An Accurate Solution of the Cylindrical Dielectric Resonator Problem

A cylindrical sample of low-loss high-epsilon/sub r/, dielectric placed between two parallel conducting plates perpendicular to the sample axis forms a microwave resonator. A new method of determining the field distribution and resonant frequency of this resonator is presented. By this method the solution is obtained in a form of successive approximations converging to the exact solution. The analysis is outlined in detail for the TE/sub 01delta/ mode and compared with previously published approximate calculations and experimental data.     

Precise Design of a Bandpass Filter Using High-Q Dielectric Ring Resonators

A precise design is presented for a bandpass filter constructed by placing TE/sub 01delta/ dielectric ring resonators coaxially in a TE/sub 01/ cutoff circular waveguide. On the basis of a rigorous analysis by the mode- matching technique, the interresonator coupling coefficients are determined accurately from the calculation of two resonant frequencies f/sub sh/ and f/sub op/ when the structurally symmetric plane is short- and open-circuited. For the TE/sub 01delta/ ring resonator,the resonant frequency f/sub 0/, the temperature coefficient tau/sub f/, the unloaded Q(Q/sub u/), and the other resonances are also calculated accurately in a similar way. From the calculations, the optimum dimensions are determined to obtain the maximum Q/sub u/, as F/sub r/ = f/sub r/ /f/sub 0/ is kept constant, where f/sub r/ is the next higher resonant frequency the ring resonator using low-loss ceramics (epsilon/sub r/ = 24.3, tan delta = 5 x 10/sup -5/) has Q/sub u/ = 16800 at 12 GHz and tau/sub f/ = 0.1+-0.5 ppm/° C, while the rod one has Q/sub u/ = 14700. A four-stage Chebyshev filter having ripple of 0.04 dB and equiripple bandwidth of 27.3 MHz at f/sub 0/ =11.958 GHz is fabricated using these resonator; the measured frequency responses agree well with theory. The insertion loss is 0.9 dB, which corresponds to Q/sub u/ = 9800.     

A Proposal of a New Dielectric Resonator Construction for MIC's

A compact and high-temperature-stable dielectric resonator having no shielding metal walls nor a conventional frequency tuning screw is described. This resonator consists of a high epsilon/sub r/ dielectric resonator element mounted on a low-loss dielectric mount, a dielectric disk with thin metal film fixed on the resonator element, and a microstrip line substrate on which to mount the constituents. The resonant frequency tuning is made by trimming the metal film on the disk. The TE/sub 01delta/ -mode resonant frequencies are analyzed through dielectric waveguide model application. Less than 1-percent analytical error is presented in comparison with the experimental data for a practical resonator. The frequency tuning limit by metal film trimming is about 7 percent. The unfoaded Q value of 2700 at 8.8 GHz and a 4.4-ppm/deg frequency temperature coefficient are obtained.     

Correction Due to a Finite Permittivity for a Ring Resonator in Free Space

To better determine the resonant fields of a dielectric resonator with high permittivity epsilon/sub r/, the asymptotic theory with1//spl radic/epsilon/sub 3/ as a small parameter is extended by adding higher order terms in 1//spl radic/epsilon /sub r/ in the fields, the resonant wavenumber, and radiation Q. Extensive data are shown for the Phi independent "nonconfined" mode of a ring resonator, which radiates as a magnetic dipole. Some results are added for the "magnetic quadruple" mode.     

Resonant Frequency of a TE//sub 01delta//spl deg/ Dielectric Resonator

The resonant frequency of a TE/sub 01delta//spl deg/ dielectric resonator was obtained by assuming a cylindrical surface containing the circumference of a dielectric resonator as a magnetic wall. In such a method, the error was less than 10 percent. In this short paper, the resonant frequency is obtained by a variational method, where the surface impedance is variated from a infinite value. The theoretical value of a resonant frequency has a good agreement with our experimental result with an error less than 1 percent.     

On the Theory and Application of the Dielectric Post Resonator (Short Papers)

This short paper deals with the modes of the dielectric post resonator when epsilon/sub r/ is large. The normalized frequency F/sub 0/ = (pi D/lambda/sub 0/) /spl radic/ as a function of D/L is discussed. The simple approximate expressions for the resonant frequencies of the lower order modes are given. The properties of the TE/sub 011/, mode are discussed in detail from the point of view of its application to the measurement of the complex permittivity of microwave dielectrics. Curves and expressions for fast and simple determination of the maximum measurement errors are given.     

Extended spectral domain approach for analysis of lossy cylindrical dielectric resonators

The spectral domain approach is extended for evaluating both the resonant frequency and Q factor of a lossy cylindrical dielectric resonator operating in TE/sub 0/ modes, taking into account the effects of conducting enclosure and supporting substrate. On the basis of the equivalence principle, the circular electric currents are introduced to simulate the fields inside and outside the cylindrical dielectric sample, which separates the original problems into two auxiliary structures with radially homogeneous multilayered dielectrics. Using the spectral immittance method in conjunction with the point-matching method, the characteristic equations are derived. The present technique has no need to determine the time-consuming, complex higher-order modes. Some typical examples are computed. The numerical results agree well with experimental data available in the literature.<>     

Dielectric resonator with discrete electromechanical frequency tuning

A novel approach for discrete frequency tuning of dielectric resonators based on electromechanical actuators such as the microelectromechanical system is presented. The concept is based on the intermodal coupling between the TE/sub 01/spl delta// mode of a cylindrical dielectric resonator and the radially arranged planar slotline resonators. The resonance frequency of the dielectric resonator is changed by switching a resistive load at the open end of each quarter-wave slotline resonator leading to a variation of the coupling between the slotline resonator mode and the TE/sub 01/spl delta// mode of the dielectric resonator. As a consequence, the resonance frequency of the TE/sub 01/spl delta// mode changes. Based on this novel tuning concept, discrete tuning by 5 MHz in 0.25-MHz frequency steps was demonstrated for a test resonator at 2 GHz. The unloaded quality factor is about 12000 and the measured switching time is about 1 ms.     

Computations of Frequencies and Intrinsic Q Factors of TE/sub 0nm/ Modes of Dielectric Resonators (Short Papers)

The Rayleigh-Ritz method is described, which is used to calculate the resonant frequencies and intrinsic Q factors due to dielectric losses of quasi TE/sub onm/ modes of dielectric resonators. Electromagnetic fields of an auxiliary post dielectric resonator are taken as an electrodynamics basis for approximate solutions of this problem. The method provides upper bounds for true resonant frequencies. Numerical results are compared with previously published complementary calculations. The influence of a dielectic substrate on resonant frequencies and intrinsic Q values is demonstrated.     

Spectral Domain Analysis of an Open Slot Ring Resonator

A full wave analysis of an open slot ring resonator on a dielectric substrate is presented. It is based upon Galerkin's method in the Hankel transform domain. The computed resonant frequencies for several slot widths agree well with the experimental values on alumina substrate with epsilon/sub r/= 9.6 in the 26-37-GHz frequency range.     

New method for complex permittivity measurement of dielectric materials

A novel technique for the measurement of dielectric properties of a homogeneous isotropic material is described. An accuracy better than 1% can be obtained on the permittivity and loss tangent values. The structure used is a cylindrical metallic cavity, carrying at its centre the circular cylindrical dielectric sample. The complex permittivity is deduced from the comparison between the experimental and the computed electromagnetic characteristics (frequencies, quality factors) of the resonant TE01? mode of the dielectric resonator.     

Microwave Measurement of High-Dielectric- Constant Materials

A particularly severe source of error in the microwave measurement of high dielectric constants has been the presence of small air gaps between dielectric surfaces and metal walls. In this paper, two precise measurement techniques are described that eliminate the effect of air gaps through the use of resonant modes, for which E/sub n/=0 at the dielectric-to-metal interface. In one method a cylindrical sample is resonated within a closely fitting circular waveguide, and in the other a cylindrical sample is placed at the center of a radial waveguide. Both methods utilize a circular-electric-mode whose electric field is parallel to the metal walls. The waveguides are dimensioned to be cut off in their air regions at the resonant frequency of the dielectric sample. Formulas yield /spl epsi//sub r/ as a function of the resonant frequency, and of diameter and length of the dielectric cylinder. Measured data on samples having /spl epsi//sub r/ /spl ap/ 85 show the two methods to agree within a few tenths of one percent. The accuracy of the methods is on the order of 0.5 percent maximum error and 0.2 percent probable error when /spl int//sub 0/ is measured within 0.1 percent and D and L within 0.0005 inch (for D/spl ap/ 0.3 inch and L /spl ap/0.1 inch).     

Dielectric ring-gap resonator for application in MMIC's

A dielectric resonator, the dielectric ring-gap resonator, is introduced and analyzed. The dielectric ring-gap resonator is obtained by sawing a narrow gap into a dielectric resonator. Resonant frequencies and unloaded Q-factors of quasi-TE_0pq mode in the ring-gap resonator have been calculated by an appropriate equivalent circuit starting from the resonant frequencies and the field distributions of the TE_0pq modes in the ring resonator. The calculated resonant frequencies of the fundamental quasi-TE₀₁₁ mode show an accuracy of <1% compared with the experimental results. Coupling techniques to couple the ring-gap resonator to a microstrip line on a thin substrate, using the electric fringing field near the gap, have been experimentally investigated. A rigorous method for determining resonant frequencies and field distributions of TE modes in a multicomposite multilayered cylindrical resonator is presented. This resonator consists of numbers of cylinders that are arbitrarily layered in the axial direction     

A Dielectric Resonator Method of Measuring Inductive Capacities in the Millimeter Range

A novel technique for the measurement of dielectric and magnetic properties of a homogeneous isotropic medium in the range of approximately 3 to 100 kmc is described. An accuracy of /l.chemc/ 1 per cent is possible in the determination of permittivity or permeability in those cases where the loss tangent is sulliciently small. The measuring structure is a resonator made up of a right circular cyndrical dielectric rod placed between two parallel conducting plates. For measurement of permittivity two or more resonant TE/sub onl/ mode frequencies are determined whereas for the measurement of permeability two or more resonant TM/sub onl/ mode frequencies are determined. The dielectric or magnetic properties are computed from the resonance frequencies, structure dimensions, and unloaded Q. Since the loss tangent is inversely proportional to the unloaded Q of the structure, the precision to which Q is measured determines the accuracy of the loss tangent.     

A new method developed in measuring the dielectric constants of metallic nanoparticles by a microwave double-cavity dielectric resonator

A microwave double dielectric resonator is implemented to measure the dielectric constants of nano-metallic powders. The metallic nanoparticles prepared by vacuum evaporation in inert gas are collected and mixed with alumina powder to fill the inner hole of a sapphire disc by which the resonant frequency and Q factor are measured at the TE/sub 011/ mode to derive the complex dielectric constant.     

Precise measurement of complex permittivity of low-loss ceramics

A novel TE/sub 01/spl delta// mode cylindrical dielectric resonator is proposed for the precise determination of the complex permittivity of low-loss ceramics. The radial mode matching technique is used to determine the expressions of the relative permittivity and the loss tangent of the sample. Some measurement results are compared with those obtained by other methods and good agreement is reported.     

The Magnetic-Dipole Resonances of Ring Resonators of Very High Permittivity

The lowest magnetic-dipole mode with symmetry of revolution is investigated in a coaxial ring resonator of height L, inner radius b, and outer radius a. Theoretical data are given about the Q of the mode, the eigen magnetic dipole at resonance, and the structure of the fields (electric and magnetic) inside and outside the resonator. The variables are the dielectric constant epsilon/sub r/ = N/sup 2/ and the dimensionless ratios b/a and L/2a. The data are valid in the limit of very high epsilon/sub r/. Experiments show them to be already useful at epsilon/sub r/ = 35.     

Improved Selectivity in Cylindrical TE/sub 011/ Filters by TE/sub 211/TE/sub 311/ Mode Control

A new method is presented for the design of low loss cylindrical TE/sub 011/-mode resonators whereby transmission nulls can be placed near the TE/sub 011/, resonance by controlling the TE/sub 211/, and TE/sub 311/, modes that are naturally excited in the same resonator. The frequencies at which the nulls occur are controlled by the angular offset of the sidewall coupling apertures and the relative amplitude of the TE/sub 011/ mode compared to the TE/sub 211/ and TE/sub 311/ modes. It is also shown that a lumped constant circuit model can be used to accurately represent the multimode response of the resonator.     

Numerical analysis of dielectric resonator antennas excited in quasi-TE modes

A numerical analysis of a half-split cylindrical dielectric resonator (CDR) antenna on a conducting ground plane excited by a coaxial probe is presented. A procedure based on the method of moments (MoM) for the coupling of a body of revolution (BOR) to a non-BOR geometry is implemented. The antenna is operating in the TE/sub 01/ and HEM/sub 12/ modes. This antenna configuration has potential uses where high power handling capabilities and wide operating bandwidth are required.<>     

The Q-Factor of Coaxial Resonators Partially Loaded with High Dielectric Constant Microwave Ceramics

The quality factor of partially loaded dielectric coaxial stepped impedance resonatop (PDSIR) has been analyzed, including analysis of the dielectric constant epsilon/sub r/ and the dielectric loss tan delta of the ceramics. The Q-factor of several resonators is also calculated and compared with the experimental results. This shows that the Q-factor degradation lessens even though the resonator length becomes small when the total length L/sub t/>1//spl radic/epsilon/sub r/ and becomes large when L/sub t/ < 1//spl radic/epsilon/sub r/.