Two-to-Four Wire Hybrid Circuits in Telecommunications

                                 Abstract
The two-to-four wire hybrid circuit enables simultaneous two way
communications down a single pair of wires, typically unshielded twisted pairs.
This electric analog circuit is employed in the POTS (“plain old telephone system”), especially with XDSL (digital subscriber lines) for broadband communication when connecting to the Internet.
In this paper we present several passive two-to-four wire hybrid circuits and endeavor to present a fairly comprehensive treatment of these devices. We develop relevant design equations via flow graphs.  The circuit topologies are  presented using the simplest implementation of components and signal sources so as not to obscure the workings of the circuit. However, various other schematic representations will also be presented, so that if he comes upon a hybrid schematic diagram in the literature, the reader can recognize the category of hybrid with which he is dealing and identify component function by referring to the basic implementation. All transformer derivations consider perfect coupling.