Optimal Allocation of Local Feedback in Multistage Amplifiers via Geometric Programming

J. L. Dawson, S. Boyd, M. Hershenson, and T. H. Lee

IEEE Transactions on Circuits and Systems I, 48(1):1-11, January 2001.
Shorter version appeared in Proceedings 43rd Midwest Symposium on Circuits and Systems (MWSCAS), Lansing, Michigan, 1:570-574, 2000.

We consider the problem of optimally allocating local feedback to the stages of a multistage amplifier. The local feedback gains affect many performance indices for the overall amplifier, such as bandwidth, gain, rise-time, delay, output signal swing, linearity, and noise performance, in a complicated and nonlinear fashion, making optimization of the feedback gains a challenging problem. In this paper we show that this problem, though complicated and nonlinear, can be formulated as a special type of optimization problem called geometric programming. Geometric programs can be solved globally and efficiently using recently developed interior-point methods. Our method therefore gives a complete solution to the problem of optimally allocating local feedback gains, taking into account a wide variety of constraints.