Analytic bounds on amplifier gain-bandwidth product from complex power flow

Authors such as Thornton, Kuh, and Glasser have considered bounds on possible oscillator frequency and amplifier bandwidth based on regions of the Laplace-transform s-plane where a set of components cannot achieve real and reactive power balance. We define a “gain” that is analytic and less than unity in magnitude for values of s where power balance cannot be achieved. We then derive bounds on amplifier bandwidth with a phase constraint (intended for feedback amplifier applications) based on analytic continuation of such a gain to the jω axis.