The influence of ground-plane width on the ohmic losses of coplanarwaveguides with finite lateral ground planes

In this paper, analytical computer-aided design (CAD)-oriented conformal-mapping approximations are presented for the high-frequency attenuation of symmetric and asymmetric coplanar waveguides (ACPWs) with finite-extent lateral ground planes. A discussion is presented on the effect of ground-plane width on the losses, and design criteria are derived     

非均匀介质中非对称耦合传输线的ABCD参数

采用新的方法推导出非均匀介质中非对称耦合传输线一般A参数(ABCD参数)的解析表达式，给出了以正规模式参量描述的A参数表达式。所得A参数表达式形式简明，物理概念明晰。通过矩阵分块运算，由z参数推导A参数，对所给表达式进行了验证。验证结果表明了所得A参数解析表达式的正确性和本文方法的有效性。并用所推导出的A参数设计计算了非对称支持宽边耦合共面波导开路节级联构成的带阻滤波器。A参数解析表达式的导出为非均匀介质中非对称耦合传输线在三维(多层)微波集成电路中的应用提供了有力的理论工具。     

Characteristics of Some Asymmetrical Coupled Transmission Lines (Short Paper)

In this paper, expressions for the characteristics of some asymmetrical coupled transmission lines are derived. These include expressions for the capacitances, impedances, and phase velocities of asymmetrical coplanar strips, asymmetric coupled striplines, and asymmetric coupled microstriplines. Accuracy of these expressions is compared against available numerical results obtained rising varous numerical methods.     

CAD models for asymmetrical, elliptical, cylindrical, andelliptical cone coplanar strip lines

By the conformal mapping method, we give analytical closed form expressions for the quasi-TEM parameters for asymmetrical coplanar strip lines (ACPSs) with finite boundary substrate. Then, based on the analysis of ACPSs, elliptical coplanar strip lines (ECPSs) and cylindrical coplanar strip lines (CCPSs), and elliptical cone coplanar strip lines (ECCPSs) are studied. Computer-aided-design oriented analytical closed-form expressions for the quasi-TEM parameters for ACPSs, ECPSs, CCPSs, and ECCPSs are obtained. All of the expressions are simple and accurate for microwave circuit designs and are useful for transmission-line theory and antenna theory. The reasonableness of the method and results are verified and various design curves are given     

Closed-Form Expressions for the Current Densities on the Ground Planes of Asymmetric Stripline Structures

In this paper, closed-form expressions for the current density on the ground planes of an asymmetric stripline structure are derived. The derivation utilizes image theory in order to obtain a suitable quasi-static Green's function for this asymmetric geometry. For the special case of a symmetric stripline geometry and the limiting case of a microstrip line, it is demonstrated that the results obtained here reduce to previously derived results. As expected, it is illustrated that the current densities on the ground planes of an arbitrary asymmetric stripline are bounded by the current distribution of a symmetric stripline and that of a microstrip line. The validity of the analytical results is investigated by comparing to numerically obtained results. Finally, expressions are presented for the total ground-plane currents as fractions of the total current on the signal trace     

Characterization of asymmetric coplanar waveguide discontinuities

A general technique to characterize asymmetric coplanar waveguide (CPW) discontinuities with airbridges where both the fundamental coplanar and slotline modes may be excited together is presented. First, the CPW discontinuity without airbridges is analyzed using the space-domain integral equation (SDIE) approach. Second, the parameters (phase, amplitude, and wavelength) of the coplanar and slotline modes are extracted from an amplitude modulated-like standing wave existing in the CPW feeding lines. Then a 2n×2n generalized scattering matrix of the n-port discontinuity without airbridges is derived which includes the occurring mode conversion. Finally, this generalized scattering matrix is reduced to an n×n matrix by enforcing suitable conditions at the ports which correspond to the excited slotline mode. For the purpose of illustration, the method is applied to a shielded asymmetric short-end CPW shunt stub, the scattering parameters of which are compared with those of a symmetric one. Experiments are performed on both discontinuities and the results are in good agreement with theoretical data. The advantages of using airbridges in CPW circuits as opposed to bond wires are also discussed     

Quasi-static analysis of asymmetric cylindrical coplanar waveguides with finite-extent ground

Quasi-static characteristics of asymmetric cylindrical coplanar waveguides (CCPWs) with finite-extent ground are analysed using the conformal mapping technique. Closed-form expressions for the effective permittivity and characteristic impedance of inside and outside asymmetric CCPWs with finite ground are derived. Using these expressions, the effect of various parameters on the characteristics of CCPWs is studied.     

Characteristics of asymmetrical coupled lines of a conductor-backedcoplanar type

This paper presents for the first time a computer-aided design-oriented (CAD) analytical formula for the determination of the characteristic parameters of asymmetrical coupled lines of a conductor-backed coplanar type. Closed-form expressions are developed for evaluating the self and mutual static capacitances based on a sequence of conformal transformations. The derived formulas show excellent accuracy compared to the results produced by a spectral-domain approach     

梯形屏蔽共面波导及共面耦合线特性阻抗的计算

提出了适用于ＭＭＩＣ设计一类新型共面传输线，它包括梯形屏蔽共面波导（ＳＭＣＰＷ）梯形屏蔽共面耦合线（ＳＭＣＣＬ）共面耦全梯形屏蔽线（ＣＣＳＭＬ）推导出用于计算这些传输线的ＴＥＭ参数的解析公式，数值计算结果显示了此类共面传输线的性质。     

Analysis of a new configuration of coplanar stripline

A new configuration of coplanar stripline is presented and analyzed. This configuration is derived by augmenting coplanar stripline (CPS) with electrically wide lateral ground planes on either side of the balanced pair of signal lines. The ground planes should replace line-to-line coupling in complex circuits and eliminate the TE₀ parasitic dielectric slab waveguide mode. Also, the spacing from signal lines to ground planes can be adjusted to change the characteristic impedance. Spectral domain analysis is used to calculate the dispersion characteristics of this transmission line. Analytical expressions for quasi-static values of the line are presented. This configuration of CPS should be useful for balanced high-impedance lines in monolithic microwave integrated circuit (MMIC) and high speed digital circuits     

非均匀介质中的非对称耦合传输线一般情况下散射参数的推导

首次采用新的方法推导出非均匀介质巾非对称耦合传输线在一般情况下的散射参数解析表达式，给出了以正规模式参量描述的非均匀介质中非对称耦合传输线的散射参数表达式，形式简明，物理概念明晰，从理论上证明了所得散射参数的正确性，并结合所得S参数，给出了非均匀介质中非对称耦合传输线的等效网络。为非均匀介质中非对称耦合传输线在三维(多层)微波集成电路中的应用提供了有力的理论工具。     

Analytical formulas for coplanar lines in hybrid and monolithic MICs

Some analytical formulas for the parameters of coplanar lines are discussed and validated; a chart is given for the design of coplanar waveguides on GaAs. The formulas discussed here, together with those presented previously by us (1983) represent a suitable set for the design of coplanar lines for hybrid and monolithic MICs (microwave integrated circuits).     

CAD models of losses for symmetric elliptical and circular cylindrical coplanar strip lines

This article addresses a CAD-oriented closed-form expressions for dispersive and conductor thickness-based line parameters for symmetrical coplanar strip lines (CPS) on a finite-thickness dielectric substrate. The conductor and dielectric losses are also computed. The models are extended to non-planar CPS – elliptical coplanar strip line (ECPS) and cylindrical coplanar strip lines (CCPS). Finally, accurate circuit model for these structures is also presented. The results between 1 and 60?GHz are compared against the results of HFSS and Sonnet and also against the experimental results. The average deviation of the model against the experimental result is 2.06%.     

Analytical analyses of v, elliptic, and circular-shaped microshieldtransmission lines

Several new types of monolithic coplanar transmission lines, v, elliptic, and circular-shaped microshield coplanar waveguide, have been proposed. The characteristic impedance expressions for those transmission lines have been derived using the conformal mapping method (CMM) under the assumption of the pure-TEM propagation and zero dispersion. In the analyses of the elliptic and the circular-shaped microshield coplanar lines, the methods using the graphical approximation and taking the geometric mean value of the upper and the lower bounds to the size of the line are put forward to calculate the characteristic impedance of this two kinds of microshield coplanar lines. The numerical results show the effects of the different shaped microshield walls on characteristic impedances     

Miniaturized Wilkinson power dividers utilizing capacitive loading

The authors report the miniaturization of a planar Wilkinson power divider by capacitive loading of the quarter wave transmission lines employed in conventional Wilkinson power dividers. Reduction of the transmission line segments from λ/4 to between λ/5 and λ/12 are reported here. The input and output lines at the three ports and the lines comprising the divider itself are coplanar waveguide (CPW) and asymmetric coplanar stripline (ACPS), respectively. The 10 GHz power dividers are fabricated on high resistivity silicon (HRS) and alumina wafers. These miniaturized dividers are 74% smaller than conventional Wilkinson power dividers, and have a return loss better than +30 dB and an insertion loss less than 0.55 dB. Design equations and a discussion about the effect of parasitic reactance on the isolation are presented for the first time     

Field distributions in supported coplanar lines using conformalmapping techniques

We use conformal mapping techniques to derive the analytical expressions for calculating the field distributions in supported coplanar lines. Our calculations agree well with the results obtained using the point matching method. Our method is an extension of the approximate technique proposed by Veyres and Hanna (1980), and provides an accurate and fast calculation of the field distributions. This method can be extended to the analysis of other coplanar lines widely used in monolithic microwave integrated circuits (MMIC) and optical integrated circuits (OIC) applications     

Analysis and synthesis of coplanar coupled lines on substrates offinite thicknesses

This paper presents two sets of newly developed CAD-oriented formulas for the evaluation of the quasi-static even and odd-mode characteristics of coplanar coupled lines on substrates of finite thicknesses. The first set of expressions is derived based on the conformal mapping method. Numerical results show that both the even- and odd-mode characteristic impedances and effective dielectric constants computed by these expressions are in good agreement with the results generated by the spectral domain method. The second set of formulas is derived based on a seminumerical approach and can be used to calculate the geometrical parameters of coplanar coupled lines directly from the given electrical parameters, without using an iterative approach. These seminumerical formulas give maximum error in impedance calculation of about 2.0% (c/h<2), over a wide range of impedance and dielectric constant values     

Circuit parameters for single and coupled microstrip lines by arigorous full-wave space-domain analysis

A rigorous full-wave analysis is applied to determine the dispersion characteristics and the impedance matrix of coplanar microstrip lines. It is shown that the impedance definition based on the propagating power and the longitudinal current is the most appropriate one. Examples are given for the single strip, for two coupled strips, either symmetric or asymmetric, and for a three-strip configuration. Some attention is also devoted to the current profiles associated with each eigenmode     

The influence of metallization thickness on the characteristics ofcascaded junction discontinuities of shielded coplanar type transmissionline

A full-wave analysis based on the mode-matching technique is applied to analyze cascaded junction discontinuities of coplanar-type transmission lines, coplanar waveguide (CPW) and finline. Results for a CPW-finline transition, a shielded CPW gap and a symmetric notch incorporating the finite metallization thickness effect are presented. The influence of metallization thickness on the coupling effect exhibited by cascaded junction discontinuities is also presented and discussed     

Third-Order Intermodulation Distortion and Harmonic Generation in Mismatched Weakly Nonlinear Transmission Lines

This paper describes a procedure to obtain analytical expressions for the spurious signals generated in nonlinear transmission lines with impedance mismatch when they are subject to small-signals. Using these expressions one can rapidly extract the nonlinear parameters describing the nonlinear effects due to the conductor, L(i) and R(i) , such as in superconductors, and/or the nonlinear parameters due to the dielectric, C(v) and G(v) , such as in ferroelectrics. The resulting closed-form expressions have been validated by equivalent circuit simulations. Spurious signal measurements on several coplanar waveguide superconducting and ferroelectric transmission lines have been explained by the use of the resulting closed-form expressions.