A Matric Representation of the Geometrically Tapered Chain of Four Terminal Networks

The geometrically tapered chain of two-terminal pairs is defined as a chain whose individual sections have transmission matrices whose diagonal elements are the same for all sections, while the antidiagonal elements for successive sections differ by a multiplicative factor which is independent of position along the chain. The transmission matrix of the chain is then expressed in terms of Tchebycheff functions. It is shown how, in special cases, the results reduce to previously known formulas. The phase shift network used in phase shift oscillators is considered briefly, as a particular case of the geometrically tapered network.