A Method of Impedance Correction

HE analysis of transmission circuits with which telephone engineers are familiar is an outgrowth of the general physical theory of the propagation of wave disturbances in continuous media. Problems analogous to the analysis of a smooth transmission line are found, for example, in optical and acoustical theory and in the theory of the vibrations of a taut string. The situations of most importance from the standpoint of general physics are those in which the continuous medium extends indefinitely in at least one direction. Since, moreover, this is also the simplest case, it has been customary to base our transmission analysis upon the analogous concept of an infinite line with distributed constants. The analysis of such a structure, since it depends upon only two quantities, the characteristic impedance and the propagation constant, is of course very simple. An actual telephone transmission circuit, however, is by no means an infinite structure containing distributed constants. Many lines, for example, are loaded. Whether loaded or unloaded, they do not extend indefinitely, but are interrupted by terminal apparatus and intermediate repeaters. Each of these, moreover, contains a miscellany of apparatus, such as modulators, transformers, amplifiers, filters, equalizers, by-pass circuits, and the like, having little physical resemblance to a continuous medium. 794 A METHOD OF IMPEDANCE C JRRECTION 795 This physical contrast between an ideal continuous medium and an actual physical telephone circuit does not necessarily mean that the application of the wave theory to circuit analysis is a difficult matter.