Fully parameterized model of a voltage-driven capacitive coupled micromachined ohmic contact switch for RF applications

Abstract

A comprehensive and completely parameterized model is proposed to determine the related electrical and mechanical dynamic system response of a voltage-driven capacitive coupled micromechanical switch. As an advantage over existing parameterized models, the model presented in this paper returns within few seconds all relevant system quantities necessary to design the desired switching cycle. Moreover, a sophisticated and detailed guideline is given on how to engineer a MEMS switch. An analytical approach is used throughout the modelling, providing representative coefficients in a set of two coupled time-dependent differential equations. This paper uses an equivalent mass moving along the axis of acceleration and a momentum absorption coefficient. The model describes all the energies transferred: the energy dissipated in the series resistor that models the signal attenuation of the bias line, the energy dissipated in the squeezed film, the stored energy in the series capacitor that represents a fixed separation in the bias line and stops the dc power in the event of a short circuit between the RF and dc path, the energy stored in the spring mechanism, and the energy absorbed by mechanical interaction at the switch contacts. Further, the model determines the electrical power fed back to the bias line. The calculated switching dynamics are confirmed by the electrical characterization of the developed RF switch. The fabricated RF switch performs well, in good agreement with the modelled data, showing a transition time of 7 µs followed by a sequence of bounces. Moreover, the scattering parameters exhibit an isolation in the off-state of >8 dB and an insertion loss in the on-state of <0.6 dB up to frequencies of 50 GHz. The presented model is intended to be integrated into standard circuit simulation software, allowing circuit engineers to design the switch bias line, to minimize induced currents and cross actuation, as well as to find the mechanical structure dimensions necessary for the desired switching time and actuation voltage waveform. Moreover, process related design rules can be automatically verified.