On the Theoretical Limits of Gain and Matching in Single‐Stage High‐Frequency Amplifiers

Active device performances are typically characterized by figures of merit, representing the best achievable values of quantities such as gain, port mismatch, noise figure, and output power. The figures identify the limits for a single-stage amplifier realized using a given active device and, from a design point of view, help to determine whether design goals can be fulfilled. Amplifier design goals always include specifications for gain and port mismatch. Various figures of merit from high-frequency linear circuit theory exist for these quantities, but most are defined under restrictive conditions: fixed impedance termination or conjugate matching at one active device port. This paper analyzes the limits of the small signal performance for a single-stage amplifier with unconstrained port terminations. For this purpose, all possible combinations of gain and port mismatch achievable by an amplifier utilizing a given active device are first investigated; the limits of those performances are then determined. New formulations for the eligible gain and mismatches are derived, and the stability conditions of the circuit corresponding to each achievable performance are addressed. Thanks to the developed analysis, the figures of merit of active devices available in the literature are easily demonstrated. Moreover, design methodologies for microwave amplifiers with a general level of matching at the ports can be developed. As an example, a mismatching chart is proposed that gives all the amplifier performance in terms of the mismatch of the ports.