A Note on Zeros of Reflection and Transmission in a Cascade of Lossless Two-Terminal-Pair Networks

Certain properties of cascade-connected, two-terminal-pair lossless networks are investigated. Particular reference is made to the duo-cascade (two-terminal-pair networks) and the trio-cascade (three two terminal-pair networks). In the first part of the paper, theorems and proofs pertaining to inter-relations among the reflection and transmission coefficients of the complete cascade and the two-terminal-pair networks are presented. In the second part of the paper, a discussion of degenerate transmission zeros is presented. In the third section, the effects on transmission coefficients of adding various right-halfs-plane zeros of reflection are investigated. Reflection zeros are added so that the real frequency magnitude of a reflection coefficient is invariant under the addition of reflection zeros.