Network Synthesis Using Lossy Reactances

Circuit designers have devoted a considerable amount of attention to the problem of precorrecting for the losses that inevitably occur in physical reactances. The most successful approach in this connection has been to assume that all reactive elements have losses of the semi-uniform type (i.e., all inductors have oneQ; all capacitors have anotherQ). This approach was first used by Darlington [1] in 1939 and, since, has been extended by many others [2]-[10]. The available literature on semi-uniform loss provides many useful design procedures for filters of the insertion loss type. The literature does not provide a coherent synthesis theory, however. Indeed, a quick survey reveals that 1) the literature is concerned almost exclusively with the insertion loss configuration; 2) the synthesis procedures that have been developed are quite complex and provide little insight into the networks considered. The authors hope that the present paper will provide a more systematic basis for the synthesis of networks that incorporate semi-uniform loss. The approach used is to transform networks that contain lossy reactances into networks that contain more dearly ideal reactances. Conventional RLCT synthesis techniques are then applied. The approach proves remarkably successful. Indeed, the final theory is almost as comprehensive as that presently available for RLCT networks. The paper treats 1) realizability conditions, 2) the Brune procedure, 3) the Darlington (driving point) procedure, 4) the BottDuffin procedure, and finally 5) the insertion loss theory.