Iterative impedance

[3] A simple generic L-circuit is shown in the diagram consisting of a series impedance Z and a shunt admittance Y.

The iterative admittance, YIT, of this circuit is given by, where, The square root term in these expressions cause them to have two solutions.

However, only solutions with a positive real part are physically meaningful since passive circuits cannot exhibit negative resistance.

Designating this half-section image impedance as ZIM we have for the L-circuit,[9] The diagrams show this result: an infinite chain of L-sections is identical to an infinite chain of alternately reversed half-sections except for the value of the initial series impedance.

[10] The model for a transmission line is an infinite chain of L-sections with infinitesimally small components.

Iterative impedance of a simple generic L-circuit
Iterative impedance of an infinite ladder of L-circuit sections
Image impedance of an infinite ladder of L-circuit half-sections