Theory of Cascaded Structures: Lossless Transmission Lines

Cascaded structures play a major role in many signal processing and signal propagating systems. The universality of such structures is particularly evident when the signals are of a wave nature, i.e., the components of the structure are representable by transmission lines rather than lumped elements. Transmission media with discontinuities are examples of such structures. Other examples include integrated, microwave, and optical circuits. Theory of distributed structures has, so far, been successfully developed only for structures whose components are lossless (or RC) transmission lines of equal electrical lengths. It is the purpose of this paper to present a theory of cascaded structures when the component elements are lossless transmission lines of arbitrary electrical lengths. Extensions of the theory developed here to other structures will be discussed in a subsequent paper.