Matching impedance of a nonuniform transmission line: application to cochlear modeling

A generalization of the concept of characteristic impedance to nonuniform transmission lines leads to an impedance having a local character. This matching impedance depends on the solution of the transmission line equations, and cannot generally be obtained in analytical form. However, when the propagation properties of the line vary only slowly (as is the case in cochlear macromechanics), a convenient analytical approximation of the matching impedance can be derived by means of the Liouville-Green method.