NEGATIVE IMPEDANCES AND THE TWIN 21-TYPE REPEATER 487 



sistance Rq in such fashion that the e.m.f. in the output circuit of the 

 ampHfier tends to increase the current. Assume now that the e.m.f. 

 E is applied and a current /o flows in the series circuit. 



E + {M - Ro- Ri - Ro)Io = 0. (1) 



The drop across the ampUfier is: 



e= {R, + R,- M)h, (2) 



and the net resistance of the whole amplifier is: 



r = y=R, + R,- M. (3) 



■i-o 



It may aid in understanding the behavior of this system to assume, 

 first, that M is zero so that the circuit consists simply of the three 

 positive resistances Ro, Ri and Rz in series and then consider what 

 happens as M is gradually increased. The e.m.f. appearing in the 

 output circuit of the amplifier acts to reduce the drop e across the 

 terminals 1, 3 and to increase the current Iq. The e.m.f. E must be 

 reduced if the current is to be kept constant. The curves of Fig. 3 

 show how the resistances and current vary as ^1/ changes, E being 

 constant. 



When M = Ri -{- R2 the drop e and the resistance r become zero. 

 The amplifier then ceases to take power from the circuit and supplies 

 its own losses. If this condition could be exactly obtained the ter- 

 minals 1, 3 might be short-circuited and the e.m.f. E removed, without 

 changing the current which would continue to flow in the amplifier. 

 If, however, the e.m.f. were removed or the circuit opened without 

 short-circuiting the terminals of the amplifier the current in the input 

 circuit, and, consequently, the e.m.f. in the output circuit of the 

 amplifier would disappear and the system would become inactive. 



If, now, M is further increased so that it approaches i<!o + -Ki + R-i 

 the current increases indefinitely, or the e.m.f. E required to sustain 

 the current at a given value approaches zero. Under these conditions 

 the drop e and the resistance r become negative and the amplifier 

 supplies not only its own losses but also part of the energy dissipated 

 by the resistance Ro- It does so under the control of the e.m.f. E, 

 however, and if this e.m.f. is removed the system becomes inactive as 

 before. At the limit when M = Ro -\- Ri -{- R^, the amplifier supplies 

 all the losses in the system and any current /o, once started, continues 

 indefinitely. 



This ideal condition is not realized in practice. Either M is slightly 

 too small, in which case the current decreases when E is removed, or it 



