Negative Impedance Boosting

The insertion of lumped negative impedances at intervals along each conductor of a cable pair has long been of interest as a means of improving bilateral transmission. In the familiar expressions for propagation constant y = a + jp = + &L)(G + juC) (1) and characteristic impedance Z, = R« + jX o = V(R + JuTJRG + ja>C), (2) if one lets both G and R go to zero on presumption that the shunt conductance of well-insulatecl cable is negligible and that the copper resistance can effectively be canceled by active devices, he encounters four challenging approximations: a « 0, (5 ^ c o y / L C , R0 ^ y/TJC 1019 and X0 tt 0.