Relation To Characteristic Impedance
Image impedance is a similar concept to the characteristic impedance used in the analysis of transmission lines. In fact, in the limiting case of a chain of cascaded networks where the size of each single network is approaching an infinitesimally small element, the mathematical limit of the image impedance expression is the characteristic impedance of the chain. That is,
The connection between the two can further be seen by noting an alternative, but equivalent, definition of image impedance. In this definition, the image impedance of a network is the input impedance of an infinitely long chain of cascaded identical networks (with the ports arranged so that like impedance faces like). This is directly analogous to the definition of characteristic impedance as the input impedance of an infinitely long line.
Conversely, it is possible to analyse a transmission line with lumped components, such as one utilising loading coils, in terms of an image impedance filter.
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