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Digital Circuit Optimization via Geometric Programming
 Operations Research
, 2005
"... informs ® doi 10.1287/opre.1050.0254 © 2005 INFORMS This paper concerns a method for digital circuit optimization based on formulating the problem as a geometric program (GP) or generalized geometric program (GGP), which can be transformed to a convex optimization problem and then very efficiently s ..."
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informs ® doi 10.1287/opre.1050.0254 © 2005 INFORMS This paper concerns a method for digital circuit optimization based on formulating the problem as a geometric program (GP) or generalized geometric program (GGP), which can be transformed to a convex optimization problem and then very efficiently solved. We start with a basic gate scaling problem, with delay modeled as a simple resistorcapacitor (RC) time constant, and then add various layers of complexity and modeling accuracy, such as accounting for differing signal fall and rise times, and the effects of signal transition times. We then consider more complex formulations such as robust design over corners, multimode design, statistical design, and problems in which threshold and power supply voltage are also variables to be chosen. Finally, we look at the detailed design of gates and interconnect wires, again using a formulation that is compatible with GP or GGP.
Disciplined convex programming
 Global Optimization: From Theory to Implementation, Nonconvex Optimization and Its Application Series
, 2006
"... ..."
A Heuristic Method for Statistical Digital Circuit Sizing
"... In this paper we give a brief overview of a heuristic method for approximately solving a statistical digital circuit sizing problem, by reducing it to a related deterministic sizing problem that includes extra margins in each of the gate delays to account for the variation. Since the method is based ..."
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In this paper we give a brief overview of a heuristic method for approximately solving a statistical digital circuit sizing problem, by reducing it to a related deterministic sizing problem that includes extra margins in each of the gate delays to account for the variation. Since the method is based on solving a deterministic sizing problem, it readily handles largescale problems. Numerical experiments show that the resulting designs are often substantially better than one in which the variation in delay is ignored, and often quite close to the global optimum. Moreover, the designs seem to be good despite the simplicity of the statistical model (which ignores gate distribution shape, correlations, and so on). We illustrate the method on a 32bit LadnerFischer adder, with a simple resistorcapacitor (RC) delay model, and a Pelgrom model of delay variation.
SilvaMartinez: “Bandwidth enhancement of multistage amplifiers using active feedback
 Proceedings of the 2004 International Symposium on Circuits and Systems, Vol.1
, 2004
"... A new topology for wideband multistage amplifiers (MA) is introduced. The proposed method uses active negative feedback in a chain of amplifiers to extend the bandwidth and improve gainbandwidth product. The topology has several advantages such as having capability of widening bandwidth as the numb ..."
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A new topology for wideband multistage amplifiers (MA) is introduced. The proposed method uses active negative feedback in a chain of amplifiers to extend the bandwidth and improve gainbandwidth product. The topology has several advantages such as having capability of widening bandwidth as the number of stage increases and enhancing bandwidth by several times that of the dominant pole of each stage. To verify the performance of topology, an 8stage amplifier in 0.35µm CMOS was designed, where more than 2.8GHz bandwidth and 40dB gain were obtained from simulations. 1.
Optimal doping profiles via geometric programming
 IEEE Transactions on Electron Devices
, 2005
"... Abstract—We first consider the problem of determining the doping profile that minimizes base transit time in a (homojunction) bipolar junction transistor. We show that this problem can be formulated as a geometric program, a special type of optimization problem that can be transformed to a convex op ..."
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Abstract—We first consider the problem of determining the doping profile that minimizes base transit time in a (homojunction) bipolar junction transistor. We show that this problem can be formulated as a geometric program, a special type of optimization problem that can be transformed to a convex optimization problem, and therefore solved (globally) very efficiently. We then consider several extensions to the basic problem, such as accounting for velocity saturation, and adding constraints on doping gradient, current gain, base resistance, and breakdown voltage. We show that a similar approach can be used to maximize the cutoff frequency, taking into account junction capacitances and forward transit time. Finally, we show that the method extends to the case of heterojunction bipolar junction transistors, in which the doping profile, as well as the profile of the secondary semiconductor, are to be jointly optimized. Index Terms—Base doping profile, base transit time minimization, cutoff frequency maximization, geometric programming, Geprofile optimization, optimal doping profile. I.
"Conefree" primaldual pathfollowing and potential reduction polynomial time interiorpoint methods
 MATH. PROG
, 2005
"... We present a framework for designing and analyzing primaldual interiorpoint methods for convex optimization. We assume that a selfconcordant barrier for the convex domain of interest and the Legendre transformation of the barrier are both available to us. We directly apply the theory and techni ..."
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We present a framework for designing and analyzing primaldual interiorpoint methods for convex optimization. We assume that a selfconcordant barrier for the convex domain of interest and the Legendre transformation of the barrier are both available to us. We directly apply the theory and techniques of interiorpoint methods to the given good formulation of the problem (as is, without a conic reformulation) using the very usual primal central path concept and a less usual version of a dual path concept. We show that many of the advantages of the primaldual interiorpoint techniques are available to us in this framework and therefore, they are not intrinsically tied to the conic reformulation and the logarithmic homogeneity of the underlying barrier function.
Deterministic Approaches to Analog Performance Space Exploration (PSE)
"... Performance space exploration (PSE) determines the range of feasible performance values of a circuit block for a given topology and technology. In this paper, we present two deterministic approaches for PSE. One approximates the feasible performance space based on linearized circuit models and is su ..."
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Performance space exploration (PSE) determines the range of feasible performance values of a circuit block for a given topology and technology. In this paper, we present two deterministic approaches for PSE. One approximates the feasible performance space based on linearized circuit models and is suitable for investigating a large number of performances. The other one computes discretizations of the Pareto front of competing performances. In addition, a motivation and application of PSE using a hierarchical design example is presented.
Synthesizable full custom mixedsignal IP
"... In this paper, we describe synthesizable custom IP, a new approach to analog circuit design. Synthesizable custom IP is created by using geometric programming techniques. We observe that both transistor behavior and performance measures for a phase locked loop can be formulated as posynomial functi ..."
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In this paper, we describe synthesizable custom IP, a new approach to analog circuit design. Synthesizable custom IP is created by using geometric programming techniques. We observe that both transistor behavior and performance measures for a phase locked loop can be formulated as posynomial functions of the design variables. As a result, these design problems can be formulated as geometric programs, 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. We present design results and silicon tests results for phaselocked loops circuits that were designed using this new approach. 1
A Tutorial on Geometric Programming
"... A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods can solve even largescale GPs extremely efficiently and reliably; at the same time a number of practical problems ..."
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A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods can solve even largescale GPs extremely efficiently and reliably; at the same time a number of practical problems, particularly in circuit design, have been found to be equivalent to (or well approximated by) GPs. Putting these two together, we get effective solutions for the practical problems. The basic approach in GP modeling is to attempt to express a practical problem, such as an engineering analysis or design problem, in GP format. In the best case, this formulation is exact; when this isn’t possible, we settle for an approximate formulation. This tutorial paper collects together in one place the basic background material needed to do GP modeling. We start with the basic definitions and facts, and some methods used to transform problems into GP format. We show how to recognize functions and problems compatible with GP, and how to approximate functions or data in a form compatible with GP (when this is possible). We give some simple and representative examples, and also describe some common extensions of GP, along with methods for solving (or approximately solving) them.