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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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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.
An Optimal Power Allocation Scheme for the STC Hybrid–ARQ over Energy Limited Networks
"... Abstract—In this paper, we show that for STC (SpaceTime Coded) HybridARQ (Automatic Repeat reQuest) schemes with (re)transmission power control over independent Rayleigh block fading channels, the problem of optimizing energy efficiency with a PER (Packet Error Rate) constraint can be solved as a ..."
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Abstract—In this paper, we show that for STC (SpaceTime Coded) HybridARQ (Automatic Repeat reQuest) schemes with (re)transmission power control over independent Rayleigh block fading channels, the problem of optimizing energy efficiency with a PER (Packet Error Rate) constraint can be solved as a geometric programming problem. The optimum transmit power increases superlinearly with each requested retransmission and the fraction of the average power optimally allocated to each ARQ round only depends on the incremental diversity gain. The energy savings increases with a decrease in the PER targets and decreases with an increase in the diversity gain. Index Terms—Energy limited networks, geometric programming, hybrid ARQ, spacetime codes. I.
Time in Yrs Annual Coupon Market Price
"... The ordinary bootstrap method for computing forward rates from zero rates generates posynomial equations as introduced in an area of optimization termed geometric programming invented by Duffin, Peterson, and Zener [6]. posynomial disc. fns e−zk(tk−t0) �k−1 = i=0 x (ti+1−ti) i,i+1, k = 1,... express ..."
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The ordinary bootstrap method for computing forward rates from zero rates generates posynomial equations as introduced in an area of optimization termed geometric programming invented by Duffin, Peterson, and Zener [6]. posynomial disc. fns e−zk(tk−t0) �k−1 = i=0 x (ti+1−ti) i,i+1, k = 1,... express the forward rates zk(tk − t0) = � k−1 i=0 fi,i+1(ti+1 − ti), where xi,i+1 = e −fi,i+1 in Tables 2–4. Note that the are n equations in m unknowns (n = m =5). Ordinary bootstrapping does not work when n � = m, eg., if there were no 0.5 time T–Bill. 1 (1)
Automated Design of FoldedCascode OpAmps with Sensitivity Analysis
 In International Conference on Electronics, Circuits and Systems
, 1998
"... We present a method for optimizing and automating component and transistor sizing in 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 expressed as geom ..."
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We present a method for optimizing and automating component and transistor sizing in 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 expressed as geometric programs, as special type of convex problems for which very efficient global optimization methods exist. A side benefit of using convex optimization is that a sensitivity analysis is obtained with the final solution with no additional computation. This information is of great interest to analog circuit designers. The method we present can be applied to a wide variety of amplifier architectures, but in this paper we apply the method to a specific twostage amplifier architecture.
Comparing Two YΔBased Methodologies for Realizable Model Reduction
, 2000
"... From a background of RC interconnect models in layouttocircuit extraction, this paper compares two realizable model reduction methodologies based on generalized Y# transformation. The first method represents admittances through a rational function in the sdomain, where the numerator and denomina ..."
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From a background of RC interconnect models in layouttocircuit extraction, this paper compares two realizable model reduction methodologies based on generalized Y# transformation. The first method represents admittances through a rational function in the sdomain, where the numerator and denominator polynomials are truncated at a userdefined order. During the Y# transformation, common factors in the numerator and denominator are identified and cancelled. The rational form of the admittances allows realization through e.g. Brune synthesis. The second method represents admittances through a moments expansion up to a userdefined order. It also allows synthesis after a Pade matching step. In that sense, the methods are equivalent. Nevertheless, a comparison shows that the former performs better in the frequency domain.
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"... The notion of convexity underlies important results in many parts of mathematics such as optimization, analysis, combinatorics, probability and number theory. The geometric foundations of the theory of convex sets date back to work of Minkowski, Carathéodory, and Fenchel around 1900. Since then, thi ..."
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The notion of convexity underlies important results in many parts of mathematics such as optimization, analysis, combinatorics, probability and number theory. The geometric foundations of the theory of convex sets date back to work of Minkowski, Carathéodory, and Fenchel around 1900. Since then, this area has expanded into a large number of directions and now includes topics such as highdimensional spaces, convex analysis, polyhedral geometry, computational convexity, approximation methods and others. In the context of optimization, both theory and empirical evidence show that problems with convex constraints allow efficient algorithms. Many applications in the sciences and engineering involve optimization, and it is always extremely advantageous when the underlying feasible regions are convex and have practically useful representations as convex sets. A situation in which convexity has been wellunderstood is the study of convex polyhedra, which are the solution sets of finitely many linear inequalities [27, 86]. A context in algebraic geometry in which convexity arises is the theory of toric varieties. These are algebraic varieties derived from polyhedra [49, 73]. Both convex polyhedra and toric varieties have satisfactory computational techniques associated to them. Linear optimization over polyhedra is linear programming which admits interiorpoint algorithms that run in polynomial time. More generally, polyhedra can be
Power Controlled FCFS Splitting Algorithm for Wireless Networks
"... We consider random access in wireless networks under the physical interference model, wherein the receiver is capable of powerbased capture, i.e., a packet can be decoded correctly in the presence of multiple transmissions if the received Signal to Interference and Noise Ratio exceeds a threshold. ..."
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We consider random access in wireless networks under the physical interference model, wherein the receiver is capable of powerbased capture, i.e., a packet can be decoded correctly in the presence of multiple transmissions if the received Signal to Interference and Noise Ratio exceeds a threshold. We propose a splitting algorithm that varies the transmission powers of users on the basis of quaternary channel feedback (idle, success, capture, collision). We show that our algorithm achieves a maximum stable throughput of 0.5518. Simulation results demonstrate that our algorithm achieves higher throughput and lower delay thanthat of the First Come First Servesplitting algorithmwith uniformtransmission power.
jpvQeecs.berkeley.edu
"... We present a method for designing operational amplifiers using reversed geometric programming, which is an extension of geometric programming that allows both convex and nonconvex constraints. Adding a limited set of nonconvex constraints can improve the accuracy of convex equationbased optimizati ..."
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We present a method for designing operational amplifiers using reversed geometric programming, which is an extension of geometric programming that allows both convex and nonconvex constraints. Adding a limited set of nonconvex constraints can improve the accuracy of convex equationbased optimization, without compromising global optimality. These constraints allow increased accuracy for critical modeling equations, such as the relationship between gm and Ips. To demonstrate the design methodology, a foldedcascode amplifier is designed in a 0.18'pm technology for varying speed requirements and is compared with simnlations and designs obtained from geometric programming. Categories and Subject Descriptors:
Some Properties of Posynomial Rings
, 2005
"... In this article we shall study some basic properties of posynomial rings with particular emphasis on rings Pos(K, Q)[¯x], and Pos(K, Z)[¯x]. The latter ring is the well known ring of Laurent polynomials. 1 ..."
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In this article we shall study some basic properties of posynomial rings with particular emphasis on rings Pos(K, Q)[¯x], and Pos(K, Z)[¯x]. The latter ring is the well known ring of Laurent polynomials. 1