Four-Dimensional Transformations of 4-Pole Matrices with Applications to the Synthesis of Reactance 4-Poles

The various matrices (impedance, admittance, chain, scattering) commonly used in 4-pole theory are shown to originate from 4-dimensional transformations on the vector formed by the input and output voltages and currents. Several particular transformations are studied and lead naturally to a matrix (the transfer matrix) already introduced by Bauer, Dicke, and Watson. This is applied to the synthesis of reactance 4-poles: in particular, their decomposition into a tandem connection of two 4-poles of lower degree, studied by Talbot, is considerably simplified.