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75
GPCAD: A Tool for CMOS OpAmp Synthesis
 IN PROCEEDINGS OF THE IEEE/ACM INTERNATIONAL CONFERENCE ON COMPUTER AIDED DESIGN
, 1998
"... We present a method for optimizing and automating component and transistor sizing for CMOS operational amplifiers. We observe that a wide variety of performance measures can be formulated as posynomial functions of the design variables. As a result, amplifier design problems can be formulated as a g ..."
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Cited by 34 (13 self)
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We present a method for optimizing and automating component and transistor sizing for CMOS operational amplifiers. We observe that a wide variety of performance measures can be formulated as posynomial functions of the design variables. As a result, amplifier design problems can be formulated as a geometric program, a special type of convex optimization problem for which very efficient global optimization methods have recently been developed. The synthesis method is therefore fast, and determines the globally optimal design; in particular the final solution is completely independent of the starting point (which can even be infeasible), and infeasible specifications are unambiguously detected. After briefly
Disciplined convex programming
 Global Optimization: From Theory to Implementation, Nonconvex Optimization and Its Application Series
, 2006
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Robust analog/RF circuit design with projectionbased posynomial modeling
 IEEE/ACM ICCAD
, 2004
"... In this paper we propose a RObust Analog Design tool (ROAD) for posttuning analog/RF circuits. Starting from an initial design derived from hand analysis or analog circuit synthesis based on simplified models, ROAD extracts accurate posynomial performance models via transistorlevel simulation and ..."
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Cited by 21 (9 self)
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In this paper we propose a RObust Analog Design tool (ROAD) for posttuning analog/RF circuits. Starting from an initial design derived from hand analysis or analog circuit synthesis based on simplified models, ROAD extracts accurate posynomial performance models via transistorlevel simulation and optimizes the circuit by geometric programming. Importantly, ROAD sets up all design constraints to include largescale process variations to facilitate the tradeoff between yield and performance. A novel convex formulation of the robust design problem is utilized to improve the optimization efficiency and to produce a solution that is superior to other local tuning methods. In addition, a novel projectionbased approach for posynomial fitting is used to facilitate scaling to large problem sizes. A new implicit power iteration algorithm is proposed to find the optimal projection space and extract the posynomial coefficients with robust convergence. The efficacy of ROAD is demonstrated on several circuit examples. 1.
RealTime Convex Optimization in Signal Processing
"... Convex optimization has been used in signal processing for a long time, to choose coefficients for use in fast (linear) algorithms, such as in filter or array design; more recently, it has been used to carry out (nonlinear) processing on the signal itself. Examples of the latter case include total ..."
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Cited by 18 (4 self)
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Convex optimization has been used in signal processing for a long time, to choose coefficients for use in fast (linear) algorithms, such as in filter or array design; more recently, it has been used to carry out (nonlinear) processing on the signal itself. Examples of the latter case include total variation denoising, compressed sensing, fault detection, and image classification. In both scenarios, the optimization is carried out on time scales of seconds or minutes, and without strict time constraints. Convex optimization has traditionally been considered computationally expensive, so its use has been limited to applications where plenty of time is available. Such restrictions are no longer justified. The combination of dramatically increased computational power, modern algorithms, and new coding approaches has delivered an enormous speed increase, which makes it possible to solve modestsized convex optimization problems on microsecond or millisecond time scales, and with strict deadlines. This enables realtime convex optimization in signal processing.
Performance tradeoff analysis of analog circuit by normal boundary intersection
 In DAC
, 2003
"... We present a new technique to examine the tradeoff regions of a circuit where its competing performances become “simultaneously optimal”, i.e. Pareto optimal. It is based on circuit simulation, sizing rules, which capture elementary topological and technological constraints, and an advanced multic ..."
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Cited by 13 (2 self)
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We present a new technique to examine the tradeoff regions of a circuit where its competing performances become “simultaneously optimal”, i.e. Pareto optimal. It is based on circuit simulation, sizing rules, which capture elementary topological and technological constraints, and an advanced multicriteria optimization formulation called normalboundary intersection. We are able to efficiently calculate a wellbalanced discretization of a Pareto surface, identify the active constraints, which prevent a further improvement, and even rank these constraints in terms of stringency. Experimental results demonstrate the efficacy and efficiency of the method and its potential for topology selection and analog synthesis.
Optimal allocation of local feedback in multistage amplifiers via geometric programming
 IEEE Transactions on Circuits and Systems I
, 2001
"... We consider the problem of optimally allocating local feedback to the stages of a multistage amplifier. The local feedback gains affect many performance indices for the overall amplifier, such as bandwidth, gain, risetime, delay, output signal swing, linearity, and noise performance, in a complicat ..."
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Cited by 9 (5 self)
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We consider the problem of optimally allocating local feedback to the stages of a multistage amplifier. The local feedback gains affect many performance indices for the overall amplifier, such as bandwidth, gain, risetime, delay, output signal swing, linearity, and noise performance, in a complicated and nonlinear fashion, making optimization of the feedback gains a challenging problem. In this paper we show that this problem, though complicated and nonlinear, can be formulated as a special type of optimization problem called geometric programming. Geometric programs can be solved globally and efficiently using recently developed interiorpoint methods. Our method therefore gives a complete solution to the problem of optimally allocating local feedback gains, taking into account a wide variety of constraints. 1 1
Analog performance space exploration by FourierMotzkin elimination with application to hierarchical sizing
 in Proc. of ICCAD
, 2004
"... Analog performance space exploration identifies the range of feasible performance values of a given circuit topology. It is an extremely challenging task of great importance to topology selection and hierarchical sizing. In this paper, a novel technique for the efficient simulationbased exploration ..."
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Cited by 8 (1 self)
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Analog performance space exploration identifies the range of feasible performance values of a given circuit topology. It is an extremely challenging task of great importance to topology selection and hierarchical sizing. In this paper, a novel technique for the efficient simulationbased exploration of highdimensional performance spaces is presented. To this end, fundamental circuit design knowledge is described by constraint functions. Based on a linearization of the latter and of the circuit performance functions, a description of the feasible performance range in the form of a polytope is derived. Moreover, the approach is integrated into a hierarchical sizing method, where it propagates topological and technological constraints bottomup. Practical application results demonstrate the efficiency and usefulness of the new method. 1.
A tutorial on convex optimization
 In Proceedings of the 23th American Control Conference
"... Abstract — In recent years, convex optimization has become a computational tool of central importance in engineering, thanks to it’s ability to solve very large, practical engineering problems reliably and efficiently. The goal of this tutorial is to give an overview of the basic concepts of convex ..."
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Cited by 8 (1 self)
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Abstract — In recent years, convex optimization has become a computational tool of central importance in engineering, thanks to it’s ability to solve very large, practical engineering problems reliably and efficiently. The goal of this tutorial is to give an overview of the basic concepts of convex sets, functions and convex optimization problems, so that the reader can more readily recognize and formulate engineering problems using modern convex optimization. This tutorial coincides with the publication of the new book on convex optimization, by Boyd and Vandenberghe [7], who have made available a large amount of free course material and links to freely available code. These can be downloaded and used immediately by the audience both for selfstudy and to solve real problems. I.
An Efficient Optimizationbased Technique to Generate Posynomial Performance Models for Analog Integrated Circuits
 in: Proc. 39th Design Automation Conf., Ernest Morial Convention
, 2002
"... This paper presents an new directfitting method to generate posynomial response surface models with arbitrary constant exponents for linear and nonlinear performance parameters of analog integrated circuits. Posynomial models enable the use of efficient geometric programming techniques for circuit ..."
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Cited by 8 (3 self)
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This paper presents an new directfitting method to generate posynomial response surface models with arbitrary constant exponents for linear and nonlinear performance parameters of analog integrated circuits. Posynomial models enable the use of efficient geometric programming techniques for circuit sizing and optimization. The automatic generation avoids the timeconsuming nature and inaccuracies of handcrafted analytic model generation. The technique is based on the fitting of posynomial model templates to numerical data from SPICE simulations. Attention is paid to estimating the relative `goodnessoffit' of the generated models. Experimental results illustrate the significantly better accuracy of the new approach.
Performancecentering optimization for systemlevel analog design exploration
 Proc. of 2005 IEEE/ACM ComputerAided Design Conference (ICCAD2005
, 2005
"... In this paper we propose a novel analog design optimization methodology to address two key aspects of topdown systemlevel design: (1) how to optimally compare and select analog system architectures in the early phases of design; and (2) how to hierarchically propagate performance specifications fr ..."
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Cited by 6 (0 self)
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In this paper we propose a novel analog design optimization methodology to address two key aspects of topdown systemlevel design: (1) how to optimally compare and select analog system architectures in the early phases of design; and (2) how to hierarchically propagate performance specifications from system level to circuit level to enable independent circuit block design. Importantly, due to the inaccuracy of earlystage systemlevel models, and the increasing magnitude of process and environmental variations, the systemlevel exploration must leave sufficient design margin to ensure a successful latestage implementation. Therefore, instead of minimizing a design objective function, and thereby converging on a constraint boundary, we apply a novel performance centering optimization. Our proposed methodology centers the analog design in the performance space, and maximizes the distance to all constraint boundaries. We demonstrate that this earlystage design margin, which is measured by the volume of the inscribed ellipsoid lying inside the performance constraints, provides an excellent quality measure for comparing different system architectures. The efficacy of our performance centering approach is shown for analog design examples, including a complete clock data recovery system design and implementation. 1.