442 BELL SYSTEM TECHNICAL JOURNAL 



of such a line of length / terminated by a resistance R = k \s readily 

 seen to satisfy the conditions (2) above for no distortion. It would 

 have an attenuation a' = '^R'G'l napiers and time-of-transmission 

 T = ■^L'C'l seconds. 



Having seen above what constitutes ideal transmission character- 

 istics, the problem of distortion correction in any practical distorting 

 circuit is that of altering the circuit in some way so as to approach this 

 ideal. In most circuits it is impossible to obtain these ideal charac- 

 teristics throughout the entire frequency range. More or less satis- 

 factory transmission results will be had, however, if this ideal is 

 approached over the range of frequencies most essential to the com- 

 position of the impressed e.m.f., as shown by its Fourier integral 

 analysis. 



How accurately an ideal attenuation characteristic has been met 

 in any case depends upon how nearly constant the attenuation is in 

 the frequency range. A simple practical measure of the degree of 

 approach to an ideal phase characteristic at the frequencies in this 

 range is furnished by a consideration of the time-of-phase-transmission 

 in the steady state, 



Tp = i/oj seconds, (7) 



in which h is defined as in (1) for the complete circuit. The more 

 nearly constant r^ is in the frequency range, the closer it approaches 

 equality with t, the time-of-transmission of the circuit for those 

 frequencies. 



In many cases approximately ideal phase characteristics already 

 exist in the desired frequency ranges so that corrections need be made 

 for attenuation only. In others, such as those in which the steady- 

 periodic state is of most importance and where the phase relations 

 between the components are immaterial, it is satisfactory to obtain 

 uniform attenuation at the desired frequencies. The method of alter- 

 ing circuit transmission characteristics to be shown in this paper 

 follows in Part 2. 



Part 2. Constant Resistance Recurrent Networks 



2.1. Fundamental Basis of Distortion Correction 



The general transmission circuit of Fig. 1 is shown as having a 

 resistance, R, at the receiving end, as in the case where the energy is 

 absorbed. Usually the circuit characteristics at this resistance with 

 respect to the sending terminals show distortion in the required 

 frequency range. If so, an ideal method of correcting the distortion 



