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Several methods are available for synthesizing three-terminal RC networks when only two of the three short-circuit admittances or two of the three open-circuit impedances are specified. This paper treats the synthesis problem in which all three functions are given; that is, in which terminal behavior of network is entirely prescribed. There is a discussion of necessary conditions which must be satisfied by a set of short-circuit admittances or open-circuit impedances in order that it correspond to a three-terminal RC network. A synthesis method is then developed by means of which networks can be found for a wide variety of specified functions. By means of well-known correspondences between networks of different kinds of elements, similar synthesis methods are easily derived for LC and RL. network, without mutual inductances.