The transmissibility reveals two very useful characteristics of a micro-electro-mechanical systems (MEMS) device, the resonant frequency and the mechanical quality factor. Real time knowledge on these two important factors can enhance application performance or avoid potential problems from environmental disturbances due to fabrication tolerances and the resulting operational differences in otherwise identical devices. Expensive laboratory equipment is typically used to measure the transmissibility. However, these test systems are not readily adaptable to field use. Therefore, it is important to be able to measure the transmissibility using a real time technique with a simplified test setup. This study proposes a technique that can compute the transmissibility in real time using a low cost microcontroller.
This technique utilizes two laser vibrometers to detect the input and output motions of the proof mass in a MEMS device, which are fed to high speed 500 KHz analog to digital converters (ADC) in the microcontroller. A filtering step is performed to decrease noise. After the sampling and pre-filtering, a Fast Fourier Transform (FFT) is performed to convert the time-domain signals to frequency domain signals. The amplitude of the output signal at each frequency is divided by the amplitude of the corresponding input signal at each frequency to obtain the transmissibility. To overcome the difficulties resulting from measurement and quantization noise, a recursive calculating algorithm and a de-quantization filter are introduced. The recursive calculating process guarantees that the system updates the results continually, which results in a transmissibility plot covering the entire bandwidth. The de-quantization filter considers the validity of the data and performs the transmissibility division step accordingly.
A cantilevered structure was chosen as the device-under-test to verify and evaluate this technique. The cantilevered device was attached to an electromechanical shaker system for vibratory stimulation. Two laser vibrometers were used to detect the input and output motion and this data was fed into a microcontroller. The microcontroller was STM32F407, which is 32-bit and 168 MHz controller. The tests demonstrated that this technique can measure the transmissibility and therefore the resonant frequency and mechanical quality factor accurately compared to a professional signal analyzer.
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