Theory of Cascaded Structures: Lossless Transmission Lines

1.1 Purpose A large class of signal processing and signal propagating systems takes the form of a cascade of elementary two-port, linear transducers. For example, in the classical filler theory cascades of constant-/c, mderived sections, etc. and in the modern network synthesis cascades of transmission-zero sections form the conceptual basis. Integrated circuits utilize RC transmission lines in cascade. In microwave filler theory, the structure takes the form of a cascade of quarter-wave transformers. Optical filters incorporate the same idea in multilayer dielectric thin-film structures. In propagation problems, one typically encounters waves (electromagnetic, acoustic, etc.) travelling in cascades of transmission media and discontinuities. These are but a few examples to indicate the importance and universality of such structures. It is the purpose of this paper to present a theory of such structures when the component two-ports are representable by uniform lossless 631 632 T H E BELL SYSTEM T E C H N I C A L J O U R N A L , A P R I L 1966