490 



BELL SYSTEM TECHNICAL JOURNAL 



and the current in the main circuit is: 



T P- - g T _L T ^1 + ^2 - M 

 h = S = /l + /2 = ^5-n «. 



i?o 



from which 



RiRi 



e 



r = -v 



R1R2 



h R1 + R2-M' 

 and the appHed voltage E is: 



E ^ Io{Rq + r) = 



(6) 



(7) 



(8) 



Fig. 4 — ^One-way amplifier connected as a shunt negative resistance. 



With this arrangement, the e.m.f. generated in the output circuit of 

 the ampUfier opposes the current I2 due to the e.m.f. E, and as M 

 increases, the current /o in the main circuit decreases and the resistance 

 of the ampUfier increases. The curves of Fig. 5 show how the resist- 

 ances and current vary as M changes, E being constant. To keep /o 

 constant, it would now be necessary to increase E. 



When M = Ri the current I2 becomes zero. 



When M = i?i + i?2 the current /o falls to zero, the potential 

 e = E, the current h has reversed in direction, the resistance r = <» 

 and the amplifier just supplies its own losses. If the circuit outside 

 the amplifier is now opened, the condition of the amplifier is the same 

 as when the short circuit was applied to Fig. 2 and the current circulat- 

 ing in the amplifier will continue. If E is removed without opening 

 the circuit, Ro will draw energy from the amplifier, thus reducing /i and 

 causing all currents and voltages to disappear. The amplifier is still 

 under the control of the e.m.f. E. 



For the arrangement of Fig. 4 to become unstable it is necessary for 

 the amplifier to maintain or increase the voltage e after the controlling 

 e.m.f. E is removed. For the amplifier to maintain the voltage e it is 

 necessary that: 



RoRi 



^-r/' 



Ro + R, 



RoR\ 

 Ro + R^ 



(9) 



+ i?2 



