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/.     

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.     

Variation of the Electrical Characteristics of an Inhomogeneous Microstrip Line with the Dielectric Constant of the Substrate and with the Geometrical Dimensions (Short Papers)

Studying systematically the variations of electrical characteristics of microstrip lines with the width w of the line, the thickness h, and the dielectric constant epsilon/sub r/ of the substrate, we have obtained a perfect linear variation with epsilon/sub r/. Then using a least squares method, we have been able to give an analytical expression of capacitances usable for 1 /spl les/ epsilon/sub r/ /spl les/ 100 and 0.04 /spl les/ w/h /spl les/ 10. The importance of this result is that we can give impedances and phase velocities without any computation.     

Design Charts for Inhomogeneous Coupled Microstrip Lines

Owing to the bear variation of the odd- and even-mode capacitances in terms of the dielectric constant epsilon/sub r/, of the substrate, it has been possible to obtain formulas giving all the electrical characteristics of the Iines for given values of the ratios, width w and separation s of the lines upon height h of the dielectric substrate. Conversely, by means of charts, it is possible to obtain the geometrical dimensions of the Iines, whatever the value of epsilon/sub r/, for the imposed matching impedance and coupling coefficient. The use of these charts is very easy, and the results are the closest to experimental data published to date.     

Cylindrical Dielectric Resonators and Their Applications in TEM Line Microwave Circuits

A cylindrical sample of low-loss high epsilon/sub r/ placed between two parallel conducting plates perpendicular to the sample axis forms a microwave resonator. A simple approximate method for predicting the resonant frequencies of the TE modes of this structure is developed. The method becomes exact for the fitting case of this structure which is known as a dielectric post resonator. In all cases, the accuracy of the method is shown to be better than 3.5 percent. The TE/sub 01delta/ mode chart presented allows the determination of the resonant frequency and the tuning range of any cylindrical dielectric resonator for which epsilon/sub r/ >or= 10. The properties of the dielectric resonator as a TEM line element are demonstrated experimentally.     

Characteristics of Transmission Lines with a Single Wire for a Multiwire Circuit Board

This paper presents the characteristic impedance Z/sub 0/ and the phase velocity v/sub p/ of transmission lines with a single wire for a multiwire circuit board (MWB) under the quasi-TEM wave approximation. The characteristics are discussed for each of three investigated strictures a: (I)H = h + r, (II)H = h, and (III)H = h - r, where r, h, and H are the radius of the wire, the thickness of the dielectric (adhesive layer), and the distance from the ground plane to the center of the wire, respectively. A charge simulation method is used for the calculation of the parameters. Z/sub 0/ and v/sub p/ are presented in graphical form for adhesive relative dielectric constants epsilon* of 1.0, 2.65, and 5.0 as a function of r/h. An approximate formula of Z/sub 0/ for the structure of case (II) with epsilon* = 5.0 is also presented.     

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.     

Some Effects of Field Perturbation Upon Cavity-Resonance and Dispersion Measurements on MIC Dielectrics

An analysis is presented of field perturbations in MIC resonators in order to examine the errors which occur in permittivity measurements made by cavity-resonance methods: Q factor, coupling effects, fringing fields, crystal misalignment (for anisotropic materials), changes in ambient temperature are all considered. Analysis of a cavity with mixed boundary conditions shows that the resonant-mode frequencies depend to the first order on that part of Q/sub 0/ associated with imperfect electric (metal) walls, but to the second order on that part associated with imperfect magnetic (open-circuit) walls. A new expression is given for the Q of an open-ended microstrip resonator when surface waves are excited in the dielectric, and it is shown that the unloaded Q (Q/sub 0/) can be dominated by this phenomenon. It is further shown that these Q-related effects, together with reactive perturbations arising from fringing, coupling structures, are the principal source of error in measurements for epsilon or epsilon/sub eff/. Such reactive effects may be treated semiquantitatively by applying Slater's perturbation theorem to the affected region. These procedures lead to the following revised values for the crystal permittivity of sapphire (monocrystalline Al/sub 2/0/sub 3/) in the microwave region: epsilon/sub ||/ (parallel to the c axis) = 11.6; epsilon/sub /spl perp// (base-plane) = 9.4.     

Characteristic Impedance of a Wide Slotline on Low-Permittivity Substrates (Short Paper)

Computed results on the characteristic impedance of wide slots etched on an electrically thin substrate of low dielectric constant epsilon/sub r/ are presented. These results combined with those in [1] provide design data for these slotlines. Curves are presented for epsilon/sub r/= 2.22, 3.0, 3.8, and 9.8. Comparison is shown for the characteristic impedance between the present calculations and those available in the literature for high-epsilon/sub r/ substrates. Empirical formulas, based on least-square curve fitting, are presented for the normalized slot wavelength lambda'/lambda/sub 0/ and the characteristic impedance Z/sub 0/ over the range 0.0015<=W/lambda/sub 0/<=1.0, 0.006<=d/lambda/sub 0/<=0.06, 2.22<=epsilon/sub r/<=9.8.     

Microwave Measurement of Dielectric Properties of Low-Loss Materials by the Dielectric Rod Resonator Method

Improvements both in accuracy and speed are described for the technique of measuring the microwave dielectric properties of low-loss materials by using a dielectric rod resonator short-circuited at both ends by two parallel conducting plates. A technique for measuring the effective surface resistance R/sub s/ of the conducting plates is proposed to allow the accurate measurement of the loss tangent tan delta. By means of the first-order approximation, the expressions are analytically derived for estimating the errors of the measured values of relative permittivity epsilon/sub r/, tan delta, and R/sub r/, for measuring the temperature coefficient of epsilon/sub r/, and for determining the required size of the conducting plates. Computer-aided measurements are realized by using these expressions. It is shown that the temperature dependence of R/sub s/, should be considered in the tan delta measurement. The copper plates used in this experiment have the relative conductivity of 91.0+-2.7 percent at 20°C, estimated from the measured R/sub s/ value. For a 99.9-percent alumina ceramic rod sample, the results measured at 7.69 GHz and 25°C show that epsilon/sub r/,= 9.687+-0.003 and tan delta = (1.6+-0.2)x 10/sup -5/. The temperature coefficients measured between 25 and 100°C are 112x10/sup -6//°C for epsilon/sub r/, and 23x10/sup -4//°C for tan delta.     

Maximum Q-Factor of Microstrip Resonators

The quality factors of microstrip half-wavelength resonators have been calculated as a function of substrate thickness for frequencies in the range 8-96 GHz, for different epsilon/sub r/. Conductor, dielectric, and radiation losses have been included. The optimum substrate thickness for the maximum Q-factor for 50-omega microstrip resonators has been derived as a function of frequency for different dielectric constants.     

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.     

A Broad-Band, Automated, Stripline Technique for the Simultaneous Measurement of Complex Permittivity and Permeability

A broad-band automated technique for making frequency-swept measurements of complex permittivity and permeability simultaneously is described. Epsilon/sub r/ and µ/sub r/ are computed from S-parameter measurements made on a strip transmission-line device loaded with the material under test. The derivation of epsilon/sub r/ and µ/sub r/ as functions of S/sub 11/ and S/sub 21/ is included, as well as a practical design for a stripline sample holder. Measured epsilon/sub r/ and µ/sub r/ data for several dielectrics and ceramic ferrites is also presented. The technique has been found to have an overall accuracy of better than +-5 percent.     

Analysis of Nonreciprocal Coupled Image Lines

The effective dielectric constant method is used to analyze the nonreciprocal coupling properties of coupled image lines separated by a Iongitudinally magnetized ferrite slab. Two structures are considered, one incorporating low-dielectric-constant image lines (epsilon/sub r/ = 2.56), the other incorporating image lines consisting of high-dielectric-constant material (epsilon/sub r/ = 9.8). Results of dispersion characteristics, coupling parameters, and field distributions are presented.     

Analysis and Evaluation of a Method of Measuring the Complex Permittivity and Permeability Microwave Insulators

Theory and experimental results are presented to show the possibility of using a resonant post technique for characterizing dielectric and magnetic materials at microwave frequencies. Results of the temperature dependence of the relative dielectric constant of nonmagnetic materials with /spl epsilon//sub r/, varying from 4 to 60 are presented and also loss tangent measurements at room temperature. The complex permittivity and permeability of a number of garnet materials has also been measured with 4/spl pi//spl gamma/M/sub s/ / /spl omega/ varying from 0.25 to 0.8. The measured real part of the permeability is in good agreement with the theoretical predictions of Schlomann and the imaginary part of the permeability agrees with measurements by Green et al. on similar materials.     

Losses on Multiconductor Transmission Lines in Multilayered Dielectric Media

For the transmission-line modes, a multiconductor transmission line in a multilayered dielectric medium can be characterized by four matrix parameters the capacitance matrices [C], the inductance matrix [L], the shunt conductance matrix [G], and the series resistance matrix [R]. The first two matrices [C] and [L] can be obtained from equivalent electrostatic and magnetostatic problems. The conductance matrix [G] can be obtained by changing all dielectric constants epsilon/sub i/ to complex dielectric constants /angle over epsilon/sub i/ in the equivalent electrostatic problem. The resistance matrix [R] can be obtained by applying a perturbation method to each mode of the transmission line. A computer program has been written for an arbitrary line, and sample computations are presented.     

Dielectric Resonator in a Waveguide Below Cutoff

A structure is considered consisting of a waveguide 2 below cutoff, connected to waveguides above cutoff, 1 and 3, by means of suitable junctions. A dielectric resonator is introduced in waveguide 2. Its effect on the transmission curve of the structure is evaluated in the limit epsilon/sub r/spl rarr/spl infin/. Theoretical results are compared with experiment.     

Microwave Bandpass Filters Containing High-Q Dielectric Resonators

This paper is concerned with dielectric disks used as resonators in microwave bandpass filters. For many years it has been known that modes of resonance occur in isolated dielectric bodies having air boundaries, and that very compact high-Q resonators can be achieved when /spl epsiv/ /sub r/, is high and tan /spl delta/ is low. High-purity TiO/sub 2/ ceramic material, for example, has an /spl epsiv/ /sub r/ about 100, tan /spl delta/ about 0.0001, and Q/sub u/ about 10 000. Practical applications of dielectric resonators have previously been limited by insufficient design information. Formulas are derived for the coupling coefficient between adjacent dielectric-disk resonators within a metal waveguide below cutoff. This metal enclosure is necessary for shielding and to prevent radiation loss. Comparisons between theoretical and experimental coupling coefficient values show very good agreement in each of the three bandpass configurations treated in this paper. Techniques of loop and probe coupling to the end resonators of a multiresonator bandpass filter are discussed and methods of supporting the resonators are suggested. The conclusion is made that microwave dielectric resonators offer important size reductions compared to conventional resonators of similar high Q, but that the center-frequency change of the dielectric resonators as a function of temperature is excessive for many applications. Temperature stabilization is one solution, but preferably a material should be developed having electrical characteristics similar to TiO/sub 2/ ceramic, but with at least an order of magnitude improvement in temperature sensitivity.     

Optical Methods for the Measurement of Complex Dielectric and Magnetic Constants at Centimeter and Millimeter Wavelengths

A method is described which permits the determination of the complex dielectric constant, epsilon* = epsilon/sub o/k/sub e/(l-j tan delta/sub e/), and the complex permeability, µ* = µ/sub o/k/sub m/ (l-j tan delta/sub m/), using free space transmission and reflection from a plane sheet of the sample dielectric. The procedure represents an extension of that used at optical frequencies. Differences arise however, due to the fact that the assumptions of k/sub m/ = 1 and tan delta/sub m/ = 0, which are made in the optical theory, are not always valid at millimeter wavelengths.     

Barium Tetratitanate MIC Technology

Experimental results on BaTi/sub 4/O/sub 9/ microwave integrated circuit (MIC) characteristics, including microstrip dispersion and loss, have shown excellent agreement with the theoretical predictions. Precision measurements of temperature stability were conducted at 14 GHz. The high dielectric constant (epsilon/sub r/ = 37) and its negative temperature coefficient can be used in specialized MIC's for application to advanced microwave subsystems.