A review of microwave techniques for measuring both complex permittivity and complex permeability of materials is given. It includes both resonant and reflection transmission methods for which limitations are discussed.

The vector network analyzer provides a versatile tool for use in the microwave characterization of material permittivity and/or permeability. An understanding of network analyzer error sources can be leveraged into better measurement results. Vector error correction not only reduces the systematic errors but can also be used to remove the effects of dielectric dams in broadband transmission/reflection measurements.

The results of the full-wave model theory for the open-ended coaxial probe with lift-off are presented and are applied to measurements of thin materials. The model allows the study of the open-ended coaxial probe as a nondestructive testing tool. The equations presented are valid for both dielectric and magnetic materials. The analysis yields insight into the effects of air gaps on probe measurements. Numerical results indicate that the probe is very sensitive to lift-off at low frequencies. This sensitivity decreases somewhat as frequency increases. In order for the field to penetrate the air gap, larger size coaxial line or higher frequencies need to be used. An application of the theory is performed by numerically solving the inverse problem using measured reflection coefficient.

Open-ended coaxial probes have been used in broadband dielectric properties measurements for several years. To aid in the ongoing numerical simulation and microwave sintering research at the University of Utah, we have found it necessary to make dielectric properties measurements up to temperatures as high as 1400 °C. The available cavity perturbation techniques were unsuitable in this application due to their relatively narrow band, and the available metal probes are also unsuitable due to the differential thermal expansions of the inner and outer conductors, which makes it difficult to carry out accurate and on-line calibration procedures for these probes.

To help us achieve both broadband and high-temperature dielectric properties measurements, we have developed a new metallized ceramic coaxial probe. The detailed design of this probe is described and the metallization procedure is discussed.

Also to optimize the design of the probe and in particular to increase the penetration of fields in samples under test and hence improve the probe sensitivity to variation in properties of a larger class of materials, and to determine the required minimum thickness of various samples to obtain accurate results, we modeled and simulated the probe performance using the Finite-Difference Time-Domain (FDTD) method. Results from the FDTD simulation are presented and some guidelines that may be used to optimize the design of the probe are discussed.

The incident, reflected and transmitted powers were measured and the reflection and transmission coefficients calculated for a liquid fuel. Two sizes of double ridge waveguide were used to cover the frequency ranges 2.5 to 7.5 and 7.5 to 18 GHz and corrections were made for waveguide losses. Strong interference effects were observed and the real part of the dielectric constant, ε', was obtained primarily from the separation of interference maxima and minima while the loss tangent, ε“/ε', was obtained by curve fitting to the normalized power loss. The final values of ε′ and ε“/ε′ were determined at each frequency by minimizing the difference between the experimental and theoretical values of the reflection coefficient and the normalized power loss. With increasing frequency ε' decreases and then becomes constant while ε“/ε' decreases throughout the frequency range within experimental accuracy.

Research into microwave firing at Staffordshire University has been carried out since 1988 and dielectric property measurements have been used to help in developing process technology. The dielectric property measurement technique (cavity perturbation [1]) is that designed by Atomic Energy of Canada Ltd (A.E.C.L) [2]. The technique was chosen because of it's ability to analyse powder samples as well as solids. In order for dielectric property data to be of use in developing microwave processing, measurements have to be made on the starting materials of the process (i.e powders). When measurements are made on powders it is important to quote the bulk density at which the measurement was made since dielectric properties vary with density as well as frequency and temperature.

We have developed a fast in-situ method for measuring the quality factor, Q, and resonant frequency, fr, for an isolated microwave resonant mode. The mode resonant frequency was continuously monitored using a phase modulation frequency tracking technique. The quality factor was determined by periodically switching off the microwave power and fitting the decay curve to an exponential. The cavity perturbation method was used with small spherical samples (ka « 1). Combining the Q and fr data with a non-contact measurement of the sample temperature permits the calculation of the temperature dependence of the real (ε′) and imaginary (ε″) dielectric constants. Because of the speed of this technique (≈1 μSce), it can be used during processing to continuously measure the dielectric constants of the material without perturbing the sample temperature. Measurements were performed using isolated TM010 and TEI11 cylindrical cavity modes. Care was taken to minimize the perturbing effects of the sample support. The accuracy of the frequency tracker was verified at room temperature from measurements on several alumina spherical samples. The decay technique was also verified from measurements on several small spherical nylon samples.

It is now possible, in a number of laboratories worldwide, to make microwave dielectric property measurements at temperatures up to about 1500°C. These measurements have shown that the loss tangent, tanδ, of a wide range of engineering ceramics increases dramatically at elevated temperatures. The interaction between the ceramic material and the impurities present during processing can have a dramatic effect on both the ease with which the material is able to extract energy from the microwave field and on the properties of the final ceramic. While the effect of impurities on the ceramic properties is relatively well understood the effect of impurities on the microwave loss mechanisms at elevated temperatures is not. This paper will review some of the recent work on the high temperature microwave dielectric property measurements performed at Nottingham.

Open reflection microwave resonator sensors have been developed for in situ measurement of the bulk moisture absorbed by nonconducting fiber-reinforced composites. These contacting sensors operate at about 4 GHz, and have sensitivities and resolutions of about 0.1% moisture. In application, two independent parameters are measured simultaneously. From these, the two components of the effective complex dielectric constant ε* (ε′= - јε″) as seen by the sensor are determined. Both ε′ and ε″ are highly linear with absorbed moisture.

Both linearly polarized sensors (for measuring anisotropie moisture absorption) and circularly polarized sensors (for measuring the average anisotropy) have been demonstrated. Moisture uptake in the polymer matrix, moisture wicking along Kevlar fibers, and the effects of moisture damage due to blistering, microcracking, etc., all have been tracked in accelerated moisture exposure tests. Where applicable, the experimentally measured profiles have been validated using a one-dimensional Fickian diffusion model.

The sensors are suitable for many applications, e.g., to map the extent of moisture contamination in composite panels, as a portable probe for aid in composite panel repairs, as a cure monitor of moisture in powder or fluid polymers, or as a permanently installed sensor for monitoring the accumulated moisture in radomes. In the latter case, exceptionally improved sensitivities and resolutions are possible.

Until now, the measurement techniques used for the dielectric characterization of materials require severe limitations in terms of sample shape, size and homogeneity. This paper considers the dielectric permittivity measurement as a non-linear inverse scattering problem. Such an approach allows to identify the quantities to be measured and suggests possible experimental arrangements. The problem is shown to be significantly simplified if the shape of the material is known and if some a priori knowledge of the averaged value of the permittivity in the material under test is available. Two test cases have been selected to illustrate the state of the art in solving such inverse problems. The first one consists of a two-dimensional configuration which is applicable to cylindrical objects, and the second one to a vector three-dimensional configuration applicable, for instance, to cubic samples. The main limitations of such an inverse scattering approach are discussed and expected improvements in the near future are analysed.

As a consequence of the BERGMAN - MILTON theory, which expresses the effective permittivity of a two phase mixture with an integral of a density function, it has been possible to evaluate the local electrical field strength inside a heterogeneous mixture. The developed formula can be used advantageously for modeling the local temperature inside a ceramic material during its microwave sintering.

Permittivity measurements from 0.2 to 20 GHz were taken on fresh peaches of three varieties at three stages of maturity during the growing season to determine whether dielectric properties might be correlated with maturity. Other physical properties of the peach tissue, such as density, moisture content, firmness, and total soluble solids content, were also determined. Two indices, based on dielectric constant and loss factor values at 0.2 and 10 GHz were found to correlate with stage of maturity, but they were dependent on the variety, and further study is necessary to determine their practical usefulness.

The surface recombination of GaAs which has a high carrier concentration layer (HCCL) formed by Si+ implantation has been investigated using the reflectance microwave probe (RMP) method. The RMP method enables us to evaluate the surface property of GaAs contactlessly and easily. The experimental results of the samples which were implanted with doses ranging from 1.0×1011 to 3.9×1012cm-2 at an energy of lOOke V indicate that the effective surface recombination velocity decreases with dosage because of HCCL formed after the annealing. On the other hand, the results of the samples which were implanted with a dose of 3.9 × 1012cm-2 at energies ranging from 30 to 180keV indicate that the effective surface recombination velocity increases with energy for energies larger than 50keV. We understood the reason by comparing with the numerical calculation results of an effective surface recombination velocity at a high-low junction interface.

The basis is presented for using a microwave resonant cavity as an effective “contactless balance”, providing information about the mass of dielectric objects inserted into the cavity. An uncertainty analysis presented in the paper confirms that the mass of small dielectric objects can be determined by this technique with an accuracy better than 4%.

Electromagnetic drying processes have been used in industrial applications for many years. New materials with different properties and structures have been recently developed which required the development of new drying systems capable of effectively drying the new materials. In this paper, we use Finite-Difference Time-Domain (FDTD) to model and simulate realistic electromagnetic drying processes including induction heating and RF drying. The power deposition patterns obtained from the FDTD code is also used in a finite-difference heat transfer code to evaluate the temperature distribution pattern and optimize rates of drying. Sample parameters used to analyze the RF drying and the induction heating processes include the sample conductivity, dielectric constant along with size, orientation and the geometric arrangement. Specifically, we analyzed the operating frequency, coil pitch, sample to coil diameter ratio, and the possible placement of multiple samples in an induction heating process. Effects investigated in a parallel plate RF drying system include: electrode spacing, electrode length and width, and the spacing between multiple samples. Results of electromagnetic power distributions and temperature patterns are presented.

We present two distinct approaches to the numerical determination of electromagnetic field intensities which must be known before the sintering of ceramics can be modelled in a multi-mode microwave cavity. In the first, a Finite Element Method, we employ edge elements to discretise Maxwell's Equations and apply the conjugate gradient algorithm to solve the resulting system of linear algebraic equations at each time step. The second, which is based on the Method of Lines, is a variant of the Finite Difference Time Domain technique and is used to transform Maxwell's Equations into a set of time-dependent ordinary differential equations. These methods are compared with the help of three examples: a small tray of mashed potatoes placed inside a cavity, a standard waveguide partially filled with a ceramic, and a cavity inhomogeneously loaded with the same material. The good agreements which we have found give us confidence in the soundness of either approach for use in numerical simulation work.

Small cylinders of high-purity alumina were encased in a “casket” of low-density zir-conia insulation and heated to sintering temperature in a large multi-mode microwave oven. Optical fiber sensors were used to monitor the temperature at several locations in the system. It was found that the alumina samples heat faster than the zirconia insulation at temperatures above 1000°C, and that the temperature distribution in the sample is essentially uniform during the heating process.

A two-dimensional mathematical model of the heat transfer process was developed which reproduces the essential features of the observed phenomena. Literature data for all temperature-dependent properties were incorporated into the model. The model suggests that the alumina samples absorb a significant fraction of the microwave energy.

An analytic approach is used for evaluation of the microwave power absorption profiles in a lossy dielectric cylinder coaxially aligned in a cylindrical cavity. This approach, based on a cylindrical shell model, also determines the normal mode frequencies and fields. Absorption profiles inside the sample will be presented for resonant modes that are intrinsically angular independent. In addition, results will be presented for special modes that are not intrinsically angular independent, but produce angular independent absorption for time average values. This new development broadens the class of modes that can be used in heating materials when isotropy about an axis is needed. We demonstrate how this model can extend the application of cavity perturbation theory for determining dielectric constants to cylinders of larger diameter. Implications of these results for microwave processing of materials are also discussed.

A hybrid microwave heating arrangement used to heat alumina fiber preforms has been modeled to determine what conditions are needed to create significant differences in temperature across the specimen while still maintaining control of the temperature. The model assumes a uniform external microwave field and dielectric properties for the specimen as a function of temperature. The results of the model show that significant differences in temperature can be attained while still having control of the temperature at the center. Experiments show that the temperature at the center can be held at 1000°C and still allow a difference in temperature of 50°C between the center and the surface of the specimen to be present.

Computer modeling and numerical simulation provide a valuable tool for providing guidelines towards a successful routine experimentation with microwave sintering of ceramics. It is also expected that continued efforts in numerical simulation will lead to establishing procedures for the scale up and commercial utilization of this new technology.

In this paper, we utilize the FDTD technique to model sintering ceramics in multimode microwave cavities. The role of using process stimulus such as SiC rods on improving the uniformity of the microwave sintering process are also simulated. To help experimentally validate the obtained results, the FDTD electromagnetic power deposition results were combined with a 3D heat transfer program to calculate temperature distribution in samples and surrounding insulation. Results from the FDTD codes and comparisons with experimental measurements of sintering experiments are presented.

To improve the efficiency of the simulation and achieve more accurate results, we developed a variable mesh FDTD code to help focus the numerical results and hence improve the resolution in critical sites inside the sintering oven. Detailed solution procedures are described. We solved some test geometries with the uniform grid and the developed variable mesh codes and compared the obtained results to validate and check the accuracy of the solution procedure. Results from these comparisons are presented.