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Circuit Optimization via Adjoint Lagrangians
 IEEE INTERNATIONAL CONFERENCE ON COMPUTERAIDED DESIGN
, 1997
"... The circuit tuning problem is best approached by means of gradientbased nonlinear optimization algorithms. For large circuits, gradient computation can be the bottleneck in the optimization procedure. Traditionally, when the number of measurements is large relative to the number of tunable paramete ..."
Abstract

Cited by 6 (3 self)
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The circuit tuning problem is best approached by means of gradientbased nonlinear optimization algorithms. For large circuits, gradient computation can be the bottleneck in the optimization procedure. Traditionally, when the number of measurements is large relative to the number of tunable parameters, the direct method [2] is used to repeatedly solve the associated sensitivity circuit to obtain all the necessary gradients. Likewise, when the parameters outnumber the measurements, the adjoint method [1] is employed to solve the adjoint circuit repeatedly for each measurement to compute the sensitivities. In this paper, we propose the adjoint Lagrangian method, which computes all the gradients necessary for augmentedLagrangianbased optimization in a single adjoint analysis. After the nominal simulation of the circuit has been carried out, the gradients of the merit function are expressed as the gradients of a weighted sum of circuit measurements. The weights are dependent on the nominal solution and on optimizer quantities such as Lagrange multipliers. By suitably choosing the excitations of the adjoint circuit, the gradients of the merit function are computed via a single adjoint analysis, irrespective of the number of measurements and the number of parameters of the optimization. This procedure requires close integration between the nonlinear optimization software and the circuit simulation program. The adjoint
Implicit MixedMode Simulation of VLSI Circuits
, 1990
"... trical and Computer engineering, with a specialty in communications and circuit theory. From 1972 to 1978 he was employed as an analog circuit designer, working primarily in the audio industry. In 1978, he founded Tatum Labs, a consulting firm, to do analog circuit design. Beginning in 1980, his wor ..."
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Cited by 3 (0 self)
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trical and Computer engineering, with a specialty in communications and circuit theory. From 1972 to 1978 he was employed as an analog circuit designer, working primarily in the audio industry. In 1978, he founded Tatum Labs, a consulting firm, to do analog circuit design. Beginning in 1980, his work became primarily software tools for circuit designers. Tatum Labs developed and marketed entry level CAD software, including a circuit simulator, for board level circuits. He sold Tatum Labs in 1986 to pursue full time graduate study.
"Relaxing"  A Symbolic Sparse Matrix Method Exploiting the Model Structure in Generating Efficient Simulation Code
, 1996
"... This paper presents a new method for symbolically solving large sets of algebraically coupled equations as they are frequently encountered in the formulation of mathematical models of physical systems in object oriented modeling. The method, called "relaxing," enables the modeler to exploit the sp ..."
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This paper presents a new method for symbolically solving large sets of algebraically coupled equations as they are frequently encountered in the formulation of mathematical models of physical systems in object oriented modeling. The method, called "relaxing," enables the modeler to exploit the special matrix structure of the type of system under study by simply placing the keyword relax at appropriate places in the model class libraries. This procedure defines an evaluation sequence for a sparse matrix Gaussian elimination scheme. The method is demonstrated at hand of several broad classes of physical systems: drive trains, electrical circuits, and treestructured multibody systems. In particular, relaxing allows a model compiler, such as Dymola, to start from a declarative, object oriented description of the model, and to automatically derive the recursive O(f) algorithm used in modern multibody programs. Keywords: Sparse matrices; symbolic formulae manipulation; objectorient...
A General Approach to Circuit Equations
, 1994
"... Computer aided circuit analysis is a complex procedure, which may be roughly divided into three steps. The first stage is device modelling, where quantitative properties of the participating electronic devices are determined. In the second step, the circuit's topology in conjunction with the device ..."
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Computer aided circuit analysis is a complex procedure, which may be roughly divided into three steps. The first stage is device modelling, where quantitative properties of the participating electronic devices are determined. In the second step, the circuit's topology in conjunction with the device equations is being exploited, in order to formulate a linearized nonsingular equation set. Eventually, the equation set is iteratively solved in the third phase, yielding a solution vector of circuit variables. This paper deals with the second and third step, where diverse sparse matrix methods are employed. Its ambition is to provide a general mathematical form, by which most matrix manipulating techniques can be described, thus enabling their classification on a theoretical level. Usually, these methods would be presented descriptively rather than strictly mathematically. The paper introduces a matrix reduction operator, from which a general matrix operator equation is deduced. This operat...