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.     

Time domain Green's functions for lossy and dispersive multilayered media

We have introduced a fast method of calculating the time domain Green's functions for multilayered media. In this paper, we demonstrate the use of this method to compute the scalar potential Green's function for a multilayer lossy dispersive medium on a PEC ground. The strength of the method lies in obtaining the Green's function for many source-to-field distances /spl rho/ and time instances t simultaneously. It only takes 6 min 28 s to compute 100/spl times/336=33 600 space time Green's function points in Matlab on a Pentium III 867 MHz processor with 1 GB of RAM for a multilayered lossy dispersive medium.     

Transient analysis using quasiperiodic forcing functions

The unit step is expressed as a convolution of frequency-modulated sinusoids. The response of a system to the step defined in this manner is then examined, and a method is indicated whereby transient information may be extracted.     

Capacitance computations in a multilayered dielectric medium usingclosed-form spatial Green's functions

An efficient method to compute the 2-D and 3-D capacitance matrices of multiconductor interconnects in a multilayered dielectric medium is presented. The method is based on an integral equation approach and assumes the quasi-static condition. It is applicable to conductors of arbitrary polygonal shape embedded in a multilayered dielectric medium with possible ground planes on the top or bottom of the dielectric layers. The computation time required to evaluate the space-domain Green's function for the multilayered medium, which involves an infinite summation, has been greatly reduced by obtaining a closed-form expression, which is derived by approximating the Green's function using a finite number of images in the spectral domain. Then the corresponding space-domain Green's functions are obtained using the proper closed-form integrations. In both 2-D and 3-D cases, the unknown surface charge density is represented by pulse basis functions, and the delta testing function (point matching) is used to solve the integral equation. The elements of the resulting matrix are computed using the closed-form formulation, avoiding any numerical integration. The presented method is compared with other published results and showed good agreement. Finally, the equivalent microstrip crossover capacitance is computed to illustrate the use of a combination of 2-D and 3-D Green's functions     

Application of Green's functions for analysis of transient thermal states in electronic circuits

This paper presents an approach to the modelling of transient thermal states in electronic circuits using an analytical solution of the heat equation. Fully three-dimensional analytical time dependent solutions are determined with the help of Green's functions. The solution method is illustrated in detail on a practical example, where the results of transient thermal simulations of a real hybrid circuit are compared with infrared measurements.     

General analytical solutions of static Green's functions forshielded and open arbitrarily multilayered media

In this paper, we present for the first time general analytical solutions of the static Green's functions for shielded and open arbitrarily multilayered media. The analytical formulas for the static Green's functions, which are expressed in the form of the Fourier series or the Fourier integrals, have simple form and are applicable to arbitrary number of the dielectric layers. The derivation of the formulas is primarily based on a technique by which a recurrence relation between L layers and L+1 layers is developed. Green's functions for a three-layered dielectric structure are given as an example of the general formulas. These general analytical solutions will provide a new and efficient tool to the analysis of the multilayered medium structures     

Transient and time-harmonic dyadic Green's functions for a perfectly conducting cone

New representations for the time-dependent dyadic Green's functions for a perfectly conducting semi-infinite cone are presented. For the special case of small cone angles and an on-axis source, simplified expressions are given for both the time-dependent and time-harmonic regimes.     

A direct discrete complex image method from the closed-form Green's functions in multilayered media

Sommerfeld integration is introduced to calculate the spatial-domain Green's functions (GF) for the method of moments in multilayered media. To avoid time-consuming numerical integration, the discrete complex image method (DCIM) was introduced by approximating the spectral-domain GF by a sum of exponentials. However, traditional DCIM is not accurate in the far- and/or near-field region. Quasi-static and surface-wave terms need to be extracted before the approximation and it is complicated to extract the surface-wave terms. In this paper, some features of the matrix pencil method (MPM) are clarified. A new direct DCIM without any quasi-static and surface-wave extraction is introduced. Instead of avoiding large variations of the spectral kernel, we introduce a novel path to include more variation before we apply the MPM. The spatial-domain GF obtained by the new DCIM is accurate both in the near- and far-field regions. The CPU time used to perform the new DCIM is less than 1 s for computing the fields with a horizontal source-field separation from 1.6/spl times/10/sup -4//spl lambda/ to 16/spl lambda/. The new DCIM can be even accurate up to 160/spl lambda/ provided the variation of the spectral kernel is large enough and we have accounted for a sufficient number of complex images.     

Rigorous coupled-wave analysis of multilayered grating structures

Using a rigorous coupled-wave analysis, a (2 /spl times/ 2) matrix method in homogenous layered media is generalized for a grating-embedded multilayer structure with (2M /spl times/ 2M) dynamic and propagation matrices in both transverse-electric and transverse-magnetic polarizations, where M is the number of harmonics retained in the field expansion. A numerically stable algorithm to implement the method is described. Numerical results are presented for a diffraction-based optoacoustic sensor that consists of a reflective movable membrane and fixed grating fingers on a transparent quartz substrate and are compared with the scalar diffraction method to illustrate the limited applicability of the scalar approach.     

New closed-form Green's functions for microstrip structures theory and results

This paper presents an efficient technique to evaluate the Green's functions of single-layer and multilayer structures. Using the generalized pencil of function method, a Green's function in the spectral domain is accurately approximated by a short series of exponentials, which represent images in spatial domain. New compact closed-form spatial-domain Green's functions are found from these images using several semi-infinite integrals of Bessel functions. With the numerical integration of the Sommerfeld integrals avoided, this method has the advantages of speed and simplicity over numerical techniques, and it leads to closed-form expressions for the method-of-moments matrix coefficients. Numerical examples are given and compared with those from numerical integration     

Analysis of microstrip wraparound antennas using dyadic Green's functions

The radiation pattern of microstrip wraparound antennas was obtained here using a theory based on dyadic Green's functions for concentric-cylindrical layered media. The dielectric layer that is usually neglected as a first-order approximation was considered here. An asymptotic expression for the dyadic Green's function that takes into account only the space wave is first obtained. Radiation patterns for various radii, permittivities, and thicknesses of the dielectric layer of a microstrip wraparound antenna were obtained using as a source a uniform annular magnetic current obtained by means of a cavity model with conducting magnetic walls. The calculated values of the percent pattern coverage decreases as the thickness and the permittivity of the dielectric layer increase. The influence of the dielectric layer is more pronounced for radiation direction near that of the axis of the cylindrical surface. It is also shown that the radiation patterns at a frequency of 2.0 GHz are not much dependent on the diameter of the antenna for values from 3 to 120 in.     

Electromagnetic dyadic Green's functions for multilayeredspheroidal structures. I: formulation

Dyadic Green's functions (DGFs) and their scattering coefficients are formulated in this paper for defining the electromagnetic fields in multilayered spheroidal structures. The principle of scattering superposition is applied, in a similar form of the DGF in an unbounded medium under spheroidal coordinates, the scattering DGFs due to multiple spheroidal interfaces are expanded in terms of the spheroidal vector wave functions. For the lack of general orthogonality of the spheroidal radial and angular functions, the Green's dyadics are expressed in a different way where the coordinate unit vectors are also combined in the construction, as compared with the conventional form of vector wave eigenfunction expansion. The matrix equation systems satisfied by the coupled scattering (i.e., reflection and transmission) coefficients of the DGFs are obtained so that these coefficients can be solved uniquely. The DGFs can be employed to investigate effects of spheroidal radomes used to protect the airborne or satellite antenna systems and of handy phone radiation near the spheroid-shaped human head, and so forth. Numerical calculations about the applications of the formulated multilayered DGFs are presented in part II of this paper     

Analysis of multilayered periodic structures using generalizedscattering matrix theory

The use of generalized scattering matrix theory is proposed as a fast, efficient approach for analyzing multilayer structures where in each layer is either a diffraction grating or a uniform dielectric slab, and all grating layers have the same periodicity. The overall scattering from the structure is determined by first evaluating a matrix of scattering parameters for each individual layer and then forming a scattering matrix for the entire structure by a procedure analogous to the cascading of networks in circuit theory. Higher-order spatial (Floquet) harmonics, including nonpropagating modes and cross-polarized fields, are taken into account as necessary. The approach is illustrated by computing the reflection coefficient of a multilayered resistive strip grating as a function of frequency     

Thermal analysis of layered electronic circuits with Green's functions

This paper presents a method for thermal simulation of electronic circuits using an analytical solution of the three-dimensional heat equation resulting from an appropriate circuit thermal model. The temperature fields in multilayered structures are computed analytically employing the Green's functions solution method. The entire solution methodology is illustrated in detail on the particular examples of electronic circuits containing multiple heat sources. Compared to the previous papers published by the authors, the method has been extended by including the possibility of simulating imperfect layer contacts. The simulation results are validated with infra-red measurements and results obtained using other methods. Additionally, the discussion of simulation errors caused mainly by different non-linear phenomena is included.     

Rigorous analysis of shielded cylindrical dielectric resonators bydyadic Green's functions

This paper presents a rigorous approach for the calculation of resonant frequencies of a metallic cavity loaded by a dielectric resonator. Tangential fields at the air-dielectric interface are derived from dyadic Green's functions and boundary conditions are applied. Dyadic Green's identity and the boundary element method are used to solve the numerical problem. In order to validate the method, resonant frequencies are calculated for a cylindrical cavity loaded with a dielectric cylinder and compared with available results in the literature. Then resonance is studied for dielectric cylinder in a rectangular cavity. In the case of multiple dielectric resonators in the cavity, the coupling coefficient is computed with an original method based on the use of symmetries     

Green's functions analysis of planar circuits in a two-layergrounded medium

A moment method analysis of planar circuits in a layered medium is developed. The Green's functions of a two-layer grounded medium are used in order to take into account the effect of the surface wave, coupling, and radiation. Interpolation techniques are used to increase computational efficiency. The embedded conductors are modeled with triangular patches. Results for several configurations, including direct and proximity coupled radiators, are in good agreement with measurements and other calculations     

Numerically efficient analysis of planar microstrip configurationsusing closed-form Green's functions

An efficient technique for the analysis of a general class of microstrip structures with a substrate and a superstrate is investigated in this paper using newly-derived closed-form spatial domain Green's functions employed in conjunction with the Method of Moments (MoM). The computed current distributions on the microstrip structure are used to determine the scattering parameters of microstrip discontinuities and the input impedances of microstrip patch antennas. It is shown that the use of the closed-form Green's functions in the context of the MoM provides a computational advantage in terms of the CPU time by almost two orders of magnitude over the conventional spectral domain approach employing the transformed version of the Green's functions     

A generalized scattering matrix method using the method of momentsfor electromagnetic analysis of multilayered structures inwaveguide

The method of moments (MoM) in conjunction with the generalized scattering matrix (GSM) approach is proposed to analyze transverse multilayered structures in a metal waveguide. The formulation incorporates ports as an integral part of the GSM formulation, thus, the resulting model can be integrated with circuit analysis. The proposed technique permits the modeling of interactive discontinuities due to the consideration of a large number of modes in the cascade. The GSM-MoM method can be successfully applied to the investigation of a variety of shielded multilayered structures, iris coupled filters, determining the input impedance of probe excited waveguides, and of waveguide-based spatial power combiners     

Transient analysis of multiple-input integrated digital structures

This paper presents an insight into the transient performance and propagation delay of complex integrated multiple-input structures in relation to a large digital system, taking into account the intrinsic parameters associated with device geometry. Modeling is therefore performed at the gate level. A piecewise linear model is used for the various transient intervals and the analysis employs fixed time steps. Experimental observations give ample evidence of good agreement between the theoretical and computed results, for which various values of input rise and fall times and different values of fan-out, β0, and fTare used. An accurate appraisal of the storage time associated with the gate is thus possible. Detailed solutions determine the main factors that offer scope for improvement for the structure studied, and suggest means of optimizing the transient response using the derived analytical expressions.     

Transient thermal analysis of sapphire wafers subjected to thermal shocks

Rapid heating and cooling are commonly encountered events in integrated circuit processing, which produce thermal shocks and consequent thermal stresses in wafers. The present paper studies the heat transfer in sapphire wafers during a thermal shock as well as the dependence of the wafer temperature on various process parameters. A three-dimensional finite-element model of a single sapphire wafer was developed to analyze the transient heat conduction in conjunction with the heat radiation and heat convection on the wafer surfaces. A silicon wafer was also investigated, for comparison. It was found that the rapid thermal loading leads to a parabolic radial temperature distribution, which induces thermal stresses even if the wafer is not mechanically restrained. The study predicted that for sapphire wafers the maximum furnace temperature of 800 /spl deg/C should be held for two hours in order to get a uniform temperature throughout the wafer.