NEGATIVE IMPEDANCE TELEPHONE REPEATERS 10G7 



Fig. 7(b) shows the same converter, but here the impedance Zx is 

 connected to terminals 1 and 2. The impedance seen at terminals 3 and 

 4 (at least over the frequency l)and of inten^st) will be Z^ divided bj^ A: 

 and shifted in phase through a positive angle of approximately 180 de- 

 grees. This impedance will (if freciuencies from zero to infinity are con- 

 sidered) fulfill the definition given above for the E3 repeater impedance. 

 Thus Fig. 7(b) can represent the operation of the E3 repeater. 



From Fig. 7, it is apparent that the same converter circuit could have 

 been used for both the E2 and the E3 repeaters. For practical reasons 

 it w^as not. However, the ratio k and the phase shift in both the con- 

 verter of the E2 and that of the E3 were made approximately the same. 



OPERATION IN TRANSMISSION LINES 



Within limitations, the E2 repeater can be represented by a negative 

 impedance, —Z, and the E3 repeater can be represented by a negative 

 admittance, — Y. With a negative impedance and a negative admittance 

 available, losses of transmission lines can be reduced in the manner 

 illustrated in Fig. 8. The transmission line is represented by two net- 

 works as shown in Fig. 8(a). One of these (Network A) is in the form 

 of a T network the series arms of which are represented by impedances 

 Z; and the shunt arm, by an admittance F. This network has a propaga- 

 tion constant ai + j/Si . The attenuation ai represents the major portion 

 of the line attenuation, and the phase shift /Si is that just sufficient to 

 make Network A realizable physically. This representation is necessary 

 because Network A has image impedances each equal to the character- 

 istic impedance (Zq) of the line. If the characteristic impedance of the 

 line w^ere a pure resistance, then the phase shift through this network 

 could be zero and I3i could be zero. But the characteristic impedances of 

 actual lines are not pure resistance; thus the phase shift i8i must be in- 

 cluded in Network A. The other network (Network B) is shown as a 

 box. It has a propagation constant a2 + j02 • Here ^2 represents the 

 remaining phase shift in the transmission line and 02 is an attenuation 

 just sufficient to make Network B physically realizable in view of the 

 image impedances which are both equal to Zo , the characteristic im- 

 pedance of the line. Fig. 8(b) shows the addition to this line of a repeater 

 consisting of a T network made up of negative impedances — Z in the 

 series arms and a negative admittance — Y in the shunt arm. The arm 

 — Z of the repeater adjacent to the line cancels Z of the line. The two 

 admittances — Y and Y cancel and the other series arms — Z and Z 

 also cancel. The result, as shown in Fig. 8(c), is that only the attenua- 

 tion and phase shift of Network B remain. 



