Unified Theory of Linear Noisy Two-Ports

Network noise invariants are introduced that lead to improved noise characterization and a complete theory of linear noisy two-ports. Minimum power-added noise temperature and minimum cold load temperature are identified as network noise invariants under lossless embedding. Associated invariant equations provide explicit relations between all known and new network invariants. From these equations, an invariant under lossless embedding is identified that defines network noise-gain coupling in the most basic terms of noise correlation, minimum noise temperature, and complex nonreciprocal gain. A noise correlation parameter q is formally introduced that is invariant to lossless input and/or output transformation. Conditions and bounds are established, and it is shown that q ≈ 2 for low-noise active devices. An exact expression for the q parameter of a minimum noise cascade network is given in terms of constituent device invariants. From a systems point of view, the cascade q parameter represents source impedance noise sensitivity. A lower bound on cascade q is determined by device invariants minimum power-added noise temperature and minimum cold load temperature. It is shown that the cascade q lower bound is realized by simultaneous noise and power match.