On the Lower Bound to the Input and Output Mismatch of Conditionally Stable Linear Two-Ports

In the design of amplifier stages based on unconditionally stable linear active two-ports, the amplifier gain can be maximized through simultaneous conjugate matching with passive loads at the input and output ports. Conversely, the optimization of linear amplifiers based on conditionally stable active devices requires a trade-off between gain, stability margin, input/output port mismatch and (for low-noise amplifiers) noise figure. Exploiting potentially in-band unstable devices can be advantageous in the design of open-loop low-noise amplifiers, since the in-band stabilization with input resistors is well known to negatively affect the amplifier minimum noise figure. Within this framework, the article derives a lower bound to the input and output mismatch of non unconditionally stable linear two-ports. The minumum mismatch is shown to only depend, in a simple way, on the stability factor $K$ and on the assumed mismatch ratio between the two ports. The minimum mismatch condition can be implemented by cascading the active, potentially in-band unstable two-port with two (input and output) reactive matching sections. The application of the theory to the design of low-noise amplifier open-loop stages based on conditionally stable active devices is discussed through CAD examples.