Slit-Coupled Strip Transmission Lines

Two types of slit-coupled strip-line configuration are presented which are especially useful for the realization of multi-section components using printed-circuit techniques. The slit-coupled configurations described consist of a pair of strips oriented face to face and either parallel or perpendicular to the outer ground planes. Coupling is achieved through a longitudinal slit. Exact conformal mapping solutions of the even- and odd-mode characteristic impedances are arranged in the forms of the design equations for both parallel and perpendicular cases. In order to facilitate design, nomograms are presented for the parallel case which give the physical line dimensions in terms of the even- and odd-mode characteristic impedances. Furthermore, the exact design equations for both parallel and perpendicular broadside-coupled strip configurations, which are considered to be special cases of the slit-coupled configurations, are presented. Formulas for the terminating lines are also included. The proposed parallel-coupled strip transmission line configurations permit smooth variation of coupling and applications to a wide variety of circuit components.     

Symmetric Strip Transmission Line Tee Junction

Several different network forms have been employed previously to characterize the symmetrical strip-line tee junction and the parameters of these networks have been obtained by various means. In this paper the available theoretical and experimental results are systematically correlated. A choice, based on design convenience, is made of the most appropriate network form, and recommendations are given for the values of each of the parameters in this representation. In some ranges, the available data were inadequate, and additional experimental results were taken in order to clarify the recommendations.     

Problems in Strip Transmission Lines

A review is given of characteristic-impedance formulas for shielded-strip transmission lines. From these formulas a set of approximate relationships for the attenuation and Q of a dielectric-filled shielded-strip transmission line is derived. The method makes the standard assumption that the current distribution is that of a lossless line and the surface resistivity that of an infinite-plane condutor. Although this method applies accurately to most other types of lines, in this case an error of the order of 10% is believed to occur due to the failure of the assumptions at the corners of the strip. However, the error is in a direction that makes the computed values conservative, and the accuracy should be sufficient for most practical purposes. The derivation of a correction term is now being attempted. In addition to the discussion of attenuation attention is given in this paper to the design considerations involved in a shielded-strip-line impedance meter, and to some preliminary data obtained with this device. Also the future topics for investigation under this research and development program are mentioned.     

Analysis of Distributed-Lumped Strip Transmission Lines

A calculation method for obtaining characteristic impedances and phase velocities of striplines, which are regarded as consisting of distributed-lumped elements such as so-called wiggly lines, is presented with numerical results. The numerical calculations have been carried out for a) single stripline with slots at the outer edges, b) coupled stripline with rectangular wiggling, and c) coupled stripline with slots at the outer edges. Experimental work has also been accomplished to verify the present method. Results show good agreement with calculations.     

Analysis of Edge-Coupled Shielded Strip and Slabline Structures

A method for the analysis of edge-coupled strip and slabline structures is presented which uses relatively simple algebraic expressions. The described procedure can be used to analyze directional couplers, interdigitated and comb line filters, and any other structures formed by an array of rectangular edge-coupled transmission lines, of arbitrary thickness, situated between two parallel plates. The analysis is complete in that it allows the conversion of the physical dimensions of the structure into a set of admittance parameters which completely describes its electrical behavior, including both conductor and dielectric losses.     

Characteristic Impedances of Multiconductor Strip Transmission Lines

The design of certain log-periodic microwave circuit elements requires a knowledge of the characteristic impedances of a system of four-coupled strip transmission lines. The system of four strip conductors between parallel ground planes is capable of supporting four different TEM modes which have different characteristic impedances. In this paper, the characteristic impedances of the four modes are determined by a variational method. The variational solution is an upper bound to the exact characteristic impedance of the line. In general, the coplanar strip conductors are located at an arbitrary (but identical) displacement from the parallel ground planes. When the separation between the broadside-coupled strips is precisely one-half the spacing between the parallel ground planes, two of the mode impedances may be determined exactly by means of conformal mapping. The variational solutions are compared to the exact solutions for this special case. Because of the "cell image" principle which holds for the problem, the mode solutions presented here also apply to various single- and two-conductor strip transmission lines with arbitrary displacements. As a result, solutions for the following strip line configurations are available from the analysis: a single strip conductor in a trough, or between parallel ground planes; two coplanar strips between ground planes; two broadside-coupled strips in a trough, or between parallel ground planes. An extensive set of curves are presented which show the characteristic impedances of the four modes as a function of the relative dimensions of the strip transmission line.     

Impedances of Offset Parallel-Coupled Strip Transmission Lines

An offset parallel-coupled strip configuration is described, in which the mechanical parameters are strip width, strip offset, and ratio of strip spacing to ground-plane spacing. The electrical parameters are dielectric constant, characteristic impedance, even and odd mode impedance. The configuration is analyzed by conformal rnapping techniques. Explicit design equations are derived in which the mechanical parameters are expressed in terms of the electrical parameters. Illustrative results are presented, and the limitations on coupling strength, characteristic impedance, and strip configuration are discussed.     

Characteristic Impedances of Broadside-Coupled Strip Transmission Lines

Formulas are given for the even- and odd-mode characteristic impedances of shielded coupled strip-transmission-line configurations that are especially useful when close coupling is desired. Applications may be made to wideband coupled-strip-line filters, 3-db directional couplers, and many other components. The cross sections considered are thin broadside-coupled strips either parallel or perpendicular to the ground planes. Modification of the formulas for thick strips is discussed. The derivations are outlined, with particular attention given to the underlying assumption that restricts the use of the formulas to cases of close coupling.     

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.     

Discontinuities in the Center Conductor of Symmetric Strip Transmission Line

A systematic measurements program has been carried out to check the validity of theoretical formulas for the equivalent circuit parameters of a variety of discontinuities in the center conductor of symmetric strip transmission line. These theoretical formulas have been in part previously available and are in part new or modified. Results indicate that, in general, these formulas are adequate for most engineering purposes and that certain of the network parameters can be neglected.     

Calculation of Characteristic Admittances and Coupling Coefficients for Strip Transmission Lines

An integral equation technique is presented which may be used to efficiently compute the Maxwellian capacitance matrix, i.e., the coefficients of capacitance and inductance, for any system of zero-thickness strip conductors located parallel to and between two ground planes, The TEM characteristic admittances for various operating modes and the coupling coefficients can then be obtained from the elements of this matrix. A single computer program based upon this technique can be used to compute the capacitance matrix for any particular strip line configuration desired and would thus be especially valuable to the design engineer who would like to quickly obtain accurate design curves for a previously unstudied configuration of ship conductors. This procedure gives much more accurate results in but a fraction of the computer time required when the more common finite difference equation approach is used, and it avoids the necessity for a separate mathematical analysis for each new strip line configuration, as would be required when using a conformal mapping technique. Illustrative results are given for several different strip-line configurations.     

Finite Element Method Applied to Skin-Effect Problems in Strip Transmission Lines

This paper describes a two-dimensional finite element approach to the quasi-static TEM analysis of shielded or open conducting strips with applications to VLSI parasitic elements and transmission line characteristics of printed circuits. The approach uses a combination of two-dimensional and one-dimensional finite elements to solve the field problems in terms of the magnetic vector potential in the frequency domain. The method and the algorithm can be applied to shielded or open conducting strips and takes into account the skin effect and proximity effect between structures. The ac resistance and reactance calculated by rising this approach can be used as input parameters to a circuit analysis program such as SPICE or similar programs.     

Capacity and Characteristic Impedance of Strip Transmission Lines with Rectangular Inner Conductors

An example of the rigorous solution of a complex region boundary value problem is presented. The particular problem, the electrostatic capacity and characteristic impedance of a strip transmission line, is solved exactly and numerical results are given for a particular geometrical configuration.     

带状传输线直角拐角不连续性问题的研究

非对称带状传输线(ASTL)在LTCC微波集成电路系统中使用广泛,在电路设计过程中经常会遇到直角拐角不连续性部件,因此在分析电路性能时应充分考虑其所产生的传输损耗。在已有的偏心带状线T型接头不连续性等效电路模型基础上,分析了非对称带状传输线直角拐角的不连续性问题。经实例验证发现,所得计算结果与IE3D软件仿真结果吻合良好。     

Unified Approach to Solve a Class of Strip and Microstrip-Like Transmission Lines

This paper presents a unified analytical approach to solve a class of shielded strip and shielded microstrip-like transmission lines with multilayer dielectrics under TEM-wave approximation. The analysis makes use of the variational technique in the space domain combined with the "transverse transmission line" method. Expressions are derived for the capacitance of a single line, coupled two-line and coupled four-line structures. The same formulas can be used for a class of such structures by the substitution of a single parameter, namely, the admittance at the charge plane, which can be obtained using the standard transmission line formulas. Numerical results of two special structures, namely, the broadside-coupled suspended microstrip lines, and broadside-coupled inverted microstrip lines, using two suspended, dielectric substrates are included. The technique presented is the simplest compared to any other analytical procedures reported in the literature.     

A Universal Approximate Formula for Characteristic Impedance of Strip Transmission Lines with Rectangular Inner Conductors

An explicit expression is developed for the characteristic impedance of a microwave strip transmission line with rectangular inner conductor of arbitrary dimensions. The expression is exact for zero thickness and arbitrary width, exact for zero width and arbitrary thickness, and quite accurate (within 3% for the extreme cases of a square inner conductor of dimensions about 0.01 of plate separation, but in most cases of practical interest within 0.1%) throughout the entire range of thickness and width.     

An Analysis of Characteristics of Coplanar Transmission Lines with Finite Conductivity and Finite Strip Thickness by the Method of Lines

The method of lines (MoL) has been applied for analyzing the characteristics of various structures of coplanar transmission lines widely. But in most previous literatures, the metallizations are considered as infinitely thin or PEC(Perfect Electric Conductor). In this paper, the characteristics of coplanar transmission lines (take an example for shielding microstrip lines) with finite conductivity and finite strip thickness are analyzed by MoL and the computation results are shown.     

Planar Transmission Lines

This paper derives formulas for the transmission properties--characteristic impedance and attenuation--in the principal mode of a transmission line consisting of one or two long strips of metal foil embedded in a dielectric material between two long metal strips considerably wider than the central ones. The width and spacing of the central strips is arbitrary, and it is also necessary to take account of their thickness in computing the attenuation. A graphical method is given for evaluating the characteristic impedance in general, and analytic approximations are given for a number of special cases. Finally the question of the leakage of power from between the outer strips is considered briefly.     

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.