Intermodulation in capacitively coupled microelectromechanical filters

A compact model for third-order intermodulation in capacitively coupled microelectromechanical filters is derived. A simple expression for the input third-order intercept point is given. This is valuable in designing micromechanical filters, for example, for communication applications. The validity of the analytic model is verified with numerical harmonic-balance simulations and experimental measurements.     

Imaging of in- and out-of-plane vibrations in micromechanical resonator

Vibrations in a micromechanical 13.1 MHz bulk acoustic mode silicon resonator have been imaged with a scanning Michelson laser interferometer. A novel detection scheme utilizing the Michelson interferometer is developed, which enables imaging the in-plane vibrations in addition to the out-of-plane component. The novel imaging technique is demonstrated by measuring the vibrations of the extensional and Lame modes in a square plate resonator     

Square-extensional mode single-crystal silicon micromechanical resonator for low-phase-noise oscillator applications

A micromechanical 13.1-MHz bulk acoustic mode silicon resonator having a high quality factor (Q=130 000) and high maximum drive level (P= 0.12 mW at the hysteresis limit) is demonstrated. The prototype resonator is fabricated of single-crystal silicon by reactive ion etching of a silicon-on-insulator wafer. A demonstration oscillator based on the new resonator shows single-sideband phase noise of -138 dBc/Hz at 1 kHz offset from the carrier.     

Variable Antenna Load for Transmitter Efficiency Improvement

A wireless radio transmitter with an integrated variable-impedance antenna is demonstrated. The transmit signal is connected via a switch to the antenna at one of several feed points that correspond to different load impedances that are optimal for the power amplifier at different transmit power levels. It is shown that this can be used to improve the efficiency of the transmission at low and medium transmit powers. The variable antenna load is demonstrated with a planar inverted-F antenna, but the method can be applied to any antenna with suitable impedances.     

Systematic design approach for capacitively coupled microelectromechanical filters

A design procedure for microelectromechanical (MEMS) band-pass filters is formulated that takes into account specifications set for carrier-to-interference ratio (C/I) and insertion loss. Since suppressing intermodulation distortion to maximize C/I in MEMS filter design typically leads to increased loss and vice versa, it is necessary to aim at a feasible compromise in filter performance that meets all of the requirements. In order to meet specifications that are typical for a handheld communication terminal, an integrated receiver architecture, where filter input and output impedances other than 50 omega can be used, is found to be more feasible than resistively terminating the front-end filter at source and load to 50 omega.     

Electrostatic transducers for micromechanical resonators: free space and solid dielectric

Three electrostatic transduction methods are analyzed for a micromechanical, longitudinal mode, beam resonator. The conventional parallel plate transducer placed at the location of maximum displacement is compared to two solid, dielectric transducers internal to the resonator. Although the solid dielectric offers higher permittivity than the free-space-filled transducers, the unfavorable locations of the internal transducers reduce or even remove the performance advantage of the higher permittivity.     

Thermokinetic actuation for batch assembly of microscale hinged structures

This paper reports on surface micromachined hinged structure assembly using thermokinetic forces in the molecular flow regime. Ultrasonic vibration energy is used to reduce the static friction making the thermokinetic force comparatively significant. The thermokinetic force, resulting from the more energetic gas molecules emanating from the heated substrate, increases with pressure and substrate temperature in the molecular flow regime. The transition from viscous to molecular regime occurs as the molecular mean-free-path approximately equals the flap length, making the pressure threshold for thermokinetic flap actuation size dependent. In addition to the experimental results, one-dimensional (1-D) and two-dimensional (2-D) force models are presented. Examples of assembled structures are shown and assembly jig suitable for automated MEMS batch assembly is demonstrated.     

Phase noise in capacitively coupled micromechanical oscillators

Phase noise in capacitively coupled microresonator-based oscillators is investigated. A detailed analysis of noise mixing mechanisms in the resonator is presented, and the capacitive transduction is shown to be the dominant mechanism for low-frequency 1/f-noise mixing into the carrier sidebands. Thus, the capacitively coupled micromechanical resonators are expected to be more prone to the 1/f-noise aliasing than piezoelectrically coupled resonators. The analytical work is complemented with simulations, and a highly efficient and accurate simulation method for a quantitative noise analysis in closed-loop oscillator applications is presented. Measured phase noise for a microresonator-based oscillator is found to agree with the developed analytical and simulated noise models.     

Third-order intermodulation in microelectromechanical filters coupled with capacitive transducers

Third-order intermodulation in capacitively coupled microelectromechanical filters is analyzed. Parallel-plate transducers are assumed and, in addition to the capacitive nonlinearities, also the usually much weaker second- and third-order mechanical resonator nonlinearities are taken into account. Closed-form expressions for the output signal-to-interference ratio (SIR) and input intercept point are derived. The analytical results are verified in experiments and in numerical harmonic-balance simulations. It is shown that intermodulation as a function of frequency is asymmetric with respect to the passband. The results are valuable in designing micromechanical filters, for example, for communication applications.