Coupled Transmission Lines

An analysis of coupling between a stripline and a rectangular waveguide is presented. Coupling is through small apertures in the form of a circular hole or a narrow rectangular slot. A closed form expression for the normalized field distribution in the stripline, required for the purpose of analysis, is also derived. The theoretical results show good agreement with the experimental results.     

Propagation Parameters of Coupled Microstrip-Like Transmission Lines for Millimeter-Wave Applications

A variational expression is derived for the propagation parameters of coupled microstrip-like transmission lines for millimeter-wave applications using the "transverse transmission line" method. Numerical results are presented for the coupled inverted microstrip lines, and for the coupled suspended microstrip lines. The effects of the top and sidewalls and also of the finite thickness of strip conductors on the even- and odd-mode impedances are studied. The use of a dielectric overlay in equalizing the even- and odd-mode phase velocities is investigated.     

Tapped-Line Coupled Transmission Lines with Applications to Interdigital and Combline Filters

Exact, general, open-wire-line equivalent circuits for tapped-line combline and interdigital arrays are derived using a combination of graph transformations and induction. A significant feature of the equivalent circuits is that they do not require commensurate length sections. The equivalent circuit for tapped-line interdigital arrays is utilzed to develop design equations for tapped-line interdigital filters.     

Time-Domain Simulation of n Coupled Transmission Lines

In this paper, a general SPICE model for n coupled transmission lines is presented. The model consists of two identical transformation networks and n single-transmission-line models. The transformation networks are realized with linear time-invariant voltage-controlled voltage sources (VCVS's) and current-controlled current sources (CCCS's) only. A simplified model designed to simulate connections on multilayer printed circuit boards is also presented. In this case, the coupling model is adequately described by a capacitance matrix C and an inductance matrix L that are Toeplitz, symmetric, and tridiagonal. The particular structure of C and L makes the computation of the parameters of the transformation network extremely easy and efficient because only simple function evaluations (cosines) are required. Furthermore, the transformation network depends only on the number of coupled lines and not on the parameters of those lines. Therefore, a library of such models needs to be determined only once, and only the characteristic impedances and time delays for the single lines have to be recomputed. The simulation results have been compared against expermental results, and the difference between the two is less than 1 percent.     

Coupled-Mode Analysis of Nonuniform Coupled Transmission Lines

The transmission-line equations describing propagation along coupled transmission lines are cast in coupled-mode form so that the roles of the different coupling coefficients and the impedance variation are more directly observable. Restrictions on the various parameters for obtaining directional coupling with nonuniform lines are then discussed and exact solutions for the coupling response of two nonuniform coupled lines with particular variations of the coupling coefficients are presented. The results obtained from the exact closed-form solutions should aid in the design of tapered couplers.     

Parameters of Microstrip Transmission Lines and of Coupled Pairs of Microstrip Lines

A theoretical analysis is presented of microwave propagation on microstrip, with particular reference to the case of coupled pairs of microstrip lines. Data on this type of transmission line are needed for the design of directional couplers, filters, and other components in microwave integrated circuits. The inhomogeneous medium, consisting of the dielectric substrate and the vacuum above it, is treated in a rigorous manner through the use of a "dielectric Green's function" which expresses the discontinuity of the fields at the dielectric-vacuum interface. Results are presented in graphical form for substrate dielectric constants of 1, 9, and 16, and a range of values of width and spacing of the strips. Numerical tables for these and other cases are also available. The tables present capacitance, characteristic impedance, and velocity of propagation of the even and odd normal modes. The method lends itself to the treatment of other geometries which are of practical interest, such as "thick" strips, presence of an unsymmetrically located upper ground plane, etc.     

Coupled Nonuniform Transmission Line and Its Applications

Theory and applications of coupled nonuniform transmission lines are described. Matrix representations of a general coupled nonuniform transmission line are presented, by means of which the behavior of any coupled nonuniform transmission line maybe completely described. Among a wide variety of applications of coupled nonuniform transmission lines, two typical networks, one the coupled nonuniform transmission-line folded all-pass network and the other the coupled nonuniform transmission-line directional coupler, are treated in detail. Equivalent circuit representatious of these two networks are presented, which enable the designer to synthesize them in a greatly simplified manner by making use of the theories now available for more conventional single nonuniform transmission lines. In addition, the properties of these two networks using coupled exponential line are investigated. Design procedure is also given for asymmetrical coupled exponential-line directional couplers having excellent characteristics.     

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.     

Time-Domain Perturbational Analysis of Nonuniformly Coupled Transmission Lines

A method of analyzing the time-domain behavior of a pair of nonuniformly coupled, dispersionless transmission lines is presented. The coupling coefficient of the system is assumed to be slowly varying with position. The set of coupled equations is transformed into a form for which the method of characteristics applies. Instead of numerically integrating the coupled equations, we decouple the equations by writing the solution in the form of a perturbational series. The resulting zeroth-order term corresponds to the inverse transform of the WKB approximation in the frequency domain, which contains only the wavefront and amplitude information. The higher order terms can be directly interpreted as reflections along the lines. Causality is satisfied to all orders. This method has the advantage of easier implementation, and is more versatile than frequency-domain methods as well as the brute-force numerical integration of the coupled partial differential equations.     

Design Parameters of Inhomogeneous Asymmetric Coupled Transmission Lines

The parameters of asymmetric coupled lines in an inhomogeneous medium (mode numbers and mode impedances) are derived in terms of self and mutual static capacitances of the system in the filled and empty structures. These capacitances are computed by using the network analog method. The effect of dispersion is accounted for by introducing an approximate dispersion model. A set of design curves for different geometric configurations are presented which can help in the design of couplers and filters. The obtained numerical results, taking into consideration the dispersion effect, were found to be in a good agreement with the only available published data.     

Dissipation Loss Effects in Isolated and Coupled Transmission Lines

This paper describes a computer-aided analysis of dissipation losses in uniform isolated or coupled transmission lines for microwave and millimeter-wave integrated-circuit applications. The analysis employs a quasi-TEM model for isolated transmission lines and for the even- and odd-mode transmission lines associated with coupled-line structures. The conductor and dielectric losses are then related to equivalent charge density distributions, which are evaluated using a method-of-moments solution. The transmission lines treated by this analysis may contain any number of Iossy conductors and inhomogeneous dielectrics, consisting of any number of different homogeneous dielectric regions. A development is provided to explicitly relate the four-port terminal-electrical performance of directional couplers to evaluated even- and odd- mode loss coefficients. Examples of evaluated losses are presented in graphical form for isolated lines of inverted microstrip and trapped inverted microstrip and edge-coupled microstrip with a dielectric overlay. The analysis accuracy has been confirmed using microstrip and coplanar waveguide configurations. A comparison is made of the total loss characteristics for microstrip, coplanar waveguide, inverted microstrip, and trapped inverted microstrip. Calculations are compared with measurements for the coupled-line structure. Accuracy of the solution and suggested refinements are discussed. Five computer programs are documented.     

Asymmetric Coupled Transmission Lines in an Inhomogeneous Medium

Terminal characteristic parameters for a uniform coupled-line four-port for the general case of an asymmetric, inhomogeneous system are derived in this paper. The parameters (impedance, admittance, etc.) are derived in terms of two independent modes that propagate in two uniformly coupled propagating systems. The four-port parameters derived are of the same form as those obtained for the symmetric case resulting in similar port equivalent circuits for various circuit configurations considered by Zysman and Johnson. The results obtained should be quite useful in designing asymmetric coupled-line circuits in an inhomogeneous medium for various known applications.     

Inductively Compensated Parallel Coupled Microstrip Lines and Their Applications

A simple method using lumped inductors to compensate unequal even- and odd-mode phase velocities in parallel coupled microstrip lines is presented. The singly and doubly compensated cases are analyzed to enable the optimum inductor values and the electrical lengths of the compensated coupled lines to be calculated from closed-form expressions. The technique proposed not only improves the performance, but also yields a more compact design. To demonstrate the technique's broad range of applicability, the compensated coupled-line structure is used to enhance the performance of a 900-MHz Lange coupler, a 1-GHz multisection 10-dB coupler, a 900-MHz planar Marchand balun, and a 1.8-GHz parallel coupled bandpass filter.     

Coupled Strip Transmission Lines with Rectangular Inner Conductors

A method is presented for determining the capacitance of electrostatic fields which have hitherto proved intractable because their solutions required the evaluation of hyperelliptic integrals. The method is illustrated by applying it to the determination of the characteristic impedance of a strip transmission line. The results compare favorably with the results of existing solutions. The method is then used to determine the characteristic impedance of coupled strip transmission lines with inner conductors of rectangular shape. Curves are included which permit the determination of this impedance over a wide range of line proportions.     

Equivalent Circuits of Binomial Form Nonuniform Coupled Transmission Lines

Equivalent circuits of nonuniform coupled transmission lines whose self and mutual characteristic admittance distributions obey binomial form are presented. Telegrapher's equations of these nonuniform coupled transmission lines can he solved exactly rising Bessel functions of fractional order. By decomposing the chain matrix, it is shown that equivalent circuits of these nonuniform conpled transmission lines consist of cascade connections of lumped reactance elements, uncoupled uniform transmission lines and ideal transformers.     

Applications of Optical Fibers for Overhead Transmission Lines

Optical fibers are increasingly in use for overhead transmission lines. Optical fiber cables for overhead transmission lines can be classified into three types; composite type, winding type, and self-supporting type. For the composite type, an FRP-covered optical fiber unit is suitable because of its good thermal and mechanical characteristics. Winding-type fiber cable is least expensive to install on existing overhead transmission lines. A dc arc test showed that the winding type can be applied to a ground wire because of its resistance to lightning. The winding type was applied to the ground wire of a 275-kV line, using a remote-controlled winding machine.     

Two-Port Equivalent Circuits of Two-Wire Parabolic Tapered Coupled Transmission Lines

Two-port equivalent circuits of two-wire parabolic tapered coupled transmission lines (PTCTL) with open or short terminal conditions on the remaining two ports are presented. First, two-port equivalent circuits of PTCTL, whose characteristic admittances increase along the lines, are shown. Second, two-port equivalent circuits of PTCTL, whose characteristic impedances increase along the lines, the dual of the previous circuits, are shown. These two-port circuits of PTCTL are expressed in terms of two equivalent representations, one having mixed, lumped and uniform distributed circuits, and the other consisting of uncoupled nonuniform distributed circuits.     

基于精细积分法的耦合传输线瞬态分析

在耦合传输线的瞬态分析中提出了一种基于精细积分法的龙格-库塔迭代法。这是一种时域内的数值解法，该方法在对电报方程进行空间离散而获得对时间的一阶微分方程之后，没有采用精细计算法，而是采用了龙格-库塔迭代法。避免了大量的矩阵运算，提高了传输线瞬态响应分析的效率。     

The Admittance Matrix of Coupled Transmission Lines (Letters)

An alternate derivation of the admittance matrix of n coupled lines is presented. The method uses the superposition of two modes of excitation analagous to the even and odd mode excitation used for the analysis of two coupled lines. Only mutual capacitance to adjacent lines is considered.     

Periodically Loaded Nonreciprocal Transmission Lines for Phase-Shifter Applications

Nonreciprocal transmission lines periodically loaded with thin metallic diaphragms are analyzed using the wave transmission matrix approach. An approximate equivalent circuit representation of the diaphragm is proposed and discussed. Using this representation, the differential phase-shift and impedance characteristics of the periodically loaded line are computed for assumed parameters, for "shunt-capacitance" and "shunt-inductance" loading. The range of validity of the approximate results is examined using a certain criterion. The differential phase shift for both capacitive and inductive loading is found to be greater than that of the unloaded line and the results show the same general trends as those previously observed experimentally.