NEGATIVE IMPEDANCES AND THE TWIN 21-TYPE REPEATER 501 



same as for the series type booster described above except that the 

 reflected waves are opposite in phase. This makes it possible to elimi- 

 nate the echo by combining two boosters in one repeating device as 

 described below. 



The shunt booster would also operate if Zj, were made a series type 

 negative impedance smaller in magnitude than Zo/2, but in this case 

 the wave traveling toward the receiver would be reversed in phase and 

 the echo wave would be greater than the transmitted wave. 



Singing Points of Various Forms of Repeaters 



When a line of characteristic impedance Zo has a certain return loss 

 Sh its impedance will lie between a maximum value of mZo and a 

 minimum of Z^/m where 



Si = 20 logio "^^ • (25) 



m — \ 



If two pieces of such a line are joined through a repeating device the 

 high and low impedances may combine in three different ways which 

 give the greatest tendency to sing with different types of apparatus. 



The series type negative impedance, whether connected in series 

 with or across the line, has the greatest tendency to sing when the 

 minimum impedances of both lines occur at the same frequency and the 

 shunt type negative impedance has the greatest tendency to sing when 

 the maximum impedances occur at the same frequency. The 21 -type 

 repeater has the greatest tendency to sing when the maximum im- 

 pedance of one line and the minimum of the other occur at the same 

 frequency, the internal connections of the repeater determining which 

 impedance must be high. In the 22-type repeater any of these com- 

 binations may be the worst, depending upon the internal arrangement 

 of the repeater circuit. 



The series booster (with series type negative impedance) will sing 

 when 



Z. + ^ = 0. (26) 



m 



Substituting Zs obtained from this relation in equation (21) and 

 remembering that the loss L becomes a gain G\ when Zs is negative, 

 the gain which will produce singing is: 



Gs= 20 logic (l -I)' (27) 



