Discussion and new proofs of the conditional stability criteria for multidevice microwave amplifiers

In the design of microwave multidevice amplifiers, criteria ensuring conditional stability allow a better trade-off between performance and stability to be obtained with respect to unconditional stability criteria. Previous results concerning conditional stability of linear two-ports are discussed, and new proofs of the conditional stability criterion ensuring stability for all the values of input and output terminations located in circular regions of the Smith chart are provided. By following the proposed proofs, it is shown for the first time that necessary and sufficient conditions for conditional stability can be ascertained by means of a single parameter. The overall stability factors are directly obtained starting from Ohtomo´s proviso on unconditional stability. Procedures to apply the conditional stability criterion to the synthesis of multidevice amplifiers are also outlined and illustrated by means of a case study concerning the design of a four-stage distributed amplifier in the 1-10 GHz frequency band.