488 BELL SYSTEM TECHNICAL JOURNAL 



is too large so that any value of E however small starts a current which 

 thereafter increases because the amplifier supplies more than enough 

 energy to sustain the current. This increase continues until checked 

 by the inability of the amplifier to deal with larger currents. In effect 

 M is reduced to the point where r is again equal to — i?o, after which the 

 current continues at a constant value. 



The arrangement shown in Fig. 2 can therefore be made to provide 

 any negative resistance between r — and r = — Rq without causing 

 instability or a tendency to sing. Such a system is stable when the 

 algebraic sum of all the resistances in series in the circuit is positive. 

 This behavior is typical of a large number of arrangements that are 

 able to furnish negative resistances. All such arrangements will be 

 referred to as series negative resistances to distinguish them from another 

 type which will be described below. 



It should be noted that if the sign of M is reversed, for example, by 

 interchanging the two wires connected with the output terminals 3, 4, 

 no negative resistance results. As M increases, the current /o de- 

 creases, or the e.m.f. E must be increased to maintain the current, 

 but no matter how large AI is made, the direction of the drop e and sign 

 of the resistance r do not change though the latter approaches <». 



The Unstable Condition 



So far nothing has been said as to the nature of the e.m.f. E. In the 

 ideal case, when the system is stable, the current wave is a copy of the 

 voltage wave as in any circuit having a pure resistance. What hap- 

 pens when the circuit is unstable depends upon the nature of the ampli- 

 fier or other device used to produce the negative resistance and not 

 upon the e.m.f. E. This may be of any kind and of minute size, such 

 as that resulting from thermal agitation in the resistances forming 

 part of the apparatus. If the amplifier is able to amplify direct cur- 

 rents, the resulting disturbance may be a direct current limited only 

 by the ability of the apparatus to supply energy to the circuit. Where 

 transformers, condensers, etc., are involved the disturbance settles 

 down to an alternating current which may contain many harmonics 

 or may be almost a pure sine wave. These effects are called "sing- 

 ing." The final frecjuency, amplitude and wave shape depend upon the 

 makeup of the apparatus in a way which is beyond the scope of this 

 paper. 



Shunt Negative Resistance 



By connecting the terminals of the ideal one-way amplifier in parallel 

 as shown in Fig. 4, a negative resistance will be obtained which is 

 typical of the second type or shunt negative resistance. 



