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The finite-element method (FEM) is applied for modal analysis of ferrite-loaded spherical resonators. To improve the efficiency of the numerical calculations, the body-of-revolution (BOR) technique is utilized. Due to the frequency-dependent ferrite permeability, FEM leads to a nonlinear eigenvalue problem that is challenging to solve. To this end, Beyn’s method is proposed. The effectiveness of the proposed approach is confirmed by comparing with the results obtained analytically and with the measured data. [ABSTRACT FROM AUTHOR]

A simple non-Maxwellian model is used for designing Bragg reflectors of cylindrical geometry and arbitrary thicknesses for the horizontal or cylindrical dielectric reflectors. Results suggest the achievement of an unloaded Q-factor of 234,000 at 9.7 GHz for the fundamental mode.

The complex permittivity and resistivity of float-zone high-resistivity silicon were measured at microwave frequencies for temperatures from 10 up to 400 K employing dielectric-resonator and composite dielectric-resonator techniques. At temperatures below 25 K, where all free carriers are frozen out, loss-tangent values of the order of 2 x [10.sup.-4] were measured, suggesting the existence of hopping conductivity or surface charge carrier conductivity in this temperature range. Use of a composite dielectric-resonator technique enabled the measurement of materials having higher dielectric losses (or lower resistivities) with respect to the dielectric-resonator technique. The real part of permittivity of silicon proved to be frequency independent. Dielectric losses of high-resistivity silicon at microwave frequencies are mainly associated with conductivity and their behavior versus temperature can be satisfactory described by dc conductivity models, except at very low temperatures. Index Terms--Conductivity measurement, dielectric losses, dielectric resonators, permittivity measurement, silicon, semiconductor materials measurements.

The application of one of the first few composite cylindrical T[E.sub.0n1] modes for measurements of the complex permittivity of ferroelectrics based on rigorous electromagnetic analysis of the structure is reported. Variable temperature measurements are performed on a Pb[Mg.sub.1/3][Nb.sub.2/3][O.sub.3] (PMN) ceramic sample, and the measured complex permittivity has shown good agreement with the results of measurements obtained on the same sample at lower frequencies.

Magnetically tunable two-pole dielectric-resonator filters containing axially and circumferentially magnetized ferrite elements have been designed and investigated. Employing axially magnetized ferrites, a 20-MHz tuning range was obtained. The Q factor of resonators was 2500 and the tuning power was 1.8 W. Filters containing circumferentially magnetized discs demonstrated a 12-MHz tuning range with the Q factor over 8000 (tuning power 3.5 W) and 28 MHz with the Q factor 3500 (tuning power 3.5 W). Index Terms--Dielectric resonators, ferrite loaded resonators, filters, tunable filters.

The anisotropic loss tanget is determined in monocrystalline sapphire for components parallel and perpendicular to the crystal axis, using the whispering gallery (WG) mode method. Sapphire dielectric material from three different manufacturers is compared over the 270-345 K temperature range and the 5-16 GHz frequency range.

A Fabry-Perot resonator operating at 39 GHz, with two pairs of quarter-wavelength single-crystal quartz Bragg reflectors is realized. Good agreement between theoretical and experimental resonant frequency and Q-factors is obtained while thermal compensation of the resonant frequency of the Fabry-Perot is proposed employing rods and cylinders made of metals with different thermal expansion coefficients.

It has been proven, based on a rigorous electromagnetic analysis, that spherical T[E.sub.10p]-mode Bragg-reflection resonators exhibit many times higher Q factors than corresponding cylindrical T[E.sub.01[delta]]-mode dielectric resonators, dielectric whispering-gallery-mode resonators, or empty spherical T[E.sup.10p]-mode cavities. Rigorous equations have been derived that allow optimally designed Q-factor and 'quarter-wavelength' reflector-multilayered-spherical Bragg-reflection resonators. Experiments have been performed on three-layer spherical resonators made of single-crystal YAG and single-crystal quartz. The unloaded Q factor for the T[E.sup.012] mode in these resonators was 1.04 x [l0.sup.5] at 26.26 GHz for YAG and 6.4 x [10.sup.4] at 27.63 GHz for quartz. Index Terms--Bragg scattering, dielectric materials, dielectric resonators, millimeter-wave technology.

The concept of the spherical Bragg reflector (SBR) resonator is introduced. The resonator is made from multiple layers of spherical dielectric, loaded within a spherical cavity, and is designed to concentrate the energy within the central region of the resonator and away from the cavity walls to minimize conductor losses.

New measurements of dielectric properties of Lanthanum gallium silicate (Langasite or LGS) conducted with the whispering-gallery mode technique at microwave frequencies is calculated along with the first measurements of the two independent components of the imaginary part of the permittivity tensor. It appears LGS is a relatively high-loss dielectric material compared with sapphire or quartz.

The frequency stability of microwave oscillators have improved considerably depending on very low loss, single crystals with frequency temperature self compensation of the resonance mode. From the isotropic materials like the calcium and lithium fluoride only one form of resonance is selected which shows whispering gallery (WG) mode electromagnetic field structure.

Lithium tantalate (LiTa[O.sub.3]) exhibits excellent electrooptical, piezoelectric, and pyroelectric properties and a very low thermal expansion. In this paper, we report measurements of loss tangent and the real part of the relative permittivity [[epsilon].sub.r[perpendicular to]] measured in c-axis LiTa[O.sub.3] crystals in the temperature range from 14 K to 295 K at a frequency of 11.4 and 10 GHz. Microwave properties of LiTa[O.sub.3] were determined by measurements of the resonance frequency and the unloaded [Q.sub.o] factor of a T[E.sub.011] mode cylindrical cavity containing the sample under test and accounting for uncalibrated cables and adaptors inside the cryocooler. The permittivity of LiTa[O.sub.3] was found to increase from 38.9 to 41.1 and the loss tangent to change from 1.1 x [10.sup.-4] to 6.5 x [10.sup.-4] over the full temperature range. Due to its low loss and relatively high permittivity, LiTa[O.sub.3] is suitable for microwave applications. Index Terms--Dielectric materials, lithium tantalate (LiTa[O.sub.3]), microwave properties, tantalates.

Investigating the results of microwave characterization of YBCO films using a SrLaAlO4 (SLAO) and a sapphire (AO) rods of 3 mm height and 5mm diameters at frequencies of 18 GHz and 24.6 GHz. is discussed. It is concluded that by swapping the sapphire rod with the SLAO, is able to measure the R(sub s) of YBCO thin films at two different frequencies without compromising the accuracy of measurements.

In this paper, we present complex permittivity data at microwave frequencies (approximately 10 GHz) for many common plastics over a temperature range of 122 to 375 K. The measurements were made with a T[E.sub.01[Delta]] dielectric resonator placed inside an environmental chamber. Data are presented for the following materials: acrylonitrile butadiene styrene, polytetrafluoroethylene, cross-linked polystyrene, tetrafluorethylene-perfluorpropylene, polypropylene, polysulfone, polymethylmethacrylate, polyvinyl chloride, polycarbonate, high-density polyethylene, polyoxy-methylene (acetal homopolymer), and polyamide. Index Terms--Complex permittivity, dielectric resonator, microwave freqeuncy, plastics, variable temperatures.

Complex permittivity measurements of irradiated high-resistivity float-zone silicon have been performed in this letter from microwave to millimeter-wave frequencies employing three different resonance techniques. It has been proven that the irradiated silicon exhibits resistivity of the intrinsic silicon at temperatures larger than 295 K and the loss tangent due to phonon absorption reaches about 10−5 at room temperature. The total loss tangent of the room-temperature irradiated silicon is smaller than $6\times10$ −5 at frequencies larger than 5 GHz. The real part of the complex permittivity of silicon linearly increases with temperature for $T $ > 200 K. [ABSTRACT FROM AUTHOR]

A new approach for designing a high-Q microwave resonator with low spurious mode density is described and discussed.

Dielectric loss tangent and permittivity of polytetrafuoroethylene (Teflon), high-density (HD) polyethylene, and cross-linked polystyrene (Rexolite) were measured at temperature range from 28 to 84 K and frequency of approximately 18 GHz. The material properties were determined by measurements of the resonant frequency and the Q factor of a T[E.sub.011] mode cylindrical superconducting cavity containing a sample under test. It has been demonstrated that these materials exhibit very low losses at cryogenic temperatures (2 x [10.sup.-6] for Teflon, 5 x [10.sup.-5] for HD polyethylene and 1.1 x [10.sup.-4] for Rexolite). Due to low losses, these materials can be useful in construction of various high-Q factor microwave devices for operation at cryogenic temperatures. Index Terms--Dielectric materials, microwave properties, polyethylene, Rexolite, Teflon.

To accurately determine the surface resistance of high-temperature superconducting films, multifrequency measurements of [S.sub.21], [S.sub.11], and [S.sub.22] and sophisticated data processing are required. As a result, surface resistance measurements and calculations for varying temperatures are very time consuming. In this paper, we introduce a simplified method for calculations of the unloaded Q ([Q.sub.o]) factor, which require measurements of [S.sub.11] and [S.sub.22] at the lowest temperature only. For all other temperatures, only [S.sub.21] measurements are needed. The method has been shown to give sufficiently accurate [Q.sub.o] values and, hence, the surface resistance of superconducting samples, as compared to results obtained from [S.sub.21], [S.sub.11], and [S.sub.22] measurements using the transmission-mode Q factor technique. The presented method has been tested under different coupling coefficients and frequencies. Index Terms--Dielectric resonator, high-temperature superconductors, surface resistance.

A new technique for compensating the frequency-temperature dependence of high-Q monolithic sapphire dielectric resonators near liquid nitrogen temperature is shown. This is accomplished by doping monocrystalline sapphire with Ti3+ ions. Calculations showed that a Ti3+ doped sapphire resonator may have its frequency-temperature dependence nulled anywhere between 4 and 80 K depending on the concentration of the Ti3+ ions.

The electromagnetic (EM) properties of shielded gyromagnetic spheres are characterized with the aid of an electrodynamic model formulated for the transverse electric (TE) modes of an isotropic sphere, in a similar way as dielectric resonators are commonly analyzed. Broadband characteristics of geometric and energy filling factors are presented. A new measure of the magnetic loss tangent is introduced which is positive despite the intrinsic permeability of the gyromagnetic medium being negative, where existing definitions yield a non-physical negative value. The sample size dependence of those quantities is also assessed. The conclusions from the analysis are applied to investigate and de-embed ferromagnetic linewidth errors which can occur in broadband measurements of magnetic garnet spheres. Magnetic anisotropy fields and the gyromagnetic $g$ -factor are also estimated from the measurement data. Experiments were performed in a two-port subwavelength cavity, covering a frequency range of up to 28 GHz. Additionally, two-port rectangular resonant cavity linewidth measurements at a few modes have been conducted. Good agreement between the two methods is found if the systematic error is accounted for. [ABSTRACT FROM AUTHOR]

A new method dedicated to the measurement of the moisture content and salinity of soil is proposed in this paper. The method takes the advantage of the most accurate permittivity sensor available at microwave frequencies based on a ${\mathrm {TE}}_{01\delta }$ mode dielectric resonator providing the effective complex permittivity of the measured mixture. The measurement has been undertaken mostly at 1 GHz due to the fact that conductive losses of liquids are substantially varying with salinity at low microwaves, thus, increasing measurement sensitivity. At first, intrinsic properties of the major components of the soil, such as sand, salt and saline water, are extracted from the effective parameters measured at microwave frequencies and compared with the Maxwell-Garnett mixing rule to extract their intrinsic properties. In case of the soil, the unknown moisture content and salinity are extracted from raw measurement results using an empirical permittivity model of a conductive mixture which, unlike to analytical dielectric mixing rules, accounts for a percolation threshold. [ABSTRACT FROM AUTHOR]

Low-loss dielectric laminates that are routinely used in the manufacturing of printed circuit boards (PCBs) are known to be anisotropic. The in-plane and the out-of-plane components of the dielectric permittivity have been so far typically determined using one of several available methods. In this article, we performed measurements of both components of complex permittivity of selected isotropic and anisotropic laminar materials employing a combination of a few split-post dielectric resonators (SPDRs) and one cylindrical cavity supporting several TM $_{0n0}$ modes in the microwave band. Based on obtained data a novel, more precise approach to measuring the out-of-plane component of complex permittivity of laminar samples has been proposed. Additionally, a detailed analysis of several sources of measurement uncertainty (e.g., due to finite tolerances of manufacturing of the sample) has been performed and some recommendations formulated. [ABSTRACT FROM AUTHOR]

Simple perovskite crystals undergo structural phase transitions on cooling to low temperatures, which significantly change the material properties of the crystal. In this work, we rigorously characterize the temperature evolution of permittivity of a perovskite crystal as it undergoes phase transitions. In particular, we have undertaken precision measurements of a single crystal of Strontium Titanate from 294.6 to 5.6 K, by measuring the frequency of multiple microwave transverse electric (TE) and magnetic resonant modes simultaneously. The multi-mode microwave measurement technique of resonant frequency used in this work allows high precision determination of any induced anisotropy of the permittivity as the crystal undergoes structural phase transitions. Compared with previous results, we unequivocally show that the permittivity has an isotropic value of 316.3±2.2 at room temperature, consistent with its well-known cubic structure, and determine the onset of dielectric anisotropy as the crystal is cooled to lower temperatures. We show that the crystal exhibits uniaxial anisotropy in the permittivity below 105 K when the structure becomes tetragonal, and exhibits biaxial anisotropy in the permittivity below 51 K when the structure becomes orthorhombic. [ABSTRACT FROM AUTHOR]

Two methods for minimizing the effect of parasitic losses on surface resistance measurements of superconductors using dielectric resonators are presented. The first technique optimizes the sapphire resonator aspect ratio to minimize the parasitic losses for given superconductor sample dimensions and measurement frequency. The second employs a reference resonator with a perfect conductor plane to cancel out the effect of parasitic losses by measurements of the resonant frequencies and Q-factors of two resonators.

Measurements on low-loss materials using closed and open cavity resonators, and dielectric resonator methods are presented. Results indicate that consistent measurement results can be obtained with a number of well-characterized fixtures. Uncertainties associated with each method are addressed. Measurements also were performed on materials used in previous intercomparisons.

Research was conducted to study a sapphire-rutile composite microwave dielectric resonator obtained from a cylindrical sapphire monocrystal that supported two thin disks of monocrystal rutile at the end. A sweep oscillator was used to determine the mode frequencies of the resonator while the N1 E-mode family frequency was represented as a function of temperature. Results indicated that the resonator can be utilized in the construction of temperature stable microwave oscillators that operate above liquid helium temperatures.

An analysis on the mono-crystalline rutile resonator was conducted to measure its dielectric properties through the use of whispering gallery mode method. The resonant frequencies were subjected to 300 to 10 K measurements. Results revealed that the loss tangent and dielectric constant of a single crystal rutile which exhibited anisotropy were obtained through the whispering gallery mode technique.

Whispering-gallery modes in axially magnetized ferrite disk samples have been studied using rigorous Rayleigh-Ritz and finite-element analyses. The influence of radial magnetization on the resonant frequencies of both WGE and WGH modes was investigated, both theoretically and experimentally. Permeability tensor components of biased ferrites were determined from measurements of the resonant frequencies of the [WGH.sub.n00] and the [WGE.sub.n00] mode families.

A wide variety of microwave ferrite phase-shifting materials have been measured in the demagnetized state. The relative magnetic permeability and loss factor were determined near and above natural gyromagnetic resonance using [H.sub.011] cylindrical dielectric ring resonators. These low-loss dielectric sleeves were dimensioned for accurate magnetic property measurements of single ferrite rod samples at logarithmically sampled resonant frequencies from 2 GHz to 25 GHz. Permeability and magnetic loss factor are computed from the measured resonant frequencies and Q factors of these resonators, with and without the ferrite sample, using exact eigenvalue equations. Generally, the real part of the complex magnetic permeability increases with decreasing saturation magnetization, while the magnetic loss factor increases nonlinearly with increasing saturation. Schloemann's theoretical model for the real part of initial permeability of a cylindrically symmetric domain configuration in the completely demagnetized state shows excellent agreement with measured data when 2[[Pi].sub.[Gamma]][M.sub.s]/[Omega] < 0.75. The data allow design optimization of circulators and dual-mode and polarization-insensitive phasers, which are widely used in antenna array systems.

A dielectric resonator technique has been used for measurements of the permittivity and dielectric loss tangent of single-crystal dielectric substrates in the temperature range 20-300 K at microwave frequencies. Application of superconducting films made it possible to determine dielectric loss tangents of about 5 X [10.sup.-7] at 20 K. Two permittivity tensor components for uniaxially anisotropic samples were measured. Generally, single-crystal samples made of the same material by different manufacturers or by different processes have significantly different losses, although they have essentially the same permittivities. The permittivity of one crystalline ferroelectric substrate, SrTi[O.sub.3], strongly depends on temperature. This temperature dependence can affect the performance of ferroelectric thin-film microwave devices, such as electronically tunable phase shifters, mixers, delay lines and filters.

The Rayleigh-Ritz method and the finite element method nongenerating spurious solutions are employed for analysis of whispering gallery modes (WGM's) in cylindrical single-crystal anisotropic dielectric resonators. These methods allow accurate computation of the resonant frequencies, the Q-factors (depending on the dielectric and on the conductor losses), and the electromagnetic field distributions for all WGM's in the presence of additional elements like metal shields, MIC substrate, or supports. Different families of modes are studied both theoretically and experimentally. The mode coupling phenomenon is investigated. A WGM single-crystal quartz resonator is presented having an unloaded Q-factor greater than 30 000 at about 100 GHz, including radiation and dielectric losses.

Surface resistances of laser-ablated YBCO films are measured accurately by using the sapphire dielectric resonator technique with copper cylindrical shield, with the replacement of the two endplates by the high temperature superlayers (HTS). The resonant system has a frequency of 18.1 giga hertz and parasitic loss factor of 12,000. The parasitic losses of the system is reduced considerably by the use of larger HTS samples. Calibration is avoided during the evaluation of the surface resistance value by the use of exact formulas.