Closed form Greens functions for general sources and stratified media

Cataloged from PDF version of article.The closed-form Green's functions of the vector and scalar potentials in the spatial domain are presented for the sources of horizontal electric, magnetic, and vertical electric, magnetic dipoles embedded in general, multilayer, planar media. First, the spectral domain Green's functions in an arbitrary layer are derived analytically from the Green's functions in the source layer by using a recursive algorithm. Then, the spatial domain Green's functions are obtained by adding the contributions of the direct terms, surface waves, and complex images approximated by the Generalized Pencil of Functions Method (GPOF). In the derivations, the main emphasis is to put these closed-form representations in a suitable form for the solution of the mixed potential integral equation (MPIE) by the method of moments in a general three-dimensional geometry. The contributions of this paper are: 1) providing the complete set of closed-form Green's functions in spectral and spatial domains for general stratified media; 2) using the GPOF method, which is more robust and less noise sensitive, in the derivation of the closed-form spatial domain Green's functions; and 3) casting the closed-form Green's functions in a form to provide efficient applications of the method of moments. © 1995 IEE

Broad-band microwave amplifier design considerations

Broad-band microwave integrated circuit (MIC) amplifier design is a complex, multi-disciplinary process. This work focuses on three important aspects: the behaviour of microstrip transmission lines, discontinuities, and related structures; the accurate measurement of components and devices mounted in microstrip circuits; and the circuit design methodology. Techniques for microstrip quasi-static analysis are reviewed in order to identify methods suitable for extension to deal with the effects of substrate anisotropy. An integral equation method is described and the anisotropic Green's function derived using an extension to the method of partial images. Proposed transform methods are assessed and the preferred option implemented by adaption of a microstrip analysis computer program. A method, by which accurate measurements of microstrip properties may be made, is developed. Involving measurements of the resonant behaviour of half-wavelength short circuit resonators with two arbitrary coupling conditions, this technique allows the unloaded properties to be deduced. Results for microstrip on a sapphire substrate concur with the analysis. A pragmatic but effective approach to the calculation of the capacity component of microstrip discontinuities, and some other three dimensional MIC structures, is described and developed to allow existing data for isotropic substrates to be applied to the anisotropic situation. The computer corrected network analyser (CCNA) is a widely used microwave measurement tool. Weaknesses in popular correction strategies are identified and remedies developed. In particular, revised calibration equations that better accommodate test port mismatch variation with s-parameter selection, and a model for quadrature error are presented. A 2-port calibration scheme suitable for use with MIC transmission lines, using only simple standards, is described. The standards are partially self-calibrating;the values of propagation constant, loss, and end effect are deduced in the calibration process. An effective jig for use with microstrip is described and the results of measurements on microwave transistors presented. Conventionally microwave amplifiers are designed using reactive components both to achieve good port matches and compensate the frequency dependent gain of the active devices. The problems associated with this approach are enumerated and the alternatives reviewed. A methodology which combines the benefits of frequency dependant dissipative networks with the elegance of reactive network synthesis is described. The device gain slope is compensated by simple lumped or distributed circuits incorporating a resistive element to produce a composite `device' with a specififed (flat) maximum available gain frequency response. Reactive matching networks are then used to interface these gain blocks. By this structured approach the amplifier gain breakdown can be defined at the outset and preserved through the design process. Other advantages stemming from the use of dissipative compensation include improved tolerance to device parameter and component value scatter, reduced group delay variations and enhanced reverse isolation. The method is demonstrated by the design and characterisation of 4 to 9 GHz amplifier having a representative specification. The close conformance of the performance of the untrimmed amplifier to that predicted by computer simulation testifies to the inherent accuracy of the design method, the microstrip (and related structures) analysis techniques and the CCNA MIC calibration scheme

ANALYSIS AND DESIGN OF PLANAR ACTIVE AND PASSIVE QUASI-OPTICAL COMPONENTS USING NEW FDTD TECHNIQUES

PhDNew Quasi-optical sensor technology, based on the millimetre and submillimetre band of the electromagnetic spectrum, is actually being implemented for many commercial and scientific applications such as remote sensing, astronomy, collision avoidance radar, etc. These novel devices make use of integrated active and passive structures usually as planar arrays. The electromagnetic design and computer simulation of these new structures requires novel numerical techniques. The Finite Difference Time Domain method (FDTD) is well suited for the electromagnetic analysis of integrated devices using active non-linear elements, but is difficult to use for large and/or periodic structures. A rigorous revision of this popular numerical technique is performed in order to permit FDTD to model practical quasi-optical devices. The system impulse response or discrete Green's function (DGF) for FDTD is determined as a polynomial then the FDTD technique is reformulated as a convolution sum. This new alternative algorithm avoids Absorbing Boundary Conditions (ABC's) and can save large amounts of memory to model wire or slot structures. Many applications for the DGF can be foreseen, going beyond quasi-optical components. As an example, the exact ABC based on the DGF for FDTD is implemented for a single grid wall is presented. The problem of time domain analysis of planar periodic structures modelling only one periodic cell is also investigated. Simple Periodic Boundary Conditions (PBC) can be implemented for FDTD, but they can not handle periodic devices (such as phased shift arrays or dichroic screens) which produce fields periodic in a 4D basis (three spatial dimensions plus time). An extended FDTD scheme is presented which uses Lorentz type coordinate transformations to reduce the problem to 3D. The analysis of non-linear devices using FDTD is also considered in the thesis. In this case, the non linear devices are always model using an equivalent lumped element circuit. These circuits are introduced into the FDTD grid by means of the current density following an iterative implicit algorithm. As a demonstration of the technique a quasi-optically feed slot ring mixer with integral lens is designed for operation at 650 GHz

High-Performance Computing for the Electromagnetic Modeling and Simulation of Interconnects

The electromagnetic modeling of packages and interconnects plays a very important role in the design of high-speed digital circuits, and is most efficiently performed by using computer-aided design algorithms. In recent years, packaging has become a critical area in the design of high-speed communication systems and fast computers, and the importance of the software support for their development has increased accordingly. Throughout this project, our efforts have focused on the development of modeling and simulation techniques and algorithms that permit the fast computation of the electrical parameters of interconnects and the efficient simulation of their electrical performance

Modeling EMI Resulting from a Signal Via Transition Through Power/Ground Layers

Signal transitioning through layers on vias are very common in multi-layer printed circuit board (PCB) design. For a signal via transitioning through the internal power and ground planes, the return current must switch from one reference plane to another reference plane. The discontinuity of the return current at the via excites the power and ground planes, and results in noise on the power bus that can lead to signal integrity, as well as EMI problems. Numerical methods, such as the finite-difference time-domain (FDTD), Moment of Methods (MoM), and partial element equivalent circuit (PEEC) method, were employed herein to study this problem. The modeled results are supported by measurements. In addition, a common EMI mitigation approach of adding a decoupling capacitor was investigated with the FDTD method

Full-wave analysis of large conductor systems over substrate

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (leaves 137-145).Designers of high-performance integrated circuits are paying ever-increasing attention to minimizing problems associated with interconnects such as noise, signal delay, crosstalk, etc., many of which are caused by the presence of a conductive substrate. The severity of these problems increases as integrated circuit clock frequencies rise into the multiple gigahertz range. In this thesis, a simulation tool is presented for the extraction of full-wave interconnect impedances in the presence of a conducting substrate. The substrate effects are accounted for through the use of full-wave layered Green's functions in a mixed-potential integral equation (MPIE) formulation. Particularly, the choice of implementation for the layered Green's function kernels motivates the development of accelerated techniques for both their 3D volume and 2D surface integrations, where each integration type can be reduced to a sum of D line integrals. In addition, a set of high-order, frequency-independent basis functions is developed with the ability to parameterize the frequency-dependent nature of the solution space, hence reducing the number of unknowns required to capture the interconnects' frequency-variant behavior.(cont.) Moreover, a pre-corrected FFT acceleration technique, conventional for the treatment of scalar Green's function kernels, is extended in the solver to accommodate the dyadic Green's function kernels encountered in the substrate modeling problem. Overall, the integral-equation solver, combined with its numerous acceleration techniques, serves as a viable solution to full-wave substrate impedance extractions of large and complex interconnect structures.by Xin Hu.Ph.D

Review on the Modeling of Electrostatic MEMS

Electrostatic-driven microelectromechanical systems devices, in most cases, consist of couplings of such energy domains as electromechanics, optical electricity, thermoelectricity, and electromagnetism. Their nonlinear working state makes their analysis complex and complicated. This article introduces the physical model of pull-in voltage, dynamic characteristic analysis, air damping effect, reliability, numerical modeling method, and application of electrostatic-driven MEMS devices

Analytical and numerical modeling to address signal integrity issues in mixed signal applications

Signal integrity issues are a major concern in highly integrated and compact mixed signal IC\u27s. This work presents a numerical and analytical method for analyzing and assessing signal integrity issues relating to discontinuities, interconnects, and irregularly shaped power planes through the development of two independent methods. To address the coupling issue the finite difference time domain (FDTD) technique has been used, which is an accurate and robust algorithm capable of analyzing an arbitrary geometry in both the frequency and time domains. The analysis of signal integrity issues is carried out using examples such as transmission lines placed in close proximity, co-planar to co-planar transitions, and board level via interconnects. To take advantage of FDTD\u27s ability to work natively in the time domain an analysis of two closely spaced transmission lines made where a series of digital pulses were applied to one transmission line while a low RF power analog signal is present on the other. Using voltage and current extraction techniques the corruption of the RF signal due to the coupling of the digital waveform is obtained. To address the resonances occurring in a power plane cavity excited due to ground/Vdd bounce an analytical method based on a segmentation technique in conjunction with the cavity model with arbitrary port placement has been developed for irregularly shaped power planes. Using this technique the resonant frequencies and noise coupling for irregular power planes can be accurately computed. Some popular power plane configurations such as the L-shaped and rectangular ring shape are considered and comparisons have been made with the equivalent circuit based transmission line matrix (TLM) method, HFSS, and experimental results. A design methodology has also been developed to shape the power planes so that no resonances occur within the frequency range of interest