776 BELL SYSTEM TECHNICAL JOURNAL 



the impedances of modulators, amplifiers and telephone lines approx- 

 imate constant resistances. The interposition of filters between lines 

 and modulating or amplifying apparatus, however, normally produces 

 large reflection coefiicients. Since the filters in addition to being the 

 apparatus immediately responsible for mismatching, are also inexpen- 

 sive and easily controlled in comparison with the line, they furnish the 

 most promising field for the reduction of reflection coefficients. 



Relation between Actual and Image Impedances 



The reflection coefficient which determines the amount of crosstalk 

 exhibited by the system involves directly only the line impedance and 

 the actual impedance characteristic of the filter system. In order to 

 understand the peculiarities of the actual impedance of a filter, how- 

 ever, it is necessary to give prior consideration to its characteristic, or 

 image impedances. The image impedances of any transmitting device 

 are defined as the impedances with which the device must be terminated 

 at both ends if the impedances looking both ways at each pair of 

 terminals are to be matched. In other words, they are the impedances 

 with which the structure must be terminated if no reflections are to 

 occur. Filter sections of different physical configuration and with 

 different attenuation characteristics often have the same image im- 

 pedance characteristics. Practical filter designs are therefore usually 

 composite structures containing several different types of sections. 

 Internal reflections are avoided by so choosing the arrangement of the 

 section that the image impedance characteristics at all section junctions 

 are matched. Under these circumstances the image impedance charac- 

 teristics of the complete structure are the same as those of its terminat- 

 ing sections. The image impedance characteristic of typical low pass 

 filter sections is shown in Fig. 4i-A . A corresponding curve for band pass 

 filters is given in Fig. 4-B. The image impedance characteristics are 

 given only for the transmitting bands of the filters since, as previously 

 indicated, the filters themselves suppress crosstalk in the attenuating 

 regions making it unnecessary to control impedances outside the 

 transmitting range. The associated equipment, such as lines and 

 modulators, with which the filters are terminated, are approximately 

 constant pure resistances, and may be represented in the trans- 

 mitting range by the block type characteristics drawn over the curves. 



The relation between the image impedance properties of filters 

 and the actual impedance presented by a repeater or terminal to the 

 line can be understood from the simplified circuit diagram of a typical 

 carrier terminal (Fig. 5). Upon examining the figure we note that 

 there are a number of junctions at which rounded filter image im- 



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