504 



BELL SYSTEM TECHNICAL JOURNAL 



Negative Impedances Arranged in T or IT Networks 



It has been pointed out by G. A. Campbell, H. Mouradian/ and 

 possibly by others, that three negative impedances can be grouped into 

 a r or a TT network which may be inserted in a telephone line. Such 

 a network is able to amplify waves traversing the line without causing 

 echoes if the values of the impedances are suitably chosen. In order 

 to avoid singing, the impedances in series with the line must be of the 

 series type, and those bridged across the line, of the shunt type. 



A Double Booster 



Fig. 14 shows a network of impedances connected between two pieces 

 of telephone line having the characteristic impedance Zq. These lines 

 are assumed at first to be free from irregularities. The branches 

 ac and he are fixed networks, each having the impedance Zq. Branches 

 ah and cd are networks whose impedances can be varied reciprocally 

 from the value Zo, that is, if one impedance is multiplied by a factor 



pZo 



LINEW 



LINEE 



Fig. 14 — Double booster. 



p, the other is divided by the same factor. The factor p may be 

 positive or negative, and may be complex. Branches ah, ac, cd and the 

 line E may be considered as forming the arms of a Wheatstone bridge, 

 of which the branch he is one diagonal and the line W is the other. 

 This bridge is balanced; consequently, the impedance connected to the 

 line W consists of two parallel circuits, one comprising the branch ah 

 in series with the line E and the other comprising the branches ac 

 and cd in series. This impedance is independent of p, being equal to 

 Zo- By symmetry, the impedance connected to the line E is also equal 

 to Zo, so no reflection occurs at the terminals of the network. 



Assuming that a wave arrives, for example, over the line W and is 



*"Long Distance Transmission Problems," by 11. Mouradian, Journal of the 

 Franklin Instilute, \'o\. 207, No. 2, February, 1929. 



