On Gain-Bandwidth Limitations for Physically Realizable Systems

Gain-bandwidth limitations for certain physical systems have been obtained in integral form by employing a generalized representation theorem for bounded-real functions. These systems are characterized by the fact that certain portions of them are fixed or prescribed. The primary interest of the paper is the determination of how the fixed portion limits the overall performance of the system and, in particular, the gain-bandwidth constraints for input-output functions. A principal feature of the procedure, and of the specific results quoted, is that it applies (within assumptions such as linearity, time-invariance, etc.) to extremely general systems. For example, no restriction such as rationality (lumped, finite systems) is imposed. The examples considered (wideband matching, optimization of laser amplifier, etc.) have been selected either for their current interest or the generality of the statements which can be made concerning them.