Felipe L. Peñaranda-Foix

Accurate determination of the complex permittivity of materials with transmission reflection measurements in partially filled rectangular waveguides

An enhanced transmission reflection technique for the precise determination of the complex permittivity of dielectric materials partially filling the cross section of a rectangular waveguide is described. Dielectric properties are determined by an iterative procedure from two-port S-parameter measurements and a numerically generated propagation constant obtained from the analysis of a partially filled waveguide. Convergence of the solution is ensured from perturbational approximations. Unlike previous approaches, an uncertainty investigation is performed, taking into account all the parameters involved in the dielectric characterization. Permittivity accuracy values are presented and, hence, an optimum measurement setup can be established. Measurements of reference materials have been carried out to validate the method.

A novel technique for deembedding the unloaded resonance frequency from measurements of microwave cavities

A novel technique to extract the influence of coupling networks on the resonant frequency of cavities in one-port measurements is presented. The determination of the unloaded resonant frequency is performed directly from measurements without either the need to obtain the electromagnetic fields in the resonator or to deembed the delay of transmission lines from the measuring equipment to the resonator. The importance of the Fosters form on the modeling of the frequency detuning of the resonators is also discussed and a criterion for the choice of the appropriate Fosters form is suggested. The procedure is validated with simulations and experimental measurements of manufactured cavities

Determination of the permittivity and permeability for waveguides partially loaded with isotropic samples

A method to measure the complex permittivity and permeability of a sample of isotropic material partially filling the rectangular waveguide cross section is presented. The method is based on a multimodal analysis of the waveguide and it does not imply any restriction on the general use of this technique for different widths, lengths or location of the samples. Electromagnetic properties of the material are determined by matching the S-parameters measured with a vector network analyser and the S-parameters calculated theoretically. Convergence to the correct solution is ensured using an optimization technique based on nonlinear minimization. A comparison between theoretical and experimental measurements is realized, which shows the feasibility of the implemented software. Besides, the accurate determination of the properties of the well-known materials validates the performance of the measurement method. Also, an error analysis is performed which confirms the reliability and robustness of our method.

Dynamic Measurement of Dielectric Properties of Materials at High Temperature During Microwave Heating in a Dual Mode Cylindrical Cavity

A microwave cavity and heating system for microwave processing and in situ dynamic measurements of the complex permittivity of dielectric materials at high temperatures ( ~ 1000 °C) has been developed. The method is based on a dual-mode cylindrical cavity where heating and testing are performed by two different swept frequency microwave sources. A cross-coupling filter isolates the signals coming from both sources. By adjusting the frequency bandwidth of the heating source and the level of coupling to the cavity, an automatic procedure allows for the establishment of a desirable level of heating rate to the dielectric sample to reach high temperatures in short cycles. Dielectric properties of materials as a function of temperature are calculated by an improved cavity perturbation method during heating. Accuracy of complex permittivity results has been evaluated and an error lower than 5% with respect to a rigorous analysis of the cavity has been achieved. The functionality of the microwave dielectric measurement system has been demonstrated by heating and measuring glass and ceramic samples up to 1000 °C. The correlation of the complex permittivity with the heating rate, temperature, absorbed power, and other processing parameters can help to better understand the interactions that take place during microwave heating of materials at high temperatures compared to conventional heating.

Design rules for the optimization of the sensitivity of open-ended coaxial microwave sensors for monitoring changes in dielectric materials

Open-ended coaxial probes are widely used for non-destructive measurement of dielectric properties of materials, and also as microwave sensors for industrial processes and quality control applications. The main design parameters of these sensors are the coaxial radii and working frequency. In this paper, the influence of these variables on the final sensitivity of the coaxial sensor when monitoring dielectric materials is analysed, and a novel expression for this parameter selection is proposed. Moreover, a method to select the optimum parameters of experimental configurations is provided. Measurements demonstrate that high discrimination can be achieved with this method when monitoring changes in the dielectric properties of materials.

Full-Wave Analysis of Dielectric-Loaded Cylindrical Waveguides and Cavities Using a New Four-Port Ring Network

In this paper, a full-wave method for the electromagnetic analysis of dielectric-loaded cylindrical and coaxial waveguides and cavities is developed. For this purpose, a new four-port ring network is proposed, and the mode-matching method is applied to calculate the generalized admittance matrix of this new structure. A number of analyses on dielectric-loaded waveguide structures and cavities have been conducted in order to validate and to assess the accuracy of the new approach. The results have been compared with theoretical values, numerical modeling from the literature, and data from commercial electromagnetic simulators. The method has been also applied to the accurate determination of dielectric properties, and we provide an example of these measurements as another way to validate this new method.

A nondestructive method of measuring the dielectric and magnetic properties of laminate materials in open cavities

A complete analysis of split-cylinder resonators is presented by means of circuital techniques for nondestructive measurement of dielectric and magnetic properties of laminate materials.

Circuital Analysis of Cylindrical Structures Applied to the Electromagnetic Resolution of Resonant Cavities

The objective of this chapter is first to describe the generalized circuital analysis as a method to solve complex electromagnetic problems and second to apply this specific technique to the determination of the resonant frequency and Q-factor of a cylindrical cavity loaded with a dielectric material when the material is introduced inside the cavity through a hole in the upper wall. The generalized circuital analysis as a method for solving electromagnetic problems consisting of the segmentation of the whole geometry of the microwave circuit into simpler structures which resolution can be solved in a easier way. Once the simpler structures have been solved separately, they can be joined or combined in order to give the complete solution of the complex structure. The resolution of the resonant frequency and Quality factor of a coaxially loaded circular cavity with a dielectric material is very interesting, for instance, for the determination of the dielectric properties (complex permittivity) of materials on this type of cavities. This type of analysis on these cavities can be found in the technical literature but in all cases, the effect of the hole to introduce the dielectric material inside the cavity is neglected and in some cases, such as it will be shown in the second part of the chapter, the effect of the hole can introduce considerable errors in the determination of the resonant frequency and quality factor whose can interfere the precision of the permittivity calculations. In next sections, the effect of the hole for the introduction of dielectric materials inside circular cavities is evaluated by solving the structure by the generalized circuital analysis. Several measurements of circular cavities with dielectric materials will confirm the effect of the hole in the precision of permittivity calculations. 7

Circuital analysis of a coaxial re-entrant cavity for performing dielectric measurement

We apply circuital analysis to the re-entrant cavity method for measuring the relative permittivity and loss tangent of dielectric material. With this new model, we are able to make use of the higher-order resonant modes of the re-entrant cavity, and are therefore able to broaden the frequency range over which we can measure the dielectric properties of the sample. We compare this new model with others in the literature and validate its capabilities through a comparison with other dielectric measurement techniques.

Noninvasive Monitoring of Polymer Curing Reactions by Dielectrometry

A microwave sensor system for the noninvasive monitoring of the curing process of a thermoset material placed inside a metallic mold is described. The microwave sensor is designed as an open-ended coaxial resonator with a curved surface adapted to the mold inner shape. The analysis of the microwave resonator comprises a recently developed method for deembedding the effect of coupling network in overcoupled resonators, so the range of permitted measurements encompass both low and high dielectric losses of polymeric materials. Results show that noninvasive, continuous monitoring of the microwave dielectric properties of the thermoset material can be performed in real time, allowing one to check initial conditions and to verify the evolution of the cure process.