The network synthesis on the insertion-loss basis
A unified and concise exposition is provided of the general insertionloss filter theory. Methods of synthesis of most important network functions are derived in terms of the prescribed steady-state network performance; also realization procedures are explained and expressed in terms of explicit formulae for direct application to the design of conventional ladder structures with an arbitrary number of branches.Two particular cases are solved in detail, namely the symmetrical and the inverse-impedance, low-pass networks, which are both unified in a single mathematical treatment. Such unification enables one to consider both of them as one general case of a low-pass analogue ladder structure.Special emphasis is given to the Cauer-Darlington method of synthesis of networks whose insertion-loss response approximates, in Chebyshev's sense, to that of the ideal wave filter; however, Taylor's approximation (maximally flat response) and the constant-k filters are also included.In the case of the maximally flat and the Cheby̅shev pass-band approximation, important explicit formulae for the ladder components are derived for a network with an arbitrary number of branches and an arbitrary termination ratio. These components (ladder coefficients) are thus directly computable from the required discrimination characteristics or the reflection factor, and from the bandwidth specifications.
