Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

Characterization of an embedded RF-MEMS switch

An RF-MEMS capacitive switch for mm-wave integrated circuits, embedded in the BEOL of 0.25μm BiCMOS process, has been characterized. First, a mechanical model based on Finite-Element-Method (FEM) was developed by taking the residual stress of the thin film membrane into account. The pull-in voltage and the capacitance values obtained with the mechanical model agree very well with the measured values. Moreover, S-parameters were extracted using Electromagnetic (EM) solver. The data observed in this way also agree well with the experimental ones measured up to 110GHz. The developed RF model was applied to a transmit/receive (T/R) antenna switch design. The results proved the feasibility of using the FEM model in circuit simulations for the development of RF-MEMS switch embedded, single-chip multi-band RF ICs

Temperature-dependent Characterization of Power Amplifiers Using an Efficient Electrothermal Analysis Technique

In this paper, we propose an efficient methodology for the electrothermal characterization of power amplifier (PA) integrated circuits. The proposed electrothermal analysis method predicts the effect of temperature variations on the key performances of PAs, such as gain and linearity, under realistic dynamic operating conditions. A comprehensive technique for identifying an equivalent compact thermal model, using data from 3-D finite element method thermal simulation and nonlinear curve fitting algorithms, is described. Two efficient methods for electrothermal analysis applying the developed compact thermal model are reported. The validity of the methods is evaluated using commercially available electrothermal computer-aided design (CAD) tools and through extensive pulsed RF signal measurements of a PA device under test. The measurement results confirm the validity of the proposed electrothermal analysis methods. The proposed methods show significantly faster simulation speed comparing to available CAD tools for electrothermal analysis. Moreover, the results reveal the importance of electrothermal characterization in the prediction of the temperature-aware PA dynamic operation

Large-signal device simulation in time- and frequency-domain: a comparison

The aim of this paper is to compare the most common time- and frequency-domain numerical techniques for the determination of the steady-state solution in the physics-based simulation of a semiconductor device driven by a time-periodic generator. The shooting and harmonic balance (HB) techniques are applied to the solution of the discretized drift-diffusion device model coupled to the external circuit embedding the semiconductor device, thus providing a fully nonlinear mixed mode simulation. The comparison highlights the strong and weak points of the two approaches, basically showing that the time-domain solution is more robust with respect to the initial condition, while the HB solution provides a more rapid convergence once the initial datum is close enough to the solution itsel

Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition

Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include high-dimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the high-level simulation. In this paper, we develop an efficient ANOVA-based stochastic circuit/MEMS simulator to extract efficiently the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensor-train decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is simulated efficiently by our simulator at the cost of only 10 minutes in MATLAB on a regular personal computer.Comment: 14 pages (IEEE double column), 11 figure, accepted by IEEE Trans CAD of Integrated Circuits and System

Fast, non-monte-carlo estimation of transient performance variation due to device mismatch

This paper describes an efficient way of simulating the effects of device random mismatch on circuit transient characteristics, such as variations in delay or in frequency. The proposed method models DC random offsets as equivalent AC pseudo-noises and leverages the fast, linear periodically time-varying (LPTV) noise analysis available from RF circuit simulators. Therefore, the method can be considered as an extension to DC match analysis and offers a large speed-up compared to the traditional Monte-Carlo analysis. Although the assumed linear perturbation model is valid only for small variations, it enables easy ways to estimate correlations among variations and identify the most sensitive design parameters to mismatch, all at no additional simulation cost. Three benchmarks measuring the variations in the input offset voltage of a clocked comparator, the delay of a logic path, and the frequency of an oscillator demonstrate the speed improvement of about 100-1000x compared to a 1000-point Monte-Carlo method

Time-domain analysis of RF and microwave autonomous circuits by vector fitting-based approach

This work presents a new method for the analysis of RF and microwave autonomous circuits directly in the time-domain, which is the most effective approach at simulation level to evaluate nonlinear phenomena. For RF and microwave autonomous circuits, time-domain simulations usually experiment convergence problems or numerical inaccuracies due to the presence of distributed elements, preventing de-facto their use. The proposed solution is based on the Vector Fitting algorithm applied directly at circuit level. A case study relative to a RF hybrid oscillator is presented for practical demonstration and evaluation of performance reliability of the proposed method