Synthesis of Transmission Systems in Terms of Tandem-Connected Quadripoles

A theory for the tandem connection of quadripoles is presented, using as basic parameters the operating factor and input and output impedances of a quadripole when operating under reference conditions between arbitrarily chosen source and load impedances. These parameters are termed the reference parameters, and the source and load impedances are called the nominal impedances. Simple extension leads to the reference loss parameters. Operating-loss and input-return-loss formulae are derived for the non-reference operation of a quadripole, and, in conjunction with return-loss formulae obtained for quadripole junctions, are used to determine overall operating-loss characteristics of a transmission system when quadripoles are added or removed. Furthermore, these formulae are used for transmission-system synthesis. A technique is developed which permits convenient and precise calculation of return and operating loss, or alternatively enables calculation of their limits. The formulae derived facilitate the rapid solution of a variety of practical transmission problems, and their application in some instances is illustrated by the inclusion of numerical examples.