On the canonic cascade synthesis for lossless one-ports

The problem of finding all possible canonic cascade syntheses for lossless one-ports Is considered. Without being able to solve it in general, the following steps in this direction are presented. For the purpose of a systematic search for canonic
LC
-cells a topological criterion is given which eliminates all nonminimal
LC
-cells, i.e. those with more elements than is their degree. Another topological criterion serves to detect a large number of minimal
LC
-cells that are not canonic. On the other hand, in order to prove an
LC
-cell to be canonic the synthesis problem is divided into a linear and a nonlinear part. A bridged
T
of degree 4 serves as an example to show how to prove the existence of a solution for the nonlinear equations and how to generate from it a canonic synthesis, using theorems about the linear part. Some of the material is new, some can be found piecewise elsewhere but is reproduced and adapted here for the sake of a unified and coherent presentation. In particular, apart from the bridged
T
already mentioned, seven different new nontrivial canonic
LC
-cells are listed.