From a Novel

A methodology for extracting high-frequency IC interconnect transmission parameters directly from S-parameter measurements has been demonstrated using on-chip test structures. The methodology consists of: (1) building on-chip interconnect structures for microwave test, (2) characterizing and subtracting measurement system parasitics, (3) extracting the transmission line impedance and propagation constant (attenuation constant and phase constant) from the calibrated data, and (4) extracting the Telegrapher's Equation transmission parameters (R, L, C, and G). Additional on-chip calibration permits subtraction of pad parasitic effects. This methodology is demonstrated over a 45-MHz to 20-GHz frequency range using an example 1-cm-long, 4- mu m-wide IC interconnect built in an advanced BiCMOS technology. Variations in interconnect impedance and capacitance indicate two signal propagation modes. Significant substrate-based loss is measured at microwave frequencies. >

S-parameter-based IC interconnect transmission line characterization

Four classes of models of the lightning return stroke are reviewed. These four classes are: (1) the gas dynamic models; (2) the electromagnetic models; (3) the distributed-circuit models; and (4) the "engineering" models. Validation of the reviewed models is discussed. For the gas dynamic models, validation is based on observations of the optical power and spectral output from natural lightning. The electromagnetic, distributed-circuit, and "engineering" models are most conveniently validated using measured electric and magnetic fields from natural and triggered lightning. Based on the entirety of the validation results and on mathematical simplicity, we rank the "engineering" models in the following descending order: MTLL, DU, MTLE, BG, and TL. When only the initial peak values of the channel-base current and remote electric or magnetic field are concerned, the TL model is preferred. Additionally discussed are several issues in lightning return-stroke modeling that either have been ignored to keep the modeling straightforward or have not been recognized, such as the treatment of the upper, in-cloud portion of the lightning channel, the boundary conditions at the ground, including the presence of a vertically extended strike object, the return-stroke speed at early times, the initial bi-directional extension of the return stroke channel, and the relation between leader and return stroke models. Various aspects of the calculation of lightning electric and magnetic fields in which return stroke models are used to specify the source are considered, including equations for fields and channel-base current, as well as a discussion of channel tortuosity and branches.

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Review and evaluation of lightning return stroke models including some aspects of their application

Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods.

Integral Equation Methods for Electromagnetic and Elastic Waves

In this paper, a new technique for preconditioning electric field integral equations (EFIEs) by leveraging Calderon identities is presented. In contrast to all previous Calderon preconditioners, the proposed preconditioner is purely multiplicative in nature, applicable to open and closed structures, straightforward to implement, and easily interfaced with existing method of moments (MoM) code. Numerical results demonstrate that the MoM EFIE system obtained using the proposed preconditioning converges rapidly, independently of the discretization density.

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A Multiplicative Calderon Preconditioner for the Electric Field Integral Equation

In the Method-of-Moments (MoM), applied to the Integral-Equation (IE) formulation for scattering or antenna problems, the solution (the unknown current) is approximated by a linear combination of a finite number of basis functions.

Spectral Filtering for Space-Domain Analysis of Periodic Structures

The basic idea of this work is to eliminate the Green's function singularity, without affecting the stability and the accuracy of the integrals, through a proper windowing of the employed Green's function spectrum.

Spectral filtering of the spatial multi-layered Green's function

A stable fast solver is proposed for the EFIE-MoM analysis of problems with significant sub-wavelength details and/or discretization, and overall sizes up to a few wavelengths. The Adaptive Cross Approximation is used to compress the EFIE-MoM matrix, while a Multiresolution preconditioner is used to improve the ill-conditioning associated to the EFIE in the low frequency and/or dense-discretization regime. Numerical results shows the effectiveness of the proposed approach.

MR-preconditioned ACA for sub-wavelength discretization

Accurate numerical models of a given antenna can be derived from measurements using the inverse source technique [1–3]. Using this technique, measured antenna patterns can currently be imported and used as numerical sources in a number of commercial Computational Electromagnetic (CEM) solvers [4–9]. This method has been validated experimentally and the achievable accuracy investigated for both stand-alone and flush-mounted antennas [10–12]. The reported validation activities have been concentrated on flush mounted antennas physically extending from the ground plane. Such antennas can easily be modelled by equivalent currents on a representative structure. In this paper, we investigate the derivation of the numerical model of a measured aperture type antenna, when mounted in a larger flat structure. Following the procedure in [10–12], a numerical model of the aperture is created from measurements of an open-ended waveguide when mounted in a representative ground plane. The accuracy of the model is investigated by comparison of the radiated Near Fields (NF) from the model and full-wave simulations. Future activities, comprise validation with measurements including different CEM tools.

Giuseppe Vecchi

Papers

Spectral Filtering for Space-Domain Analysis of Periodic Structures

Spectral filtering of the spatial multi-layered Green's function

MR-preconditioned ACA for sub-wavelength discretization

Measured antenna models for numerical simulations of antenna placement scenarios

Synthetic Function Expansion with Multi-Grid Approach