On the Optimum Noise-Gain Locus of Two-Ports

A novel result is presented concerning the locus, on the source reflection coefficient plane, of the optimum tradeoff between noise factor and available gain. Although this locus has been discussed and exploited in previous contributions, here, it is shown in a simple manner that it must be an arc of a circumference with center Ctc and radius ρtc (tangency circle). A handy transformation (a reversible, conformal one) of two-port networks is adopted to study the problem in a simplified, yet general, representation. Properties of the tangency circle are observed in this 'noise-centered' representation which are preserved under the conformal transformation, thus providing two equivalent, closed-form approaches to computing Ctc and ρtc. The second method presented lends itself to being easily implemented in commercial circuit simulators, thus serving as the basis of a simple design method for single-stage low-noise amplifiers.