Considerations on the 4 NTₒ / Tₘ Ratio and the Noise Correlation Matrix of Active and Passive Two-Port Networks

The constraint on the Wiatr–Pospieszalski (WP) parameterΘ W\!P= 4 NTₒ / Tₘ 2, whereNis the Lange invariant andTₘthe minimum equivalent noise temperature andTₒ=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 onΘ W\!Pthat is used to investigate noisy linear two-port networks. In particular, parallel feedback is discussed thoroughly in order to understand its effect on theΘ W\!Pparameter and determine the conditions for whichΘ W\!Pis larger or smaller than 2. A suitable expression that explains the conditions forΘ W\!Pof 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 ofΘ W\!P=2. The broad result of this paper's investigation is that the constraintΘ W\!P 2is not a property of the noise parameter matrix as the constraint1 Θ W\!Pis; yet, the thresholdΘ W\!P=2is demonstrated to have unique features for both active and passive two-port networks. Alternative and original demonstrations of the1 Θ W\!Pconstraint are also obtained as a byproduct of the investigation.