NEGATIVE IMPEDANCES AND THE TWIN 2 1 -TYPE REPEATER 505 



transmitted to the line E, the ratio of the voltage across the terminals 

 a, d to that impressed on the hne £ is (1 + p)/l and the transmission 

 loss through the network is: 



L = 20 login (1 + p). (31) 



This loss becomes a gain when p becomes negative and the network 

 acts as an amplifier. 



Examination of Fig. 14 shows that the branches ab and cd are each 

 connected to a constant impedance Zo, hence, if p lies between and — 1 , 

 the branch ab must be a series type negative impedance and cd of the 

 shunt type. If p lies between —1 and -co, these types must be 

 interchanged. 



The physical behavior of this network may be readily understood 

 if the properties of negative impedances are kept in mind. At first 

 let p be infinite and assume that a wave arrives over the line W. 

 This wave tends to produce a current in the upper conductor which at 

 a given instant flows in the direction indicated by the short solid arrow^ 

 This wave will be absorbed by the impedance Zo of the branch ac. 

 If now p is made negative the series type negative impedance in the 

 branch ab will cause additional currents to flow in the lines E and W 

 the directions and relative magnitudes of which are indicated by the 

 longer solid arrows. The shunt type negative impedance in the branch 

 cd tends to produce currents having the directions indicated by the 

 dotted arrows, thus further increasing the wave in the line E but an- 

 nulling the effect of the series type impedance in the line W. The 

 network of Fig. 12, therefore, amplifies waves traveling in either 

 direction without causing echoes to return to the source. It resembles, 

 in this respect, a 22-type repeater, but it cannot give different gains in 

 the two directions. 



Putting a shunt type impedance in the branch ab and a series type 

 in the branch cd would reverse the sign of the amplified wave. 



For such a network to function as described above, it is not necessary 

 for the ratio p to be independent of frequency. Phase shifts in the 

 negative impedances are permissible provided they are kept equal so 

 that the echoes will be eliminated. It is, therefore, possible to use 

 filters and other apparatus to cause the gain to vary with frequency 

 in a desired manner without encountering the troubles which occur 

 in the single booster. 



It is further possible to couple the series branch ab of the network of 

 Fig. 12 to the line by means of a transformer and the bridged branch 

 cd by means of a condenser without seriously altering the reciprocal 



