Measurement of resonant frequency and quality factor of microwave resonators: Comparison of methods

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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A MEMS PPA Based Active Vibration Isolator - STUDENT AWARD 3RD PLACE $500

Additional Conferences (Device Packaging HiTEC HiTEN & CICMT) ◽

10.4071/2016dpc-tp33 ◽

2016 ◽

Vol 2016 (DPC) ◽

pp. 000853-000880

Author(s):

Chong Li ◽

C. Lavinia Elana ◽

Robert N. Dean ◽

George T. Flowers

Keyword(s):

Resonant Frequency ◽

Quality Factor ◽

Proof Mass ◽

Control Voltage ◽

Stable Range ◽

Vibration Isolator ◽

Operating Range ◽

Stable Operating ◽

Mass Damper ◽

Active Vibration

Several types of micro-devices are adversely affected by high frequency mechanical vibrations present in the operating environment. Examples include MEMS vibratory gyroscopes and resonators, and micro-optics. Various types of MEMS vibration isolators have been developed for use in the packaging of these vibration sensitive devices. Passive isolators consist of a spring-mass-damper MEMS device and usually have a very high mechanical quality factor, which makes them susceptible to ringing at the isolator's resonant frequency. Active isolators have been realized by using state sensing of the proof mass motion and feeding one or more of these states back through an actuator to adjust the frequency response of the isolator. For example, the technique known as skyhook damping uses velocity feedback to adjust, and typically increase, the damping of the isolator. Although these technique are doable, they require state sensing or state estimation, with feedback electronics to drive the actuator. A simpler MEMS active vibration isolator architecture employs only a parallel plate actuator (PPA) with the MEMS spring-mass-damper structure. The PPA driven with a DC voltage, in its stable operating range, displaces the proof mass, which results in a change in the effective system spring constant due to the electrostatic spring softening effect. This results in a change in the resonant frequency and the quality factor of the isolator. However, due to the nonlinearities inherent in this type of device, the stable operating range is reduced as the PPA voltage is increased. Furthermore, even when the isolator is stable in steady-state, a sufficiently large transient response can also drive it into the unstable regime, resulting in the electrodes snapping into contact. In this study, the PPA based active vibrator isolator is developed and its performance is evaluated. The characteristics of the transient instability are investigated and its stable range of operation is specified, for booth external disturbances and rapid application of the control voltage. This MEMS PPA based active vibration isolator can improve performance compared to passive isolators, while being much simpler than state feedback active isolators.

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A Geometrical Study on the Roof Tile-Shaped Modes in AlN-Based Piezoelectric Microcantilevers as Viscosity–Density Sensors

Sensors ◽

10.3390/s19030658 ◽

2019 ◽

Vol 19 (3) ◽

pp. 658 ◽

Cited By ~ 4

Author(s):

Víctor Ruiz-Díez ◽

Javier Toledo ◽

Jorge Hernando-García ◽

Abdallah Ababneh ◽

Helmut Seidel ◽

...

Keyword(s):

Resonant Frequency ◽

Quality Factor ◽

Q Factor ◽

Liquid Media ◽

Roof Tile ◽

Aln Film ◽

Monitoring Applications ◽

Media Monitoring ◽

Comprehensive Study

Cantilever resonators based on the roof tile-shaped modes have recently demonstrated their suitability for liquid media monitoring applications. The early studies have shown that certain combinations of dimensions and order of the mode can maximize the Q-factor, what might suggest a competition between two mechanisms of losses with different geometrical dependence. To provide more insight, a comprehensive study of the Q-factor and the resonant frequency of these modes in microcantilever resonators with lengths and widths between 250 and 3000 µm and thicknesses between 10 and 60 µm is presented. These modes can be efficiently excited by a thin piezoelectric AlN film and a properly designed top electrode layout. The electrical and optical characterization of the resonators are performed in liquid media and then their performance is evaluated in terms of quality factor and resonant frequency. A quality factor as high as 140 was measured in isopropanol for a 1000 × 900 × 10 µm3 cantilever oscillating in the 11th order roof tile-shaped mode at 4 MHz; density and viscosity resolutions of 10−6 g/mL and 10−4 mPa·s, respectively are estimated for a geometrically optimized cantilever resonating below 1 MHz.

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Analysis of a circular microstrip antenna on isotropic or uniaxially anisotropic substrate using neurospectral approach

COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering ◽

10.1108/compel-10-2012-0225 ◽

2013 ◽

Vol 33 (1/2) ◽

pp. 567-580 ◽

Cited By ~ 5

Author(s):

Sami Bedra ◽

Siham Benkouda ◽

Tarek Fortaki

Keyword(s):

Resonant Frequency ◽

Quality Factor ◽

Microstrip Antenna ◽

Numerical Results ◽

Spectral Domain ◽

Quality Factors ◽

Resonant Frequencies ◽

Content Type ◽

Anisotropic Substrate ◽

Circular Microstrip Antenna

Purpose – The paper aims to propose an artificial neural network (ANN) in conjunction with spectral domain formulation for fast and accurate determination of the resonant frequency and quality factor of circular microstrip antenna printed on isotropic or anisotropic substrate. This neurospectral approach reduces the problem complexity. Design/methodology/approach – The moment method implemented in the spectral domain provides good accuracy but its computational cost is high due to the evaluation of the slowly decaying integrals and the iterative nature of the solution process. The paper introduces the electromagnetic knowledge combined with ANN in the analysis of circular microstrip antenna on isotropic or uniaxially anisotropic substrate to reduce the complexity of the spectral approach and to minimize the CPU time necessary to obtain the numerical results. Findings – The resonant frequency results obtained from the neural model are in very good agreement with the experimental and theoretical results available in the literature. Finally, numerical results for the substrate anisotropy effect on the resonant frequency, quality factor and radiation pattern are also presented. Originality/value – The paper develops fast and accurate model based on ANN technique to calculate the resonant frequencies and quality factors of circular microstrip antennas. ANN is used to model the relationship between the parameters of the microstrip antenna and the resonant frequencies and quality factors obtained from the spectral domain approach. This relatively simple model allows designers to predict accurately the resonant frequencies and quality factors for a given design without having to develop or run the spectral method codes themselves. The main advantages of the method are: less computing time than the spectral model, results with accuracy equivalent to that of full-wave models and cost effectiveness, since the client can use a simple PC for implementation. Another advantage of the proposed ANN model is that it takes into account the uniaxial anisotropy in the substrate without increasing the network size. This is done by combining ANN with electromagnetic knowledge.

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Microwave dielectric properties of Ca[(Li1/3Nb2/3)1−xMx]O3−δ (M = Sn, Ti) ceramics

Journal of Materials Research ◽

10.1557/jmr.1999.0483 ◽

1999 ◽

Vol 14 (9) ◽

pp. 3567-3570 ◽

Cited By ~ 56

Author(s):

Ji-Won Choi ◽

Chong-Yun Kang ◽

Seok-Jin Yoon ◽

Hyun-Jai Kim ◽

Hyung-Jin Jung ◽

...

Keyword(s):

Dielectric Constant ◽

Dielectric Properties ◽

Resonant Frequency ◽

Temperature Coefficient ◽

Quality Factor ◽

Single Phase ◽

Microwave Dielectric Properties ◽

Multiphase Materials ◽

Microwave Dielectric ◽

Orthorhombic Perovskite

The microwave dielectric properties of Ca[(Li1/3Nb2/3)1−xMx]O3−δ (M = Sn, Ti, 0 ≤ x ≤ 0.5) ceramics were investigated. In general, the ceramics prepared were multiphase materials. However, single-phase specimens having orthorhombic perovskite structure similar to CaTiO3 could be obtained in the vicinity of Sn = 0.2 to 0.3, and Ti = 0.2. As Sn concentration increased, the dielectric constant (εr) decreased and the quality factor (Q) significantly increased within the limited Sn concentration. As Ti concentration increased, the dielectric constant (εr) increased, the quality factor (Q) decreased, and the temperature coefficient of resonant frequency (τf) changed from a negative to positive value. The temperature coefficient of resonant frequency of 0 ppm/°C was realized at Ti = 0.2. The Q · fo value and εr for this composition were found to be 26100 GHz and 38.6, respectively.

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