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.     

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.     

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.     

The Inverse Problem for Biaxial Materials

Theory and measurements for the determination of the constitutive parameters of an anisotropic material are described, when a slab of the material is inserted in a rectangular waveguide. If both epsilon and µ tensors have zero off-diagonal elements (biaxial material), then the six diagonal elements can be determined by measuring amplitude and phase of reflection and transmission coefficients. If the material is nondispersive, two sets of measurements at two different frequencies are sufficient, under TE/sub 10/ excitation. In the more general case of a lossy and dispersive material, two sets of measurements at the same frequency under TE/sub10/ and TE/sub20/ excitations are needed. An experimental setup for the latter case is described.     

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.     

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.     

Dispersion Characteristics for Wide Slotlines on Low-Permittivity Substrates (Short Paper)

This paper provides additional dispersion data on slotlines not available in the literature to date. In particular, data are presented on wide slots etched on an electrically thin substrate of low-dielectric constant. The range of parameters covered in this paper are 0.006<= d/lambda/sub 0/ <=0.06, 0.005 <= W/lambda/sub 0/ <=2.0, and epsilon /sub r/ =2.22, 3.0, 3.8, 9.8. The problem is formulated using the spectral-domain technique, and the spectral Galerkin's method is employed to compute the slot wavelength. Numerical results are compared to the experimental data over 2-6 GHz for slotlines on a 1.57-mm substrate (epsilon/sub r/ = 2.55). Agreement to within 2.0 percent is obtained.     

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.     

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/.     

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.     

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.     

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.     

Metallized Dielectric Horn and Waveguide Structures for Millimeter-Wave Oscillator/Mixer Systems

A new method of producing millimeter-wave oscillator/mixers and associated antenna horns has been developed. This uses the technique of metal coating of dielectric body, and hence avoids the expensive and difficult machining of conventional metal cavities. A sensitive self-oscillating mixer has been tested in this structure and shown to be free from the unstable operation associated with surface radiation of unshielded dielectric waveguide. Low epsilon/sub r/ dielectric was used, thus facilitating ease of matching in contrast with the high epsilon/sub r/ necessary with the unshielded guide.     

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.     

A Graphical Method for Measuring Dielectric Constants at Microwave Frequencies

This paper describes a graphical method for measuring the real and imaginary parts of the dielectric constant epsilon/epsilon/sub 0/ = epsilon' - j epsilon" of materials at microwave frequencies. The method is based on the network approach to dielectric measurements proposed by Oliner and Altschuler in which the dielectric sample fills a section of transmission line or waveguide. In contrast to their method, the network representing the dielectric sample is analyzed in terms of the bilinear transformation Gamma'=(aGamma+b)/(cGamma+d); ad-bc=4. The analysis proceeds from the geometric properties of the image circle in the r plane obtained by terminating the output line in a calibrated sliding short. The technique described retains the desirable features of the network approach but avoids the necessity of measuring both scattering coefficients. As a result the procedure is more direct and, in the case of the TEM configuration, leads to an entirely graphical solution in which the complex dielectric constant can be read from a Smith chart overlay.     

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.     

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.     

New View on an Anisotropic Medium and Its Application to Transformation from Anisotropic to Isotropic Problems

The metric factor is defined as m(epsilon*/sub x/, epsilon*/sub y/, theta/sub x/) = /spl radic/ cos/sup 2/theta/sub x/ / epsilon*/sub x/ + sin/sup 2/theta/sub x/ / epsilon*/sub y/ in the radial direction, with the angle theta/sub x/ from the x axis being one of the principal axes in an anisotropic dielectric medium filling the two-dimensional space. The normalized metric factor is defined as n(epsilon*/sub x/, epsilon*/sub y/, theta/sub x/, beta) /spl equiv/ m(epsilon*/sub x/, epsilon*/sub y/, theta/sub x/) / m(epsilon*/sub x/, epsilon*/sub y/, beta) in the form normalized by the metric factor in the direction with the angle beta from the x axis. The effective path length d'/sub P1P2/ between the points P1 and P2 is defined as d'/sup P1P2/ = n(epsilon*/sub x/, epsilon*/sub y/, theta/sub x/, beta)d/sub P1P2/ where d/sub P1P2/ is the actual path length of the straight line P1P2 with the angle theta/sub x/ from the x axis. We propose the minimun principle of the effective path length for electric flux in the region with multilayered anisotropic media. It is applied to solving the electrostatic problem with two anisotropic media whose principal axes are different. We show by using the normalized metric factor that the anisotropic problem can be transformed into the isotropic problem.