Analysis of the modified MOS Wilson current mirror: a pedagogical exercise in signal flow graphs, Mason´s gain rule, and driving-point impedance techniques

A pedagogical analysis of the modified MOS Wilson current mirror using signal flow graphs (SFGs), Mason´s gain rule and driving-point impedance (DPI) techniques is presented as an exercise for undergraduate electrical engineering students learning to analyze transistor-level circuits with multiple-feedback loops. While students often prefer the SFG representation for single feedback loops, they often abandon it in favor of the more familiar nodal analysis methods for multiple loops. Yet these methods can be long and cumbersome and contribute little to intuition. In an attempt to preserve the intuitive grasp of tradeoffs, this paper presents an exercise of several well-established analytical techniques for generating and analyzing SFGs. The modified Wilson current mirror is used to compare three analytical approaches: (1) fundamental laws with brute-force algebra; (2) fundamental laws with Mason´s gain rule; and (3) DPI technique with Mason´s gain rule. The concepts reinforced in this paper include: (1) tradeoffs between gain and other quantities such as output resistance or bandwidth; (2) how Mason´s gain rule simplifies the analysis of closed-loop gain; and (3) how DPI techniques simplify the generation of SFGs