IMPEDANCE CORRECTION OF WAVE FILTERS 771 



itself, various transmission networks, amplifiers, modulators, electro- 

 acoustic apparatus, etc. are quite dissimilar physically and as we might 

 naturally expect, these physical differences manifest themselves in 

 many instances as pronounced dissimilarities in the forms of the im- 

 pedance-frequency characteristics. For example, the characteristic 

 impedance of a uniform line varies smoothly with frequency, but that 

 of a wave filter changes abruptly as we go from the transmitting to the 

 attenuating range. In spite of the possibility of changing the general 

 impedance level by the insertion of a transformer such inherent 

 "incompatibilities of temperament" between the characteristic im- 

 pedances of the various components of the telephone circuit must lead 

 normally to impedances which resemble each other only in narrow 

 frequency bands and which may differ widely over large and important 

 portions of the frequency spectrum. In default of some method of 

 extending the range of similarity, most long telephone circuits will 

 exhibit wide impedance mismatches or irregularities at numerous junc- 

 tion points. 



TERMINAL. 

 APPARATUS 



Z| Z2 LINE 

 — o o 



REFLECTION COEFFICIENT^ 



Z1-Z2 

 Z|+ Z2 



Fig. 1 — Junction of line and terminal apparatus illustrating impedances which 



determine the reflection coefficient. 



In voice frequency circuits or in carrier circuits which are not in 

 close physical association, impedance irregularities are of importance 

 only insofar as they affect transmission efficiency.* In addition to 

 modifying the current which proceeds onward toward the receiving 

 device, however, an impedance difference at any junction produces a 

 reflected wave which retraverses the circuit toward the sending end. 

 A convenient measure of this second effect is found in the "reflection 

 coefficient" which may be defined as the vector difference of the two 

 impedances looking both ways from any junction divided by their 

 vector sum (see Fig. 1) and is equal both in magnitude and phase to 

 the ratio between the reflected wave and the wave originally propa- 

 gated. 



The effect of reflection of considerable magnitude on transmission is 

 slight. Indeed relatively large reflection may actually improve the 

 transmission characteristic of certain circuits. In voice frequency 

 circuits and in carrier circuits which are not operated over lines in close 



* In two wire repeatered circuits reflection causes echoes which are one of the limit- 

 ing factors of such circuits. These circuits are, however, outside the scope of this paper. 



