The insertion loss synthesis of communication networks using non-ideal elements.

The purpose of the research work described in this dissertation was a explore available methods for the synthesis of networks from non-ideal elements and to find a new theory upon which a practically tractable synthesis procedure can be founded for circuits with arbitrarily distributed losses. Since the theory providing the basis for this novel design method turned out to be closely related to the insertion loss synthesis technique, a detailed explanation of the latter was required. It has been provided in Chapter I. Apart from some new derivations involving the relation between the form of the characteristic function and the circuit configuration, and the approximating synthesis procedure for filter-combinations, the fundamental theory described in the first chapter is available in the literature. The construction of realizable transfer functions for some practical requirements is treated in Chapter II. There the proof of the non-realizability of a quasielliptic response, some realizability-considerations involving elliptic filters, the Section on harmonic suppression filter-sets and the step-by-step design method for Chebyshev pass-band filters are original; the rest of Chapter II recapitulates existing theory. Chapter III provides a summary of miscellaneous analysis and synthesis methods which take into account the effects of non-ideal elements. The improved temperature-compensation procedure is new; the other results have been previously published. The derivations contained in Para. III.2.c. have been worked out by the writer, at least one of them, however, probably duplicates Darlington's original (unpublished) calculations. The new synthesis method and its supporting theorems are described in Chapter IV. First, a large variety of formulae are obtained for the derivatives of various network parameters. These formulae are utilized in the derivation of the main theory; they are also directly applicable to circuit analysis. The formulae can be deduced from the determinant forms of the driving-point and transfer immittances. The effects of losses on the transfer characteristics are then studied indirectly by examining the changes in various parameters of the transfer function (natural frequencies, attenuation poles, proportionality factor) due to the added dissipation. Using series expansions, from the variation of these parameters the increment of the transfer function itself could be found to a first-order approximation. These results were used to find expressions, in which contributions of individual lossy elements to the distortion of the ideal characteristics were displayed. Even more important, they led to a relatively simple synthesis procedure allowing precorrection (often called predistortion) for the detrimental effects of individual losses. Since the calculations giving rise to the final formulae involve series expansions and terms containing powers of loss factors greater than unity are omitted, the accuracy decreases with increasing losses. Even for quality-factors in the order of 10, however, examples proved the results to be sufficiently exact for any practical purposes. Using some special properties of the lossy ladder-networks found in the course of this investigation the general expressions were simplified for this important configuration. For the import-art case of semi-homogeneous loss distribution (all coils have identical quality-factors, and so do all capacitors, but the quality-factors of the two groups differ), topological considerations were applied to achieve extremely compact formulae. Procedures to improve the accuracy for extreme cases (large losses, sharply changing response) have been developed; however these are seldom needed. Some alternative procedures applicable in special cases have also been derived. Finally, the theory was tested with excellent results by applying it to a large number of design problems, a representative cross-section of which has been included in Chapter IV to illustrate the simplicity and usefulness of the method