1072 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1954 



as apply to the single series repeater. If A'' is 2 the gain is infinite and the 

 circuit will sing. This similarity goes further. Assume that a single 

 negative impedance Za equal to A'Zo/lSO" is inserted in series in an 

 electrically long line and N is adjusted for stability. If this series element 

 is removed and the bridged T of Fig. 12 is inserted in the same place 

 and adjusted by changing A^ until the system is stable it will be found 

 that A^ will have the same value in the bridged T structure as it had 

 for the single series negative impedance. 



Thus, if A^ is the same in the case of the bridged T as in the single 

 series impedance, the gain advantage can be obtained by comparing 

 formulas on Figs. 12 and 13 from w^hich it can be seen that the gain 

 advantage of the bridged T is equal in db to 20 logio [1 + (A^/2)]. If a 

 single series repeater can be used in a line to give an insertion gain of 

 6 db {N = 1) then a bridged T can be used to provide 20 logio (1 + 0.5) 

 or 3.5 db additional. Thus, in this case the series repeater gives 6 db 

 gain as compared to 6 + 3.5 or 9.5 db for the bridged T. These gains are 

 theoretical; in actual lines with simply constructed repeaters the com- 

 parison may not be c^uite so favorable to the bridged T. 



THE NEGATIVE IMPEDANCE CONVERTER 



So far the discussion of the E2 and E3 repeaters has been in terms of 

 a "black box" which translates a positive impedance into a negative 



INSERTION LOSS _ o„ , „^ I; 

 IN DECIBELS ""^O LOG,o — 



INSERTION GAIN _ -,„ , nr -^3 



IN DECIBELS " ^0 LOG,o -^ 



= -20 LOGio- 



20 LOGio 



(b) 



2Zo 



(c) 



Fig. 1,3 — • Insertion gain of the E2 repeater. 



