Basic nonuniform transmission lines

Abstract

It is shown that for any given nonuniform transmission line (n.u.t.l.) ℒ, (which may be a multilayered RC network or a multiwire transmission line), with a per-unit-length series impedance Z(x) and shunt admittance Y(x), there always exists an electrically equivalent ‘inverse line’ ℒE, for which ZY is constant. Further, two more electrically equivalent lines may be found for which either Z or Y is constant. Although the study of any n.u.t.l. can be carried out directly, it is often advantageous to do so in terms of its equivalents. At present, the inverse line seems to be very attractive from a constructional point of view. It is also shown that for 2-wire lines, the different classes of n.u.t.l.s (including all their generalisations) known to have hyperbolic solutions are all equivalent to one of the ‘basic lines‘, namely the uniform line, the exponential line, the algebraic line z = z0(l + kx)±2, y = y0(l + kx)±2, the trigonometric line z = z0 cos ±2 (mx + n), y = y0 cos±2 (mx + n), or the hyperbolic line z = z0 cosh±2 (mx + n), y = y0 cosh±2 (mx + n). Thus, the study of networks containing n.u.t.l.s with hyperbolic solutions may be carried out in terms of these basic lines.