A 5 GHz Resonant Cavity for Complex Permittivity Measurements: Design, Test Performances and Application

2006 ◽  
Vol 514-516 ◽  
pp. 1561-1565 ◽  
Author(s):  
Luís Cadillon Costa ◽  
Susana Devesa ◽  
François Henry
Keyword(s):  
Perturbation Theory ◽  
Quality Factor ◽  
Small Perturbation ◽  
Complex Permittivity ◽  
Resonant Cavity ◽  
Cavity Resonator ◽  
Finite Conductivity ◽  
Theoretical Treatment ◽  
Resonance Frequencies ◽  
5 Ghz

The theoretical treatment of a cavity resonator consists of solving the Maxwell equations in that cavity, respecting the boundary conditions. The resonance frequencies appear as conditions in the solutions of the differential equation involved and are not significantly affected by the fact that the cavity walls have a finite conductivity. Solutions for rectangular cavities and for the lowest resonant mode, where the probability of mistaking one mode from another is slight, are readily obtained. The measurement of the complex permittivity, ε* = ε´-iε´´, can be made using the small perturbation theory. In this method, the resonance peak frequency and the quality factor of the cavity, with and without a sample, can be used to obtain the complex dielectric permittivity of the material. We measure the shift in the resonant frequency of the cavity, f, caused by the insertion of the sample, which can be related to the real part of the complex permitivitty, ε´, while the change in the inverse of the quality factor of the cavity, (1/Q), gives the imaginary part, ε´´. In this work we report the construction details, the performance tests of the cavity to confirm the possibility of the use of the small perturbation theory, and the application of the technique to measure the complex permittivity of a reinforced plastic.

Sectorial substrate-integrated half-mode near-field sensors for biological liquid characterization

2014 ◽  
Vol 6 (3-4) ◽  
pp. 305-312 ◽  
Author(s):  
Nora Meyne ◽  
Arne F. Jacob
Keyword(s):  
Factor Analysis ◽  
Perturbation Theory ◽  
Aqueous Solutions ◽  
Quality Factor ◽  
Near Field ◽  
Calibration Method ◽  
Biological Liquid ◽  
Suitable Reference ◽  
5 Ghz

Two compact resonant near-field sensors are introduced for the characterization of aqueous solutions at 5 GHz. They are based on folded substrate-integrate circular half-mode resonators with a planar sensing tip. Owing to the planar design, the sensor is simple and cheap to manufacture, and a sample can be easily coupled to the resonator from the top. The operating principle of the sensor is explained and verified by both simulation and measurement. The radiation of the sensors is quantified by means of a quality factor analysis. Finally, a previously introduced calibration method based on the perturbation theory is applied to the sensors and its accuracy is improved by choosing more suitable reference materials.

scholarly journals Continuous Characterization of Permittivity over a Wide Bandwidth Using a Cavity Resonator

2020 ◽  
Vol 20 (1) ◽  
pp. 39-44
Author(s):  
Rehab S. Hassan ◽  
Sung Ik Park ◽  
Ashwini Kumar Arya ◽  
Sanghoek Kim
Keyword(s):  
Complex Permittivity ◽  
Cavity Resonator ◽  
Dielectric Materials ◽  
Wide Frequency Range ◽  
Wide Bandwidth ◽  
Frequency Independent ◽  
5 Ghz ◽  
Continuous Determination

We examine a rectangular cavity resonator method to accurately characterize the complex permittivity of dielectric materials over a wide frequency range of 1–5 GHz by exploiting the fundamental mode and higher-order TE<sub>(1,0,<i>l</i>)</sub> modes. For this purpose, a rectangular waveguide is coupled with a cavity resonator through a large inductive aperture. The permittivity characterization at both even and odd TE<sub>(1,0,<i>l</i>)</sub> modes enables continuous determination of the permittivity over operating frequencies. The characterization of the permittivity for even TE<sub>(1,0,<i>l</i>)</sub> modes suffers from potential errors due to the displacement of materials. This paper also proposes a method to compensate for these errors and improve the accuracy in the even modes. The experimental results of the fabricated cavity are presented using different materials (frequency-independent and frequency-dependent). The measured complex permittivity results show a good agreement with the reported results over a wide bandwidth available in the literature.

Nonlinear Sloshing in Fixed and Vertically Excited Containers

2002 ◽  
Author(s):  
Jannette B. Frandsen ◽  
Alistair G. L. Borthwick
Keyword(s):  
Perturbation Theory ◽  
Free Surface ◽  
Small Perturbation ◽  
Numerical Solutions ◽  
Vertical Direction ◽  
Nonlinear Effects ◽  
Breaking Waves ◽  
Surface Flow ◽  
Nonlinear Behaviour ◽  
Computational Domain

Nonlinear effects of standing wave motions in fixed and vertically excited tanks are numerically investigated. The present fully nonlinear model analyses two-dimensional waves in stable and unstable regions of the free-surface flow. Numerical solutions of the governing nonlinear potential flow equations are obtained using a finite-difference time-stepping scheme on adaptively mapped grids. A σ-transformation in the vertical direction that stretches directly between the free-surface and bed boundary is applied to map the moving free surface physical domain onto a fixed computational domain. A horizontal linear mapping is also applied, so that the resulting computational domain is rectangular, and consists of unit square cells. The small-amplitude free-surface predictions in the fixed and vertically excited tanks compare well with 2nd order small perturbation theory. For stable steep waves in the vertically excited tank, the free-surface exhibits nonlinear behaviour. Parametric resonance is evident in the instability zones, as the amplitudes grow exponentially, even for small forcing amplitudes. For steep initial amplitudes the predictions differ considerably from the small perturbation theory solution, demonstrating the importance of nonlinear effects. The present numerical model provides a simple way of simulating steep non-breaking waves. It is computationally quick and accurate, and there is no need for free surface smoothing because of the σ-transformation.

MEMS-based LC tank with extended tuning range for low phase-noise VCO

2015 ◽  
Vol 9 (2) ◽  
pp. 249-258 ◽  
Author(s):  
Alessandro Cazzorla ◽  
Paola Farinelli ◽  
Laura Urbani ◽  
Fabrizio Cacciamani ◽  
Luca Pelliccia ◽  
...  
Keyword(s):  
Phase Noise ◽  
Quality Factor ◽  
Ohmic Contacts ◽  
Tuning Range ◽  
Design System ◽  
High Resistivity ◽  
Continuous Tuning ◽  
5 Ghz ◽  
Lc Tank ◽  
Low Phase Noise

This paper presents the modeling, manufacturing, and testing of a micro-electromechanical system (MEMS)-based LC tank resonator suitable for low phase-noise voltage-controlled oscillators (VCOs). The device is based on a variable MEMS varactor in series with an inductive coplanar waveguide line. Two additional parallel stubs controlled by two ohmic MEMS switches have been introduced in order to increase the resonator tunability. The device was fabricated using the FBK-irst MEMS process on high resistivity (HR) silicon substrate. Samples were manufactured with and without a 0-level quartz cap. The radio frequency characterization of the devices without 0-level cap has shown a continuous tuning range of 11.7% and a quality factor in the range of 33–38. The repeatability was also tested on four samples and the continuous tuning is 11.7 ± 2%. Experimental results on the device with a 0-level cap, show a frequency downshift of about 200 MHz and a degradation of the quality factor of about 20%. This is, most likely, due to the polymeric sealing ring as well as to a contamination of the ohmic contacts introduced by the capping procedure. A preliminary design of a MEMS-based VCO was performed using Advanced Design System and a hardwired prototype was fabricated on Surface Mount Technology on RO4350 laminate. The prototype was tested resulting in a resonance frequency of 5 GHz with a phase noise of −105 and −126 dBc at 100 KHz and 1 MHz, respectively, and a measured output power of −1 dBm.

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