Considerations on the ${{ 4 {{NT}}_{\rm o} }/{ {T}_{\rm m}}}$ Ratio and the Noise Correlation Matrix of Active and Passive Two-Port Networks

The constraint on the Wiatr-Pospieszalski (WP) parameter Θ_WP = 4 NT_o/T_m ≤ 2, where N is the Lange invariant and T_m the minimum equivalent noise temperature and T_o=290 ( K ), has been suggested as a validation tool for the characterization of active microwave devices, despite its acknowledged limitations. This paper provides a solid theoretical background on Θ_WP that is used to investigate noisy linear two-port networks. In particular, parallel feedback is discussed thoroughly in order to understand its effect on the Θ_WP parameter and determine the conditions for which Θ_WP is larger or smaller than 2. A suitable expression that explains the conditions for Θ_WP of on-chip devices to be less than 2 is obtained. The theoretical results are supported by a scalable GaN device model extracted from measurements providing further insight into the noise performance of microwave devices. Finally, the investigation is applied to passive two-port networks to highlight the singular properties of Θ_WP=2. The broad result of this paper´s investigation is that the constraint Θ_WP=2 is not a property of the noise parameter matrix as the constraint 1≤ Θ_WP is; yet, the threshold Θ_WP=2 is demonstrated to have unique features for both active and passive two-port networks. Alternative and original demonstrations of the 1≤ Θ_WP constraint are also obtained as a byproduct of the investigation.