The Presence of the Fibonacci Numbers in Passive Ladder Networks: The Case of Forbidden Bands [Historical Corner]

This paper takes into consideration a number of different ladder networks showing links with the so-called Golden Ratio φ = 1.6180339..., which is embedded into the Fibonacci sequence. Discreteness and periodicity in electronic ladder networks seem to appear as the main features able to include Fibonacci numbers. For instance, in the telecommunication environment, transmission lines can be studied with a given approximation by simplified discrete ladder networks made by a sequence of passive identical cells, such as R-R; R-C; R-L; C-R; L-R; L-C; C-L; directly and electrically coupled each other. In this context, the so called Golden Ratio frequently appears in particular conditions, without a specific reason, at least to our best knowledge, and its presence, so far, still does represent a sort of mystery.