12 BELL SYSTEM TECHNICAL JOURNAL 



Zf) -\- Zt Zo ~r Zr 



(6) 



This applies to the same circuit as equations 3 and 4, the only difference 

 being that for telephone purposes the ratio EtlVr is used rather than 

 VilVr since in the telephone case the internal voltage of the generating 

 apparatus rather than the terminal voltage is the more convenient 

 reference voltage. Otherwise the two equations are identical consist- 

 ing simply of a rearrangement of terms. The outstanding feature of 

 the arrangement shown in equation 6 is that it consists of the product 

 of a number of terms rather than the sum of a series of terms 

 as in equation 4. The first term represents the ratio of voltages 



Z + Zr 

 which would be obtained if there were no line present, namely ' —. 



The second term illustrates the effect of propagation over the line it- 

 self without allowance for reflection at the terminals. The next three 

 terms, two in the numerator and one in the denominator are the 

 factors which make allowance for this reflection. Each is dependent 

 upon simply the magnitude of two impedances, and their inclusion in 

 the equation represents the fact that inserting the line between the 

 two impedances inserts the reflection factors between the line and the 

 transmitting impedance at one end, and the line and receiving im- 

 pedance at the other end, and takes out the reflection factor directly 

 between the transmitting and receiving impedances. The reflection 

 factor becomes unity in any case in which the two impedances are 

 equal. The last term of the equation is called the interaction factor 

 because it represents the effect of multiple reflection back and forth 

 between the two terminals of the line. This factor necessarily is 

 complicated as it depends upon the characteristics of the line and on 

 both transmitting and receiving impedances. It will be noted that 

 this factor becomes substantially equal to unity in case either the 

 transmitting impedance and the line impedance are approximately 

 equal, the receiving impedance and the line impedance are approxi- 

 mately equal, or the attenuation of the circuit is considerable. In most 

 practical telephone circuits these conditions are approximated suffi- 

 ciently closely so that the departure of this factor from unity can usu- 

 ally be neglected. 



In general, practical telephone circuits are, of course, a good deal 



