724 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



systems. Converselj^ these methods raay be used in the design of pulse 

 modulation systems to evaluate requirements imposed on the transmis- 

 sion characteristics for a given transmission perfoiTnance. 



Transmission impaiiTnents may result from S3'stem imperfections other 

 than characteristic distortion, which require a different theoretical ap- 

 proach and are not considered here. Among them are erratic timmg of 

 pulses, thermal and other noise within the transmission system and in- 

 terference from outside sources, such as other communication systems or 

 atmospheric disturbances. 



1. PROPERTIES OF TRANSMISSION-FREQUENCY CHARACTERISTICS 



A basic parameter of transmission systems is the transmission-fre- 

 quency characteristic 



T(tco) = A(o:)e-''^^"\ (1.01) 



in which w = 27r/ is the radian frequency, ^4(co) is the amplitude and 

 \l/(u) the phase characteristic. The transmission-frequency characteristic 

 may designate the ratio of received voltage to transmitted current, of 

 received current to transmitted voltage, of received to transmitted cur- 

 rent or of received to transmitted voltage. The two latter ratios are not 

 the same except for sjTnmetrical networks \\ith impedance matching at 

 both ends. For symmetrical structures having appreciable attenuation, 

 such as transmission lines between repeaters, the ratios are virtually the 

 same with impedance matching at the receiving end. In the following, 

 T{io}) will designate any of the above ratios, as the case ma}^ be. 



When a number of networks are connected in series, as is usually the 

 case in transmission systems, the resultant transmission characteristic 

 is 



where Ti , To ■ • ■ Tn are the transmission characteristics of the individual 

 networks with the same impedance terminations as encountered in the 

 series arrangement, i.e. as measured in place or with equivalent termina- 

 tions. 



The phase characteristic \l/ can in general be regarded as the sum of 

 three components. The first is the minimum phase shift component, 

 1^", which has a definite relation to the amplitude characteristic of the 

 system, and is of particular interest in connection with phase distortion 

 with different types of amplitude characteristics. The second is a 



