M. Hershenson et al, "Optimal design of a CMOS op-amp via Geometric Programming", IEEE Trans. CAD, No.1, 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....space in which the designer is interested is fully covered. Therefore the expressions are suited to be used over a larger part of the design space during circuit design. 6. The technique generates posynomial expressions [25] This allows to formulate the sizing problem as a geometric program [26], 27] The paper is organized as follows. Section 2 will provide some theoretical background. In section 3, we will discuss our approach in detail. The proposed approach has been implemented in a software prototype. The experimental results obtained with this prototype are described in section ....

....if it has the form m i=1 # c i x (7) with c i #Rand #R. If we restrict all c i to be positive (c i R ) then the expression f is called posynomial. Whereas the former has better fitting properties, the latter allows to formulate analog circuit sizing as a geometric program [26], 27] A (primal) geometric program is the constrained optimization problem: minimize f0 (X) with the constraints: f i (X) 1,i=1, p (8) g j (X) 1,j=1, q xk 0,k=1, n with all f i (X) posynomial and all g j (X) monomial. By substituting all variables x i by zk = log (xk ) and ....

M. Hershenson, S. P. Boyd, and T. H. Lee, "Optimal design of a CMOS op-amp via geometric programming," IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, vol. 20, pp. 1--21, Jan. 2001.

....(e.g. temperature and supply voltage) must be taken into account as early as possible in the design cycle. Furthermore a high degree of automation is needed for analog circuit design in order to cope with the demand of an ever shorter time to market [9] Powerful tools for nominal design, e.g. [5, 14, 15], were developed and some are commercially available. Nominal design usually does not consider process fluctuations and variations of the operating conditions. Therefore, nominal design can only guarantee that the given specifications are fulfilled for the typical process and nominal operating ....

M. del Mar Hershenson, S. P. Boyd, and T. H. Lee. Optimal design of a CMOS Op-Amp via geometric programming. IEEE TCAD, 20(1), 2001.

....of the existing approach from [5]and the novel proposed direct fitting approach In the course of that research, it was demonstrated that the sizing of analog integrated circuits, like amplifiers, switched capacitor filters, LC oscillators, etc. can be formulated as a geometric program [1, 2]. In that approach, the performance characteristics of the circuits are represented as symbolic equations written in posynomial format. The advantages of a geometric program are multiple [3] 1. The problem is convex and has only one global optimum. 2. The optimization is not dependent on the ....

....2. The optimization is not dependent on the starting point. 3. Infeasible sets of constraints can be identified. 4. The geometric program s optimum can be found extremely efficiently, using interior point methods [4] even for relatively large problems. The problem with the approaches in [1]and[2] however, is that the symbolic equations have to be derived manually, and that nonposynomial expressions have to be approximated manually into posynomial format. Both steps are time consuming and can result in large inaccuracies, since e.g. also the device models have to be cast in ....

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M. Hershenson, S. P. Boyd, and T. H. Lee, "Optimal design of a CMOS op--amp via geometric programming," IEEE Transactions on Computer--Aided Design of Integrated Circuits and Systems, vol. 20, no. 1, pp. 1--21, Jan. 2001.

....each case, the resulting noise power expression is still posynomial, and therefore can be handled by geometric programming. Another extension is to couple the design of the feedback together with the actual component level design of the amplifier (for example, transistor widths and lengths) as in [15]. We envision several situations where the methods de scribed in this paper would be very useful to a circuit designer. Whenever the number of stages is at least three, and the number of important specifications is at least three (say) the problem of optimally allocating local feedback gains ....

M. Hershenson, S. Boyd, and T. H. Lee. Optimal design of a CMOS op-amp via geometric programming. In B. Datta, editor, Applied and Computational Control, Signals, and Circuits, volume 2. Birkhauser, 2000.

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M. Hershenson, S. Boyd, and T. H. Lee, Optimal design of a CMOS op-amp via geometric programming IEEE TCAD March 2001

....each case, the resulting noise power expression is still posynomial, and therefore can be handled by geometric programming. Another extension is to couple the design of the feedback together with the actual componentlevel design of the amplifier (for example, transistor widths and lengths) as in [14]. We envision several situations where the methods described in this paper would be very useful to a circuit designer. Whenever the number of stages is at least three, and the number of important specifications is at least three (say) the problem of optimally allocating local feedback gains ....

M. Hershenson, S. Boyd, and T. H. Lee. Optimal design of a CMOS op-amp via geometric programming. In B. Datta, editor, Applied and Computational Control, Signals, and Circuits, volume 2. Birkhauser, 2000. 21

....This gives a very useful quantitative measure of how tight each constraint is, or how much it a#ects the objective. In this paper we considered only one op amp circuit, but the general method is applicable to many other circuits, as will be reported in papers currently under preparation [48]. For the op amp considered here, the analytical expressions for the constraints and specifications were derived by hand, but in a more general setting this step could be automated by the use of symbolic circuit simulators like ISAAC [36] SYNAP [83] and ASAP [32] A CAD tool for optimization of ....

M. Hershenson, S. Boyd, and T. H. Lee. Optimal design of a CMOS op-amp via geometric programming. Submitted to IEEE Transactions on Computer-Aided Design, November 1997.

....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 introducing the method, which is described in more detail in [1], we show how the method can be applied to six common op amp architectures, and give several example designs. 1 Introduction As the demand for mixed mode integrated circuits increases, the design of analog circuits such as operational amplifiers (op amps) in CMOS technology becomes more critical. ....

....for mixed mode integrated circuits increases, the design of analog circuits such as operational amplifiers (op amps) in CMOS technology becomes more critical. Many authors have noted the disproportionately large design time devoted to the analog circuitry in mixed mode integrated circuits. In [1] we introduced a new method for determining the component values and transistor dimensions for CMOS op amps. The method handles a wide variety of specifications and constraints, is extremely fast, and results in globally optimal designs. We have developed a simple op amp synthesis tool, called ....

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M. Hershenson, S.Boyd, and T. Lee. Optimal design of a CMOS op-amp via geometric programming. http://wwwisl. stanford.edu/people/boyd (submitted to IEEE Transactions on Computer-Aided Design).

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M. Hershenson et al, "Optimal design of a CMOS op-amp via Geometric Programming", IEEE Trans. CAD, No.1, 2001.

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M. Hershenson, S. P. Boyd, and T. H. Lee. Optimal design of a CMOS op--amp via geometric programming. IEEE Transactions on Computer--Aided Design of Integrated Circuits and Systems, 20(1):1--21, Jan. 2001.

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