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.     

Accurately Approximate Formula of Effective Filling Fraction for Microstrip Line with Isotropic Substrate and its Application to the Case with Anisotropic Substrate

The accurately approximate formula of effective filling fraction q/sub w/ is obtained for the microstrip line with zero-thickness strip and isotropic substrate. The line capacitance per unit length C/epsilon/sub 0/ for the case with anisotropic substrate can easily be obtained by using the approximate formula of q/sub w/ and C/sub 0//epsilon/sub 0/ tabulated for the wide range of shape ratio w/h. The parameters Z, v, and lambda for such a line can be calculated by using C/ epsilon/sub 0/ and C/sub 0//espsilon/sub 0/.     

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.     

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.     

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.     

Quasi-Static Characteristics of Microstrip on an Anisotropic Sapphire Substrate

The well-defined and repeatable electrical properties of single-crystal sapphire make it an attractive substrate material for microstrip, but its dielectric anisotropy constitutes an important design complication. This paper describes investigations into the quasi-static characteristics of single microstrip lines on sapphire substrates cut with a specified orientation. To account for anisotropy, a new permittivity parameter epsilon/sub req/ is introduced, which is a function of the Iinewidth to substrate-height ratio W/h. The variation of epsilon/sub req/ with W/h is derived by finite-difference methods. Universal curves for microstrip on correctly orientated sapphire are presented, showing 1) epsilon/sub req/, 2) the low-frequency limit of effective microstrip permittivity epsilon/sub e0/, and 3) the characteristic impedance of the line Z/sub 0/, all as functions of W/h.     

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.     

Accurate Analysis Equations and Synthesis Technique for Unilateral Finlines

Accurate analysis equations and synthesis techniques are presented for unilateral finlines, valid over a wide range of structural parameters and substrate dielectic constants (1/spl les/epsilon/sub r//spl les/3.75). These expressions are usable for computing the cutoff wavelength to within +-0.6 percent, the guided wavelength to within +-2 percent, and the characteristic impedance (based on the power-voltage definition) to within +-2 percent, of the spectral-domain method, over the normalized frequency range 0.25/spl les/b/lambda/spl les/0.6.     

Microstrip-Slot Coupler Design-Part II: Practical Design Aspects

Practical aspects of designing microstrip-slot couplers on an Al/sub 2/O/sub 3/ ceramic substrate (epsilon/sub r/ = 9.8) are treated in supplementation of the theoretical analysis of the coupler presented in Part I. Comparison with implemented couplers yields rules for specification of the reference planes at the ends of the coupling section, for the appropriate choice of definition for the slot-line characteristic impedance. Design data of the standard versions of the microstrip transmission line, the slot line are shown to be adequate for the microstrip-slot coupler. Computed S -parameter curves plotted for various 3-dB couplers yield information on realizable transmission characteristics.     

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.     

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.     

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.     

Measurements of the Photo-Induced Complex Permittivity of Si, Ge, and Te at 9 GHz

The photo-induced complex permittivity Delta epsilon /sub r/(=Delta epsilon'/sub r/--j Delta epsilon"/subr/)of single, crystal silicon, germanium, and tellurium samples was studied using a transmission microwave bridge method at frequencies of about 9 GHz. The measurements were made at temperatures in a range from 100 to 300 K over an optical wavelength range from about 0.6 to 1.4 µm for silicon, 0.8 to 2.0 µm for germanium, and 1.5 to 4.2 µm for tellurium. The incident monochromatic illumination was chopped at about 90 Hz. It was found that the spectral variation of Delta epsilon'/sub r/ was similar to that for Delta epsilon"/sub r/ over the wavelength ranges with the incident monochromatic light intensity in the order of 100 µw/cm²². The spectral peaks (for Si and Ge samples) of both Delta epsilon'/sub r/ and Delta epsilon"/sub r/ were found to shift towards shorter wavelengths as the temperature was decreased. From the photo-induced complex permittivity results, the collision time of the free carriers was derived.     

The Dependence of Reflection on Incidence Angle

A Iossy dielectric sheet has complex dielectric constant epsilon = epsilon (x) and complex permeability µ = µ(x), where x is the distance to one interface. This sheet is backed by a conducting surface and used as an absorber. If | epsilon (x)µ(x) | >>epsilon/sub 0/µ/sub 0/, so that (epsilon/epsilon/sub0/)(µ/µ/sub0/) - sin² theta is nearly independent of the incidence angle theta, then the amplitude reflection R(theta) is wholly determined by R(0). Typical results: When R(theta/sub0/) = 0 at one polarization, then at theta=theta/sub 0/ the reflection for the other polarization corresponds to a voltage standing-wave ratio SWR =sec² theta/sub 0/. At perpendicular polarization max | R(theta) | on (theta/sub 1/, theta/sub 2/) is least, for given | R(0) I, if R(0) is real and positive; and then R(theta) = 0 at tan²theta/2 = R(0). But for parallel polarization R(0) must be real and negative to get optimum performance. When the absorber functions at both polarizations the best obtainable result is | R(theta) | = tan²theta/2, no matter what interval (theta/sub 1/, theta/sub 2/) is specified. The error in the approximation is investigated theoretically and experimentally. A complete set of graphs is included, suitable for design of those absorbers to which the theory applies. The analysis also yields an exact expression for the limiting behavior of the reflection at grazing incidence. This can be used in problems such as computation of the field due to a dipole over a plane earth. Finally, the theory of the Salisbury screen is re-examined as an aid in checking the other developments.     

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.     

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.     

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/.     

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.