Optimal design of a CMOS op-amp via geometric programming

TLDR

Design objectives and constraints for CMOS op‑amps are posynomial functions, allowing the amplifier design problem to be expressed as a geometric programming optimization with efficient global methods. The paper introduces a method to determine component values and transistor dimensions for CMOS op‑amps and applies it to a widely used architecture by formulating the design as a geometric program. The method models CMOS op‑amp design as a geometric program, enabling efficient global optimization of component values and transistor dimensions, and supports robust sizing that satisfies specifications across process variations. The approach yields globally optimal CMOS op‑amp designs and trade‑off curves among power, open‑loop gain, and bandwidth, enabling fully automated sizing directly from specifications.

Abstract

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 tradeoffs among competing performance measures such as power, open-loop gain, and bandwidth. Our method, therefore, yields completely automated sizing 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 tradeoff curves relating performance measures such as power dissipation, unity-gain bandwidth, and open-loop gain. We show how the method can he used to size robust designs, i.e., designs guaranteed to meet the specifications for a variety of process conditions and parameters.