A Normalized Model of a Microelectromechanical Relay Calibrated by Laser-Doppler Vibrometry

Abstract

This work presents a behavioral model for a microelectromechanical (MEM) relay for use in circuit simulation. Models require calibration, and other published relay models require over a dozen parameters for calibration, many of which are difficult to extract or are only available after finite element analysis. This model improves on prior work by taking advantage of model normalization, which often results in models that require fewer parameters than un-normalized models. This model only needs three parameters extracted from experiment and one dimension known from device fabrication to represent its non-contact behavior, and two additional extracted parameters to represent its behavior when in contact. The extracted parameters–quality factor, resonant frequency, and the pull-in voltage–can be found using laser Doppler vibrometry. The device dimension is the actuation gap size, which comes from process data. To demonstrate this extraction process, a series of velocity step responses were excited in MEM relays, the measured velocity responses were used to calibrate the model, and then then simulations of the model (implemented in Verilog-A) were compared against the measured data. The error in the simulated oscillation frequency and peak velocity, two values selected as figures of merit, is less than 10% across many operating voltages.