Computation of Coplanar-Type Strip-Line Characteristics by Relaxation Method and its Application to Microwave Circuits

The characteristics of new strip lines [i.e., a single strip-conductor coplanar-type strip line (S-CPS), a two symmetrical strip-conductor coplanar-type strip line (T-CPS), and a coupled strip-conductor coplanar-type strip line (C-CPS), which consists of single two-center strip conductors or coupled strip conductors and ground plates on a dielectric substrate and outer ground conductor] are calculated by the relaxation method. The effect of the outer ground conductor and side wall on these lines is analyzed and the characteristic impedance and phase-velocity ratio are determined. The characteristic impedance is determined experimentally and the maximum values of the discrepancies compared with the calculated value of each of the lines are 2.0-3.0 percent. Application examples of the coplanar-type strip line to microwave transistor amplifier and parallel-coupled filter are shown. A transistor amplifier of small size, light weight, wide bandwidth, and improved reliability is achieved. A parallel-coupled filter small in size (reduction ratio is more than 50 percent), with good frequency symmetry and featuring easy resonance frequency fine tuning is obtained.     

Uniform Multimode Transmission Lines (Short Papers)

A consistent normal-mode theory for coupled uniform transmission lines is developed which properly accounts for the fact that some propagation constants may be equal. Explicit responses are calculated. The results are interpreted in terms of transmission-line networks which consist of simple lines and which are coupled via conductor sharing.     

Multilayer Microstrip Transmission Lines (Short Papers)

A method used to treat covered microstrip is extended to multilayer microstrip. Detailed results are obtained for the general three-layer problem. Series expansion and term-by-term integration are used to obtain a closed form expression for the Green's function. Matrix methods are then used to obtain the characteristic impedance. Data obtained agree closely with experiment.     

Spectral-Domain Approach for Calculating the Dispersion Characteristics of Microstrip Lines (Short Papers)

The boundary value problem associated with the open microstrip line structure is formulated in terms of a rigorous, hybird-mode representation. The resulting equations are subsequently transformed, via the application of Galerkin's method in the spectral domain, to yield a characteristic equation for the dispersion properties of the open microstrip line. Numerical results are included for several different structural parameters. These are compared with other available data and with some experimental measurements.     

Solution to Waveguide Problems by Successive Extrapolated Relaxation (Short Papers)

A successive extrapolated relaxation (SER) technique has been developed to solve elliptic partial difference equations iteratively. SER is more efficient than optimized successive over-relaxation (SOR) and permits useful solutions of waveguide modes using finite difference methods.     

A Technique for Computing Dispersion Characteristics of Shielded Microstrip Lines (Short Papers)

The boundary value problem associated with the shielded microstripline structure is formulated in terms of a rigorous hybrid-mode representation. The resulting equations are subsequently transformed, via the application of Galerkin's method in the spectral domain, to yield a characteristic equation for the dispersion properties of shielded microstrip lines. Among the advantages of the method are its simplicity and rapid convergence. Numerical results are included for several different structural parameters. These are compared with other available data and with some experimental results.     

Dielectric Loss in Microstrip Lines (Short Papers)

A new technique is presented for calculating dielectric loss in microstrip lines. Numerical results for several different substrates are included. These are compared with other available results and experimental data.     

Quasi-Static Characteristics of Asymmetrical and Coupled Coplanar-Type Transmission Lines

In this paper, variational expressions for the capacitances of' asymmetrical and coupled coplanar-type transmission lines are derived. The methods employed are quite general, and are useful for analyzing various types of coplanar-type transmission lines, with either an isotropic or anisotropic substrate. An accurate and efficient method of calculation is provided for the variational expressions, and some numerical results are presented.     

Loss Calculations of Coupled Microstrip Lines (Short Papers)

Loss calculations have been performed to yield useful data relevant to the complementary odd and even modes propagating along a pair of identical coupled microstrip lines. The calculations are based on methods applied to the single-line case and indicate substantial differences in attenuation occurring between the odd and even modes for particular geometries.     

Multiconductor Transmission Lines and the Green's Matrix (Short Papers)

It is shown that the study of arbitrarily terminated multiconductor transmission lines which may in general be lossy and subjected to excitation applied at an arbitrary point along the lines, may be effectively performed with the aid of the appropriate Green's matrix. The procedure is illustrated using the Chipman method of impedance measurement as well as coupled microstrip lines.     

Wave Propagation on Nonuniform Transmission Lines (Short Papers)

The problem of wave propagation on nonuniform transmission lines is studied. Equations are presented not only for the reflection coefficient but for the transmission and admittance properties as well. They are valid under the assumption that only one mode of propagation exists on the line and that the properties do not change so rapidly that the fundamental transmission line equations are no longer applicable. Since all equations are derived for arbitrary load conditions, an extremely versatile solution of the problem has been obtained.     

Time-Delay Limits Set by Dispersion in Magnetostatic Delay Lines (Short Papers)

Analysis and experiments show the extreme dispersion of magnetostatic delay lines. A suitable parameter to characterize the amount of dispersion present has been found to be the maximum output energy contained in a time interval equal to the input pulse duration. The time occurrence of this maximum value gives a convenient measure of the group delay. The pulse shape and energy content versus delay have been determined both theoreticaly and experimentally for axially magnetized circular rods. The results show that delays beyond two to three times the input pulse duration cannot be obtained with more than 50 percent of the output energy contained within the original pulse duration.     

Normalized Impedance Graphs for Exponential Transmission Lines (Short Papers)

Sign errors in an existing closed form solution for the reflection coefficient along an exponentially tapered transmission line have been corrected and the solution has been modified by the use of electrical line length. This allows useful graphs for the input impedance of the tapered line to be computed which are normalized with respect to frequency and system impedance. The graphs clearly demonstrate both the broad-band and narrow-band properties of the tapered line.     

A Method for Computing Edge Capacitance of Finite and Semi-Infinite Microstrip Lines (Short Papers)

This short paper describes a method for computing the edge capacitance of finite or semi-infinite sections of microstrip transmission lines. The approach is based on Galerkin's method applied in the Fourier-transform domain. It is mathematically simple and requires the inversion of rather small-size matrices.     

Dimensions of Microstrip Coupled Lines and Interdigital Structures (Short Papers)

A method is presented for finding dimensions of coupled lines and interdigital structures on microstrip given the electrical properties. Both a graphical approach and computer approach using polynomial approximations are given. These results are within 1 percent of Bryant and Weiss' dimensions for coupled lines for most practical stripwidths and spacings. Experimental data for a 10-percent bandwidth microstrip interdigital filter are given.     

Equivalent Circuit of a Narrow Axial Strip in Waveguide (Short Papers)

A theoretical determination is made of the two-port equivalent circuit of a narrow strip located axially in a rectangular waveguide such that it extends partially or completely across the waveguide narrow dimension. The analysis is based upon derivation of a variational expression for a field quantity from which can be determined the reflection coefficient and the equivalent-circuit parameters. Experimental input susceptance values agree closely with the theory. The analysis shows that the T-equivalent network of a nontouching strip has a series-resonant shunt circuit. This element has application in filter and impedance-transforming networks, in planar circuits, and in fin-line structures.     

The Method of Series Expansion in the Frequency Domain Applied to Multidielectric Transmission Lines (Short Papers)

In this short paper a method of expanding the phase constant and the field of a multidielectric transmission line as a power series of the frequency is developed. The method provides a theoretical justification for the widely used "static" approximations and indicates the reason why their accuracy is frequently good. This expansion may also be useful for estimating an upper limit to the frequency band in which the dispersion does not exceed a specified value. A numerical example is included.     

Higher Order Mode Cutoff in Polygonal Transmission Lines (Short Papers)

This paper provides an analytical solution to the problem of determining the cutoff wavelength of the first higher order mode in any transmission line having as its conductors a pair of coaxial, similar, similarly oriented regular polygons. The method is based on the cross-sectional resonance technique. It is shown that, under certain circumstances, the requirement that the polygons be coaxial can be relaxed and a solution still obtained in this way.     

Open-End and Edge Effect in Microstrip Transmission Lines (Short Papers)

An empirically derived relation is reported which accurately describes the open-end effect in microstrip transmission lines on alumina substrates. This empirical equation was used to describe the edge-correction term in Wheeler's general expression for the characteristic impedance for wide lines. It is shown that with this modification there exists a distinct crossover (w/h /spl ap/ 1) between the narrow- and wide-line approximations.     

Computation of the Impedance of an Infinitely Long Helical Transmission Line by Numerical Methods (Short Papers)

A numerical method is given for the determination of the impedance of an infinitely long thin-wire helix. The propagation constant of the current for zero tangential electric field is found and used in a variational expression for impedance. Asymptotic values of resistance versus pitch are compared with resistances of infinitely long straight-wire antennas.