## GPCAD: A Tool for CMOS Op-Amp Synthesis (1998)

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Citations: | 29 - 10 self |

### BibTeX

@MISC{Hershenson98gpcad:a,

author = {Maria del Mar Hershenson and Stephen P. Boyd and Thomas H. Lee},

title = {GPCAD: A Tool for CMOS Op-Amp Synthesis},

year = {1998}

}

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### Abstract

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 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 su...

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- 1995
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- Duffin, Peterson, et al.
- 1967
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- Koh, Séquin, et al.
- 1990
(Show Context)
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- 1997
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- 1990
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TILOS: A polynomial programming approach to transistor sizing
- Fishburn, Dunlop
- 1985
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Integer programming based topology selection of cell-level analog circuits,” Computer-Aided Design of Integrated Circuits and Systems
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- 1995
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et al. A top-down constraint-driven design methodology for analog integrated circuits
- Chang
- 1992
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- 1995
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- 1989
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Degrauwe et al. Towards an analog system design environment
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- 1989
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- 1992
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