A new boundary description in two-dimensional TLM models ofmicrowave circuits

A boundary representation for the two-dimensional transmission line matrix (TLM) method of numerical analysis is described. In conventional TLM simulations, boundary conditions are realized by introducing the appropriate impulse reflection coefficients halfway between two nodes. Since the total field quantities are only defined on the nodes, their values at the boundary are not directly available from TLM solutions. The TLM procedure is modified so that boundaries can be placed across the nodes. The boundary conditions in TLM can then be formulated in terms of the field boundary conditions derived from Maxwell's equations rather than in terms of impulse reflection coefficients. The essential differences between the conventional TLM and the proposed procedure are presented. Examples are given for several typical problems, and the results obtained with the two methods are compared. These are found to be in excellent agreement     

TLM coefficients with distributed losses

In TLM modelling of lossy systems, instead of concentrating losses in lumped resistors or stubs, an attempt is made to model the losses as distributed, in the `connect' or `propagate' stage, while leaving the scattering lossless. TLM transmission and reflection coefficients are derived using a novel, distributed, quasi-black box approach. The coefficients agree with those from lumped resistor analysis. The implications are discussed in the context of lossy TLM modelling in general     

Modeling of general constitutive relationships in SCN TLM

The modeling of general constitutive relationships in SCN (symmetrical condensed node) TLM is presented. The technique consists of decoupling the impulse scattering at the nodes from equations describing the medium by using equivalent node sources with state-variable formulation of the constitutive relationships. The procedure requires few modifications of TLM. Numerical examples are presented     

Moment method solution of double step discontinuities in waveguides

The problem of scattering of a double step waveguide discontinuity is investigated. Two coupled sets of equations in terms of the unknown magnetic current sheets on the apertures are obtained and solved for the electric field distribution using the moment method. The scattering matrix coefficients describing reflection, transmission, and mode conversions at a symmetric double step waveguide discontinuity are obtained and presented graphically for specific junctions.     

Spectral estimation for the transmission line matrix method

The transmission line matrix (TLM) method for microwave circuit analysis calculates the time-domain variation of the electromagnetic fields in response to an arbitrarily chosen excitation. Spectral estimation for the TLM method by use of the discrete fourier transform and fast Fourier transform is reviewed. Error bounds are given and checked by means of a numerical example. A spectral estimation method based on Prony's method for use with TLM is presented. A numerical example shows that the method allows an order of magnitude reduction in the number of iterations in the TLM method for equal accuracy     

The frequency-domain transmission line matrix method-a new concept

A frequency-domain transmission line matrix (TLM) method for the frequency-selective S-matrix computation of 3D waveguide discontinuities is presented. It combines the flexibility of the conventional TLM method with the computational efficiency of frequency-domain methods. The basis for this technique is the excitation of an impulse train of sinusoidally modulated magnitude, which retains the form of an impulse while its envelope contains the information of the structure at the modulation frequency. Utilizing the diakoptics technique in conjunction with the concept of the intrinsic scattering matrix, the original electromagnetic field problem is simplified to a matrix algebra problem. A variety of structures have been analyzed in order to check the accuracy of the approach, and excellent agreement has been observed in all cases. S-parameters for CPW air-bridges including finite thickness and conductivity of the metallizations are computed. The effect of superconducting air-bridges is analyzed     

Application of the TLM method to transient thermal simulation ofmicrowave power transistors

The transmission line matrix (TLM) explicit method of numerical simulation has been used to model the transient thermal properties of various microwave heterojunction bipolar transistor (HBT's) power structures, used in a pulsed mode. Control of the time step during the simulation is of paramount importance and the paper outlines some of the problems encountered using time step control methods currently published and describes an improved algorithm. This improved time step control method has been implemented in a general purpose 3D TLM transient thermal simulator. Some simulation results are described for a variety HBT transistor structures with very different thermal time constants     

Synthesis of Cascaded Lossless Commensurate Lines

A scattering transfer matrix factorization based algorithm for cascaded lossless commensurate line synthesis is presented. The characteristic impedances of the extracted commensurate lines and the reflection factors of the remaining networks are formulated in terms of reflection factor coefficients of the whole circuit. There is no need to use root search routines so as to cancel common terms, to get degree reduction. The formulation of the method is explained, and an example is included, to illustrate the implementation of the synthesis algorithm.     

An analysis method for high-speed circuit systems

A new method for analyzing high-speed circuit systems is presented. The method adds transmission line end currents to the circuit variables of the classical modified nodal approach. Then the matrix equation describing high-speed circuit system can be formulated directly and analyzed conveniently for its normative form. A time-domain analysis method for transmission lines is also introduced. The two methods are combined together to efficiently analyze high-speed circuit systems having general transmission lines. Numerical experiment is presented and the results are compared with that calculated by Hspice.     

An efficient algorithm for transmission line matrix analysis ofelectromagnetic problems using the symmetrical condensed node

A study of the symmetrical condensed TLM (transmission line matrix) node is presented. The study reveals not only that the characteristic scattering matrix satisfies the law of conservation of energy but also that electromagnetic fields are conserved even for finite node spacing. Using the results of this study, the authors develop an efficient algorithm for TLM analysis using the symmetrical condensed node. This algorithm significantly reduces the number of floating point operations so that the speed of computation is comparable to that of other expanded node analysis schemes. The case of a lossy medium is also discussed. With a better understanding of this symmetrical node and equipped with a fast algorithm, TLM analysis of three-dimensional electromagnetic problems can improve the computer-aided design of microwave and millimeter-wave circuits     

有内置薄板腔体的HEMP屏蔽效能研究

在HEMP(高空核电磁脉冲)平面波照射下,依据传输线理论和波导理论,结合电路原理,分别建立了HEMP在金属腔内传播时的等效电路模型和信号流图,得到了腔体各部分的等效阻抗以及HEMP 在腔体内传播过程中的传输矩阵和散射矩阵。采用了传输线法(TLM)和广义Beam-Liu-Tesche(BLT)方程法两种快速算法计算有内置薄板的开孔矩形金属腔的屏蔽效能,与仿真计算进行了对比,验证了扩展算法的准确性,并分析了内置薄板的宽度和位置对腔体屏蔽效能的影响。结果表明:两种快速算法均能准确地计算腔体的屏蔽效能;内置薄板越宽,且越靠近中央位置,腔体的屏蔽效能越高,谐振频率越大。研究所得结论可以为电子设备的HEMP防护提供重要的理论依据。     

Application of the TLM method to half-space and remote-sensingproblems

The problem of scattering and radiation in the presence of a material half-space is solved using the transmission line matrix (TLM) method. The TLM method is a general numerical method for obtaining an approximate solution to the time-dependent form of Maxwell's equations in the presence of complex environments. The method requires the discretization of the entire spatial domain of the problem and provides the transient response as well as (through discrete Fourier transform) the frequency domain response. The three-dimensional symmetric-condensed TLM node is applied. A total/scattered field formulation is applied to excite the space. The source used is an electrically short electric dipole and is described analytically in the time-domain. The method is used to calculate near field distributions (in both the time and frequency domain) and the change in source input impedance of a dipole radiator in the presence of a half-space. Numerical simulations relevant to the detection of buried objects are provided     

Representation of symmetrical condensed TLM node

A new and simple transmission line junction to represent the symmetrical condensed TLM node is presented. The required scattering is achieved without the use of ideal transformers, though at the expense of a redefinition of the ports. The junction is intended as a conceptual model but with minor modifications could actually be built.<>     

用TLM法模拟二维三维电磁散射近场和远场

数值模拟二维等腰直角三角形导电柱体和三维方形导电柱体对高斯脉冲平面波的电磁散射近场和远场分布。数值结果表明在三角柱体的电磁散射近场中镜面反射并不明显,但在远场却非常明显并且成为最主要的散射方向。三维电磁散射的数值结果表明,二次辐射是电磁散射的主要机理,并且在多个导体目标情况下,各自的散射场将互相干涉形成总的散射场。     

A class of symmetrical condensed node TLM methods derived directlyfrom Maxwell's equations

A series of general transmission line matrix (TLM)-type methods, which include the symmetrical condensed node method, are derived directly from Maxwell's curl equations without recourse to transmission line models. Written as a system of conservation laws, Maxwell's equations in 3-D plus time are decomposed along the orthogonal characteristic directions of a rectangular grid. The Riemann invariants in this method correspond to the voltage pulses of the TLM method. A new method of handling inhomogeneous media is proposed based on a new transfer event. The dispersive nature of these schemes is also investigated     

Differential equation solutions of MOS transmission line models generalized to lossy cases

Lumped transmission line equivalent circuit models offer a proven technique for calculating small signal admittances of MOS capacitors. Typically, this is done by means of 6 × 6 matrix multiplications. Recently, however, we derived for the lossless MOSC a set of three differential equations which are easier and more convenient to solve than the more general matrix method.Here we review simple circuit topology to explore the fundamental limitations of the three differential equation system and find that minority carrier scattering and bulk recombination losses can be included. Each of these losses contributes an additional term to each of the three lossless equations, resulting in a system of equations that is modular with respect to the inclusion of either of these two losses. The majority carrier scattering loss is more easily taken care of by the matrix method, but is only important at very high frequency (e.g. 10⁷ Hz).     

Huygens and the computer-a powerful alliance in numericalelectromagnetics

A time domain technique based on equivalent transmission line interconnections, referred to as the transmission line matrix model (TLM), is presented. The author retraces the history of TLM, from the original concepts of Huygens to the pioneering work of Peter B. Johns, and on to the latest developments in TLM modeling. The most important two-dimensional and three-dimensional TLM algorithms are explained, and new concepts in time-domain representation of frequency-dispersive boundaries are discussed. Some typical applications are described     

Dispersion in anisotropic media modeled by three-dimensional TLM

The dispersion in anisotropic media modeled by three-dimensional TLM is investigated. Two nodes, the symmetrical condensed node with stubs and the symmetrical super-condensed node are considered. Simple closed-form expressions for the dispersion relations do not exist in general, therefore the investigations are restricted to wave propagation in isotropic media and to wave propagation along the mesh axes and the mesh diagonals. The dispersion analysis for the symmetrical super-condensed node yields a direct relationship between the relative permittivity and relative permeability and the parameters of the scattering matrix     

A New Four-Port Automatic Network Analyzer: Part II--Theory

This paper presents a comprehensive theory of the new four-port network analyzer using only one power detector and one electronically adjustable reference load, (e.g., an adjustable short circuit or a varactor diode) described in a companion paper. A method based on annihilation operators for describing an n-port is introduced. This method is found convenient for analyzing different measurement situations. Hence, schemes for reflection measurements and transmission measurements are analyzed in detail. For evaluation of the reflection (or transmission) coefficient, it is shown that seven (or five) parameters defining the system have to be determined. Calibration schemes for precision reflection and transmission measurements are described.