Transient analysis of coupled, tapered transmission lines witharbitrary nonlinear terminations

A fast and efficient method of simulating the time-domain transient response of coupled, tapered transmission lines is presented. A time-domain scattering parameter formulation is used to derive the simple closed-form expression for the voltage variables for uniform lossless lines; this expression is applied to tapered lines by dividing the lines into many uniform section. Computational efficiency and stability are achieved using recursive time-domain algorithms. When a quasi-TEM propagation mode is assumed, the method is applicable to nonlinear terminations and inhomogeneous dielectric media. Memory requirements are minimized and are independent of the number of time steps. Simulation results showed good agreement with experimental results     

Coupled mode analysis of forward and backward coupling in multiconductor transmission lines

The nonorthogonal coupled mode theory is extended to the analysis of multiconductor transmission lines by including backward coupling. Coupling coefficients are expressed as overlap integrals of the eigenfields and currents belonging to individual lines. These eigenmode solutions are calculated using the finite-difference time-domain method, which can provide a broadband solution through a single simulation. General termination conditions are given, and scattering parameters of a multiconductor transmission line can be obtained directly by solving the coupled mode equations subject to these termination conditions. As illustrative examples, several configurations of coupled microstrip lines are analyzed, and numerical results are presented. It is observed that both the forward and backward coupling results agree fairly well with results from Advanced Design System Momentum software.     

Dispersionless coupled microstrip over fused silica-like anisotropic substrates

A Green's function for coupled microstrip with cover over anisotropic substrates has been obtained in integral and series form. It is applied to obtain the even- and odd-mode characteristic impedances and normalised phase velocities for fused silica-like substrates. It is shown that, for certain anisotropies, the transmission lines are dispersionless.     

A frequency-domain approach to interconnect crosstalk simulation and minimization

A frequency-domain approach to efficiently simulate and minimize the crosstalk between high speed interconnects is proposed in this paper. Several methods for modeling coupled microstrip transmission lines are discussed. Several possible simulation strategies are also considered. A straightforward yet rigorous frequency-domain approach is followed. This approach can be used for linearly and non-linearly terminated microstrip coupled lines, since it exploits the harmonic balance technique. A typical example of microstrip interconnects is simulated and the results are compared with those obtained in previous work by other authors using time-domain methods. The simulation method proposed in this work yields good accuracy. A crosstalk minimization problem is formulated and solved following the method proposed.     

Radiation from a microstrip amplifier

A full-wave method is presented to investigate radiation from a microstrip amplifier. The spectral-domain dyadic Green's function, which takes into account both radiation and surface waves, is used to formulate an integral equation. The method of moments is then employed to find the current densities in microstrips and, subsequently, the scattering parameters of the amplifier. The radiated space and surface waves that are launched from the amplifier can be further expressed in terms of the dyadic Green's function and current densities. To verify the numerical results of scattering parameters and far-field radiation patterns, a UHF-band microstrip amplifier matching with single stubs has been implemented and measured. The comparison between simulation and measurement shows excellent agreement.     

Spherical wave expansion of the time-domain free-space dyadic Green's function

The importance of expanding Green's functions, particularly free-space Green's functions in terms of orthogonal wave functions is practically self-evident when frequency domain scattering problems are of interest. With the relatively recent and widespread interest in time-domain scattering problems, similar expansions of Green's functions are expected to be useful in the time-domain. In this paper, an expression, expanded in terms of orthogonal spherical vector wave functions, for the time-domain free-space dyadic Green's function is presented and scattering by a perfectly conducting sphere is studied as an application to check numerically the validity and to demonstrate the utility of this expression.     

Frequency- and time-domain analyses of nonuniform lossy coupledtransmission lines with linear and nonlinear terminations

A new technique for the frequency- and time-domain characterization of nonuniform coupled transmission lines is presented in this paper. In the frequency domain, a method-of-moments-based approach is used to compute the 2N×2N scattering parameter matrix of the N-coupled lines using special frequency-dependent basis functions that give good accuracy over very large bandwidths. In the time domain, the structure's S-parameters are used as its Green's function and are combined with source and terminating load conditions to obtain its transient response. The proposed method can account for loss and is particularly suitable for wideband microwave component designs and ultrahigh-speed/large-bandwidth digital interconnects, including nonlinear terminating loads. A detailed formulation of both the frequency- and time-domain approaches is presented. Several examples of two- and three-line structures are analyzed and the results are compared to published results and other computer-aided-design simulations     

A numerical formulation of dyadic Green's functions for planarbianisotropic media with application to printed transmission lines

An integral equation (IE) method with numerical solution is presented to determine the complete Green's dyadic for planar bianisotropic media. This method follows directly from the linearity of Maxwell's equations upon applying the volume equivalence principle for general linear media. The Green's function components are determined by the solution of two coupled one-dimensional IE's, with the regular part determined numerically and the depolarizing dyad contribution determined analytically. This method is appropriate for generating Green's functions for the computation of guided-wave propagation characteristics of conducting transmission lines and dielectric waveguides. The formulation is relatively simple, with the kernels of the IE's to be solved involving only linear combinations of Green's functions for an isotropic half-space. This method is verified by examining various results for microstrip transmission lines with electrically and magnetically anisotropic substrates, nonreciprocal ferrite superstrates, and chiral substrates. New results are presented for microstrip embedded in chiroferrite media     

Condition of modal analysis in time domain of lossy coupled lines

Modal decomposition in the time domain is shown to be applicable to lossy coupled transmission lines of equal width. It is rigorous for two lines and is a good approximation for more than two lines. This allows a direct time-domain simulation of buses made of microstrip lossy lines on chip or on board in digital circuits     

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.     

Effect of the Dielectric Anisotropy on the Propagation Properties of Microstrip Tapers with Height Variations

This paper deals with the design and application of nonuniform microstrip transmission lines on anisotropic substrates. A rigorous analysis is based on the use of Hertz vector potentials, moment method and transmission line theory to determine the dispersion characteristics of single and coupled tapered microstrip lines for accurate performance prediction. Results are presented for the main parameters providing the necessary information to design several devices on tapered microstrip, with variation on the strip width and dielectric height, for (M)MIC and antennas applications. A good agreement was observed with the results available in the literature for tapered lines on isotropic substrates.     

Dispersion characteristics of square pulse with finite rise time insingle, tapered, and coupled microstrip lines

The distortion of an electrical pulse, with finite risetime (quadratic-linear-quadratic transition) caused by dispersion as it propagates along a uniform microstrip, a tapered microstrip and a coupled pair of microstrips is investigated. Closed-form analysis equations for single and coupled microstrips are used to find the frequency-dependent phase velocities. Results are presented for two different taper profiles: exponential and triangular distributions. It is concluded that the optimization of the profile will provide the least pulse distortion     

Speedy computation of time-domain Green's function for microstripstructures

A speedy computation of the time-domain Green's function for microstrip structures is performed. The spatial Green's function in the frequency domain is written as the sum of real- and complex-image terms, which are respectively converted into the time domain analytically and numerically via fast Fourier transforms. The coefficients of the complex-image terms are both space and frequency independent and are computed only once, which results in a speedy algorithm     

Time-domain Green's functions for microstrip structures using Cagniard-de hoop method

Time-domain Green's functions are required for transient analyzes of many structures using the time-domain integral equation method. In this paper, we express the generalized reflection coefficient of the microstrip structure in terms of a geometric optics series so that by applying the Cagniard-de Hoop method to each term of the series, we can derive the time-domain Green's function. It is demonstrated that this series converges rapidly and there are two contributing waves from each source image if the observation point is beyond the total internal refraction location. The two waves are the direct wave from the image and the head wave from the image to the critical point, and then laterally along the surface to the observer. Each contribution is a definite integral that is evaluated for each point in space and time. Therefore, the derived Green's function is efficient for time-domain simulations compared with conventional approach, in which for each point in space and frequency a Sommerfeld type integral is involved and then the frequency-domain data is converted into time-domain by discrete Fourier transform. This rigorous Green's function can also be used to check the accuracy of other approximate methods such as those using the discrete complex image theory.     

Simulation of high-frequency integrated circuits incorporatingfull-wave analysis of microstrip discontinuities

Incorporates full-wave simulation of microstrip interconnects into circuit analysis and shows how predicted responses diverge from those based on models from a modern microwave-circuit CAD package. A method is presented for characterizing microstrip interconnects and discontinuities through the method of moments applied to a mixed-potential integral equation. The speed is greatly improved through the use of a recently published techniques for rapid evaluation of microstrip spatial Green's functions. A microstrip circuit element is analyzed separately with this procedure, and scattering parameters are extracted from the computed current density. These parameters are passed to a circuit simulator, where small- and large-signal analyses reveal how differences in interconnect modeling affect predicted responses     

A compact recursive trans-impedance Green's function for the inhomogeneous ferrite microwave circulator

A detailed analytical investigation of the circular ferrite circulator is provided in this paper. The ferrite is assumed to be radially inhomogeneous as a result of an azimuthally invariant demagnetization field. The cavity model of Bosma and the stratified ferrite model of Krowne and Neidert are used to construct a compact recursive Green's function in terms of wave impedances and azimuthal modes. The Green's function logarithmic singularity is treated separately and extracted to improve the convergence characteristics of the modal series. The impedance parameters of the circulator are obtained via an integration of the Green's function and its singular term; to obtain the scattering parameters, various matrix manipulations of the impedance parameters are invoked. Data are provided and compared with independent sources to demonstrate the veracity of the Green's function approach. Finally, a circulator design is offered using the Green's function method and scattering-parameter data associated with that design are compared with data from a three-dimensional finite-element electromagnetic simulation of a microstrip circulator. The correlation between both data sets further supports the validity of the inhomogeneous cavity model and the Green's function approach.     

一种小型平面超宽带天线的设计与研究

提出了一种新颖的小型平面超宽带(UWB)天线.该天线由微带槽天线的基本结构变形而来,为获得超宽带频率特性,设计时馈电微带线采用了渐变结构的叉形调谐支节,金属底板的开槽设计成对称多边形.首先通过数值计算来获得最佳的天线几何尺寸,并制作了实际的样品.对天线的反射特性、方向图以及增益都进行了测试,然后利用时域有限差分(FDTD)方法计算了天线收发脉冲信号的保真度.研究结果显示该天线具有良好的超宽带特性.     

Nonuniformly coupled microstrip transversal filters for analog signal processing

The Fourier transform relationship between frequency response and impedance profile for single nonuniform transmission lines is used to derive the time-domain step response of single and coupled nonuniform lines. The expression for the step response of a characteristically terminated nonuniformly coupled transmission line structure is shown to correspond to the characteristic impedance profile. By using this relationship, any arbitrary step response can be realizing by utilizing nonuniformly coupled strip or microstrip lines for possible applications as waveform-shaping networks and chirp filters. A numerical procedure to compute the step response of the nonuniform coupled line four-port is also formulated in terms of frequency-domain parameters of an equivalent cascaded uniform coupled line model with a large number of sections. Sinusoidal and chirp responses are presented as examples that are readily implemented using coupling microstrip structures. The step response of an experimental nonuniformly coupled microstrip structure is presented to validate the theoretical results.<>     

Riccati matrix differential equation formulation for the analysisof nonuniform multiple coupled microstrip lines

A Riccati matrix differential equation (RMDE) is formulated for analyzing nonuniform coupled microstrip lines (NCML's) in the frequency domain. The formulation is based on a reciprocity-related definition in the theory of multiconductor transmission lines under quasi-TEM assumption. The hybrid-mode nature of modal phase velocities and strip characteristic impedances for multiconductor microstrip structure is included. The nonlinear RMDE is first transformed into a first-order linear differential matrix equation which can be efficiently solved using method of moments. A convergence study is performed to investigate the sufficient number of basis functions used in the method. The voltage-scattering parameters of a tapered microstrip and two three-line structures are presented. The frequency responses of a pair of nonuniform coupled lines are measured and compared with calculated results     

An asymptotic closed-form microstrip surface Green's function forthe efficient moment method analysis of mutual coupling in microstripantennas

A relatively simple closed-form asymptotic representation for the single-layer microstrip dyadic surface Green's function is developed. The large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the air-dielectric interface. This asymptotic solution remains surprisingly accurate even for very small (a few tenths of a free-space wavelength) lateral separation of the source and field points. Thus, using the present asymptotic approximation of the Green's function can lead to a very efficient moment method (MM) solution for the currents on an array of microstrip antenna patches and feed lines. Numerical results based on the efficient MM analysis using the present closed-form asymptotic approximation to the microstrip surface Green's function are given for the mutual coupling between a pair of printed dipoles on a single-layer grounded dielectric slab. The accuracy of the latter calculation is confirmed by comparison with numerical results based on a MM analysis which employs an exact integral representation for the microstrip Green's function