Optimal Design of a CMOS Op-amp via Geometric Programming
M. Hershenson, S. Boyd, T. Lee
IEEE Transactions on Computer-Aided Design, 20(1):1-21, January 2001.
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We describe a new method for determining component values and transistor dimensions for CMOS operational amplifiers (op-amps). We observe that a wide variety of design objectives and constraints have a special form, i.e., they are posynomial functions of the design variables. As a result the amplifier design problem can be expressed as a special form of optimization problem called geometric programming, for which very efficient global optimization methods have been developed. As a consequence we can efficiently determine globally optimal amplifier designs, or globally optimal trade-offs among competing performance measures such as power, open-loop gain, and bandwidth. Our method therefore yields completely automated synthesis of (globally) optimal CMOS amplifiers, directly from specifications. In this paper we apply this method to a specific, widely used operational amplifier architecture, showing in detail how to formulate the design problem as a geometric program. We compute globally optimal trade-off curves relating performance measures such as power dissipation, unity-gain bandwidth, and open-loop gain. We show how the method can be used to synthesize robust designs, i.e., designs guaranteed to meet the specifications for a variety of process conditions and parameters.