Analysis of Lossy Transmission Lines with Arbitrary Nonlinear Terminal Networks

A novel method for transient analysis of Iossy transmission lines with arbitrary nonlinear terminal networks is presented. The uniqueness of this approach is that we develop time-domain Green's functions for the multiport transmission-line systems by terminating the ports in quasi-matched loads. This ensures Green's functions of a short duration. Hence, the amount of frequency-domain data necessary to obtain time-domain Green's functions is modest. These Green's functions are then convolved with the line port voltages. With this technique one can analyze responses of multiconductor transmission lines with arbitrary nonlinear loads (even with memory) as we have at any instant of time Thévenin's equivalent of the linear portion of the system. An example is presented to illustrate the application of this technique to multiconductor nonlinearly loaded transmission lines.     

The time-domain characteristics of a traveling-wave linear antenna with linear and nonlinear parallel loads

The time-domain characteristics of a traveling-wave linear antenna with linear and nonlinear parallel loads are discussed. The fast Fourier transform (FFT) is used to analyze the antenna with a linear parallel load. A numerical time-stepping finite-difference equation method is used to analyze the antenna with a nonlinear parallel load. The nonlinear effect is treated by the Newton-Raphson iteration technique. The effects of various linear and nonlinear parallel loads are examined. Physical insight into the nonlinear parallel loading of the antenna is also given in terms of detected time-domain sinusoidal electromagnetic (EM) waves.     

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     

The Pulsed-Field Multiport Antenna System Reciprocity Relation and Its Applications—A Time-Domain Approach

A novel time-domain approach to the derivation of the pulsed electromagnetic field multiport antenna system reciprocity theorem is presented. The theorem interrelates the field and system properties in two states: the transmitting state and the receiving state. General time-domain Thevenin (voltage-source, impedance-based) and Norton (electric-current source, admittance-based) type equivalent circuits are constructed for antenna systems whose local properties are described in terms of multiport Kirchhoff circuits. Applications to an indoor wireless communication performance analysis and the analysis of cosmic microwave background radiation measurement are briefly indicated. Numerical results are provided for the pulsed-field transfer between two wire loops, a configuration that is representative for the operation of wireless telecommunication systems and for the pulsed-field EM interference analysis in nano-electronic integrated circuit devices.     

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.     

Causal-convolution-a new method for the transient analysis oflinear systems at microwave frequencies

A new convolution-type method is presented for the transient analysis of causal linear systems described in the frequency-domain. The central novelty lies in the proposed method of determining impulse responses in the time-domain, which are interpreted as truly discrete functions corresponding to periodically-extended system functions in the frequency-domain. Such impulse responses map be computed with high numerical efficiency, while having excellent interpolation properties with respect to the original system function. The convolution operations which result are also naturally in the form of a sum-of-products calculation. The method is capable of handling arbitrary excitation signals, and may in principle be readily extended to more general nonlinear analysis. Several examples of the technique are given, including comparisons and validation both using existing methods, analytical results and experimental measurements     

Investigation of tapered multiple microstrip lines for VLSIcircuits

The analysis of tapered, coupled microstrip transmission lines is presented. These lines, used as interconnects between integrated circuit devices, are modeled using an iteration-perturbation approach applied in the spatial domain. From this model, a frequency-dependent scattering parameter characterization is determined. A time-domain simulation of pulse propagation through the tapered, coupled microstrip lines is performed. The frequency-domain scattering parameters are inverse Fourier transformed to obtain the time-domain Green's function. The input pulse is convolved with the Green's function, and a Newton-Raphson algorithm is applied to account for nonlinear loads. Some experimental results are shown, and a simulation approximation is proposed     

A stable solution of time domain electric field Integral equation for thin-wire antennas using the Laguerre polynomials

In this paper, a numerical method to obtain an unconditionally stable solution of the time domain electric field integral equation for arbitrary conducting thin wires is presented. The time-domain electric field integral equation (TD-EFIE) technique has been employed to analyze electromagnetic scattering and radiation problems from thin wire structures. However, the most popular method to solve the TD-EFIE is typically the marching-on in time (MOT) method, which sometimes may suffer from its late-time instability. Instead, we solve the time-domain integral equation by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically and stable results can be obtained even for late-time. Furthermore, the excitation source in most scattering and radiation analysis of electromagnetic systems is typically done using a Gaussian shaped pulse. In this paper, both a Gaussian pulse and other waveshapes like a rectangular pulse or a ramp like function have been used as excitations for the scattering and radiation of thin-wire antennas with and without junctions. The time-domain results are compared with the inverse discrete Fourier transform (IDFT) of a frequency domain analysis.     

A two-dimensional transmission line matrix microwave fieldsimulator using new concepts and procedures

A two-dimensional field simulator for microwave circuit modeling is described. It incorporates a number of recently developed concepts and advanced transmission line matrix (TLM) procedures. In particular, a discrete Green's function concept based on P.B. John's and K. Akhlarzad's time-domain diakoptics is realized, providing a high level of processing power through modularization of large structures at the field level, simulation of wideband matched loads or absorbing walls, modeling of frequency-dispersive boundaries in the time domain, and large-scale numerical preprocessing of passive structures. Nonlinear field modeling concepts are also implemented in the TLM field simulator. It can analyze two-dimensional circuits of arbitrary geometry containing both linear and nonlinear media. The circuit topology is input graphically. Both time-domain and frequency-domain responses can be computed and displayed. The capabilities and limitations of the simulator are discussed, and several microstrip and waveguide components are modeled to demonstrate its important features     

A mixed FDTD-integral equation approach for on-site safetyassessment in complex electromagnetic environments

A mixed finite-difference time-domain (FDTD)-integral equation approach for the evaluation of the power deposition in the human body model immersed in a complex electromagnetic environment is proposed. The advantage of the proposed approach is that safety assessment for exposure to generic sources may be performed on-site, in a few minutes, with high accuracy and without the need of a high-power workstation. The method uses previously stored FDTD-computed impulse responses (Green's functions) of the human body model by integrating them with the complex incident electromagnetic field distribution that can be measured on site. The application of this method to the dosimetry of cellular telephone base station antennas is presented to show its versatility and ease of use     

Transient temperature fields with general nonlinear boundary conditions in electronic systems

Green's function representations of the solution of the heat conduction equation for general boundary conditions are generalized for the nonlinear, i.e., temperature dependent case. Temperature dependent heat transfer coefficients lead to additional terms in the Green's function representation of the temperature field. For a rectangular structure with averaged homogeneous material parameters several types of Green's functions can be chosen especially simple, because of the new representation with the possibility of differing types of boundary conditions for the temperature field and the Green's function. Exact finite closed form expressions for three-dimensional-Green's functions in the time domain using elliptic theta functions are presented. The temperature field is a solution of a nonlinear integral equation which is solved numerically by iteration. The resulting algorithm is very robust, stable and accurate with reliable convergence properties and avoids matrix inversions completely. The algorithm can deal with all sizes of volume heat sources without additional grid generation. Large and small size volume heat sources are treated simultaneously in the calculations that will be presented. Heat transfer coefficients are chosen representing radiative and convective boundary conditions. An extension of the solution algorithm to composed multilayer systems of arbitrary geometry is outlined.     

Hybridization of FDTD and device behavioral-modeling techniques [interconnected digital I/O ports]

We present a systematic methodology for the electromagnetic modeling of interconnected digital I/O ports. Digital drivers and receivers are represented through behavioral models based on radial basis functions expansions. Such a technique allows a very accurate representation of nonlinear/dynamic effects as well as switching behavior of real-world components by means of carefully identified discrete-time models. The inclusion of these models into a finite-difference time-domain solver for full-wave analysis of interconnected systems is presented. A rigorous stability analysis shows that use of nonlinear/dynamic discrete-time models can be easily integrated with standard full-wave solvers, even in the case of unmatched sampling time. A set of numerical examples illustrates the feasibility of this method.     

Application of Deschamps' Graphical Method to Measurements of the Scattering Coefficients of Multiport Waveguide Junctions

A method for measuring scattering coefficients of a multiport waveguide junction is presented. It is based on the application of Deschamps' graphical technique to reduced multiport junctions, and analysis of measurements done with either matched or nearly matched loads terminated at all but the input and output ports. Averaging and least-square fitting are introduced to reduce errors from measurements.     

Scattering parameter transient analysis of transmission linesloaded with nonlinear terminations

An approach for the time-domain simulation of transients on a dispersive and lossy transmission line terminated with active devices is presented. The method combines the scattering matrix of an arbitrary line and the nonlinear causal impedance functions at the loads to derive expressions for the signals at the near and far ends. The problems of line losses, dispersion, and nonlinearities are first investigated. A time-domain formulation is then proposed using the scattering-matrix representation. The algorithm assumes that dispersion and loss models for the transmission lines are available and that the frequency dependence is known. Large-signal equivalent circuits for the terminations are assumed to be given. Experimental and computer-simulated results are compared for the lossless dispersionless case, and the effects of losses and dispersion are predicted     

Dyadic Green's functions inside/outside a dielectric elliptical cylinder: theory and application

Dyadic Green's functions in two regions separated by an infinitely long elliptical dielectric cylinder are formulated in this paper. As an application, the plane electromagnetic wave scattering by an isotropic elliptical dielectric cylinder is revisited by applying these dyadic Green's functions and the scattering-to-radiation transform. First, the dyadic Green's functions are formulated and expanded in terms of elliptical vector wave functions. The general equations are derived from the boundary conditions and expressed in matrix form. Then the scattering and transmission coefficients coupled to each other are solved from the matrix equations. To verify the theory developed and its applicability, we revisit the plane electromagnetic wave scattering (of TE- and TM-polarizations) by an infinitely long elliptical cylinder, and consider it as a special case of electromagnetic radiation using the dyadic Green's function technique. The derived equations and computed numerical results are then compared with published results and a good agreement in each case is found. Special cases where the elliptical cylinder degenerates to a circular cylinder and where the material of the cylinder is isorefractive are also considered, and the same analytical solutions in both cases are obtained.     

Numerical electromagnetic simulator termination de-embeddingtechnique

The authors report a novel approach whereby transmission-line end effects can be assessed by numerical simulation without recourse to the evaluation of the propagation properties of the line interconnecting the termination and excitation signal launch planes. As an example of the new technique, a microstrip open-ended line termination simulated by the finite-difference time-domain method is reported. The simulated results are compared with those obtained for the same structure but by a conventional numerical de-embedding scheme. The method presented is completely general and can be applied to any numerical electromagnetic field simulation method solving one-port or multiport networks     

Derivation of closed-form Green's functions for a generalmicrostrip geometry

The derivation of the closed-form spatial domain Green's functions for the vector and scalar potentials is presented for a microstrip geometry with a substrate and a superstrate, whose thicknesses can be arbitrary. The spatial domain Green's functions for printed circuits are typically expressed as Sommerfeld integrals, which are inverse Hankel transforms of the corresponding spectral domain Green's functions and are time-consuming to evaluate. Closed-form representations of these Green's functions in the spatial domains can only be obtained if the integrands are approximated by a linear combination of functions that are analytically integrable. This is accomplished here by approximating the spectral domain Green's functions in terms of complex exponentials by using the least square Prony's method     

Spectral dyadic Green's function formulation for planar integratedstructures

The problem of the complete determination of the dyadic spectral Green's function for an integrated planar structure with a grounded dielectric slab has been considered and solved in a rigorous way by using the spectral theory of the electromagnetic field. The reciprocity theorem and the geometrical symmetry of the structure have demonstrated the different roles played by the independent terms of the spectral Green's function in the evaluation of the electromagnetic characteristics of the grounded slab excited with a general source. Furthermore, an equivalent circuit representation of the structure, allowing a noteworthy simplification in the determination of the total power, has been obtained. These equivalent circuits and the derived spectral Green's function presented here can be used to analyze and design microstrip antennas of arbitrary shape with a general type of loading, such as matched or unmatched loads, parasitic, and shorting pins     

Extension of Volterra Analysis to Weakly Nonlinear Electromagnetic Field Problems with Application to Whistler Propagation

In this study, Volterra analysis is extended to weakly nonlinear electromagnetic field problems. Generalized Green's functions and their Fourier transforms are introduced. These are used to express the nth order system response explicitly in terms of the system input, Although the theory is developed in general, homogeneous media are assumed in the examples for simplicity. Application of the Volterra approach is illustrated by investigating whistler-mode propagation in a cold collisionless electron plasma. After defining the nonlinear differential equations for propagation at an angle theta to the uniform magnetic field, exponential probing inputs are used to generate the generalized Green's functions. The second-order responses, which are expressed in terms of the generalized Green's functions, are examined in detail. Computer programs are used to numerically evaluate the second-order response to a sinusoidally varying time function.     

An analysis of an N-port microstrip planar disk devicewith an arbitrarily located short circuit post of arbitrary radius

An analysis technique is presented which allows the performance of a multiport microstrip planar disk device with an arbitrarily located internal short circuit (S/C) post of arbitrary radius to be predicted. The analysis approach does not rely on the determination of eigenvalues and yields analytical expressions which are ideal for CAD implementation. The technique allows the electromagnetic fields at the periphery of the disk to be dramatically altered by an appropriate choice of post size and offset. Since the operation of N-port devices is dependent on the peripheral fields, this technique offers a potentially very powerful design tool for the production of planar disk devices