A coupled pendula system as an analogy to coupled transmission lines

The aim of this paper is to present a practical and easy to analyze coupled pendula system in order to demonstrate, by analogy, the behavior of coupled transmission lines and related devices. The importance of the Coupled Mode Theory is first explained and its derivation is worked out through the use of the spring-coupled pendula, followed by a statement of the theory and its restrictions. The theory is then used for coupled transmission lines in general and a comparison is made between the coupled pendula and coupled transmission lines in order to extract analogous quantities and to recognize the limitations of such an analogy. The coupled pendula are then used to demonstrate the behavior of a forward coupler, tunable filter, optical switch, and parametric amplifier.