A graphical approach to the synthesis of general insertion attenuation functions

When a network is required to give an attenuation which is frequency dependent, the specification is usually given in the form of a graph or a table. If the insertion-parameter theory is to be used in finding the network, the specification has to be converted into a rational function. Known methods of achieving this seldom lead to satisfactory results, and a new method has been developed which is applicable to the most general form of the wanted rational function. The numerator and the denominator are composed of factors, each representing a certain group of permissible zeros in the complex frequency plane. The influence of the single factors can be plotted on log-log paper, the sum of the curves obtained representing the attenuation of the complete function. On the other hand, a given graphical characteristic can be approximated by a sum of curves whose functions are known. It is found that only a comparatively small selection of different curves is needed for the solution of practical problems. By way of example, the function for a network meeting the requirements of the C.C.I.F. (Paris, 1947) psophometer weighting-characteristic for commercial telephone circuits is determined. Although, in principle, the method could be applied to filter design, certain difficulties arise, and the chief application may be limited to the design of equalizers and similar networks, in which the attenuation/frequency characteristics do not exhibit excessively sudden changes of slope.