An Original Demonstration of the $T_{\min}/T_{o}\leq 4N$ Inequality for Noisy Two-Port Networks

The inequality T
_min
/T
₀
les 4N for any noisy linear two-port network is completely demonstrated for the first time. A graphical interpretation to link the Lange invariant N to the minimum noise performance T
_min
or F
_min
is also presented. A new term DeltaN is defined and demonstrated to be invariant to lossless transformations. Its sign is important for the network to contribute as little noise as possible. Finally, conditions required for a two-port's noise figure to be either minimum or maximum are pointed out.