The modelling of EM leakage into advanced composite enclosures using the TLM technique

The TLM technique has been enhanced to allow the accurate modelling of EM diffusion through advanced composite material shells. This is a significant development owing to the rapidly increasing use of conducting composite materials in aerospace vehicle design. The accurate EM modelling of this class of materials is important for correct design of vehicles with regard to electromagnetic compatibility (EMC). Existing 3-D time-domain TLM models a non-perfectly conducting shell using a resistive sheet (or sheets) to simulate the surface. The results from this model are shown to be slightly inaccurate and require lengthy computer solution times. A separate 1-D, frequency-domain transmission-line model has been developed elsewhere to better analyse the diffusion properties of composite materials. The incorporation of the results from this frequency domain code into the 3-D time-domain TLM algorithm is outlined.     

A METHOD FOR INCORPORATING CHARGED PARTICLE MOTION WITHIN A 2-D TLM FIELD CODE

Charged particle motion is incorporated within a transmission line modelling (TLM) field code to establish a new model which allows the investigation of field-particle interactions. The model is validated by using it to predict the trajectory of moving particles and the field and potential distributions inside a planar diode for which analytical solutions are available. The effect of space charge on the operation of the diode is also investigated. The model is then applied to study in detail a practical electron gun design.     

Spatially weighted numerical models for the two-dimensional wave equation: FD algorithm and synthesis of the equivalent TLM model

In this paper a new TLM model for the two-dimensional wave equation is introduced. It is synthesized directly from a FD algorithm. The FD algorithm is second-order-accurate in both space and time, and is explicitly time-stepped. The spatial derivatives in the FD algorithm are approximated by the weighted combination of two standard central difference stencils, one oriented as usual, the other rotated by 45° with its arms extended by a factor of (2)^1/2. The TLM model is realized as the weighted connection of two original models (with the same geometrical configuration as the FD algorithm). The weighting in the TLM model is accomplished by using a variable intrinsic impedance for specific elemental transmission lines. The FD and TLM methods possess identical dispersion relations if the former is operated at its upper limit of stability. Therefore, under these conditions both represent identical models for the simulation of wave propagation. The propagation characteristics of the new model are investigated and the conditions for approximate numerical isotropy are provided. The numerical implementation (scattering matrix and transfer event) is described. To validate the new model, the calculation of cutoff frequencies of various modes in rectangular waveguide is performed. Comparison with analytical results (for an unfilled waveguide) and other numerical results (for a waveguide partially filled with a dielectric) validate the implementation of the model.     

A computer-aided design of EMC microstrip dipole arrays using nonlinear optimization techniques

This paper describes a method for designing electromagnetically coupled (EMC) printed dipole arrays. The advantages of EMC dipoles include greater bandwidth, higher efficiency, and an easier match to the feed lines, when compared to classically fed printed antennae. The excitation mechanism is provided by a strip transmission line embedded inside the substrate which couples energy parasitically to the microstrip antenna. Electromagnetically coupled microstrip dipoles have been investigated by empirical or approximate analysis techniques. As a result an approximate model has been derived for microstrip dipoles. The method is based on the method of moments solution to an integral equation derived from the approximate Green function for a grounded dielectric slab. The element lengths and offsets and the stub length of the EMC dipole array are determined by the direct search optimization method of Hooke and Jeeves. To show the feasibility of the proposed method, a mathematical formulation and numerical results are presented for Chebyshev arrays. © 1998 Scripta Technica, Electr Eng Jpn, 125(4): 60–66, 1998     

An investigation of the different TLM configurations used in the modelling of diffusion problems

The commonly used transmission-line modelling (TLM) network of one-dimensional diffusion problems often results in unwanted oscillations. Two different TLM configurations (line boundary (LB) and resistance boundary (RB)), are investigated with some techniques necessary to reduce the oscillations. Comparisons between the various LB and RB models addressed in this paper, indicate that, in general, two-dimensional TLM models produce consistently more accurate results.     

Management of spatial and temporal thermal dynamics using TLM

The design of a preliminary spatial thermal control algorithm is described. This is based on the traditional state‐space servo design and exploits the analogy between the transmission line matrix (TLM) method and state‐space. The TLM algorithm involves not only temporal dynamics but also spatial ones. The control algorithm presented here involves estimating an analogous TLM model for the process to be controlled, the states of which are then used to calculate the control signals, across space, to be employed. The performance of the control algorithm is briefly investigated over a range of design parameter values, in order to seek a preliminary insight into parameter selection. Copyright © 2008 John Wiley & Sons, Ltd.     

TRANSIENT ANALYSIS OF n-TIER GaAs MESFET MATRIX AMPLIFIERS BY THE TLM METHOD

The performances of n-tier GaAs MESFET matrix amplifiers are studied in the time domain. The model is developed incorporating the parasitic resistive loss and internal coupling capacitance of the active device. Techniques are contemplated to transform the matrix amplifier into a set of coupled multi-conductor transmission lines. The resultant model is analysed by the TLM method. Impulse responses of 2 × 4 and 3 × 3 matrix amplifiers are investigated. The frequency responses of the amplifiers are obtained through a Fourier transform. Agreement is observed between results obtained by the TLM model and those obtained by other analytical methods or a complicated circuit analysis program. A 5 × 7 matrix amplifier is also analysed to show the advantage of the developed method.     

The efficiency of transmission-line matrix modelling—a rigorous viewpoint

The difference equations of the scalar linear transmission-line matrix (TLM) routine as introduced by Johns for numerically solving the diffusion equation are shown to be isomorphic to Goldstein's correlated random walk model of diffusion. For the infinite homogeneous bar their exact solution is derived algebraically and given in the form of Jacobi polynomials. This puts the TLM algorithm on a sounder mathematical and physical basis. The accuracy in solving the diffusion equation is investigated in general form and thus its astonishing efficiency explained. Several other basic questions of this numerical technique are also discussed.     

Boundary conditions in TLM diffusion modelling

The connection algorithms used in transmission‐line matrix (TLM) modelling of diffusion processes for describing boundary conditions in both link‐line and link‐resistor nodal configurations have been derived. The new algorithms regarding the inhomogeneous Robin condition enhance the capability of the TLM method in simulating thermal or particle diffusion phenomena. A number of boundary treatments in the existing literature have been found to be special cases of our results. The Dirichlet‐type boundary condition is also discussed. TLM numerical results using the new algorithms, particularly with the link‐resistor model for achieving signal synchronization, are shown to be in excellent agreement with the available analytical solutions. Copyright © 2006 John Wiley & Sons, Ltd.     

A TLM MODEL OF TRANSIENT, 2-DIMENSIONAL STRESS PROPAGATION

A TLM nodal structure suitable for modelling the propagation of transient stresses is described. The nodal structure is analysed algebraically using the analogy between TLM and discrete state space control theory. A numerical implementation based on this nodal structure is validated by comparing results generated using the TLM model with those produced using the finite difference approach for the case of pressure applied to a semi-infinite plate.     

Use of lossless transmission‐line segments and shunt resistors for TLM diffusion modelling

In diffusion modelling by means of the transmission‐line matrix (TLM) method, a nodal arrangement of using lossless transmission‐line segments and series resistors is almost exclusively adopted and is currently considered as a standard approach. In this paper, the use of shunt resistors instead of series resistors is shown to represent an equally valid configuration. As a starting point, we have derived the telegrapher's equation in its most general form for TLM modelling of diffusion processes. A general algorithm based on the shunt‐resistor TLM model for implementing a numerical solution of the diffusion equation in multiple dimensions is given. Fundamental analysis and calculated examples confirm that the alternative shunt‐resistor configuration does not exhibit the unwanted absorption effects suggested by a recent paper (Internat. J. Numerical Model.: Electronic Networks, Devices and Fields 2002; 15 :261). Copyright © 2003 John Wiley & Sons, Ltd.     

TLM representation of the hyperbolic heat conduction equation

Many heat transfer situations are adequately described by the parabolic thermal diffusion equation. However, in situations in which very rapid heating occurs or in slower heating regimes for particular materials, the hyperbolic heat conduction equation is a better representation. Here, a parameterized nodal structure for transmission line modelling (TLM) representation of hyperbolic heat conduction processes is devised. A TLM model based on the nodal structure is implemented and temperature field predicted by the model are compared with analytical results for the same physical situation. Copyright © 2002 John Wiley & Sons, Ltd.     

The calculation of radar cross-section (RCS) using the TLM method

The calculation of the radar cross-section (RCS) of complex bodies using the symmetrical condensed TLM method is presented. The technique is based on a near-to-far field transformation of the TLM calculated near fields. Several two-dimensional examples are presented which validate the method. The main advantage of utilizing techniques such as TLM for RCS computation lies in the ability to model arbitrary bodies with complex material compositions.     

Application of the TLM method to two-dimensional scattering problems

In this paper the application of the TLM method to electromagnetic scattering problems is investigated. To achieve the full computational benefits of using a time-domain numerical method, pulse excitation can be applied together with Fourier transformation of an output impulse response to yield frequency-domain results over a wide bandwidth. The configuration of the mesh is the same as that used in FD–TD scattering simulations (i.e., separation of the simulation space into total and scattered field regions). To terminate the exterior boundaries of the mesh, absorbing boundary conditions are applied to absorb the outward travelling waves. The effect of the absorbing boundaries on both time- and frequency-domain results is investigated. Frequency-domain scattered far-field patterns are presented for perfectly conducting square and circular cylinders illuminated by an incident plane wave (TM case). Forward and back scattering cross-section results obtained from a single TLM simulation indicate both the accuracy and efficiency of the method for calculating frequency-domain results over a wide bandwidth.     

建筑物雷电保护系统内部最大磁场强度的计算

雷击建筑物引起的电磁干扰和电磁兼容问题是建筑物雷电防护的重要研究课题。为此,研究了雷击建筑物时防雷系统暂态电流分布以及内部磁场分布的计算。采用传输线模型对防雷系统进行等效,采用时频变换技术对该模型进行求解,并根据电流分布的计算结果采用解析方法对建筑物内部磁场分布情况进行了求解。然后根据计算结果,从参数变化的角度对IEC标准给出的磁场近似计算公式的合理性和适用性进行了分析和验证。结果表明,IEC标准中的近似公式所忽略的"空间位置"和"接地电阻"两个因素对建筑物雷电保护系统内部最大磁场强度的计算精确度影响较大,而其他因素的影响较小。     

On the dispersion of a non‐orthogonal TLM cell

The numerical dispersion of a non‐orthogonal transmission line matrix (TLM) algorithm is for the first time investigated. First of all, the dispersion relation is derived in the most general possible case. Then, the validation is carried out in the analysis of a simple one‐dimensional example. Results show that the theory is in excellent agreement with the numerical simulation. Numerical results concerning various cell shape dispersion characteristics are presented and show some relatively weak numerical dispersion even for rather highly distorted cells. Finally, some indications concerning cell shape selection to minimize the non‐orthogonal TLM cell are proposed. Copyright © 2007 John Wiley & Sons, Ltd.     

A MODIFIED FINITE DIFFERENCE METHOD FOR MODELLING DIFFUSION PROCESSES

A time domain unconditionally stable explicit method is presented which may be used to model processes governed by the diffusion equation such as transient heat flow. Unlike the explicit finite difference routine, the method models the diffusion process within the time step (MPWT). Being explicit, the method (MPWT) may easily account for non-linear physical parmeters and may be compared with the transmission line matrix (TLM) method of diffusion modelling in terms of its utility. Unlike the TLM model, however, the equivalent circuit does not contain inductive components which have no clear physical meaning. The MPWT method is based on a simple resistive and capacitive circuit model, which for short time steps reduces to the explicit finite difference formulation but is stable for large time steps. Good agreement has been found when results obtained using this algorithm are compared with other numerical methods and analytical results.     

Transmission-line modelling of nonlinear reactive components and mutual inductances

Transmission-line models (TLMs) for nonlinear reactive components and mutual inductances are derived. The model for nonlinear reactive components is shown to be an improvement on the previous one. TLM results with the mutual inductance model are compared with the exact solution, and good agreement is found.     

某气象雷达对高度表电磁干扰的预测和分析

为确定系统内电子电气设备协调工作的可能性,应进行系统电磁兼容性的预测分析。分析的结果既可以预测系统满足电磁兼容性的条件,也是为保障电子设备的电磁兼容性而采取实际措施的基础。但是,目前国内对电磁兼容性工程试验和测量的研究还很缺乏。本文以机载无线电高度表和某地面气象雷达组成的系统为例,介绍了一种接收机敏感度的测量方法。依据高度表的敏感度,分析其是否受气象雷达发射的电磁波的干扰。该项测试和分析是气象雷达建设的依据,对解决国内同类问题具有指导意义。     

Application of the symmetrized transmission-line matrix method to the cold modelling of magnetrons

Two- and three-dimensional electromagnetic resonance calculations have been performed on rising-sun magnetron structures. These calculations have been made using the transmission-line matrix method. Cylindrical coordinates have been used in order to facilitate modelling of the essentially cylindrical device. Recent improvements to the TLM technique, such as the development of the symmetric condensed node for electromagnetics, have been fully exploited. The numerical procedure is described, the modelling process is discussed, and the results obtained are evaluated in comparisons with corresponding empirical data.