Showing papers in "IEEE Transactions on Microwave Theory and Techniques in 1972"

Narrow-Bandpass Waveguide Filters

Abstract: A procedure is described whereby narrow-bandpass waveguide filters having ripple in both the passbands and stopbands can be synthesized in the form of coupled waveguide cavities. Orthogonal modes in square or circular waveguides are employed to enable negative coupling elements to be realized. As a consequence, very compact filters can be constructed. Experimental results on an 8-cavity orthogonal-mode narrow-bandpass filter are shown to agree well with theory.

Hairpin-Line and Hybrid Hairpin-Line/Half-Wave Parallel-Coupled-Line Filters

Abstract: A new class of microwave filters, hairpin-line and hybrid hairpin-line/half-wave parallel-coupled-line filters, is reported. This class of filters is particularly well suited for microstrip and TEM printed-circuit realizations because grounding of the filter resonators is generally not required. Hairpin-line filters have been divided into two types. The first (Type A) is characterized by having its input and output lines open-circuited at their ends. The Type A filter has been found to yield practical impedance levels for narrow to approximately 25-percent bandwidths. The second (Type B) is characterized by having its input and output lines short-circuited at their ends. However, because of space limitations, details of the Type B filter are not presented in this paper. Theoretical background and design equations for Type A bandpass filters are presented. Experimental data for several stripline filters of 5- and 20-percent bandwidths are given. Experimental results for two microwave-integrated-circuit (MIC) filters are discussed.

A Microstripline Slot Antenna (Short Papers)

Abstract: A microstripline slot antenna is treated experimentally at X-band frequency. First, the input impedances of the slots for various geometries and the radiation patterns for the matched slots are measured. Second, the dependence of input impedances and radiation patterns on the slot-to-reflector spacing is tested. Finally, a two-dimensional X-band Dolph-Chebyshev slot-array antenna is designed and fabricated as an application of this type of slot.

Finite-Element Solution of Unbounded Field Problems

Abstract: An unbounded region is divided into local picture-frame regions where a partial differential-equation solution is obtained, with the remaining unbounded region represented by an integral equation. (The method permits the use of free-space Green's functions, and thus special problem-dependent Green's functions need not be found.) The integral equation is formulated as a constraint upon the local picture-frame solutions, whence these local solutions are solved directly by a variational method, using finite elements, in a manner such that the problem of the Green's-function singularity is side-stepped. The technique is applicable where sources and media inhomogeneities and anisotropies are local, and can all be placed within one or several picture frames. It is in these cases that the integral-equation approach is at a particular disadvantage, and the use of a partial differential-equation technique is advisable if not necessary. Examples presented include the static and harmonic fields of a parallel-plate capacitor, a microstrip line on a dielectric substratum, and a radiating antenna with dielectric obstacles.

Broad-Band Diode Phase Shifters

Abstract: Design figures are presented for four types of diode phase shifters: switched line, reflection, loaded line, and a new type using lumped-element high-pass and low-pass circuits. Comparison of their bandwidths shows that most of them can work over an octave bandwidth.

The Planar Circuit - An Approach to Microwave Integrated Circuitry

Abstract: Three principal categories have been known in electrical circuitry so far. They are the lumped-constant (0-dimensional) circuit, distributed-constant (1-dimensional) circuit, and waveguide (3-dimensional) circuit. The planar circuit to be discussed in general in this paper is a circuit category that should be positioned as a 2-dimensional circuit. It is defined as an "electrical circuit having dimensions comparable to the wavelength in two directions, but much less thickness in one direction." The main subject of this paper is the computer analysis of an arbitrarily shaped, triplate planar circuit. It is shown that a computer analysis based upon a contour-integral solution of the wave equation offers an accurate and efficient tool in the design of the planar circuit. Results of some computer calculations are described. It is also shown that the circuit parameters can be derived directly from Green's function of the wave equation when the shape of the circuit is relatively simple. Examples of this sort of analysis are also shown for comparison with the computer analysis.

Equivalent Capacitances for Microstrip Gaps and Steps

Abstract: The excess charge density distribution near gaps and steps in microstrip transmission lines is calculated by the solution of singular integral equations. Data are presented for gaps in microstrips of width-to-substrate-thickness ratios of 0.5, 1.0, and 2.0 and relative dielectric constants ranging from 1.0 to 15.0. For steps in a microstrip line results are given for width-to-thickness ratio of unity, relative dielectric constants of 1.0 and 9.6, while the change of width-to-height ratio is from 0.1 to 10.0. The excess charges are calculated explicitly in relatively short computing times, and the results are believed to be accurate to within a few percent.

Analytical and Numerical Studies of the Relative Convergence Phenomenon Arising in the Solution of an Integral Equation by the Moment Method

Abstract: The relative convergence phenomenon that occurs in the numerical solution of the integral equation for the iris discontinuity problem is studied both analytically and numerically. It is shown that the solution for the aperture field can be highly dependent upon the manner in which the kernel and the unknown function are approximated in the process of constructing a matrix equation by the moment method. An analytical explanation is provided for the above phenomenon and the theoretical predictions are verified numerically. Also incIuded is a suggested numerical algorithm for detecting and alleviating the relative convergence behavior for more general problems.

Analysis and Design of Dispersive Interdigital Surface-Wave Transducers

Abstract: A comprehensive circuit model characterization of dispersive interdigital transducers with nonuniform electrode spacing is presented. The model is an extension of a three-port circuit which has been useful for representing periodic transducers. The extended model includes the effects of strong piezoelectric coupling whereby the acoustic waves and electric circuits interact, and it also accounts for reflections of acoustic waves which result from perturbations of the crystal surface by the metal electrodes. The inclusion of the latter effect is shown to be essential for explaining observed levels of triple-transit echos in filters and delay lines. The circuit model is used to derive a transducer design procedure which determines the electrode positions and the anodization function (acoustic aperture taper) required to reproduce a desired waveform. This procedure is applicable to the design of weighted dispersive filters and broad-band nondispersive delay lines. In order to verify the theory a low-loss octave-bandwidth nondispersive delay line was designed using linear FM dispersive transducers on YZ LiNbO/sub 3/. The performance of this device was found to be in good agreement with the circuit model predictions.

Electric and Magnetic Coupling through Small Apertures in Shield Walls of Any Thickness

Abstract: A method is presented for evaluating the coupling between two identical resonant cavities coupled by a small aperture in a plane common wall of arbitrary thickness. The coupling is related to the frequencies of the symmetric and asymmetric modes of oscillation of the coupled cavity structure, and a variational technique is used to determine those frequencies. The method is applied to circular and rectangular apertures, and it is shown that the coupling is separable into electric and magnetic terms. The results enable theoretical solutions to be obtained for the electric and magnetic polarizabilities of circular and rectangular apertures in walls of zero thickness, and equivalent polarizabilities to be obtained when the wall thickness is nonzero. Curves of numerical values are given for circular and rectangular apertures. With zero wall thickness, the results obtained are the same as those of Bethe for a circular aperture and give good agreement with Cohn's experimental results for rectangular apertures.

An Analysis of Gap in Microstrip Transmission Lines

Abstract: Although microstrip transmission lines have been widely used in microwave integrated circuits, the discontinuity structures in the microstrip transmission lines such as a gap, an abruptly ended strip conductor, and so on, have hardly been analyzed. An analytical method and numerical results for a gap capacitance in the microstrip transmission line are described. The equivalent circuit parameters are formulated with three-dimensional Green's functions, based on a variational principle. The numerical results are in good agreement with the published experimental data. The fringing effect of an abruptly ended strip conductor is also investigated.

Equivalent Capacitances of Microstrip Open Circuits

Abstract: The integral equations that describe the charge distribution near an open-circuited microstrip end are formulated and subsequently solved by a projective method. The solution hinges on development of computationally efficient techniques for dealing with the singularities that occur by special quadrature formulas. The necessary formulas are described and tabulated. These techniques are then used to find open-circuit capacitance values for microstrip. It is found that the curves of excess capacitance versus width are easily describable by empirical equations; such equations are presented, along with the curves themselves. For strip widths between 0.1 and 10 times the substrate thickness and for dielectric constants in the range 1-51, the given data are believed accurate to within a few percent.

Microstrip Propagation on Magnetic Substrates - Part I: Design Theory

Abstract: Formulas and graphs are presented for the effective relative permeability and the filling factors of magnetic substrates in microstrip. Both the propagation and the magnetic loss filling factors are included. In the calculation of these quantities, use was made of the filling factors for dielectric substrates obtained from Wheeler's analysis and a duality relationship between magnetic and dielectric substrates derived in this paper.

A Near-Optimum Matching Section without Discontinuities

Abstract: The optimum tapered matching section requires impedance steps at the taper ends, which exclude in most cases its application for synthesizing waveguide tapers. A new "near" optimum design is described which avoids the impedance steps and yields tapers only a fractional part longer in taper length (or narrower in bandwidth) than the exactly optimum taper. A table of values of a transcendental function has been calculated to simplify the synthesis. An example compares both types of matching sections.

Matrix Methods for Microstrip Three-Dimensional Problems

Abstract: The matrix methods are applied to three-dimensional microstrip problems with emphasis upon the general problem of discontinuities in microstrip. Discontinuities considered are 1) open circuits, 2) change of width, and 3) gap in microstrip. Also, the capacitance of rectangular sections of microstrip is computed. Computed data agree well with experiment and data in the literature.

Practical Least pth Optimization of Networks

Abstract: A new and practical approach to computer-aided design optimization is presented. Central to the process is the application of least pth approximation using extremely large values of p, typically 1000 to 1 000 000. It is shown how suitable and reasonably well conditioned objective functions can be formulated, giving particular emphasis to more general approximation problems as, for example, in filter design. It is demonstrated how easily and efficiently extremely near minimax results can be achieved on a discrete set of sample points. Highly efficient gradient methods can be employed and, in network design problems, the use of the adjoint network approach for evaluating gradients results in greater savings in computer effort. A comparison between the Fletcher-Powell method and the more recent Fletcher method is made on the application of least pth approximation, using a range of values of p up to 1 000 000 000 000 on transmission-line transformer problems for which optimal minimax solutions are known. This is followed by filter design examples subject to certain constraints.

Capacitance of Parallel Rectangular Plates Separated by a Dielectric Sheet

Abstract: To determine the capacitance between two rectangular parallel plates separated by a dielectric sheet, the charge distribution on the plates is formulated in terms of a Fredholm integral equation of the first kind. This equation is solved numerically by a projective method using polynomial approximants. The resulting capacitance values are given in normalized graphical form, permitting capacitance determination for any practical values of dielectric constant and geometric parameters to within a few percent.

Frequency-Dependent Characteristics of MicrostripTransmission Lines

Abstract: A method for determining the frequency-dependent characteristics of both single and coupled lines in shielded microstrip is presented. Numerical results are given for a variety of dielectric configurations and the effects of geometry on the dispersion characteristics are examined in detail. Of particular interest are the characteristics of coupled lines on compensated dielectric structures, i.e., structures that are capable of achieving equal even- and odd-mode phase velocities, and the effects of dispersion on the directivity characteristics of such lines are discussed. In addition, the variation of impedance as a function of frequency, where the impedance is defined as the ratio of the power to the square of the longitudinal current, is presented for representative cases of single and coupled lines.

On the Use of Describing Functions in the Study of Nonlinear Active Microwave Circuits

Abstract: It is shown that a nonlinear microwave circuit can easily be represented by a feedback model. This formalistic identity with nonlinear control systems suggests that methods and results can be borrowed from nonlinear control theory. The describing function technique, a concept that has been developed to a high degree of sophistication in control theory, is applied to the problem of phase-locking of microwave oscillators. The use of describing functions in the study of nonlinear microwave circuits may give a simple conceptual understanding of locking phenomena, for example, and thereby reduce computational efforts.

Computer Analysis of the Fundamental and Higher Order Modes in Single and Coupled Microstrip

Abstract: By means of finite difference methods, dispersion curves are obtained for the fundamental and higher order hybrid modes in both single and coupled microstrip. Structures of realistic proportions are investigated by the use of a graded finite difference mesh. Variational methods are used in deriving the finite difference equations. The higher order modes are found to be similar to LSM slab line modes. A spurious nonphysical class of solutions is found to exist in this and similar formulations, the characteristics of which are described.

Propagation Mode and Scattering Loss of a Two-Dimensional Dielectric Waveguide with Gradual Distribution of Refractive Index

Abstract: An analytical discussion of the mode property and the scattering loss of a two-dimensional dielectric waveguide with gradual refractive-index distribution in the transverse direction is presented. To describe scattering loss, a transverse correlation as well as an axial correlation of the irregular variation of the refractive index have been used. The field distribution, the group delay, and the maximum film thickness of a single-mode waveguide scarcely depends on the shape of the distribution. The maximum value of the film thickness in the single-mode transmission region optimizes the scattering loss and the energy confinement. The scattering loss of a waveguide with a gradual index distribution is smaller than that of a three-layer waveguide when the transverse correlation is small, but it is not much altered when the transverse correlation is large.

Wave Sensitivities of Networks

Abstract: A theoretical foundation is presented for the efficient computation of first- and second-order sensitivities of networks with respect to network parameters in terms of wave variables. The concept of the adjoint network is used. First-order sensitivity formulas for a wide variety of elements are presented, including lumped and uniformly distributed elements, active and passive elements, and reciprocal and nonreciprocal elements. Parameters include electrical quantities, geometrical dimensions, and frequency. It is shown how gradients related to wave-based least pth and minimax objective functions can be computed. A comparison with a method which avoids the need for analysis of adjoint networks is made. Applications in the computer-aided design of networks using efficient gradient minimization methods are envisaged.

Applications of Time-Domain Metrology to the Automation of Broad-Band Microwave Measurements

Abstract: It is only recently that measurement of the transient response of microwave systems directly in the time domain has become practicable. It has led to growing interest in the concept of specifying broad-band performance solely by a transient-response measurement. Results of the use of time-domain techniques to obtain, within the range 0.1 to 10 GHz, such data as the S parameters of networks, the constitutive parameters of microwave materials, the driving-point impedance and transfer function of microwave antennas, and the frequency-domain scattering parameters of conducting surfaces in free space are described.

Microstrip Propagation on Magnetic Substrates - Part II: Experiment

Abstract: Experimental data taken on microstrip built on ferrite and garnet substrates are presented and compared with theoretical values calculated from formulas derived in a previous paper which were extended to gyromagnetic media. Good agreement has been obtained between experiment and theory. In particular the observed increase in wave attenuation at frequencies near /spl omega//sub m/ is fully explained when the frequency dependence of the characteristic impedance is taken into account.

Waveguide Bandstop Elliptic Function Filters

Abstract: Using the "natural prototype" for elliptic function filters, a design procedure is presented for a class of waveguide bandstop filters, which exhibit equiripple passband and stopband responses. Due to the availability of explicit formulas for element values in the natural prototype elliptic function filter, the design procedure is entirely analytic and does not require numerical synthesis techniques. The resulting physical structure is the familiar uniform guide with iris-coupled series stubs. Unlike the bandstop filters designed from maximally flat or Chebyshev prototypes, the elliptic function design results in stubs that are not exactly three-quarter-wave coupled.

Broadside-Coupled Strips in a Layered Dielectric Medium

Abstract: Coupling coefficient, odd- and even-mode impedances, and the mode phase velocities are calculated for a pair of broadside-coupled strips embedded in a layered dielectric medium and enclosed by a rectangular shield. Large ratios of mode phase velocities can be achieved with this structure leading to novel performance characteristics for familiar coupled-line configurations such as the microwave C section.

Stability Criteria for Phase-Locked Oscillators

Abstract: Stability criteria for negative conductance oscillators or amplifiers are derived in terms of the total circuit admittance. A figure of merit for phase locking at small injected powers is derived. The influence of large injected signals is studied. The conclusions drawn from the calculations are in good qualitative agreement with experimental observations on phase-locked IMPATT-diode oscillators.

Transmission Distortion in Multimode Random Waveguides

Abstract: We consider the coupled line equations for two-mode random media in which both modes travel in the same (forward) direction as a model for multimode millimeter waveguides and optical fibers, in which mode conversion at imperfections occurs primarily in the forward direction. Some exact general properties satisfied by the transfer function and the impulse response of such a system are given for an arbitrary coupling coefficient. A random stationary coupling coefficient with statistically independent successive values, and consequently a white spectrum (e.g., a white Gaussian or a Poisson noise), permits exact determination of transmission statistics; we obtain first- and second-order statistics in the time and frequency domains. No perturbation or other approximations are made in any of the above results, which are obtained directly from the coupled line equations. These results are used to study signal distortion in long guides. By straightforward extension of this work more complicated calculations can treat more forward modes, but not backward modes or nonwhite coupling coefficient spectra. In this paper the coupling coefficient is assumed frequency independent, and under certain conditions the signal distortion decreases as the mode conversion increases. In practical cases the coupling coefficients are frequency dependent and the above behavior is modified; the present work is extended to this important case in a companion paper.

Octave-Band Microstrip DC Blocks (Short Papers)

Abstract: The design of octave-bandwidth microstrip interdigital dc blocks is presented. Data for a 7.75- to 16.3-GHz design are given and correlated with an approximate equivalent circuit based on even and odd mode propagation in coupled microstrip. Additional data are tabulated reflecting the ability to shift the frequency band of operation.