Two-Mesh Tuned Coupled Circuit Filters

Tuned coupled circuits have been the subject of many investigations, but few of these have produced results which are useful to the design engineer. A direct attack, avoiding the special terminology and procedures of general filter theory, seems the most effective. Several such attacks have been made, but either the results have not been fully developed, or serious restrictions have been placed upon the circuits. One common restriction is that the circuits are identical; another, that they are coupled by a pure reactance. These limitations made the resulting theory inapplicable to the study of such important matters as detuning, unequal circuit resistances, resistance in the coupling impedance, etc. In this paper, a reasonably simple analysis is developed which is free from the foregoing objections. The results include and collect into a correlated whole many relations which have been derived before, as cvell as a number of new ones. Circuits which are tuned alike and coupled by a pure reactance are treated first. Universal resonance curves are developed which make it possible to determine rapidly the characteristics of any pair of isochronous circuits, once their constants are known. Formulas are derived for band width at any given number of decibels down, ratio of height of peaks to valley, etc. It is shown that the concept of critical coupling is inadequate when the circuit resistances are unequal, and a new quantity, transitional coupling, is introduced. Methods for the design of a tunable filter of constant band width are developed.