To maintain an acceptable level of quality in the production of analog-to-digital converters (ADCs), the linearity metrics of every ADC has to be measured and checked against performance specification limits. As ADCs continue to improve in resolution, their testing has becoming increasingly demanding in terms of test time. In this paper, we demonstrate a technique for reducing the test time for ADCs. The technique is shown to be significantly better than currently available techniques and can be easily integrated into current production test methodologies. Experimental results in simulation and on actual hardware are shown to demonstrate the technique.

The delay time of an inverter or NAND chain at a gate length yielding equal standby current and active current is used as the definition of a maximum Figure of Merit (FOM), FOMmax. The circuit power that occurs under this condition of equal standby and active currents is an equally important measure. This FOMmax technique is particularly useful in characterizing complementary metal-oxide-semiconductor (CMOS) technologies in the deep submicron regime. A knowledge of the exact value of gate length is not necessary to apply the FOMmax methodology.For a fixed supply voltage and gate oxide thickness, node capacitance and transistor drive, and off currents determine the value of FOMmax. The value of gate length at which FOMmax occurs decreases with decreasing supply voltage. FOMmax analysis is applied to the comparison of CMOS technologies using gate oxide thicknesses of 5.7 and 3.8 nm.

The first part of the paper presents the implementation and performance of a new absorbing boundary condition (ABC) for truncating finite element meshes. This ABC can be applied conformally to the surface of the structure for scattering and antenna radiation calculations. Consequently, the computational domain is reduced dramatically, thus allowing the simulation of much larger structures, and results are presented for three-dimensional bodies. The latter part of the paper discusses optimization issues relating to the solver's CPU speed on parallel and vector processors. It is shown that a jagged diagonal storage scheme leads to a four-fold increase in the FLOP rate of the code, and a standard matrix profile reduction algorithm substantially reduces the inter-processor communication.

The focus of the article is the code FEMATS, developed at the Radiation Laboratory of the University of Michigan. FEMATS is a general-purpose code for computing the radar cross-section (RCS) of arbitrary three dimensional targets with material inhomogeneities. It employs state-of-the-art techniques in finite element modeling of open structures, the latest sparse matrix solutions and graphical user interface for pre- and post-processing of the geometry and data files. Although the code has been primarily used for finding the echo-area of targets, FEMATS can be easily extended to solve open domain problems related to antennas, microwave circuits and cellular phones. The power of FEMATS comes from two features inherent in the technique: (i) the ability to model complicated geometries in three dimensions having arbitrary material fillings without code modification; (ii) the O(N) memory requirement of the method due to the employed local mesh termination techniques conformal to the target. This feature essentially implies that the technique scales favorably with problem size and thus very large problems can be tackled with minimal usage of computer memory and time.

Vector absorbing boundary conditions (ABCs) for doubly curved surfaces are presented, and their applicability to finite elements for scattering calculations are discussed. A performance study of these ABCs is carried out in terms of accuracy and computational requirement, and scattering patterns for several targets are included for validation purposes. It is found that accurate far-field results can be obtained by terminating the finite element mesh a fraction of a wavelength from the scattering structure.< >

This paper reviews two hybrid (frequency domain) finite element methods for electromagnetic scattering applications. Specifically, the progress over the last five years or so is reviewed as it pertains to the finite element method when combined with the boundary integral or the absorbing boundary conditions for truncating the computational domain. After a brief presentation of the associated mathematical formulations, we review two and three dimensional applications of the aforementioned methods. In addition, a brief review section on the popular element shape functions is included.

We review the finite-element method for three-dimensional scattering. A feature of this study is the construction of the weak form of the wave equation for dielectric volumes encompassing impedance and resistive surfaces, thus avoiding the introduction of a variational functional. Formulations based on absorbing boundary conditions, and the boundary integral equation for truncating the mesh, are described, and their corresponding discretization schemes are discussed. We place emphasis on large-scale simulations and solution schemes for achieving low memory requirements and code performance on parallel computing architectures. The results that we present demonstrate the robustness and the versatility of the method for large-scale computations.

Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the finite element method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid finite element methods for simulating composite scatterers, conformal microstrip antennas and finite periodic arrays. Specifically, we discuss the finite element method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods and solvers for achieving low memory requirements and code performance on parallel computing architectures.

The computation of scattering from 3D geometries has been carried out using partial differential equation (PDE) techniques and integral equation (IE) methods. As the problem size increases, PDE techniques become more attractive since the required computational resources scale linearly with the number of unknowns. However, for open domain problems like radiation or scattering, one must also consider the efficiency and accuracy of the mesh termination scheme. As is well known, the mesh truncation condition can be exact or approximate. Exact boundary conditions like the combined finite element-boundary integral formulation implemented in Yuan (1990) result in full submatrices that severely limit the problem size. Approximate boundary conditions or absorbing boundary conditions (ABCs) are local in nature and preserve the sparsity of the finite element matrix. The ideal situation would be to enclose the scatterer inside a mesh termination boundary which is of the same shape as the scattering body. In Chatterjee and Volakis (1993), a new absorbing boundary conditions was derived which can be employed on mesh truncation surfaces conforms to the surface of the target. The present authors show how the ABCs in Chatterjee and Volakis can be incorporated into the finite element equations. They also comment on the symmetry of the system for doubly curved surfaces. In the last section, they examine the performance of these ABCs, in terms of computational cost, when applied on mesh termination surfaces conformal to the scattering object.<>

An edge-based finite element formulation with conformal absorbing boundary conditions (ABCs) is presented for scattering by composite three dimensional structures having boundaries satisfying impedance and/or transition conditions. The methodology with its O(N) storage requirement is amenable to large-scale parallelization. Tests have been carried out on a massively parallel architecture with impressive speedups

The finite element method (FEM) with local absorbing boundary conditions has been recently applied to compute electromagnetic scattering from large 3-D geometries. In this paper, we present details pertaining to code implementation and optimization. Various types of sparse matrix storage schemes are discussed and their performance is examined in terms of vectorization and net storage requirements. The system of linear equations is solved using a preconditioned biconjugate gradient (BCG) algorithm and a fairly detailed study of existing point and block preconditioners (diagonal and incomplete LU) is carried out. A modified ILU preconditioning scheme is also introduced which works better than the traditional version for our matrix systems. The parallelization of the iterative sparse solver and the matrix generation/assembly as implemented on the KSR1 multiprocessor is described and the interprocessor communication patterns are analysed in detail. Near-linear speed-up is obtained for both the iterative solver and the matrix generation/assembly phases. Results are presented for a problem having 224,476 unknowns and validated by comparison with measured data.

This brief presents the experimental transient thermal profiles of the cathode surface of a practical potted heater cathode structure (standard 250 Spectra-Mat heater-cathode packaging). Temperature-time history has been obtained experimentally for various input heater power levels. The experimental results have been compared with the theoretical predictions earlier reported [3], and it has been found that in all the cases, the theoretical predictions are within 10% of the experimental results, thus validating the earlier reported theory.

The heat transfer through the porous and/or infiltrated potted heater-cathode structure is simulated by a numerical model. The model includes heat conduction through the porous potting having isometric pore shape and uniform size (310 mum in alumina potting and 20 mum in tungsten cathode pellet), imperfect interface heat transfer effect and radiative boundaries. In addition to the transient state study, a steady-state analysis using the numerical model has also been done on a commercial Spectra-Mat cathode. The predicted results have been compared with the experimental measurements and are found to be in good agreement.

An edge-based finite element formulation with vector absorbing boundary conditions is presented for scattering by composite structures having boundaries satisfying impedance and/or transition conditions. Remarkably accurate results are obtained by placing the mesh a small fraction of a wavelength away from the scatterer.<>

We have investigated the effects of self-heating on the high current I-V characteristics of semiconductor structures using a fully coupled electrothermal device simulator. The underlying physical mechanisms are highlighted from analyses of simulation results for basic resistors and reverse-biased diodes. It is shown that the breakdown in both resistors and diodes is caused by conductivity modulation due to minority carrier generation. In isothermal simulations with T = 300 K, avalanche generation is the source of minority carriers. In simulations with self-heating, both avalanche and thermal generation of minority carriers can contribute to the breakdown mechanism. The voltage and current at breakdown are dependent on the structure of the device and the doping concentration in the region with lower doping. For all structures, except highly doped resistors with poor heat sinking at the contacts, the temperature at thermal breakdown ranged from 1.25T(i) to 3T(i), where T(i) is the temperature at which the semiconductor goes intrinsic. Hence, it is found that T = T(i) is not a general condition for thermal (or second) breakdown. From these studies, an improved condition for thermal breakdown is proposed, based on the rate of minority carrier generation as a function of temperature increase and the rate at which temperature increases with power dissipation in the device. We have numerically verified this condition for the devices studied here.

The authors present the implementation details of a FE-ABC (finite-element absorbing boundary condition) code and describe the numerical considerations involved in optimizing this code. The linear equation solver and the sparse matrix generation were parallelized on the KSR1 (Kendall Square Research) shared-address space distributed-cache architecture with substantial speedup. Benchmarking was also done on the CM-5 (Connection Machine) with encouraging results. The parallel version of the FE-ABC code was run for a 1.5/spl lambda/ /spl times/ 1/spl lambda/ /spl times/ 1/spl lambda/ pec inlet and the monostatic radar cross section compared with measured data for HH-polarization.<>

The eigenvalues of a cavity resonator are computed using edge-based elements, and it is shown that these elements offer significant improvements in accuracy, in addition to being suitable for modeling arbitrarily shaped inhomogeneous regions. A performance comparison between the edge-based tetrahedra and rectangular brick elements is also carried out.<>

A hybrid finite-element formulation has been proposed for characterization of the scattering and radiation properties of microstrip patch antennas and arrays residing in a cavity (Jin and Volakis, 1991). The technique combines the finite-element (FE) and boundary integral (BI) methods to formulate a system for the solution of the fields at the aperture and those within the substrate. In the previous implementation, rectangular bricks/patches were used for a discretization of the cavity volume/superstrate. These elements inherently limit the applicability of the method to rectangular shape patches and cavities, and to specific feed structures. To avoid such restrictions on the geometrical adaptability of the FE-BI method, the authors consider its implementation using tetrahedral/triangular elements for discretizing the cavity volume/aperture. The tetrahedral elements permit excellent geometrical adaptability. The characterization (scattering/radiation) of nonrectangular patches and broadband radiators is considered. The method's ability to model practical shape and corporate feeds is demonstrated and results are presented for the antenna/array radar cross section in and out of the operating band.<>

A FE-ABC (finite-element absorbing boundary condition) solution of the scattering by arbitrary 3-D structures is considered. The computational domain is discretized using edge-based tetrahedral elements. The specifics of the FE-ABC implementation are discussed. Some results are presented in order to demonstrate that remarkably accurate solutions can be obtained by enforcing the ABC a small fraction of a wavelength from the scatterer.< >