The Theory of Special Noise Invariants

Abstract

This paper reports a novel systematic theory of the noise invariants of two-port linear noisy networks under lossless reciprocal input and output impedance transformations. The theory clarifies the relationship between the circuit theory of linear noisy networks and the theory of four noise parameters, which are widely applied in the design of low-noise amplifiers (LNAs). In particular, we prove that the fundamental noise invariants under input and output impedance transformations are the eigenvalues of a permuted version of the noise correlation matrix and that there is no feedback operation that preserves them. Known invariants, such as the minimum equivalent noise temperature ${T}_{{N}{min}}$ and ${N}$ , may be expressed in terms of such eigenvalues. In addition, we provide a complete characterization of the four noise parameters of two-port passive dissipative networks in terms of their gain parameters and derive the condition under which the invariant ${4N}{T}_{{0}}{/}{T}_{{N}{min}}$ of passive nonreciprocal networks is lower than two. We also extend the theory of special noise invariants to LNAs with lossy input matching network. Overall, the impact of the findings emerging from the theory is highlighted through theorems, remarks, circuit examples, and studies on widespread design methodologies.