incorporating microresonators which utilize electrostatic drive and sense is accompanied by a need for a convenient method to experimentally extract the circuit elements modelling the microresonators. Previously, techniques which electrically detect microresonator motional current using only off-chip electronics have been seriously hampered by parasitic feedthrough currents arising from probe-to-probe capacitance, which mask the tiny motional current.
In this report, equivalent circuits for electrostatic-comb driven and parallel-plate driven microresonators are derived. Resonance frequency, quality factor, and dC/dxare found to be the key measurable parameters in determining equivalent circuit elements. Using the derived circuit models, parasitic-induced distortion of microresonator electrical performance is quantified. Measurements and simulation of low frequency fr= 20kHz) microresonators conclude that ac drive voltages on the order of millivolts define the threshold C * L whereby motional current can be measured with acceptable interference from probe-to-probe parasitics without the need for special parasitic suppression techniques.
Techniques allowing off-chip electrical detection of microresonator motional current without interference from parasitics are then introduced. These detection strategies operate by separating motional current from parasitics in either the time or frequency domains; effectively, they eliminate all dc capacitance and sense only ac (motional) capacitance. The time-domain technique (GSED) detects motional current during the zero-input period of a gated-sinusoid excitation signal, and thus, depends upon the high-Q of the microresonator for sustainance of oscillation during detection, The frequency domain technique (EAM) is implemented by biasing the microresonator with a high-frequency carrier signal in addition to the required dc-bias. Qualitatively, the carrier signal and its time-derivative are multiplied by capacitive elements of microstructure motion, resulting in motional current, frequency-shifted to sidebands around the carrier frequency and separated from dc parasites still at the drive frequency.
Application of these techniques (particularly EAM) to microresonator circuit model extraction, ground plane design, and system performance verification will be demonstrated. A novel microelectromechanical filter implemented using parallel microresonators will be introduced in the process.
April 30, 1991
Nguyen, T. C. (1991). Electromechanical Characterization of Microresonators for Circuit Applications. United States: University of California, Berkeley.