A Novel Power Estimation Method for On-chip VLSI Distributed RLCG Global Interconnects Using Model Order Reduction Technique

Coupling Of Synthesis And Layout: Challenges And Solutions

This paper deals with the optimal design of different VLSI circuits, namely, the CMOS voltage reference circuit and the CMOS ring oscillator (RO). The optimization technique used here is the multiobjective differential evolution algorithm (MDEA). All the circuits are designed for 90 nm technology. The main objective of the CMOS voltage reference circuit is to minimize the voltage variation at the output. The targeted value of the reference voltage is 550 mV. A CMOS ring oscillator (RO) is designed depending on the performance parameters such as power consumption and phase noise. The optimal transistor sizing of each circuit is obtained from MDEA. Each circuit is implemented in SPICE by taking the optimal dimensions of the transistors, and the performance parameters are achieved. The designed voltage reference circuit achieves a reference voltage of 550 mV with 600 nW power dissipation. The reference voltage variation of 8.18% is observed due to temperature variation from −40°C to + 125°C. The MDEA-based optimal design of RO oscillates at 2.001 GHz frequency, has a phase noise of −87 dBc/Hz at 1 MHz offset frequency, and consumes 71 μW power. This work mainly aims to optimize the MOS transistors’ sizes using MDEA for better circuit performance parameters. SPICE simulation has been carried out by using the optimal values of MOS transistor sizes to exhibit the performance parameters of the circuit. Simulation results establish that design specifications are closely met. SPICE results show that MDEA is a better technique for the optimal design of the above-mentioned VLSI circuits.

During lamination, residual thermo-mechanical stresses are induced in the encapsulated solar cells composing photovoltaic (PV) modules. Depending on the material and geometrical configuration of the layers of the laminate, this residual stress field can be beneficial since it may lead to a compressive stress state in Silicon and therefore crack closure effects in the presence of cracks, with a recovery of electrical conductivity in cracked solar cells. It is therefore important to investigate the distribution of thermo-mechanical stresses within the PV laminate with a view to optimizing the coupling between the electrical response and elastic deformation in the operation of PV modules. A promising approach proposed in the present thesis regards the prediction of residual stresses in composite laminates by using a shear-lag theory to model the epoxy-vinil-acetate polymeric layers, accounting for their thermo-visco-elastic response. Moreover, it will be shown that thermomechanical formulations for stress analysis of a PV laminate lead to a system of higher order ordinary differential equations or partial differential equations in which the exact solutions may be impossible to be determined in closed form and hence numerical schemes become desirable. However, the computational cost associated with the implementation of the numerical scheme may be significantly expensive. Therefore, a method to reduce the computational complexity is expected to be very important. To this aim, Model Order Reduction (MOR) techniques are applied hierarchically, first to the thermal system of a PV module in service, and then extended to coupled thermo-mechanical problems. A combination of proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM) with a modified formulation is proposed for the first-order thermal equations of photovoltaic system during service and a new coupled second-order Krylov based formulation is developed for model order reduction of the coupled thermo-mechanical model of the photovoltaic module. The results of these reduction schemes show a huge computational gain in the reduced system solutions and a high accuracy of the reduced system outputs

In this work, a model order reduction (MOR) technique for heat-transfer system-level modeling is presented. A heat transfer solver using the finite difference method (FDM), which is appropriate for MEMS thermal analysis, is implemented. The numerical models generated by the FDM solver then were successfully reduced into low-order compact models by an Arnoldi-based model-order-reduction technique. The compact macromodels can be easily inserted into system-level or circuit simulators. We have demonstrated that the macromodel results for a thermal actuator are in good agreement with the experimental results. We also use the same technique on periodic surface heat flux problems to observe the relationship between frequency and minimum required order of the reduced model under specific error tolerance.

In steam turbines (STs), evaluation technology of thermal deformations during transient operations is increasingly important, because of a demand for improvement of operability such as shortening startup time. However, it is still difficult to predict temperatures of metal parts with sufficient accuracy due to complexity of heat transfer phenomena. The present study puts its focus on developing a method to identify metal temperatures of STs during start-up operations using particle filter (PF), a kind of sequential Bayesian filter utilizing ensemble approximation, and model order reduction (MOR) technique. In this method, a self-organizing state-space model is used to calculate time evaluations of metal temperatures, and heat transfer coefficient (HTC) parameters and steam bulk temperature parameters. And an optimal estimate of these is obtained through iterations of a short-time prediction and a correction of variables using measured temperatures. In this state-space model, state variables including HTC and bulk temperature parameters are treated as random variables, and the time evolution of each variable is modeled as follows; (1) Metal temperature is modeled using a reduced order model (ROM) in order to reduce computational time of PF. The ROM is constructed from a finite element model for unsteady heat transfer analysis using MOR technique. (2) HTC is modeled as a random walk model where its changes during one time step is randomly determined using Gaussian noise. Here, the magnitude of this noise is adjusted automatically. (3) Bulk temperature is modeled using prediction formulas with Gaussian noise added. As a validation problem, a cold start-up operation of a ST unit of a gas turbine combined cycle (GTCC) is considered. The proposed method is applied to the problem, and boundary conditions (BCs) are identified using measured temperatures at 68 measurement points. Then, the heat transfer analysis based on finite element analysis (FEA) is performed using the identified BCs. As a result of this FEA, it is confirmed that the calculated metal temperature tends to agree better with measurements compared with that of initial FEA, and that the errors of the calculated temperature at measurement points reduce by 41% on average compared with initial FEA. From this result, it is concluded that this proposed method is effective for metal temperature identification during start-up operations.

Microgrids (MGs) concepts are a systematic way to integrate the supply and demand side along with the storage devices. These mostly use renewable energy resources (RESs) viz. solar PV and wind turbines, interfaced to the low voltage distribution network via an inverter. As several components are involved, MGs has a system of systems (SoSs) architecture and its modeling leads to form a high order system. Hence, for the controllers' design purposes, these models had to be brought down to a reduced lower order system. This paper performs a comparative study of various model order reduction (MOR) techniques viz. aggregation, balanced truncation (BT), singular perturbation (SP) and Hankel norm approximation (HNA) on a two-source autonomous MG system. The standard performance evaluation methods used for a multi-input multi-output (MIMO) system i.e. the step and impulse responses, eigenvalue analysis and Bode plots were considered to determine the effectiveness of these MOR method.

The proposed research work intends to present a design methodology for obtaining a robust PID/PI controller for interval systems. This research work makes use of Model-Order Reduction (MOR) technique along with Model-Matching approach for attaining the desired controller parameters. The model-matching approach is used to consider a lower-order open-loop transfer function that embodies the desired time-domain / frequency-domain specifications. The primary objective is to make the step response of BLDC motor along with controller in closed-loop that match the open-loop response of the modeled system for the required time-domain characteristics. MOR technique is implemented for the approximation of high-order controller transfer function that has been attained by using a model-matching approach. In the current research paper, the differentiation technique for approximating the higher-order system is adopted along with Kharitonov's theorem for expanding the bounded parameter variation of a Linear BLDC-Motor, which is considered here as a case study.

The reduction of the large order models of complex systems into a sufficiently low dimensional order in such a way that important dynamic characteristics of the real system are preserved, is a nontrivial task. The motivations for such a model order reduction are either to reduce computations for analysis and practical control design or to simplify the control system structure. In the present article, major techniques in model order reduction are briefly discussed. The characteristic similarities and differences are highlighted, their advantages and disadvantages are underlined, and further research requirements and trends are commented upon. Introduction and Perspective One of the central issues in the active control of complex systems such as large flexible space structures (LFSS) is the derivation of a correct mathematical model for both the controlled and the uncontrolled dynamical systems. Theoretically, there are infinitely many elastic modes or degrees of freedom (DOF) in the distributed parameter (DP) models of LFSS, usually with very low natural damping. Moreover, the flexible modes contribute to the actual deformation of the structure.' The truly infinite dimensional character of LFSS models has to be approximated by some fidelity finite (but usually very large) dimensional model. The normal approach taken by engineers to achieve this end is via modal models with a large number of modes that provide a reasonable representation of the spacecraft dynamic characteristics. However, a difficult problem still remains to be the development of a model of lowenough dimensional order that it can be utilized by the onboard controller, yet high enough dimensional order that it preserves the dynamic characteristics of the real system represented and controlled. The motivations for such a reduction are either to reduce computations for analysis and practical control design or to simplify the control system structure. Discretization procedures will not be discussed herein and it will be assumed that a large finite dimensional model has been generated somehow and for implementation and other practical considerations, the model needs to be further reduced. *This work was-supported, in part, by the Air Force Wright Aeronautical, Air Force Systems Command, Flight Dynamics Lab, Structures and Dynamics Division, while the author was employed with HR-Textron, Valencia, California. There are various approaches to model order reduction; some are or pseudo-optimal and others are ad-hoc methods based on practical considerations and engineering experience and judgment. These techniques are known by different names such as reduction, condensation, economization, aggregation, optimal projection, and other combinations thereof. It has often been pointed out that such techniques generally constitute application of Rayleigh-Ritz/Galerkin optimization, and matrix transformation methods to the eigenvalue/eigenvector formulation for structural dynamic problems. The reduction or the condensation methods are based on transformations of the coordinates in the equations of motion that essentially maintain the invariance of the quadratic forms of the potential and kinetic energies. An important feature of these methods is that the reduced order model often loses the basic characteristics of the original system. Considerable progress was made by Likins, Ohkami, and wong5 in this respect. However, they failed to develop a general enough criterion that could reduce the system model in an sense without significantly affecting the eigenvalues of the original model. The optimization or the mathematical reduction procedure, on the other hand, is based on the reduction of the eigenvalue problem to a smaller size based on some optimality criterion (usually quadratic). In these techniques, the reductions are carried out without actually resorting to approximations, i .e. , without truncatiag any coordinates or states of the original system. Balanced model reduction of linear timeinvariant dynamical systems is essentially based on the controllability and observability relations of the states of the system. Subsystem models are obtained by deleting those states that contribute the least to the controllability and observability (or the impulse response) of the original system7 and thus are only in this sense. A more recent approach to model reduction is proposed in Skelton's work,* where each state of the system model is assigned a relative to a given basis, via a quadratic criterion, and the states with the least cost are deleted in a systematic manner. The resulting reduced model is a function of the state-space basis, and thus there is no guarantee for optimality for all choices. The latest development in model order reduction techniques is the work by Hyland and erns stein.^ Herein first order necessary conditions for reduced order modeling of linear time-invariant systems are derived via a pair of modified Lyapunov equations coupled by a nonorthogonal projection. This approach reveals the possibility of multiple extrema forsome of the abovementioned methods. Copyright @ 1988 by the American Institute of Aeronautics and Astronautics. Inc. All Rights Reserved.

With the ever-increasing complexity, circuit verification at the full-chip level is a major bottleneck in the design of VLSI circuits. This paper presents procedures that verify a given CMOS/BiCMOS VLSI circuit for its compliance to a set of pre-defined rules or design styles. Predefined rules range from simple connectivity and sizing rules to specific circuit topologies ensuring acceptable circuit speed, reliability, and signal integrity. Our compliance checks operate on transistor-level circuit netlists, which may contain back-annotated parasitics. The procedures and rules have been implemented in a checker called Elecdra. VLSI circuits with over 3 million devices have been successfully verified by Elecdra at the full-chip level.

Many new promising model order reduction (MOR) methods and algorithms were developed during the last decade. Industry and academic research institutions intend to test, validate, compare, and use these new promising MOR techniques with their own models. Therefore, an MOR toolbox bridging the gap between theoretical, algorithmic, and numerical developments to an end-user-oriented program, usable by non-experts, was developed called ‘Model Order Reduction of Elastic Multibody Systems’ (Morembs). A C++ implementation as well as a Matlab implementation including an intuitive graphical user interface is available. Import from various FE programs is possible, and the reduced elastic bodies can be exported to a variety of programs to simulate the compact models. In the course of the various projects, many improvements on the algorithmic side were added. As we learned over the years, there is not one ‘optimal’ MOR method. ‘Optimal’ MOR depends on circumstances, like boundary conditions, excitation spectra, further model usage. The toolbox is now used, e.g., in solid mechanics, biomechanics, vehicle dynamics, control of flexible structures, or crash simulations. In all these use cases, the toolbox allows the user to facilitate their well-known modeling and simulation environment. Only the critical MOR process during preprocessing is performed with Morembs, which helps to compare the various MOR techniques to find the most suited one.

Design and Analysis of VLSI Circuits Based on Directed Acyclic Graphs

The computation time required for the analysis and optimization of a complete circuit can be too long. The use of symbolic analysis together with model order reduction techniques can reduce it and make the optimization a practicable way in the circuit design. To evaluate the possibilities offered by the technique, firstly a linear test case has been considered. The problem of an inductor simulation has been analyzed by introducing simplified analytical expressions and different optimization algorithms in the fitting/optimization process. Then the optimization technique has been applied to a real circuit, a voltage reference, trying to improve the stability of the reference over the temperature.

In this paper the analysis and design of next-generation VLSI circuits using accurate electromagnetics-based models result in numerical problems of very large scale is presented. Typically, the solution of a problem with N parameters requires at least O(N) computation. With next generation VLSI circuits, however, even O(N) is prohibitively high since N is very large. The method that partially addresses this issue was developed for full-wave modeling of large-scale interconnect structures. In this method, a number of seeds (a seed has a unique cross section) are first recognized from an interconnect structure. In each seed, the original wave propagation problem is represented as a generalized eigenvalue problem. The complexity of solving 3D interconnects of O(N) is then overcome by seeking the solution of a few 2D seeds, which is then post-processed to obtain the solution of the original 3D problem through the development of an on-chip mode-matching technique. The computational bottleneck is the solution of a generalized eigenvalue problem. Efficient algorithms such as ARPACK [2] still require O(M2) storage and operations due to a dense matrix-vector multiplication. We present an algorithm that provides a solution to the generalized eigenvalue problem with O(M) complexity, thus paving the way for the full-wave simulation of next generation VLSI circuits.

Wave-pipelined intra-chip signaling for on-FPGA communications

The development of an MOS transistor charge and capacitance model for the analysis and design of VLSI circuits is described. The total stored charge in each of the gate, bulk, and channel regions is obtained by integrating the distributed charge densities over the thin-oxide area. Charge conservation is guaranteed in this model by using the terminal charges as the state variables. The capacitance expressions have the nonreciprocal property. Partition of channel charge into the drain and source components is 40/60 in the saturation region. In the triode region, this partition changes asymptotically to 50/50 as the gate voltage increases. The carrier-velocity saturation effect is incorporated through both the modification of channel quasi-Fermi level and the determination of drain saturation voltage. Implementation of the model in the SPICE circuit simulator has been achieved. Modeled results compare well with experimental data for transistors with channel lengths as small as 0.75 mu m.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>