Simplified treatment of the transconductance linearization problem employing any number of coupled differential pairs

摘要

This paper is a step toward a rigorous mathematical analysis of the transconductance linearization problem. Using the apparatus of approximation theory, we show that the transconductance linearization problem is a function approximation problem. We elaborate two separate methods for solving this problem: (i) Pade and (ii) Pade-type methods. Both methods are of the maximum flatness type because they are particular cases of the generalized Taylor series method. As a by-product of our mathematical analysis, we develop new linearization techniques. In particular, we show that maximum flatness can be derived by the Pade-type method by simply choosing distinct gate voltages. This characterizes new extensions of known design guidelines.