Analog Circuit Design via Geometric Programming

Maria del Mar HERSHENSON  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E87-A   No.2   pp.298-310
Publication Date: 2004/02/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: INVITED PAPER (Special Section on Analog Circuit Techniques and Related Topics)
geometric programming,  posynomial,  analog circuits,  optimization,  synthesis,  

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In this paper we describe a method for the automated design of analog circuits. The method simultaneously sizes the different components (transistors, capacitors, etc.) in a pre-defined circuit topology and places them according to a pre-defined slicing tree. The method is based on formulating the circuit physical and electrical behavior in a special convex form. More specifically, we cast the design problem as a geometric program, a special type of convex optimization problem. Therefore, all design constraints are formulated as posynomial inequality or monomial equality constraints. Very efficient numerical algorithms are then used to solve the resulting geometric program and to create the design that meets the desired specifications. The formulation is hierarchical and modular, allowing easy topology re-use and process porting. The synthesis method is fast, and determines the globally optimal design; in particular the final solution is completely independent of the starting point, and infeasible specifications are unambiguously detected. After a brief overview of current analog design automation solutions, we describe our method and provide some design examples for op-amps and analog-to-digital converters.