The Invariance Properties of a Multivalue n-Port in a Linear Embedding

A set of four
n
-port networks placed in an identical linear time-invariant
m+n
-port
(m \geq n)
embedding admits at least
n
characteristic "spot-frequency" algebraic expressions involving the four networks of the set left unaffected by the embedding. A general method for deriving such invariant expressions is given. Starting from this basic case, the conditions under which invariant expressions can be found for sets containing an arbitrary number of networks are investigated. Known invariants are derived as particular cases of the theory together with the conditions for their existence, and new invariants are proposed. Other applications are possible in the field of quasi-power theorems and network sensitivity.