NEGATIVE IMPEDANCES AND THE TWIN 21-TYPE REPEATER 497 



the e.m.f. generated in the output circuit of the ampHfier to the voltage 

 impressed on its input terminals, instead of the mutual impedance of 

 the amplifier, because the input current is negligibly small. This 

 ratio may be adjusted by some suitable means such as a potentiometer. 

 Referring to Fig. 8, let Z be the positive of any desired negative 

 impedance such that a network having the impedance, Z.v = Z/M^ — 1, 

 may be constructed of physically available parts, M^ being a real 



Fig. 9 — Shunt type negative impedance. 



number greater than 1. Rk = Ro/My — 1 is a pure positive resistance. 

 Next assume that a current, /, is flowing through the circuit between 

 terminals 5 and 6. The e.m.f. generated in the output circuit of the 

 amplifier is {Rs + Z\)IMy. It acts in the direction which tends to 

 increase the current. The voltage e required at the terminals 5, 6 to 

 produce this current is, then. 



e = {Ry + Zv + R2)I - (Rx + Zx)IM,, 

 from which the impedance Zz is: 



-z, 



(17) 



(18) 



which is the desired negative impedance. Due to the arrangement of 

 the circuit this impedance has series characteristics. 



Referring to Fig. 9, Z,v is a positive network. Assuming that an 

 e.m.f. e is applied to the terminals 7, 8, the e.m.f. generated in the 

 output circuit of the amplifier is eM,, which acts in opposition to e to 

 reduce or reverse the current. The current at the terminals 7, 8 is, 

 then, 



_ e — eM„ 



i?2 + Zat ' 



(19) 



