778 BELL SYSTEM TECHNICAL JOURNAL 



magnitude in traversing the filters intervening between the line term- 

 inals and the junctions at which mismatches occur. The attenuation 

 of most filters within transmitting bands is so small however, that the 

 waves may be of appreciable magnitude even after several reflections. 

 The filter phase shift within these frequency bands, on the other hand, 

 is large and varies rapidly with frequency. The reflected waves may 

 therefore combine at the input terminals in almost any fashion, and 

 the efi^ect they produce upon the input current will vary rapidly and 

 violently as we proceed along the frequency scale. With given line 

 impedance and voltage, however, the actual impedance of the terminal 

 is related in simple fashion to the actual current entering it. The im- 

 pedance, therefore, shows correspondingly wide fluctuations. The 

 extremely irregular impedance and reflection coefficient characteristics 

 of Fig. 2 exemplify the effect of reflections from the further junction 

 points of the system. Another example is furnished by the curve of 

 Fig. 7, which shows the reflection coefficient between the actual imped- 

 ance of the filter of Fig. 6 when terminated in the line resistance, 

 and that resistance. The humps of the curve come at frequencies 

 whose phase shift is such that the wave reflected from the far end 

 accentuates the departure of the near end image impedance from 

 the desired value. The valleys correspond either to points at which 

 the image impedances are ideal or to values of filter phase shift which 

 cause the reflections at the two ends of the filter to correct one another. 



Terminal Impedances Best Corrected by Special Type of Filter Section 



Close impedance correction of these complicated characteristics 

 seems hopeless. In order to keep the problem within manageable 

 limits it is necessary to destroy the reflected waves at their source by 

 preventing mismatches at all junctions between filters and other ap- 

 paratus within the transmitting bands. The technical problem can 

 consequently be reduced to the construction of a new type of filter 

 section for use at terminations, the image impedance of the new section 

 showing at one end a close approximation to the block type terminating 

 impedance characteristic of Fig. 4:-A or 4-3 (i.e. a constant resistance) 

 while at the other end it has the conventional rounded filter image 

 impedances also shown on these figures, thus matching the standard 

 sections forming the main bulk of the structure. 



Early Improvements 



Methods of approximating these characteristics to some extent were 

 already available when the need for reducing crosstalk by impedance 

 correction appeared. The first and longest step in this direction was 



