498 BELL SYSTEM TECHNICAL JOURNAL 



and the impedance Zi at the terminals 7, 8 is: 



^■' = 7 = A - ^' (20) 



which consists of the desired negative impedance —Z and a negative 

 resistance if Mv > 1- By connecting the positive resistance, 

 7?3 = R^/Mv — 1, in series with Z/ this negative resistance is neu- 

 traUzed and the desired negative impedance is found between the 

 terminals 8 and 9. This impedance has shunt characteristics. 



In both of these arrangements it is possible, without changing the 

 constants of the network Z.v, to give the negative impedance any 

 desired magnitude by adjusting the value of AIv and making the cor- 

 responding change in the resistance Rn or R3. 



Boosters 



The name "booster" has been applied to a negative impedance of 

 suitable characteristics connected in series with or bridged across a 

 telephone circuit in order to introduce energy when a wave passes and 

 so produce a transmission gain. Such devices have certain interesting 

 theoretical properties. 



Series Booster 



Fig. 10 shows an impedance Zs connected in series between the two 

 parts of a telephone line having the characteristic impedance Zq. 



Zs 



^/MAAAMp 



Fig. 10 — The series booster. 



Assume first that Zs is a positive impedance having the same angle 

 as Zo and that a wave is traveling over the line, for example, from left 

 to right. The effect of the inserted impedance is to reduce the current 

 in the line wires at the point of insertion, weakening the wave that 

 passes on to the receiver and causing a reflected wave to return to the 

 source. The transmission loss^ caused by the inserted impedance is: 



L= 20 1og:o(l+;^J, (21) 



"The values of losses, return losses and gains will be e.\pressed in decibels (db) 

 throughout this paper. 



